2015-09-30
Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves Lian Shen St. Anthony Falls Laboratory and Department of Mechanical...on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves...interaction of surface and internal gravity waves in the South China Sea. We will seek answers to the following questions: 1) How does the wind-wave
Causal properties of nonlinear gravitational waves in modified gravity
Suvorov, Arthur George; Melatos, Andrew
2017-09-01
Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial f (R ) gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial f (R ) gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient a2 of the Taylor expansion of f (R ) is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of a2. Anisotropic solutions are found, whose wave fronts trace out time- or spacelike hypersurfaces with complicated geometric properties. We show that the solutions exist in f (R ) theories that are consistent with Solar System and pulsar timing experiments.
Directory of Open Access Journals (Sweden)
S.-D. Zhang
2000-10-01
Full Text Available By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides
Experimental investigation of gravity wave turbulence and of non-linear four wave interactions..
Berhanu, Michael
2017-04-01
Using the large basins of the Ecole Centrale de Nantes (France), non-linear interactions of gravity surface waves are experimentally investigated. In a first part we study statistical properties of a random wave field regarding the insights from the Wave Turbulence Theory. In particular freely decaying gravity wave turbulence is generated in a closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonl-inear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, non-linear and dissipative time scales to test the time scale separation. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov constant of the weak turbulence theory is evaluated. In a second part, resonant interactions of oblique surface gravity waves in a large basin are studied. We generate two oblique waves crossing at an acute angle. These mother waves mutually interact and give birth to a resonant wave whose properties (growth rate, resonant response curve and phase locking) are fully characterized. All our experimental results are found in good quantitative agreement with four-wave interaction theory. L. Deike, B. Miquel, P. Gutiérrez, T. Jamin, B. Semin, M. Berhanu, E. Falcon and F. Bonnefoy, Role of the basin boundary conditions in gravity wave turbulence, Journal of Fluid Mechanics 781, 196 (2015) F. Bonnefoy, F. Haudin, G. Michel, B. Semin, T. Humbert, S. Aumaître, M. Berhanu and E. Falcon, Observation of resonant interactions among surface gravity waves, Journal of Fluid Mechanics (Rapids) 805, R3 (2016)
On the nonlinear shaping mechanism for gravity wave spectrum in the atmosphere
Directory of Open Access Journals (Sweden)
I. P. Chunchuzov
2009-11-01
Full Text Available The nonlinear mechanism of shaping of a high vertical wave number spectral tail in the field of a few discrete internal gravity waves in the atmosphere is studied in this paper. The effects of advection of fluid parcels by interacting gravity waves are taken strictly into account by calculating wave field in Lagrangian variables, and performing a variable transformation from Lagrangian to Eulerian frame. The vertical profiles and vertical wave number spectra of the Eulerian displacement field are obtained for both the case of resonant and non-resonant wave-wave interactions. The evolution of these spectra with growing parameter of nonlinearity of the internal wave field is studied and compared to that of a broad band spectrum of gravity waves with randomly independent amplitudes and phases. The calculated vertical wave number spectra of the vertical displacements or relative temperature fluctuations are found to be consistent with the observed spectra in the middle atmosphere.
Analytical and numerical investigation of nonlinear internal gravity waves
Directory of Open Access Journals (Sweden)
S. P. Kshevetskii
2001-01-01
Full Text Available The propagation of long, weakly nonlinear internal waves in a stratified gas is studied. Hydrodynamic equations for an ideal fluid with the perfect gas law describe the atmospheric gas behaviour. If we neglect the term Ͽ dw/dt (product of the density and vertical acceleration, we come to a so-called quasistatic model, while we name the full hydro-dynamic model as a nonquasistatic one. Both quasistatic and nonquasistatic models are used for wave simulation and the models are compared among themselves. It is shown that a smooth classical solution of a nonlinear quasistatic problem does not exist for all t because a gradient catastrophe of non-linear internal waves occurs. To overcome this difficulty, we search for the solution of the quasistatic problem in terms of a generalised function theory as a limit of special regularised equations containing some additional dissipation term when the dissipation factor vanishes. It is shown that such solutions of the quasistatic problem qualitatively differ from solutions of a nonquasistatic nature. It is explained by the fact that in a nonquasistatic model the vertical acceleration term plays the role of a regularizator with respect to a quasistatic model, while the solution qualitatively depends on the regularizator used. The numerical models are compared with some analytical results. Within the framework of the analytical model, any internal wave is described as a system of wave modes; each wave mode interacts with others due to equation non-linearity. In the principal order of a perturbation theory, each wave mode is described by some equation of a KdV type. The analytical model reveals that, in a nonquasistatic model, an internal wave should disintegrate into solitons. The time of wave disintegration into solitons, the scales and amount of solitons generated are important characteristics of the non-linear process; they are found with the help of analytical and numerical investigations. Satisfactory
Energy Technology Data Exchange (ETDEWEB)
Mitsotakis, Dimitrios, E-mail: dmitsot@gmail.com [Victoria University of Wellington, School of Mathematics, Statistics and Operations Research, PO Box 600, Wellington 6140 (New Zealand); Dutykh, Denys, E-mail: Denys.Dutykh@univ-savoie.fr [LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus Scientifique, F-73376 Le Bourget-du-Lac Cedex (France); Assylbekuly, Aydar, E-mail: asylbekuly@mail.ru [Khoja Akhmet Yassawi International Kazakh–Turkish University, Faculty of Natural Science, Department of Mathematics, 161200 Turkestan (Kazakhstan); Zhakebayev, Dauren, E-mail: daurjaz@mail.ru [Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics, Department of Mathematical and Computer Modelling, 050000 Almaty (Kazakhstan)
2017-05-25
In this Letter we consider long capillary–gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott–Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well. - Highlights: • A model for long capillary–gravity weakly dispersive and fully nonlinear water waves is derived. • Shallow capillary–gravity waves are classified using phase plane analysis. • Peaked travelling waves are found in the critical regime. • The dynamics of peakons in Serre–Green–Naghdi equations is studied numerically.
The evolution of a localized nonlinear wave of the Kelvin-Helmholtz instability with gravity
Orazzo, Annagrazia; Hoepffner, Jérôme
2012-11-01
At the interface between two fluids of different density and in the presence of gravity, there are well known periodic surface waves which can propagate for long distances with little attenuation, as it is for instance the case at the surface of the sea. If wind is present, these waves progressively accumulate energy as they propagate and grow to large sizes—this is the Kelvin-Helmholtz instability. On the other hand, we show in this paper that for a given wind strength, there is potential for the growth of a localized nonlinear wave. This wave can reach a size such that the hydrostatic pressure drop from top to bottom equals the stagnation pressure of the wind. This process for the disruption of the flat interface is localized and nonlinear. We study the properties of this wave using numerical simulations of the Navier-Stokes equations.
Energy Technology Data Exchange (ETDEWEB)
Huang, K.M. [Wuhan Univ. (China). School of Electronic Information; Chinese Academey of Sciences, Hefei (China). Key Lab. of Geospace Environment; Embry Riddle Aeronautical Univ., Daytona Beach, FL (United States). Dept. of Physical Science; Ministry of Education, Wuhan (China). Key Lab. of Geospace Environment and Geodesy; State Observatory for Atmospheric Remote Sensing, Wuhan (China); Liu, A.Z.; Li, Z. [Embry Riddle Aeronautical Univ., Daytona Beach, FL (United States). Dept. of Physical Science; Zhang, S.D.; Yi, F. [Wuhan Univ. (China). School of Electronic Information; Ministry of Education, Wuhan (China). Key Lab. of Geospace Environment and Geodesy; State Observatory for Atmospheric Remote Sensing, Wuhan (China)
2012-07-01
Nonlinear interactions of gravity waves are studied with a two-dimensional, fully nonlinear model. The energy exchanges among resonant and near-resonant triads are examined in order to understand the spectral energy transfer through interactions. The results show that in both resonant and near-resonant interactions, the energy exchange between two high frequency waves is strong, but the energy transfer from large to small vertical scale waves is rather weak. This suggests that the energy cascade toward large vertical wavenumbers through nonlinear interaction is inefficient, which is different from the rapid turbulence cascade. Because of considerable energy exchange, nonlinear interactions can effectively spread high frequency spectrum, and play a significant role in limiting wave amplitude growth and transferring energy into higher altitudes. In resonant interaction, the interacting waves obey the resonant matching conditions, and resonant excitation is reversible, while near-resonant excitation is not so. Although near-resonant interaction shows the complexity of match relation, numerical experiments show an interesting result that when sum and difference near-resonant interactions occur between high and low frequency waves, the wave vectors tend to approximately match in horizontal direction, and the frequency of the excited waves is also close to the matching value. (orig.)
Merkel, A; Tournat, V; Gusev, V
2014-08-01
We report the experimental observation of the gravity-induced asymmetry for the nonlinear transformation of acoustic waves in a noncohesive granular phononic crystal. Because of the gravity, the contact precompression increases with depth inducing space variations of not only the linear and nonlinear elastic moduli but also of the acoustic wave dissipation. We show experimentally and explain theoretically that, in contrast to symmetric propagation of linear waves, the amplitude of the nonlinearly self-demodulated wave depends on whether the propagation of the waves is in the direction of the gravity or in the opposite direction. Among the observed nonlinear processes, we report frequency mixing of the two transverse-rotational modes belonging to the optical band of vibrations and propagating with negative phase velocities, which results in the excitation of a longitudinal wave belonging to the acoustic band of vibrations and propagating with positive phase velocity. We show that the measurements of the gravity-induced asymmetry in the nonlinear acoustic phenomena can be used to compare the in-depth distributions of the contact nonlinearity and of acoustic absorption.
Acoustic-gravity nonlinear structures
Directory of Open Access Journals (Sweden)
D. Jovanović
2002-01-01
Full Text Available A catalogue of nonlinear vortex structures associated with acoustic-gravity perturbations in the Earth's atmosphere is presented. Besides the previously known Kelvin-Stewart cat's eyes, dipolar and tripolar structures, new solutions having the form of a row of counter-rotating vortices, and several weakly two-dimensional vortex chains are given. The existence conditions for these nonlinear structures are discussed with respect to the presence of inhomogeneities of the shear flows. The mode-coupling mechanism for the nonlinear generation of shear flows in the presence of linearly unstable acoustic-gravity waves, possibly also leading to intermittency and chaos, is presented.
Directory of Open Access Journals (Sweden)
A. V. Vikulin
2014-01-01
Full Text Available Gravity phenomena related to the Earth movements in the Solar System and through the Galaxy are reviewed. Such movements are manifested by geological processes on the Earth and correlate with geophysical fields of the Earth. It is concluded that geodynamic processes and the gravity phenomena (including those of cosmic nature are related. The state of the geomedium composed of blocks is determined by stresses with force moment and by slow rotational waves that are considered as a new type of movements [Vikulin, 2008, 2010]. It is shown that the geomedium has typical rheid properties [Carey, 1954], specifically an ability to flow while being in the solid state [Leonov, 2008]. Within the framework of the rotational model with a symmetric stress tensor, which is developed by the authors [Vikulin, Ivanchin, 1998; Vikulin et al., 2012a, 2013], such movement of the geomedium may explain the energy-saturated state of the geomedium and a possibility of its movements in the form of vortex geological structures [Lee, 1928]. The article discusses the gravity wave detection method based on the concept of interactions between gravity waves and crustal blocks [Braginsky et al., 1985]. It is concluded that gravity waves can be recorded by the proposed technique that detects slow rotational waves. It is shown that geo-gravitational movements can be described by both the concept of potential with account of gravitational energy of bodies [Kondratyev, 2003] and the nonlinear physical acoustics [Gurbatov et al., 2008]. Based on the combined description of geophysical and gravitational wave movements, the authors suggest a hypothesis about the nature of spin, i.e. own moment as a demonstration of the space-time ‘vortex’ properties.
Nonlinear internal gravity waves and their interaction with the mean wind
International Nuclear Information System (INIS)
Grimshaw, R.
1975-01-01
The interaction of a wave packet of internal gravity waves with the mean wind is investigated, for the case when there is a region of wind shear and hence a critical level. The principal equations are the Doppler-shifted dispersion relation, the equation for conservation of wave action and the mean momentum equation, in which the mean wind is accelerated by a 'radiation stress' tensor, due to the waves. These equations are integrated numerically to study the behaviour of a wave packet approaching a critical level, where the horizontal phase speed matches the mean wind. The results demonstrate the exchange of energy from the waves to the mean wind in the vicinity of the critical level. The interaction between the waves and the mean wind is also studied in the absence of any initial wind shear. (author)
International Nuclear Information System (INIS)
Pinheiro, R.
1979-01-01
The properties and production of gravitational radiation are described. The prospects for their detection are considered including the Weber apparatus and gravity-wave telescopes. Possibilities of gravity-wave astronomy are noted
Directory of Open Access Journals (Sweden)
Antonio Gledson Goulart
2013-12-01
Full Text Available In this paper, the equation for the gravity wave spectra in mean atmosphere is analytically solved without linearization by the Adomian decomposition method. As a consequence, the nonlinear nature of problem is preserved and the errors found in the results are only due to the parameterization. The results, with the parameterization applied in the simulations, indicate that the linear solution of the equation is a good approximation only for heights shorter than ten kilometers, because the linearization the equation leads to a solution that does not correctly describe the kinetic energy spectra.
Huang, N. E.; Long, S. R.; Bliven, L. F.; Tung, C.-C.
1984-01-01
On the basis of the mapping method developed by Huang et al. (1983), an analytic expression for the non-Gaussian joint probability density function of slope and elevation for nonlinear gravity waves is derived. Various conditional and marginal density functions are also obtained through the joint density function. The analytic results are compared with a series of carefully controlled laboratory observations, and good agreement is noted. Furthermore, the laboratory wind wave field observations indicate that the capillary or capillary-gravity waves may not be the dominant components in determining the total roughness of the wave field. Thus, the analytic results, though derived specifically for the gravity waves, may have more general applications.
Pizzo, Nick
2017-11-01
A simple criterion for water particles to surf an underlying surface gravity wave is presented. It is found that particles travelling near the phase speed of the wave, in a geometrically confined region on the forward face of the crest, increase in speed. The criterion is derived using the equation of John (Commun. Pure Appl. Maths, vol. 6, 1953, pp. 497-503) for the motion of a zero-stress free surface under the action of gravity. As an example, a breaking water wave is theoretically and numerically examined. Implications for upper-ocean processes, for both shallow- and deep-water waves, are discussed.
Nonlinear effects in water waves
International Nuclear Information System (INIS)
Janssen, P.A.E.M.
1989-05-01
This set of lecture notes on nonlinear effects in water waves was written on the occasion of the first ICTP course on Ocean Waves and Tides held from 26 September until 28 October 1988 in Trieste, Italy. It presents a summary and unification of my knowledge on nonlinear effects of gravity waves on an incompressible fluid without vorticity. The starting point of the theory is the Hamiltonian for water waves. The evolution equations of both weakly nonlinear, shallow water and deep water gravity waves are derived by suitable approximation of the energy of the waves, resulting in the Korteweg-de Vries equation and the Zakharov equation, respectively. Next, interesting properties of the KdV equation (solitons) and the Zakharov equation (instability of a finite amplitude wave train) are discussed in some detail. Finally, the evolution of a homogeneous, random wave field due to resonant four wave processes is considered and the importance of this process for ocean wave prediction is pointed out. 38 refs, 21 figs
Khait, A.; Shemer, L.
2018-05-01
The evolution of unidirectional wave trains containing a wave that gradually becomes steep is evaluated experimentally and numerically using the Boundary Element Method (BEM). The boundary conditions for the nonlinear numerical simulations corresponded to the actual movements of the wavemaker paddle as recorded in the physical experiments, allowing direct comparison between the measured in experiments' characteristics of the wave train and the numerical predictions. The high level of qualitative and quantitative agreement between the measurements and simulations validated the kinematic criterion for the inception of breaking and the location of the spilling breaker, on the basis of the BEM computations and associated experiments. The breaking inception is associated with the fluid particle at the crest of the steep wave that has been accelerated to match and surpass the crest velocity. The previously observed significant slow-down of the crest while approaching breaking is verified numerically; both narrow-/broad-banded wave trains are considered. Finally, the relative importance of linear and nonlinear contributions is analyzed.
Scattering of internal gravity waves
Leaman Nye, Abigail
2011-01-01
Internal gravity waves play a fundamental role in the dynamics of stably stratified regions of the atmosphere and ocean. In addition to the radiation of momentum and energy remote from generation sites, internal waves drive vertical transport of heat and mass through the ocean by wave breaking and the mixing subsequently produced. Identifying regions where internal gravity waves contribute to ocean mixing and quantifying this mixing are therefore important for accurate climate ...
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Nonlinear surface Alfven waves
International Nuclear Information System (INIS)
Cramer, N.F.
1991-01-01
The problem of nonlinear surface Alfven waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schroedinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field. (author)
The physics of orographic gravity wave drag
Directory of Open Access Journals (Sweden)
Miguel A C Teixeira
2014-07-01
Full Text Available The drag and momentum fluxes produced by gravity waves generated in flow over orography are reviewed, focusing on adiabatic conditions without phase transitions or radiation effects, and steady mean incoming flow. The orographic gravity wave drag is first introduced in its simplest possible form, for inviscid, linearized, non-rotating flow with the Boussinesq and hydrostatic approximations, and constant wind and static stability. Subsequently, the contributions made by previous authors (primarily using theory and numerical simulations to elucidate how the drag is affected by additional physical processes are surveyed. These include the effect of orography anisotropy, vertical wind shear, total and partial critical levels, vertical wave reflection and resonance, non-hydrostatic effects and trapped lee waves, rotation and nonlinearity. Frictional and boundary layer effects are also briefly mentioned. A better understanding of all of these aspects is important for guiding the improvement of drag parametrization schemes.
Numerical simulations of convectively excited gravity waves
International Nuclear Information System (INIS)
Glatzmaier, G.A.
1983-01-01
Magneto-convection and gravity waves are numerically simulated with a nonlinear, three-dimensional, time-dependent model of a stratified, rotating, spherical fluid shell heated from below. A Solar-like reference state is specified while global velocity, magnetic field, and thermodynamic perturbations are computed from the anelastic magnetohydrodynamic equations. Convective overshooting from the upper (superadiabatic) part of the shell excites gravity waves in the lower (subadiabatic) part. Due to differential rotation and Coriolis forces, convective cell patterns propagate eastward with a latitudinally dependent phase velocity. The structure of the excited wave motions in the stable region is more time-dependent than that of the convective motions above. The magnetic field tends to be concentrated over giant-cell downdrafts in the convective zone but is affected very little by the wave motion in the stable region
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Rogue waves in nonlinear science
International Nuclear Information System (INIS)
Yan Zhenya
2012-01-01
Rogue waves, as a special type of solitary waves, play an important role in nonlinear optics, Bose-Einstein condensates, ocean, atmosphere, and even finance. In this report, we mainly review on the history of the rogue wave phenomenon and recent development of rogue wave solutions in some nonlinear physical models arising in the fields of nonlinear science.
The wave of the future - Searching for gravity waves
International Nuclear Information System (INIS)
Goldsmith, D.
1991-01-01
Research on gravity waves conducted by such scientists as Gamov, Wheeler, Weber and Zel'dovich is discussed. Particular attention is given to current trends in the theoretical analysis of gravity waves carried out by theorists Kip Thorne and Leonid Grishchuk. The problems discussed include the search for gravity waves; calculation of the types of gravity waves; the possibility of detecting gravity waves from localized sources, e.g., from the collision of two black holes in a distant galaxy or the collapse of a star, through the Laser Interferometer Gravitational Wave Observatory; and detection primordial gravity waves from the big bang
Huang, N. E.; Tung, C.-C.
1977-01-01
The influence of the directional distribution of wave energy on the dispersion relation is calculated numerically using various directional wave spectrum models. The results indicate that the dispersion relation varies both as a function of the directional energy distribution and the direction of propagation of the wave component under consideration. Furthermore, both the mean deviation and the random scatter from the linear approximation increase as the energy spreading decreases. Limited observational data are compared with the theoretical results. The agreement is favorable.
Laser Source for Atomic Gravity Wave Detector
National Aeronautics and Space Administration — The Atom Interferometry (AI) Technology for Gravity Wave Measurements demonstrates new matter wave Interferometric sensor technology for precise detection and...
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Periodic waves in nonlinear metamaterials
International Nuclear Information System (INIS)
Liu, Wen-Jun; Xiao, Jing-Hua; Yan, Jie-Yun; Tian, Bo
2012-01-01
Periodic waves are presented in this Letter. With symbolic computation, equations for monochromatic waves are studied, and analytic periodic waves are obtained. Factors affecting properties of periodic waves are analyzed. Nonlinear metamaterials, with the continuous distribution of the dielectric permittivity obtained, are different from the ones with the discrete distribution. -- Highlights: ► Equations for the monochromatic waves in transverse magnetic polarization have been studied. ► Analytic periodic waves for the equations have been obtained. ► Periodic waves are theoretically presented and studied in the nonlinear metamaterials.
Solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere
International Nuclear Information System (INIS)
Li Ziliang
2008-01-01
By introducing a new transformation, a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system, which extends Fan's direct algebraic method to the case when r > 4. The solutions of a first-order nonlinear ordinary differential equation with a higher degree nonlinear term and Fan's direct algebraic method of obtaining exact solutions to nonlinear partial differential equations are applied to the combined KdV-mKdV-GKdV equation, which is derived from a simple incompressible non-hydrostatic Boussinesq equation with the influence of thermal forcing and is applied to investigate internal gravity waves in the atmosphere. As a result, by taking advantage of the new first-order nonlinear ordinary differential equation with a fifth-degree nonlinear term and an eighth-degree nonlinear term, periodic wave solutions associated with the Jacobin elliptic function and the bell and kink profile solitary wave solutions are obtained under the effect of thermal forcing. Most importantly, the mechanism of propagation and generation of the periodic waves and the solitary waves is analysed in detail according to the values of the heating parameter, which show that the effect of heating in atmosphere helps to excite westerly or easterly propagating periodic internal gravity waves and internal solitary waves in atmosphere, which are affected by the local excitation structures in atmosphere. In addition, as an illustrative sample, the properties of the solitary wave solution and Jacobin periodic solution are shown by some figures under the consideration of heating interaction
Mayr, Hans G.; Mengel, J. G.; Chan, K. L.; Huang, F. T.
2010-01-01
As Lindzen (1981) had shown, small-scale gravity waves (GW) produce the observed reversals of the zonal-mean circulation and temperature variations in the upper mesosphere. The waves also play a major role in modulating and amplifying the diurnal tides (DT) (e.g., Waltersheid, 1981; Fritts and Vincent, 1987; Fritts, 1995a). We summarize here the modeling studies with the mechanistic numerical spectral model (NSM) with Doppler spread parameterization for GW (Hines, 1997a, b), which describes in the middle atmosphere: (a) migrating and non-migrating DT, (b) planetary waves (PW), and (c) global-scale inertio gravity waves. Numerical experiments are discussed that illuminate the influence of GW filtering and nonlinear interactions between DT, PW, and zonal mean variations. Keywords: Theoretical modeling, Middle atmosphere dynamics, Gravity wave interactions, Migrating and non-migrating tides, Planetary waves, Global-scale inertio gravity waves.
International Nuclear Information System (INIS)
Cui Weiguang; Zhang Pengjie; Yang Xiaohu
2010-01-01
A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify the Gadget-2 code and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. The modified gravity model that we investigate in the present paper is characterized by a single parameter ζ, which determines the enhancement of particle acceleration with respect to general relativity (GR), given the identical mass distribution (ζ=1 in GR). The first nonlinear statistics we investigate is the nonlinear matter power spectrum at k < or approx. 3h/Mpc, which is the relevant range for robust weak lensing power spectrum modeling at l < or approx. 2000. In this study, we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. This particular statistics highlights the imprint of modified gravity in the nonlinear regime and the importance of including the nonlinear regime in testing GR. By design, it is less susceptible to the sample variance and numerical artifacts. We adopt a mass assignment method based on wavelet to improve the power spectrum measurement. We run a series of tests to determine the suitable simulation specifications (particle number, box size, and initial redshift). We find that, the nonlinear power spectra can differ by ∼30% for 10% deviation from GR (|ζ-1|=0.1) where the rms density fluctuations reach 10. This large difference, on one hand, shows the richness of information on gravity in the corresponding scales, and on the other hand, invalidates simple extrapolations of some existing fitting formulae to modified gravity cosmology.
Nonlinear waves and weak turbulence
Zakharov, V E
1997-01-01
This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.
Collapse of nonlinear Langmuir waves
International Nuclear Information System (INIS)
Malkin, V.M.
1986-01-01
The dispersion of sufficiently intensive Langmuir waves is determined by intrinsic (electron) nonlinearity. During Langmuir collapse the wave energy density required for the appearance of electron nonlinearity is attained, generally speaking, prior to the development of dissipative processes. Up to now, the effect of electron nonlinearity on the collapse dynamics and spectrum of strong Langmuir turbulence ( which may be very appreciable ) has not been studied extensively because of the difficulty of describing nonlinear Langmuir waves. In the present paper the positive determinacy of the electron nonlinear hamiltonian is proven, the increment of modulation instability of a nonlinear Langmuir wave cluster localized in a cavity is calculated, and the universal law of their collapse is found
Nonlinear modulation of ionization waves
International Nuclear Information System (INIS)
Bekki, Naoaki
1981-01-01
In order to investigate the nonlinear characteristics of ionization waves (moving-striations) in the positive column of glow discharge, a nonlinear modulation of ionization waves in the region of the Pupp critical current is analysed by means of the reductive perturbation method. The modulation of ionization waves is described by a nonlinear Schroedinger type equation. The coefficients of the equation are evaluated using the data of the low pressure Argon-discharge, and the simple solutions (plane wave and envelope soliton type solutions) are presented. Under a certain condition an envelope soliton is propagated through the positive column. (author)
Gravity induced wave function collapse
Gasbarri, G.; Toroš, M.; Donadi, S.; Bassi, A.
2017-11-01
Starting from an idea of S. L. Adler [in Quantum Nonlocality and Reality: 50 Years of Bell's Theorem, edited by M. Bell and S. Gao (Cambridge University Press, Cambridge, England 2016)], we develop a novel model of gravity induced spontaneous wave function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength ξ of the complex metric fluctuations with available experimental data. We show that ξ ≥10-26 in order for the model to guarantee classicality of macro-objects, and at the same time ξ ≤10-20 in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of ξ ˜10-21.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations...
Wave transmission in nonlinear lattices
International Nuclear Information System (INIS)
Hennig, D.; Tsironis, G.P.
1999-01-01
The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation properties quite distinct from those appearing in continuous nonlinear systems. For a large variety of condensed matter and optics applications the continuous wave approximation is not appropriate. In the present review we discuss wave transmission properties in one dimensional nonlinear lattices. Our paradigmatic equations are discrete nonlinear Schroedinger equations and their study is done through a dynamical systems approach. We focus on stationary wave properties and utilize well known results from the theory of dynamical systems to investigate various aspects of wave transmission and wave localization. We analyze in detail the more general dynamical system corresponding to the equation that interpolates between the non-integrable discrete nonlinear Schroedinger equation and the integrable Albowitz-Ladik equation. We utilize this analysis in a nonlinear Kronig-Penney model and investigate transmission and band modification properties. We discuss the modifications that are effected through an electric field and the nonlinear Wannier-Stark localization effects that are induced. Several applications are described, such as polarons in one dimensional lattices, semiconductor superlattices and one dimensional nonlinear photonic band gap systems. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
The sources of atmospheric gravity waves
International Nuclear Information System (INIS)
Nagpal, O.P.
1979-01-01
The gravity wave theory has been very successful in the interpretation of various upper atmospheric phenomena. This article offers a review of the present state of knowledge about the various sources of atmospheric gravity waves, particularly those which give rise to different types of travelling ionospheric disturbance. Some specific case studies are discussed. (author)
An introduction to atmospheric gravity waves
Nappo, Carmen J
2012-01-01
Gravity waves exist in all types of geophysical fluids, such as lakes, oceans, and atmospheres. They play an important role in redistributing energy at disturbances, such as mountains or seamounts and they are routinely studied in meteorology and oceanography, particularly simulation models, atmospheric weather models, turbulence, air pollution, and climate research. An Introduction to Atmospheric Gravity Waves provides readers with a working background of the fundamental physics and mathematics of gravity waves, and introduces a wide variety of applications and numerous recent advances. Nappo provides a concise volume on gravity waves with a lucid discussion of current observational techniques and instrumentation.An accompanying website contains real data, computer codes for data analysis, and linear gravity wave models to further enhance the reader's understanding of the book's material. Companion web site features animations and streaming video Foreword by George Chimonas, a renowned expert on the interac...
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
Stochastic inflation and nonlinear gravity
International Nuclear Information System (INIS)
Salopek, D.S.; Bond, J.R.
1991-01-01
We show how nonlinear effects of the metric and scalar fields may be included in stochastic inflation. Our formalism can be applied to non-Gaussian fluctuation models for galaxy formation. Fluctuations with wavelengths larger than the horizon length are governed by a network of Langevin equations for the physical fields. Stochastic noise terms arise from quantum fluctuations that are assumed to become classical at horizon crossing and that then contribute to the background. Using Hamilton-Jacobi methods, we solve the Arnowitt-Deser-Misner constraint equations which allows us to separate the growing modes from the decaying ones in the drift phase following each stochastic impulse. We argue that the most reasonable choice of time hypersurfaces for the Langevin system during inflation is T=ln(Ha), where H and a are the local values of the Hubble parameter and the scale factor, since T is the natural time for evolving the short-wavelength scalar field fluctuations in an inhomogeneous background
On nonlinear periodic drift waves
International Nuclear Information System (INIS)
Kauschke, U.; Schlueter, H.
1990-09-01
Nonlinear periodic drift waves are investigated on the basis of a simple perturbation scheme for both the amplitude and inverse frequency. The coefficients for the generation of the forced harmonics are derived, a nonlinear dispersion relation is suggested and a criterion for the onset of the modulational instability is obtained. The results are compared with the ones obtained with the help of a standard KBM-treatment. Moreover cnoidal drift waves are suggested and compared to an experimental observation. (orig.)
2015-05-07
associated with the lattice background; the nonlinearity is derived from the inclusion of cubic nonlinearity. Often the background potential is periodic...dispersion branch we can find discrete evolution equations for the envelope associated with the lattice NLS equation (1) by looking for solutions of...spatial operator in the above NLS equation can be elliptic, hyperbolic or parabolic . We remark that further reduction is possible by going into a moving
Oscillating nonlinear acoustic shock waves
DEFF Research Database (Denmark)
Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth
2016-01-01
We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show that at resona......We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....
Upper atmospheric planetary-wave and gravity-wave observations
Justus, C. G.; Woodrum, A.
1973-01-01
Previously collected data on atmospheric pressure, density, temperature and winds between 25 and 200 km from sources including Meteorological Rocket Network data, ROBIN falling sphere data, grenade release and pitot tube data, meteor winds, chemical release winds, satellite data, and others were analyzed by a daily-difference method, and results on the magnitude of atmospheric perturbations interpreted as gravity waves and planetary waves are presented. Traveling planetary-wave contributions in the 25-85 km range were found to have significant height and latitudinal variation. It was found that observed gravity-wave density perturbations and wind are related to one another in the manner predicted by gravity-wave theory. It was determined that, on the average, gravity-wave energy deposition or reflection occurs at all altitudes except the 55-75 km region of the mesosphere.
New approaches to nonlinear waves
2016-01-01
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the app...
The instability of internal gravity waves to localised disturbances
Directory of Open Access Journals (Sweden)
J. Vanneste
1995-02-01
Full Text Available The instability of an internal gravity wave due to nonlinear wave-wave interaction is studied theoretically and numerically. Three different aspects of this phenomenon are examined. 1. The influence of dissipation on both the resonant and the nonresonant interactions is analysed using a normal mode expansion of the basic equations. In particular, the modifications induced in the interaction domain are calculated and as a result some modes are shown to be destabilised by dissipation. 2. The evolution of an initial unstable disturbance of finite vertical extent is described as the growth of two secondary wave packets travelling at the same group velocity. A quasi-linear correction to the basic primary wave is calculated, corresponding to a localised amplitude decrease due to the disturbance growth. 3. Numerical experiments are carried out to study the effect of a basic shear on wave instability. It appears that the growing secondary waves can have a frequency larger than that of the primary wave, provided that the shear is sufficient. The instability of waves with large amplitude and long period, such as tides or planetary waves, could therefore be invoked as a possible mechanism for the generation of gravity waves with shorter period in the middle atmosphere.
Statistical properties of nonlinear one-dimensional wave fields
Directory of Open Access Journals (Sweden)
D. Chalikov
2005-01-01
Full Text Available A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.
Statistical properties of nonlinear one-dimensional wave fields
Chalikov, D.
2005-06-01
A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.
Nonlinear waves in solar plasmas - a review
International Nuclear Information System (INIS)
Ballai, I
2006-01-01
Nonlinearity is a direct consequence of large scale dynamics in the solar plasmas. When nonlinear steepening of waves is balanced by dispersion, solitary waves are generated. In the vicinity of resonances, waves can steepen into nonlinear waves influencing the efficiency of energy deposition. Here we review recent theoretical breakthroughs that have lead to a greater understanding of many aspects of nonlinear waves arising in homogeneous and inhomogeneous solar plasmas
Tidal and gravity waves study from the airglow measurements at ...
Indian Academy of Sciences (India)
The other waves may be the upward propagating gravity waves or waves resulting from the interaction of inter-mode tidal oscillations, interaction of tidal waves with planetary waves and gravity waves. Some times, the second harmonic wave has higher vertical velocity than the corresponding fundamental wave. Application ...
Nonlinear waves and pattern dynamics
Pelinovsky, Efim; Mutabazi, Innocent
2018-01-01
This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physi...
Nonlinear positron acoustic solitary waves
International Nuclear Information System (INIS)
Tribeche, Mouloud; Aoutou, Kamel; Younsi, Smain; Amour, Rabia
2009-01-01
The problem of nonlinear positron acoustic solitary waves involving the dynamics of mobile cold positrons is addressed. A theoretical work is presented to show their existence and possible realization in a simple four-component plasma model. The results should be useful for the understanding of the localized structures that may occur in space and laboratory plasmas as new sources of cold positrons are now well developed.
Relic gravity waves from braneworld inflation
International Nuclear Information System (INIS)
Sahni, Varun; Sami, M.; Souradeep, Tarun
2002-01-01
We discuss a scenario in which extra dimensional effects allow a scalar field with a steep potential to play the dual role of the inflaton as well as dark energy (quintessence). The post-inflationary evolution of the universe in this scenario is generically characterized by a 'kinetic regime' during which the kinetic energy of the scalar field greatly exceeds its potential energy resulting in a 'stiff' equation of state for scalar field matter P φ ≅ρ φ . The kinetic regime precedes the radiation dominated epoch and introduces an important new feature into the spectrum of relic gravity waves created quantum mechanically during inflation. The amplitude of the gravity wave spectrum increases with the wave number for wavelengths shorter than the comoving horizon scale at the commencement of the radiative regime. This 'blue tilt' is a generic feature of models with steep potentials and imposes strong constraints on a class of inflationary braneworld models. Prospects for detection of the gravity wave background by terrestrial and space-borne gravity wave observatories such as LIGO II and LISA are discussed
Laser Source for Atomic Gravity Wave Detector Project
National Aeronautics and Space Administration — The Atom Interferometry (AI) Technology for Gravity Wave Measurements demonstrates new matter wave Interferometric sensor technology for precise detection and...
Wave modulation in a nonlinear dispersive medium
International Nuclear Information System (INIS)
Kim, Y.C.; Khadra, L.; Powers, E.J.
1980-01-01
A model describing the simultaneous amplitude and phase modulation of a carrier wave propagating in a nonlinear dispersive medium is developed in terms of nonlinear wave-wave interactions between the sidebands and a low frequency wave. It is also shown that the asymmetric distribution of sidebands is determined by the wavenumber dependence of the coupling coefficient. Digital complex demodulation techniques are used to study modulated waves in a weakly ionized plasma and the experimental results support the analytical model
Nonlinear lattice waves in heterogeneous media
International Nuclear Information System (INIS)
Laptyeva, T V; Ivanchenko, M V; Flach, S
2014-01-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry–André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations. (topical review)
Gravity's kiss the detection of gravitational waves
Collins, Harry
2017-01-01
Scientists have been trying to confirm the existence of gravitational waves for fifty years. Then, in September 2015, came a "very interesting event" (as the cautious subject line in a physicist's email read) that proved to be the first detection of gravitational waves. In Gravity's Kiss, Harry Collins -- who has been watching the science of gravitational wave detection for forty-three of those fifty years and has written three previous books about it -- offers a final, fascinating account, written in real time, of the unfolding of one of the most remarkable scientific discoveries ever made. Predicted by Einstein in his theory of general relativity, gravitational waves carry energy from the collision or explosion of stars. Dying binary stars, for example, rotate faster and faster around each other until they merge, emitting a burst of gravitational waves. It is only with the development of extraordinarily sensitive, highly sophisticated detectors that physicists can now confirm Einstein's prediction. This is...
Nonlinear Electron Waves in Strongly Magnetized Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans; Juul Rasmussen, Jens
1980-01-01
Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...... dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed....
Gravity the quest for gravitational wave
Binétruy, Pierre
2018-01-01
What force do the Big Bang, the expansion of the Universe, dark matter and dark energy, black holes, and gravitational waves all have in common? This book uncovers gravity as a key to understanding these fascinating phenomena that have so captivated public interest in recent years. Readers will discover the latest findings on how this familiar force in our everyday lives powers the most colossal changes in the Universe. Written by the widely recognized French public scientist and leading astrophysicist Pierre Binetruy, the book also explains the recent experimental confirmation of the existence of gravitational waves.
Seeding and layering of equatorial spread F by gravity waves
International Nuclear Information System (INIS)
Hysell, D.L.; Kelley, M.C.; Swartz, W.E.; Woodman, R.F.
1990-01-01
Studies dating back more than 15 years have presented evidence that atmospheric gravity waves play a role in initiating nighttime equatorial F region instabilities. This paper analyzes a spectabular spread F event that for the first time demonstrates a layering which, the authors argue, is controlled by a gravity wave effect. The 50-km vertical wavelength of a gravity wave which they have found is related theoretically to a plasma layering irregularity that originated at low altitudes and then was convected, intact, to higher altitudes. Gravity waves also seem to have determined bottomside intermediate scale undulations, although this fact is not as clear in the data. The neutral wind dynamo effect yields wave number conditions on the gravity wave's ability to modulate the Rayleigh-Taylor instaiblity process. Finally, after evaluating the gravity wave dispersion relation and spatial resonance conditions, we estimate the properties of the seeding wave
The Impact of Dam-Reservoir-Foundation Interaction on Nonlinear Response of Concrete Gravity Dams
International Nuclear Information System (INIS)
Amini, Ali Reza; Motamedi, Mohammad Hossein; Ghaemian, Mohsen
2008-01-01
To study the impact of dam-reservoir-foundation interaction on nonlinear response of concrete gravity dams, a two-dimensional finite element model of a concrete gravity dam including the dam body, a part of its foundation and a part of the reservoir was made. In addition, the proper boundary conditions were used in both reservoir and foundation in order to absorb the energy of outgoing waves at the far end boundaries. Using the finite element method and smeared crack approach, some different seismic nonlinear analyses were done and finally, we came to a conclusion that the consideration of dam-reservoir-foundation interaction in nonlinear analysis of concrete dams is of great importance, because from the performance point of view, this interaction significantly improves the nonlinear response of concrete dams
Nonlinear evolution of astrophysical Alfven waves
Spangler, S. R.
1984-01-01
Nonlinear Alfven waves were studied using the derivative nonlinear Schrodinger equation as a model. The evolution of initial conditions, such as envelope solitons, amplitude-modulated waves, and band-limited noise was investigated. The last two furnish models for naturally occurring Alfven waves in an astrophysical plasma. A collapse instability in which a wave packet becomes more intense and of smaller spatial extent was analyzed. It is argued that this instability leads to enhanced plasma heating. In studies in which the waves are amplified by an electron beam, the instability tends to modestly inhibit wave growth.
Nonlinear waves in plasma with negative ion
International Nuclear Information System (INIS)
Saito, Maki; Watanabe, Shinsuke; Tanaca, Hiroshi.
1984-01-01
The propagation of nonlinear ion wave is investigated theoretically in a plasma with electron, positive ion and negative ion. The ion wave of long wavelength is described by a modified K-dV equation instead of a K-dV equation when the nonlinear coefficient of the K-dV equation vanishes at the critical density of negative ion. In the vicinity of the critical density, the ion wave is described by a coupled K-dV and modified K-dV equation. The transition from a compressional soliton to a rarefactive soliton and vice versa are examined by the coupled equation as a function of the negative ion density. The ion wave of short wavelength is described by a nonlinear Schroedinger equation. In the plasma with a negative ion, the nonlinear coefficient of the nonlinear Schroedinger equation changes the sign and the ion wave becomes modulationally unstable. (author)
Modelization of highly nonlinear waves in coastal regions
Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre
2015-04-01
The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.
Nonlinear coupled Alfven and gravitational waves
International Nuclear Information System (INIS)
Kaellberg, Andreas; Brodin, Gert; Bradley, Michael
2004-01-01
In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field and the coupling to compressional Alfven waves. The gravitational waves are considered in the high-frequency limit and the plasma is modeled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schroedinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected
Solitary waves on nonlinear elastic rods. I
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction betwe...... nonlinearity. The balance between dispersion and nonlinearity in the equation is investigated.......Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...... the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic...
Nonlinear wave collapse and strong turbulence
International Nuclear Information System (INIS)
Robinson, P.A.
1997-01-01
The theory and applications of wave self-focusing, collapse, and strongly nonlinear wave turbulence are reviewed. In the last decade, the theory of these phenomena and experimental realizations have progressed rapidly. Various nonlinear wave systems are discussed, but the simplest case of collapse and strong turbulence of Langmuir waves in an unmagnetized plasma is primarily used in explaining the theory and illustrating the main ideas. First, an overview of the basic physics of linear waves and nonlinear wave-wave interactions is given from an introductory perspective. Wave-wave processes are then considered in more detail. Next, an introductory overview of the physics of wave collapse and strong turbulence is provided, followed by a more detailed theoretical treatment. Later sections cover numerical simulations of Langmuir collapse and strong turbulence and experimental applications to space, ionospheric, and laboratory plasmas, including laser-plasma and beam-plasma interactions. Generalizations to self-focusing, collapse, and strong turbulence of waves in other systems are also discussed, including nonlinear optics, solid-state systems, magnetized auroral and astrophysical plasmas, and deep-water waves. The review ends with a summary of the main ideas of wave collapse and strong-turbulence theory, a collection of open questions in the field, and a brief discussion of possible future research directions. copyright 1997 The American Physical Society
Internal Gravity Waves in the Magnetized Solar Atmosphere. I. Magnetic Field Effects
Energy Technology Data Exchange (ETDEWEB)
Vigeesh, G.; Steiner, O. [Kiepenheuer-Institut für Sonnenphysik, Schöneckstrasse 6, D-79104 Freiburg (Germany); Jackiewicz, J., E-mail: vigeesh@leibniz-kis.de [New Mexico State University, Department of Astronomy, P.O. Box 30001, MSC 4500, Las Cruces, NM 88003 (United States)
2017-02-01
Observations of the solar atmosphere show that internal gravity waves are generated by overshooting convection, but are suppressed at locations of magnetic flux, which is thought to be the result of mode conversion into magnetoacoustic waves. Here, we present a study of the acoustic-gravity wave spectrum emerging from a realistic, self-consistent simulation of solar (magneto)convection. A magnetic field free, hydrodynamic simulation and a magnetohydrodynamic (MHD) simulation with an initial, vertical, homogeneous field of 50 G flux density were carried out and compared with each other to highlight the effect of magnetic fields on the internal gravity wave propagation in the Sun’s atmosphere. We find that the internal gravity waves are absent or partially reflected back into the lower layers in the presence of magnetic fields and argue that the suppression is due to the coupling of internal gravity waves to slow magnetoacoustic waves still within the high- β region of the upper photosphere. The conversion to Alfvén waves is highly unlikely in our model because there is no strongly inclined magnetic field present. We argue that the suppression of internal waves observed within magnetic flux concentrations may also be due to nonlinear breaking of internal waves due to vortex flows that are ubiquitously present in the upper photosphere and the chromosphere.
Atmospheric gravity waves in the Red Sea: a new hotspot
Magalhaes, J. M.
2011-02-03
The region of the Middle East around the Red Sea (between 32° E and 44° E longitude and 12° N and 28° N latitude) is a currently undocumented hotspot for atmospheric gravity waves (AGWs). Satellite imagery shows evidence that this region is prone to relatively high occurrence of AGWs compared to other areas in the world, and reveals the spatial characteristics of these waves. The favorable conditions for wave propagation in this region are illustrated with three typical cases of AGWs propagating in the lower troposphere over the sea. Using weakly nonlinear long wave theory and the observed characteristic wavelengths we obtain phase speeds which are consistent with those observed and typical for AGWs, with the Korteweg-de Vries theory performing slightly better than Benjamin-Davis-Acrivos-Ono theory as far as phase speeds are concerned. ERS-SAR and Envisat-ASAR satellite data analysis between 1993 and 2008 reveals signatures consistent with horizontally propagating large-scale internal waves. These signatures cover the entire Red Sea and are more frequently observed between April and September, although they also occur during the rest of the year. The region\\'s (seasonal) propagation conditions for AGWs, based upon average vertical atmospheric stratification profiles suggest that many of the signatures identified in the satellite images are atmospheric internal waves. © Author(s) 2011.
Linear superposition solutions to nonlinear wave equations
International Nuclear Information System (INIS)
Liu Yu
2012-01-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed
A case study of gravity waves in noctilucent clouds
Directory of Open Access Journals (Sweden)
P. Dalin
2004-06-01
Full Text Available We present a case study of a noctilucent cloud (NLC display appearing on 10-11 August 2000 over Northern Sweden. Clear wave structures were visible in the clouds and time-lapse photography was used to derive the parameters characterising the gravity waves which could account for the observed NLC modulation. Using two nearby atmospheric radars, the Esrange MST Radar data and Andoya MF radar, we have identified gravity waves propagating upward from the upper stratosphere to NLC altitudes. The wave parameters derived from the radar measurements support the suggestion that gravity waves are responsible for the observed complex wave dynamics in the NLC.
Nonlinear dynamics of resistive electrostatic drift waves
DEFF Research Database (Denmark)
Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.
1999-01-01
The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... polarity, i.e. a pair of electrostatic convective cells....
Modulated Langmuir waves and nonlinear Landau damping
International Nuclear Information System (INIS)
Yajima, Nobuo; Oikawa, Masayuki; Satsuma, Junkichi; Namba, Chusei.
1975-01-01
The nonlinear Schroedinger euqation with an integral term, iusub(t)+P/2.usub(xx)+Q/u/ 2 u+RP∫sub(-infinity)sup(infinity)[/u(x',t)/ 2 /(x-x')]dx'u=0, which describes modulated Langmuir waves with the nonlinear Landau damping effect, is solved by numerical calculations. Especially, the effects of nonlinear Landau damping on solitary wave solutions are studied. For both cases, PQ>0 and PQ<0, the results show that the solitary waves deform in an asymmetric way changing its velocity. (auth.)
How to turn gravity waves into Alfven waves and other such tricks
International Nuclear Information System (INIS)
Newington, Marie E; Cally, Paul S
2011-01-01
Recent observations of travelling gravity waves at the base of the chromosphere suggest an interplay between gravity wave propagation and magnetic field. Our aims are: to explain the observation that gravity wave flux is suppressed in magnetic regions; to understand why we see travelling waves instead of standing waves; and to see if gravity waves can undergo mode conversion and couple to Alfven waves in regions where the plasma beta is of order unity. We model gravity waves in a VAL C atmosphere, subject to a uniform magnetic field of various orientations, considering both adiabatic and radiatively damped propagation. Results indicate that in the presence of a magnetic field, the gravity wave can propagate as a travelling wave, with the magnetic field orientation playing a crucial role in determining the wave character. For the majority of magnetic field orientations, the gravity wave is reflected at low heights as a slow magneto-acoustic wave, explaining the observation of reduced flux in magnetic regions. In a highly inclined magnetic field, the gravity wave undergoes mode conversion to either field guided acoustic waves or Alfven waves. The primary effect of incorporating radiative damping is a reduction in acoustic and magnetic fluxes measured at the top of the integration region. By demonstrating the mode conversion of gravity waves to Alfven waves, this work identifies a possible pathway for energy transport from the solar surface to the upper atmosphere.
Shear waves in inhomogeneous, compressible fluids in a gravity field.
Godin, Oleg A
2014-03-01
While elastic solids support compressional and shear waves, waves in ideal compressible fluids are usually thought of as compressional waves. Here, a class of acoustic-gravity waves is studied in which the dilatation is identically zero, and the pressure and density remain constant in each fluid particle. These shear waves are described by an exact analytic solution of linearized hydrodynamics equations in inhomogeneous, quiescent, inviscid, compressible fluids with piecewise continuous parameters in a uniform gravity field. It is demonstrated that the shear acoustic-gravity waves also can be supported by moving fluids as well as quiescent, viscous fluids with and without thermal conductivity. Excitation of a shear-wave normal mode by a point source and the normal mode distortion in realistic environmental models are considered. The shear acoustic-gravity waves are likely to play a significant role in coupling wave processes in the ocean and atmosphere.
Nonlinear plasma waves excited near resonance
International Nuclear Information System (INIS)
Cohen, B.I.; Kaufman, A.N.
1977-01-01
The nonlinear resonant response of a uniform plasma to an external plane-wave field is formulated in terms of the mismatch Δ/sub n l/ between the driving frequency and the time-dependent, complex, nonlinear normal mode frequency at the driving wavenumber. This formalism is applied to computer simulations of this process, yielding a deduced nonlinear frequency shift. The time dependence of the nonlinear phenomena, at frequency Δ/sub n l/ and at the bounce frequency of the resonant particles, is analyzed. The interdependence of the nonlinear features is described by means of energy and momentum relations
Nonlinear interactions of counter-travelling waves
International Nuclear Information System (INIS)
Matsuuchi, Kazuo
1980-01-01
Nonlinear interactions between two waves travelling in opposite directions are investigated. When a nonlinear Klein-Gordon equation is adopted as a model equation, it is shown that such a wave system is governed by a simple set of equations for their complex amplitudes. Steady progressive waves governed by this set are investigated for various cases classified according to the signs of the coefficients. It is then found that one wave travelling in one direction appears from a certain point and the other travelling in the opposite direction has a constant amplitude from that point. This phenomenon may be regarded as a sort of reflection in spite of no rigid boundary. (author)
Evolution Of Nonlinear Waves in Compressing Plasma
International Nuclear Information System (INIS)
Schmit, P.F.; Dodin, I.Y.; Fisch, N.J.
2011-01-01
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size Δ during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches Δ. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Evolution Of Nonlinear Waves in Compressing Plasma
Energy Technology Data Exchange (ETDEWEB)
P.F. Schmit, I.Y. Dodin, and N.J. Fisch
2011-05-27
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size {Delta} during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches {Delta}. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Intercomparison of AIRS and HIRDLS stratospheric gravity wave observations
Meyer, Catrin I.; Ern, Manfred; Hoffmann, Lars; Trinh, Quang Thai; Alexander, M. Joan
2018-01-01
We investigate stratospheric gravity wave observations by the Atmospheric InfraRed Sounder (AIRS) aboard NASA's Aqua satellite and the High Resolution Dynamics Limb Sounder (HIRDLS) aboard NASA's Aura satellite. AIRS operational temperature retrievals are typically not used for studies of gravity waves, because their vertical and horizontal resolution is rather limited. This study uses data of a high-resolution retrieval which provides stratospheric temperature profiles for each individual satellite footprint. Therefore the horizontal sampling of the high-resolution retrieval is 9 times better than that of the operational retrieval. HIRDLS provides 2-D spectral information of observed gravity waves in terms of along-track and vertical wavelengths. AIRS as a nadir sounder is more sensitive to short-horizontal-wavelength gravity waves, and HIRDLS as a limb sounder is more sensitive to short-vertical-wavelength gravity waves. Therefore HIRDLS is ideally suited to complement AIRS observations. A calculated momentum flux factor indicates that the waves seen by AIRS contribute significantly to momentum flux, even if the AIRS temperature variance may be small compared to HIRDLS. The stratospheric wave structures observed by AIRS and HIRDLS often agree very well. Case studies of a mountain wave event and a non-orographic wave event demonstrate that the observed phase structures of AIRS and HIRDLS are also similar. AIRS has a coarser vertical resolution, which results in an attenuation of the amplitude and coarser vertical wavelengths than for HIRDLS. However, AIRS has a much higher horizontal resolution, and the propagation direction of the waves can be clearly identified in geographical maps. The horizontal orientation of the phase fronts can be deduced from AIRS 3-D temperature fields. This is a restricting factor for gravity wave analyses of limb measurements. Additionally, temperature variances with respect to stratospheric gravity wave activity are compared on a
Intercomparison of AIRS and HIRDLS stratospheric gravity wave observations
Directory of Open Access Journals (Sweden)
C. I. Meyer
2018-01-01
Full Text Available We investigate stratospheric gravity wave observations by the Atmospheric InfraRed Sounder (AIRS aboard NASA's Aqua satellite and the High Resolution Dynamics Limb Sounder (HIRDLS aboard NASA's Aura satellite. AIRS operational temperature retrievals are typically not used for studies of gravity waves, because their vertical and horizontal resolution is rather limited. This study uses data of a high-resolution retrieval which provides stratospheric temperature profiles for each individual satellite footprint. Therefore the horizontal sampling of the high-resolution retrieval is 9 times better than that of the operational retrieval. HIRDLS provides 2-D spectral information of observed gravity waves in terms of along-track and vertical wavelengths. AIRS as a nadir sounder is more sensitive to short-horizontal-wavelength gravity waves, and HIRDLS as a limb sounder is more sensitive to short-vertical-wavelength gravity waves. Therefore HIRDLS is ideally suited to complement AIRS observations. A calculated momentum flux factor indicates that the waves seen by AIRS contribute significantly to momentum flux, even if the AIRS temperature variance may be small compared to HIRDLS. The stratospheric wave structures observed by AIRS and HIRDLS often agree very well. Case studies of a mountain wave event and a non-orographic wave event demonstrate that the observed phase structures of AIRS and HIRDLS are also similar. AIRS has a coarser vertical resolution, which results in an attenuation of the amplitude and coarser vertical wavelengths than for HIRDLS. However, AIRS has a much higher horizontal resolution, and the propagation direction of the waves can be clearly identified in geographical maps. The horizontal orientation of the phase fronts can be deduced from AIRS 3-D temperature fields. This is a restricting factor for gravity wave analyses of limb measurements. Additionally, temperature variances with respect to stratospheric gravity wave activity are
Nonlinear Electrostatic Wave Equations for Magnetized Plasmas
DEFF Research Database (Denmark)
Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans
1984-01-01
The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....
Solitons and Weakly Nonlinear Waves in Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans
1985-01-01
Theoretical descriptions of solitons and weakly nonlinear waves propagating in plasma media are reviewed, with particular attention to the Korteweg-de Vries (KDV) equation and the Nonlinear Schrödinger equation (NLS). The modifications of these basic equations due to the effects of resonant...
New Gravity Wave Treatments for GISS Climate Models
Geller, Marvin A.; Zhou, Tiehan; Ruedy, Reto; Aleinov, Igor; Nazarenko, Larissa; Tausnev, Nikolai L.; Sun, Shan; Kelley, Maxwell; Cheng, Ye
2011-01-01
Previous versions of GISS climate models have either used formulations of Rayleigh drag to represent unresolved gravity wave interactions with the model-resolved flow or have included a rather complicated treatment of unresolved gravity waves that, while being climate interactive, involved the specification of a relatively large number of parameters that were not well constrained by observations and also was computationally very expensive. Here, the authors introduce a relatively simple and computationally efficient specification of unresolved orographic and nonorographic gravity waves and their interaction with the resolved flow. Comparisons of the GISS model winds and temperatures with no gravity wave parameterization; with only orographic gravity wave parameterization; and with both orographic and nonorographic gravity wave parameterizations are shown to illustrate how the zonal mean winds and temperatures converge toward observations. The authors also show that the specifications of orographic and nonorographic gravity waves must be different in the Northern and Southern Hemispheres. Then results are presented where the nonorographic gravity wave sources are specified to represent sources from convection in the intertropical convergence zone and spontaneous emission from jet imbalances. Finally, a strategy to include these effects in a climate-dependent manner is suggested.
Radiation from nonlinear coupling of plasma waves
International Nuclear Information System (INIS)
Fung, S.F.
1986-01-01
The author examines the generation of electromagnetic radiation by nonlinear resonant interactions of plasma waves in a cold, uniformly magnetized plasma. In particular, he considers the up-conversion of two electrostatic wave packets colliding to produce high frequency electromagnetic radiation. Efficient conversion of electrostatic to electromagnetic wave energy occurs when the pump amplitudes approach and exceed the pump depletion threshold. Results from the inverse scattering transform analysis of the three-wave interaction equations are applied. When the wave packets are initially separated, the fully nonlinear set of coupling equations, which describe the evolution of the wave packets, can be reduced to three separate eigenvalue problems; each can be considered as a scattering problem, analogous to eh Schroedinger equation. In the scattering space, the wave packet profiles act as the scattering potentials. When the wavepacket areas approach (or exceed) π/2, the wave functions are localized (bound states) and the scattering potentials are said to contain solitons. Exchange of solitons occurs during the interaction. The transfer of solitons from the pump waves to the electromagnetic wave leads to pump depletion and the production of strong radiation. The emission of radio waves is considered by the coupling of two upper-hybrid branch wave packets, and an upper-hybrid and a lower hybrid branch wave packet
NONLINEAR GRAVITATIONAL-WAVE MEMORY FROM BINARY BLACK HOLE MERGERS
International Nuclear Information System (INIS)
Favata, Marc
2009-01-01
Some astrophysical sources of gravitational waves can produce a 'memory effect', which causes a permanent displacement of the test masses in a freely falling gravitational-wave detector. The Christodoulou memory is a particularly interesting nonlinear form of memory that arises from the gravitational-wave stress-energy tensor's contribution to the distant gravitational-wave field. This nonlinear memory contributes a nonoscillatory component to the gravitational-wave signal at leading (Newtonian-quadrupole) order in the waveform amplitude. Previous computations of the memory and its detectability considered only the inspiral phase of binary black hole coalescence. Using an 'effective-one-body' (EOB) approach calibrated to numerical relativity simulations, as well as a simple fully analytic model, the Christodoulou memory is computed for the inspiral, merger, and ringdown. The memory will be very difficult to detect with ground-based interferometers, but is likely to be observable in supermassive black hole mergers with LISA out to redshifts z ∼< 2. Detection of the nonlinear memory could serve as an experimental test of the ability of gravity to 'gravitate'.
Variation principle for nonlinear wave propagation
International Nuclear Information System (INIS)
Watanabe, T.; Lee, Y.C.; Nishikawa, Kyoji; Hojo, H.; Yoshida, Y.
1976-01-01
Variation principle is derived which determines stationary nonlinear propagation of electrostatic waves in the self-consistent density profile. Example is given for lower-hybrid waves and the relation to the variation principle for the Lagrangian density of electromagnetic fluids is discussed
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Interpretation of nonlinearity in wind generated ocean surface waves
Digital Repository Service at National Institute of Oceanography (India)
Varkey, M.J.
of sinusoidal component waves; a consequent idea arising out of Fourier analysis. It is hypothesised that a sea state which is always nonlinear to various degrees is a result of interaction, both linear and nonlinear, between nonlinear component waves...
Propagation of internal gravity waves in the inhomogeneous atmosphere
International Nuclear Information System (INIS)
Deminov, M.G.; Ponomareva, L.I.
1988-01-01
Equations for disturbances of the density, temperature and speed of large-scale horizontally propagating internal gravity wave (IGM) wind are presented with regard to non-linearity, dispersion, molecular viscosity, thermal conductivity and background horizontal density and wind speed gradients. It is shown that values of wind speed and background atmosphere density decrease, typical of night conditions, provide for IGV amplitude increase near 250 km above the equator about 1.5 times, which with regard to the both hemispheres, fully compensates the effect of viscosity and thermal conductivity under increased solar activity. Speed and density decrease along IGW propagation can be provided both by background distribution of thermosphere parameters and by the front of a large-scale IGW on the background of which isolated IGW amplitude can grow
Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.
Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G
2016-12-02
We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.
Directory of Open Access Journals (Sweden)
O. Onishchenko
2013-03-01
Full Text Available In this paper, we have investigated vortex structures (e.g. convective cells of internal gravity waves (IGWs in the earth's atmosphere with a finite vertical temperature gradient. A closed system of nonlinear equations for these waves and the condition for existence of solitary convective cells are obtained. In the atmosphere layers where the temperature decreases with height, the presence of IGW convective cells is shown. The typical parameters of such structures in the earth's atmosphere are discussed.
Nonlinear theory of localized standing waves
Denardo, Bruce; Larraza, Andrés; Putterman, Seth; Roberts, Paul
1992-01-01
An investigation of the nonlinear dispersive equations of continuum mechanics reveals localized standing-wave solutions that are domain walls between regions of different wave number. These states can appear even when the dispersion law is a single-valued function of the wave number. In addition, we calculate solutions for kinks in cutoff and noncutoff modes, as well as cutoff breather solitons. Division of Engineering and Geophysics of the Office of Basic Energy Science of U.S. DOE for su...
Gravity waves from tachyonic preheating after hybrid inflation
Energy Technology Data Exchange (ETDEWEB)
Dufaux, Jean-Francois [Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Felder, Gary [Department of Physics, Clark Science Center, Smith College, Northampton, MA 01063 (United States); Kofman, Lev [CITA, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8 (Canada); Navros, Olga, E-mail: jeff.dufaux@uam.es, E-mail: gfelder@email.smith.edu, E-mail: kofman@cita.utoronto.ca, E-mail: navros@email.unc.edu [Department of Mathematics, University of North Carolina Chapel Hill, CB3250 Philips Hall, Chapel Hill, NC 27599 (United States)
2009-03-15
We study the stochastic background of gravitational waves produced from preheating in hybrid inflation models. We investigate different dynamical regimes of preheating in these models and we compute the resulting gravity wave spectra using analytical estimates and numerical simulations. We discuss the dependence of the gravity wave frequencies and amplitudes on the various potential parameters. We find that large regions of the parameter space leads to gravity waves that may be observable in upcoming interferometric experiments, including Advanced LIGO, but this generally requires very small coupling constants.
Nonlinear extraordinary wave in dense plasma
Energy Technology Data Exchange (ETDEWEB)
Krasovitskiy, V. B., E-mail: krasovit@mail.ru [Russian Academy of Sciences, Keldysh Institute of Applied Mathematics (Russian Federation); Turikov, V. A. [Russian University of Peoples’ Friendship (Russian Federation)
2013-10-15
Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.
Nonlinear ultrasonic imaging with X wave
Du, Hongwei; Lu, Wei; Feng, Huanqing
2009-10-01
X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.
Experimental Observation of Negative Effective Gravity in Water Waves
Hu, Xinhua; Yang, Jiong; Zi, Jian; Chan, C. T.; Ho, Kai-Ming
2013-01-01
The gravity of Earth is responsible for the formation of water waves and usually difficult to change. Although negative effective gravity was recently predicted theoretically in water waves, it has not yet been observed in experiments and remains a mathematical curiosity which is difficult to understand. Here we experimentally demonstrate that close to the resonant frequency of purposely-designed resonating units, negative effective gravity can occur for water waves passing through an array of resonators composing of bottom-mounted split tubes, resulting in the prohibition of water wave propagation. It is found that when negative gravity occurs, the averaged displacement of water surface in a unit cell of the array has a phase difference of π to that along the boundary of the unit cell, consistent with theoretical predictions. Our results provide a mechanism to block water waves and may find applications in wave energy conversion and coastal protection. PMID:23715132
Investigating gravity waves evidences in the Venus upper atmosphere
Migliorini, Alessandra; Altieri, Francesca; Shakun, Alexey; Zasova, Ludmila; Piccioni, Giuseppe; Bellucci, Giancarlo; Grassi, Davide
2014-05-01
We present a method to investigate gravity waves properties in the upper mesosphere of Venus, through the O2 nightglow observations acquired with the imaging spectrometer VIRTIS on board Venus Express. Gravity waves are important dynamical features that transport energy and momentum. They are related to the buoyancy force, which lifts air particles. Then, the vertical displacement of air particles produces density changes that cause gravity to act as restoring force. Gravity waves can manifest through fluctuations on temperature and density fields, and hence on airglow intensities. We use the O2 nightglow profiles showing double peaked structures to study the influence of gravity waves in shaping the O2 vertical profiles and infer the waves properties. In analogy to the Earth's and Mars cases, we use a well-known theory to model the O2 nightglow emissions affected by gravity waves propagation. Here we propose a statistical discussion of the gravity waves characteristics, namely vertical wavelength and wave amplitude, with respect to local time and latitude. The method is applied to about 30 profiles showing double peaked structures, and acquired with the VIRTIS/Venus Express spectrometer, during the mission period from 2006-07-05 to 2008-08-15.
Topological horseshoes in travelling waves of discretized nonlinear wave equations
International Nuclear Information System (INIS)
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
2014-01-01
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)
2014-04-15
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
Nonlocal nonlinear coupling of kinetic sound waves
Directory of Open Access Journals (Sweden)
O. Lyubchyk
2014-11-01
Full Text Available We study three-wave resonant interactions among kinetic-scale oblique sound waves in the low-frequency range below the ion cyclotron frequency. The nonlinear eigenmode equation is derived in the framework of a two-fluid plasma model. Because of dispersive modifications at small wavelengths perpendicular to the background magnetic field, these waves become a decay-type mode. We found two decay channels, one into co-propagating product waves (forward decay, and another into counter-propagating product waves (reverse decay. All wavenumbers in the forward decay are similar and hence this decay is local in wavenumber space. On the contrary, the reverse decay generates waves with wavenumbers that are much larger than in the original pump waves and is therefore intrinsically nonlocal. In general, the reverse decay is significantly faster than the forward one, suggesting a nonlocal spectral transport induced by oblique sound waves. Even with low-amplitude sound waves the nonlinear interaction rate is larger than the collisionless dissipation rate. Possible applications regarding acoustic waves observed in the solar corona, solar wind, and topside ionosphere are briefly discussed.
Intercomparison of stratospheric gravity wave observations with AIRS and IASI
Directory of Open Access Journals (Sweden)
L. Hoffmann
2014-12-01
Full Text Available Gravity waves are an important driver for the atmospheric circulation and have substantial impact on weather and climate. Satellite instruments offer excellent opportunities to study gravity waves on a global scale. This study focuses on observations from the Atmospheric Infrared Sounder (AIRS onboard the National Aeronautics and Space Administration Aqua satellite and the Infrared Atmospheric Sounding Interferometer (IASI onboard the European MetOp satellites. The main aim of this study is an intercomparison of stratospheric gravity wave observations of both instruments. In particular, we analyzed AIRS and IASI 4.3 μm brightness temperature measurements, which directly relate to stratospheric temperature. Three case studies showed that AIRS and IASI provide a clear and consistent picture of the temporal development of individual gravity wave events. Statistical comparisons based on a 5-year period of measurements (2008–2012 showed similar spatial and temporal patterns of gravity wave activity. However, the statistical comparisons also revealed systematic differences of variances between AIRS and IASI that we attribute to the different spatial measurement characteristics of both instruments. We also found differences between day- and nighttime data that are partly due to the local time variations of the gravity wave sources. While AIRS has been used successfully in many previous gravity wave studies, IASI data are applied here for the first time for that purpose. Our study shows that gravity wave observations from different hyperspectral infrared sounders such as AIRS and IASI can be directly related to each other, if instrument-specific characteristics such as different noise levels and spatial resolution and sampling are carefully considered. The ability to combine observations from different satellites provides an opportunity to create a long-term record, which is an exciting prospect for future climatological studies of stratospheric
Simulating nonlinear steady-state traveling waves on the falling liquid film entrained by a gas flow
International Nuclear Information System (INIS)
Yu Tsvelodub, O
2016-01-01
The article is devoted to the simulation of nonlinear waves on a liquid film flowing under gravity in the known stress field at the interface. In the case of small Reynolds numbers the problem is reduced to the consideration of solutions of the nonlinear integral-differential equation for film thickness deviation from the undisturbed level. Weakly nonlinear steady-state traveling solutions of the equation with wave numbers in a vicinity of neutral wave numbers are constructed analytically. The nature of the wave branching from the undisturbed solution is investigated. Steady-state traveling solutions, whose wave numbers within the instability area are far from neutral wave numbers, are found numerically. (paper)
Solitons and nonlinear waves in space plasmas
International Nuclear Information System (INIS)
Stasiewicz, K.
2005-01-01
Recent measurements made on the ESA/NASA Cluster mission to the Earth's magnetosphere have provided first detailed measurements of magnetosonic solitons in space. The solitons represent localized enhancements of the magnetic field by a factor of 2-10, or depressions down to 10% of the ambient field. The magnetic field signatures are associated with density depressions/enhancements A two-fluid model of nonlinear electron and ion inertial waves in anisotropic plasmas explains the main properties of these structures. It is shown that warm plasmas support four types of nonlinear waves, which correspond to four linear modes: Alfvenic, magnetosonic, sound, and electron inertial waves. Each of these nonlinear modes has slow and fast versions. It is shown by direct integration that the exponential growth rate of nonlinear modes is balanced by the ion and electron dispersion leading to solutions in the form of trains of solitons or cnoidal waves. By using a novel technique of phase portraits it is shown how the dispersive properties of electron and ion inertial waves change at the transition between warm and hot plasmas, and how trains of solitons ('' mirror modes '') are produced in a hot, anisotropic plasma. The applicability of the model is illustrated with data from Cluster spacecraft. (author)
New exact travelling wave solutions of nonlinear physical models
International Nuclear Information System (INIS)
Bekir, Ahmet; Cevikel, Adem C.
2009-01-01
In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The ((G ' )/G )-expansion method presents a wider applicability for handling nonlinear wave equations.
Nonlinear wave equation with intrinsic wave particle dualism
International Nuclear Information System (INIS)
Klein, J.J.
1976-01-01
A nonlinear wave equation derived from the sine-Gordon equation is shown to possess a variety of solutions, the most interesting of which is a solution that describes a wave packet travelling with velocity usub(e) modulating a carrier wave travelling with velocity usub(c). The envelop and carrier wave speeds agree precisely with the group and phase velocities found by de Broglie for matter waves. No spreading is exhibited by the soliton, so that it behaves exactly like a particle in classical mechanics. Moreover, the classically computed energy E of the disturbance turns out to be exactly equal to the frequency ω of the carrier wave, so that the Planck relation is automatically satisfied without postulating a particle-wave dualism. (author)
Gravity waves from quantum stress tensor fluctuations in inflation
International Nuclear Information System (INIS)
Wu, Chun-Hsien; Hsiang, Jen-Tsung; Ford, L. H.; Ng, Kin-Wang
2011-01-01
We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a nonscale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both in the CMB radiation and in gravity wave detectors, and could offer a probe of trans-Planckian physics. The fact that they have not yet been observed might be used to constrain the duration and energy scale of inflation. However, this conclusion is contingent upon including the contribution of modes which were trans-Planckian at the beginning of inflation.
Gravity waves from quantum stress tensor fluctuations in inflation
Wu, Chun-Hsien; Hsiang, Jen-Tsung; Ford, L. H.; Ng, Kin-Wang
2011-11-01
We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a nonscale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both in the CMB radiation and in gravity wave detectors, and could offer a probe of trans-Planckian physics. The fact that they have not yet been observed might be used to constrain the duration and energy scale of inflation. However, this conclusion is contingent upon including the contribution of modes which were trans-Planckian at the beginning of inflation.
Jefrey, A
1964-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
Nonlinear waves: some biomedical applications
International Nuclear Information System (INIS)
Rudenko, Oleg V
2007-01-01
The field of nonlinear physics, item No. 11 on Ginzburg's list of 'the most important and interesting problems', is reviewed. An example at the intersection of applied physics, medicine, and instrument engineering is discussed to illustrate the range and scope of the field and how deep the ideas and approaches it involves are incorporated in modern natural science and engineering. Results of relevant research and development, which has attracted much recent interest and financial support, are briefly examined. (oral issue of the journal 'uspekhi fizicheskikh nauk')
pp waves of conformal gravity with self-interacting source
International Nuclear Information System (INIS)
Ayon-Beato, Eloy; Hassaine, Mokhtar
2005-01-01
Recently, Deser, Jackiw and Pi have shown that three-dimensional conformal gravity with a source given by a conformally coupled scalar field admits pp wave solutions. In this paper, we consider this model with a self-interacting potential preserving the conformal structure. A pp wave geometry is also supported by this system and, we show that this model is equivalent to topologically massive gravity with a cosmological constant whose value is given in terms of the potential strength
Topics in nonlinear wave theory with applications
International Nuclear Information System (INIS)
Tracy, E.R.
1984-01-01
Selected topics in nonlinear wave theory are discussed, and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasi-periodic solutions to several nonlinear wave equations, which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schroedinger equation, an equation with general applicability in one-dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in the numerical studies, and the numerical work of other authors. The method of solution (related to the inverse scattering method) is then analyzed within the context of Hamiltonian dynamics where it is shown that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation, which appears here and in the work of other authors, is shown to be a special form of Liouville's transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's inversion problem, is surveyed briefly
Solitary waves on nonlinear elastic rods. II
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1987-01-01
In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results ar...... are compared with predictions of conservation theorems for energy and momentum....
Four Wave Mixing using Intermodal Nonlinearities
DEFF Research Database (Denmark)
Rishøj, Lars Søgaard
The nonlinear process of four-wave mixing (FWM) enables coupling of energy between wavelengths. This is useful for both optical amplification and wavelength conversion. A crucial prerequisite for the process is phase matching. This PhD project investigates how higher order modes (HOMs) in fibers...
Nonlinear wavenumber of an electron plasma wave
International Nuclear Information System (INIS)
Vidmar, P.J.; Malmberg, J.H.; Starke, T.P.
1976-01-01
The wavenumber of a large-amplitude electron plasma wave propagating on a collisionless plasma column is measured. The wavenumber is shifted from that of a small-amplitude wave of the same frequency. This nonlinear wavenumber shift, deltak/subr/, depends on position, frequency, and initial wave amplitude, Phi. The observed spatial oscillations of deltak/subr/ agree qualitatively with recent theories. Experimentally deltak/subr/proportionalk/subi/S (Phi) rootPhi where k/subi/ is the linear Landau damping coefficient, S (Phi) equivalentk/subi/(Phi)/k/subi/, and k/subi/(Phi) is the initial damping coefficient which depends on Phi
Nonlinear MHD Waves in a Prominence Foot
Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.
2015-11-01
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ˜ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5-11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5-14 G. For the typical prominence density the corresponding fast magnetosonic speed is ˜20 km s-1, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
Energy Technology Data Exchange (ETDEWEB)
Ofman, L. [Catholic University of America, Washington, DC 20064 (United States); Knizhnik, K.; Kucera, T. [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States); Schmieder, B. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cit, 5 place Jules Janssen, F-92195 Meudon (France)
2015-11-10
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
No further gravitational wave modes in F(T) gravity
Energy Technology Data Exchange (ETDEWEB)
Bamba, Kazuharu, E-mail: bamba@kmi.nagoya-u.ac.jp [Kobayashi–Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Capozziello, Salvatore, E-mail: capozziello@na.infn.it [Kobayashi–Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Dipartimento di Fisica, Università di Napoli “Federico II” (Italy); INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126 Napoli (Italy); De Laurentis, Mariafelicia, E-mail: felicia@na.infn.it [Kobayashi–Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Dipartimento di Fisica, Università di Napoli “Federico II” (Italy); INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126 Napoli (Italy); Nojiri, Shin' ichi, E-mail: nojiri@phys.nagoya-u.ac.jp [Kobayashi–Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Sáez-Gómez, Diego, E-mail: diego.saezgomez@uct.ac.za [Kobayashi–Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Astrophysics, Cosmology and Gravity Centre (ACGC) and Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town (South Africa); Fisika Teorikoaren eta Zientziaren Historia Saila, Zientzia eta Teknologia Fakultatea, Euskal Herriko Unibertsitatea, 644 Posta Kutxatila, 48080 Bilbao (Spain)
2013-11-25
We explore the possibility of further gravitational wave modes in F(T) gravity, where T is the torsion scalar in teleparallelism. It is explicitly demonstrated that gravitational wave modes in F(T) gravity are equivalent to those in General Relativity. This result is achieved by calculating the Minkowskian limit for a class of analytic function of F(T). This consequence is also confirmed by the preservative analysis around the flat background in the weak field limit with the scalar–tensor representation of F(T) gravity.
No further gravitational wave modes in F(T) gravity
International Nuclear Information System (INIS)
Bamba, Kazuharu; Capozziello, Salvatore; De Laurentis, Mariafelicia; Nojiri, Shin'ichi; Sáez-Gómez, Diego
2013-01-01
We explore the possibility of further gravitational wave modes in F(T) gravity, where T is the torsion scalar in teleparallelism. It is explicitly demonstrated that gravitational wave modes in F(T) gravity are equivalent to those in General Relativity. This result is achieved by calculating the Minkowskian limit for a class of analytic function of F(T). This consequence is also confirmed by the preservative analysis around the flat background in the weak field limit with the scalar–tensor representation of F(T) gravity
Electromagnetic internal gravity waves in the Earth's ionospheric E-layer
International Nuclear Information System (INIS)
Kaladze, T.D.; Tsamalashvili, L.V.; Kaladze, D.T.
2011-01-01
In the Earth's ionospheric E-layer existence of the new waves connecting with the electromagnetic nature of internal gravity waves is shown. They represent the mixture of the ordinary internal gravity waves and the new type of dispersive Alfven waves. -- Highlights: ► Existence of electromagnetic internal gravity waves in the ionospheric E-layer is shown. ► Electromagnetic nature of internal gravity waves is described. ► Appearance of the new dispersive Alfven waves is shown.
Directory of Open Access Journals (Sweden)
Colin C. Triplett
2017-01-01
Full Text Available The meteorological control of gravity wave activity through ﬁltering by winds and generation by spontaneous adjustment of unbalanced ﬂows is investigated. This investigation is based on a new analysis of Rayleigh LiDAR measurements of gravity wave activity in the upper stratosphere-lower mesosphere (USLM,40–50kmon 152 nights at Poker Flat Research Range (PFRR, Chatanika, Alaska (65◦ N, 147◦ W, over 13 years between 1998 and 2014. The LiDAR measurements resolve inertia-gravity waves with observed periods between 1 h and 4 h and vertical wavelengths between 2 km and 10 km. The meteorological conditions are deﬁned by reanalysis data from the Modern-Era Retrospective Analysis for Research and Applications (MERRA. The gravity wave activity shows large night-to-night variability, but a clear annual cycle with a maximum in winter,and systematic interannual variability associated with stratospheric sudden warming events. The USLM gravity wave activity is correlated with the MERRA winds and is controlled by the winds in the lower stratosphere through ﬁltering by critical layer ﬁltering. The USLM gravity wave activity is also correlated with MERRA unbalanced ﬂow as characterized by the residual of the nonlinear balance equation. This correlation with unbalanced ﬂow only appears when the wind conditions are taken into account, indicating that wind ﬁltering is the primary control of the gravity wave activity.
Nonlinear water waves: introduction and overview
Constantin, A.
2017-12-01
For more than two centuries progress in the study of water waves proved to be interdependent with innovative and deep developments in theoretical and experimental directions of investigation. In recent years, considerable progress has been achieved towards the understanding of waves of large amplitude. Within this setting one cannot rely on linear theory as nonlinearity becomes an essential feature. Various analytic methods have been developed and adapted to come to terms with the challenges encountered in settings where approximations (such as those provided by linear or weakly nonlinear theory) are ineffective. Without relying on simpler models, progress becomes contingent upon the discovery of structural properties, the exploitation of which requires a combination of creative ideas and state-of-the-art technical tools. The successful quest for structure often reveals unexpected patterns and confers aesthetic value on some of these studies. The topics covered in this issue are both multi-disciplinary and interdisciplinary: there is a strong interplay between mathematical analysis, numerical computation and experimental/field data, interacting with each other via mutual stimulation and feedback. This theme issue reflects some of the new important developments that were discussed during the programme `Nonlinear water waves' that took place at the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) from 31st July to 25th August 2017. A cross-section of the experts in the study of water waves who participated in the programme authored the collected papers. These papers illustrate the diversity, intensity and interconnectivity of the current research activity in this area. They offer new insight, present emerging theoretical methodologies and computational approaches, and describe sophisticated experimental results. This article is part of the theme issue 'Nonlinear water waves'.
Nonlinear wave forces on large ocean structures
Huang, Erick T.
1993-04-01
This study explores the significance of second-order wave excitations on a large pontoon and tests the feasibility of reducing a nonlinear free surface problem by perturbation expansions. A simulation model has been developed based on the perturbation expansion technique to estimate the wave forces. The model uses a versatile finite element procedure for the solution of the reduced linear boundary value problems. This procedure achieves a fair compromise between computation costs and physical details by using a combination of 2D and 3D elements. A simple hydraulic model test was conducted to observe the wave forces imposed on a rectangle box by Cnoidal waves in shallow water. The test measurements are consistent with the numerical predictions by the simulation model. This result shows favorable support to the perturbation approach for estimating the nonlinear wave forces on shallow draft vessels. However, more sophisticated model tests are required for a full justification. Both theoretical and experimental results show profound second-order forces that could substantially impact the design of ocean facilities.
Symmetry, phase modulation and nonlinear waves
Bridges, Thomas J
2017-01-01
Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
Nonlinear waves in waveguides with stratification
Leble, Sergei B
1991-01-01
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki
2017-06-01
We investigate the influence of collective self-gravity forces on the nonlinear evolution of the viscous overstability in Saturn's dense rings. Local N-body simulations, incorporating vertical and radial collective self-gravity are performed. Vertical self-gravity is mimicked through an increased frequency of vertical oscillations, while radial self-gravity is approximated by solving the Poisson equation for a thin disk in Fourier space. Direct particle-particle forces are omitted, while the magnitude of radial self gravity is controlled by assigning a variable surface mass density to the system's homogeneous ground state. We compare our simulations with large-scale isothermal and non-isothermal hydrodynamic model calculations, including radial self-gravity and employing transport coefficients derived in Salo et al. (2001). We concentrate on optical depths τ=1.5-2, appropriate to model Saturn's dense rings. Our isothermal and non isothermal hydrodynamic results in the limit of vanishing self-gravity compare very well with the studies of Latter&Ogilvie (2010) and Rein&latter (2013), respectively.With non-vanishing radial self-gravity we find that the wavelengths of saturated overstable wave trains are located in close vicinity of the local minimum of the nonlinear dispersion relation for a particular surface density. Good agreement is found between non-isothermal hydrodynamics and N-body simulations for disks with strong radial self-gravity, while the largest deviations occur for a weak but non-vanishing self-gravity.The resulting saturation wavelengths of the viscous overstability for moderate and strong radial self-gravity (λ~ 200-300m) agree reasonably well with the length scale of periodic micro structure in Saturn's inner A and B ring, as found by Cassini.
VHF radar observations of gravity waves at a low latitude
Directory of Open Access Journals (Sweden)
G. Dutta
1999-08-01
Full Text Available Wind observations made at Gadanki (13.5°N by using Indian MST Radar for few days in September, October, December 1995 and January, 1996 have been analyzed to study gravity wave activity in the troposphere and lower stratosphere. Horizontal wind variances have been computed for gravity waves of period (2-6 h from the power spectral density (PSD spectrum. Exponential curves of the form eZ/H have been fitted by least squares technique to these variance values to obtain height variations of the irregular winds upto the height of about 15 km, where Z is the height in kilometers. The value of H, the scale height, as determined from curve fitting is found to be less than the theoretical value of scale height of neutral atmosphere in this region, implying that the waves are gaining energy during their passage in the troposphere. In other words, it indicates that the sources of gravity waves are present in the troposphere. The energy densities of gravity wave fluctuations have been computed. Polynomial fits to the observed values show that wave energy density increases in the troposphere, its source region, and then decreases in the lower stratosphere.Key words. Meteorology and atmospheric dynamics (middle atmosphere dynamics; turbulence; waves and tides
Nonlinear massive spin-2 field generated by higher derivative gravity
International Nuclear Information System (INIS)
Magnano, Guido; Sokolowski, Leszek M.
2003-01-01
We present a systematic exposition of the Lagrangian field theory for the massive spin-2 field generated in higher-derivative gravity upon reduction to a second-order theory by means of the appropriate Legendre transformation. It has been noticed by various authors that this nonlinear field overcomes the well-known inconsistency of the theory for a linear massive spin-2 field interacting with Einstein's gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called '(Helmholtz-)Jordan frame' and 'Einstein frame'. In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-2 field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame (each frame therefore provides a self-contained theory). The full equations of motion and the (variational) energy-momentum tensor for the spin-2 field in Einstein frame are given, and a simple but non-trivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-2 field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-2 field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected
Properties of surface waves in granular media under gravity
International Nuclear Information System (INIS)
Zheng He-Peng
2014-01-01
Acoustical waves propagating along the free surface of granular media under gravity are investigated in the framework of elasticity theory. The influence of stress on a surface wave is analyzed. The results have shown that two types of surface waves, namely sagittal and transverse modes exist depending on initial stress states, which may have some influence on the dispersion relations of surface waves, but the influence is not great. Considering that the present experimental accuracy is far from distinguishing this detail, the validity of elasticity theory on the surface waves propagating in granular media can still be maintained. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
Planetary wave-gravity wave interactions during mesospheric inversion layer events
Ramesh, K.; Sridharan, S.; Raghunath, K.; Vijaya Bhaskara Rao, S.; Bhavani Kumar, Y.
2013-07-01
lidar temperature observations over Gadanki (13.5°N, 79.2°E) show a few mesospheric inversion layer (MIL) events during 20-25 January 2007. The zonal mean removed SABER temperature shows warm anomalies around 50°E and 275°E indicating the presence of planetary wave of zonal wave number 2. The MIL amplitudes in SABER temperature averaged for 10°N-15°N and 70°E-90°E show a clear 2 day wave modulation during 20-28 January 2007. Prior to 20 January 2007, a strong 2day wave (zonal wave number 2) is observed in the height region of 80-90 km and it gets largely suppressed during 20-26 January 2007 as the condition for vertical propagation is not favorable, though it prevails at lower heights. The 10 day mean zonal wind over Tirunelveli (8.7°N, 77.8°E) shows deceleration of eastward winds indicating the westward drag due to wave dissipation. The nightly mean MF radar observed zonal winds show the presence of alternating eastward and westward winds during the period of 20-26 January 2007. The two dimensional spectrum of Rayleigh lidar temperature observations available for the nights of 20, 22, and 24 January 2007 shows the presence of gravity wave activity with periods 18 min, 38 min, 38 min, and vertical wavelengths 6.4 km, 4.0 km, 6.4 km respectively. From the dispersion relation of gravity waves, it is inferred that these waves are internal gravity waves rather than inertia gravity waves with the horizontal phase speeds of ~40 m/s, ~37 m/s, and ~50 m/s respectively. Assuming the gravity waves are eastward propagating waves, they get absorbed only in the eastward local wind fields of the planetary wave thereby causing turbulence and eddy diffusion which can be inferred from the estimation of large drag force due to the breaking of gravity wave leading to the formation of large amplitude inversion events in alternate nights. The present study shows that, the mesospheric temperature inversion is caused mainly due to the gravity wave breaking and the inversion
Second generation diffusion model of interacting gravity waves on the surface of deep fluid
Directory of Open Access Journals (Sweden)
A. Pushkarev
2004-01-01
Full Text Available We propose a second generation phenomenological model for nonlinear interaction of gravity waves on the surface of deep water. This model takes into account the effects of non-locality of the original Hasselmann diffusion equation still preserving important properties of the first generation model: physically consistent scaling, adherence to conservation laws and the existence of Kolmogorov-Zakharov solutions. Numerical comparison of both models with the original Hasselmann equation shows that the second generation models improves the angular distribution in the evolving wave energy spectrum.
Gravitational waves from quasicircular black-hole binaries in dynamical Chern-Simons gravity.
Yagi, Kent; Yunes, Nicolás; Tanaka, Takahiro
2012-12-21
Dynamical Chern-Simons gravity cannot be strongly constrained with current experiments because it reduces to general relativity in the weak-field limit. This theory, however, introduces modifications in the nonlinear, dynamical regime, and thus it could be greatly constrained with gravitational waves from the late inspiral of black-hole binaries. We complete the first self-consistent calculation of such gravitational waves in this theory. For favorable spin orientations, advanced ground-based detectors may improve existing solar system constraints by 6 orders of magnitude.
Nonlinear quantum gravity on the constant mean curvature foliation
International Nuclear Information System (INIS)
Wang, Charles H-T
2005-01-01
A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system to be quantized. This permits the Hamiltonian constraint equation to be consistently turned into an expectation value equation on quantization that describes the scale factor on each spatial hypersurface characterized by a constant mean exterior curvature. This expectation value equation augments the dynamical quantum evolution of the unconstrained conformal three-geometry with a transverse traceless momentum tensor density. The resulting quantum theory is inherently nonlinear. Nonetheless, it is unitary and free from a nonlocal and implicit description of the Hamiltonian operator. Finally, by imposing additional homogeneity symmetries, a broad class of Bianchi cosmological models are analysed as nonlinear quantum minisuperspaces in the context of the proposed theory
Linear and Nonlinear Electrostatic Waves in Unmagnetized Dusty Plasmas
International Nuclear Information System (INIS)
Mamun, A. A.; Shukla, P. K.
2010-01-01
A rigorous and systematic theoretical study has been made of linear and nonlinear electrostatic waves propagating in unmagnetized dusty plasmas. The basic features of linear and nonlinear electrostatic waves (particularly, dust-ion-acoustic and dust-acoustic waves) for different space and laboratory dusty plasma conditions are described. The experimental observations of such linear and nonlinear features of dust-ion-acoustic and dust-acoustic waves are briefly discussed.
Nonlinear instability and chaos in plasma wave-wave interactions
International Nuclear Information System (INIS)
Kueny, C.S.
1993-01-01
Conventional linear stability analysis may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipitation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, which leads to explosive growth. In the dissipationaless case, it is conjectured that intrinsic chaotic behavior may allow initially non-resonant systems to reach resonance by diffusion in phase space. This is illustrated for a simple equilibrium involving cold counter-streaming ions. The system is described in the fluid approximation by a Hamilitonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamilitonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, which occur generically for long enough wavelengths. Three-wave interactions which occur in isolated, but numerous, regions of parameter space can drive either decay instability or explosive instability. When the resonance for explosive growth is detuned, a stable region exists around the equilibrium point in phase space, while explosive growth occurs outside of a separatrix. These interactions may be described exactly if only one resonance is considered, while multiple nonlinear terms make the Hamiltonian nonintegradable. Simple Hamiltonians of two and three degrees of freedom are studied numerically using symplectic integration algorithms, including an explicit algorithm derived using Lie algebraic methods
Nonlinear magnetoacoustic wave propagation with chemical reactions
Margulies, Timothy Scott
2002-11-01
The magnetoacoustic problem with an application to sound wave propagation through electrically conducting fluids such as the ocean in the Earth's magnetic field, liquid metals, or plasmas has been addressed taking into account several simultaneous chemical reactions. Using continuum balance equations for the total mass, linear momentum, energy; as well as Maxwell's electrodynamic equations, a nonlinear beam equation has been developed to generalize the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a fluid with linear viscosity but nonlinear and diffraction effects. Thermodynamic parameters are used and not tailored to only an adiabatic fluid case. The chemical kinetic equations build on a relaxing media approach presented, for example, by K. Naugolnukh and L. Ostrovsky [Nonlinear Wave Processes in Acoustics (Cambridge Univ. Press, Cambridge, 1998)] for a linearized single reaction and thermodynamic pressure equation of state. Approximations for large and small relaxation times and for magnetohydrodynamic parameters [Korsunskii, Sov. Phys. Acoust. 36 (1990)] are examined. Additionally, Cattaneo's equation for heat conduction and its generalization for a memory process rather than a Fourier's law are taken into account. It was introduced for the heat flux depends on the temperature gradient at an earlier time to generate heat pulses of finite speed.
Nonlinear diffuse scattering of the random-phased wave
International Nuclear Information System (INIS)
Kato, Yoshiaki; Arinaga, Shinji; Mima, Kunioki.
1983-01-01
First experimental observation of the nonlinear diffuse scattering is reported. This new effect was observed in the propagation of the random-phased wave through a nonlinear dielectric medium. This effect is ascribed to the diffusion of the wavevector of the electro-magnetic wave to the lateral direction due to the randomly distributed nonlinear increase in the refractive index. (author)
Nonlinear effects on mode-converted lower-hybrid waves
International Nuclear Information System (INIS)
Kuehl, H.H.
1976-01-01
Nonlinear ponderomotive force effects on mode-converted lower-hybrid waves are considered. The nonlinear distortion of these waves is shown to be governed by the cubic nonlinear Schroedinger equation. The threshold condition for self-focusing and filamentation is derived
Optimization of nonlinear wave function parameters
International Nuclear Information System (INIS)
Shepard, R.; Minkoff, M.; Chemistry
2006-01-01
An energy-based optimization method is presented for our recently developed nonlinear wave function expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions, using the graphical unitary group approach (GUGA). The wave function is expanded in a basis of product functions, allowing application to closed-shell and open-shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational function that depends on a relatively small number of nonlinear parameters called arc factors. The energy-based optimization is formulated in terms of analytic arc factor gradients and orbital-level Hamiltonian matrices that correspond to a specific kind of uncontraction of each of the product basis functions. These orbital-level Hamiltonian matrices give an intuitive representation of the energy in terms of disjoint subsets of the arc factors, they provide for an efficient computation of gradients of the energy with respect to the arc factors, and they allow optimal arc factors to be determined in closed form for subspaces of the full variation problem. Timings for energy and arc factor gradient computations involving expansion spaces of > 10 24 configuration state functions are reported. Preliminary convergence studies and molecular dissociation curves are presented for some small molecules
Nonlinear radial propagation of drift wave turbulence
International Nuclear Information System (INIS)
Prakash, M.
1985-01-01
We study the linear and the nonlinear radial propagation of drift wave energy in an inhomogeneous plasma. The drift mode excited in such a plasma is dispersive in nature. The drift wave energy spreads out symmetrically along the direction of inhomogeneity with a finite group velocity. To study the effect of the nonlinear coupling on the propagation of energy in a collision free plasma, we solve the Hasegawa-Mima equation as a mixed initial boundary-value problem. The solutions of the linearized equation are used to check the reliability of our numerical calculations. Additional checks are also performed on the invariants of the system. Our results reveal that a pulse gets distorted as it propagates through the medium. The peak of the pulse propagates with a finite velocity that depends on the amplitude of the initial pulse. The polarity of propagation depends on the initial parameters of the pulse. We have also studied drift wave propagation in a resistive plasma. The Hasegawa-Wakatani equations are used to investigate this problem
Integrability and Linear Stability of Nonlinear Waves
Degasperis, Antonio; Lombardo, Sara; Sommacal, Matteo
2018-03-01
It is well known that the linear stability of solutions of 1+1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N× N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N=3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.
Generating gravity waves with matter and electromagnetic waves
International Nuclear Information System (INIS)
Barrabes, C.; Hogan, P A.
2008-01-01
If a homogeneous plane lightlike shell collides head on with a homogeneous plane electromagnetic shock wave having a step-function profile then no backscattered gravitational waves are produced. We demonstrate, by explicit calculation, that if the matter is accompanied by a homogeneous plane electromagnetic shock wave with a step-function profile then backscattered gravitational waves appear after the collision
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066
An axisymmetric inertia-gravity wave generator
Maurer, P.; Ghaemsaidi, S. J.; Joubaud, S.; Peacock, T.; Odier, P.
2017-10-01
There has been a rich interplay between laboratory experimental studies of internal waves and advancing understanding of their role in the ocean and atmosphere. In this study, we present and demonstrate the concept for a new form of laboratory internal wave generator that can excite axisymmetric wave fields of arbitrary radial structure. The construction and operation of the generator are detailed, and its capabilities are demonstrated through a pair of experiments using a Bessel function and a bourrelet (i.e., ring-shaped) configuration. The results of the experiments are compared with the predictions of an accompanying analytical model.
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Weakly nonlinear electron plasma waves in collisional plasmas
DEFF Research Database (Denmark)
Pecseli, H. L.; Rasmussen, J. Juul; Tagare, S. G.
1986-01-01
The nonlinear evolution of a high frequency plasma wave in a weakly magnetized, collisional plasma is considered. In addition to the ponderomotive-force-nonlinearity the nonlinearity due to the heating of the electrons is taken into account. A set of nonlinear equations including the effect...
Active Absorption of Irregular Gravity Waves in BEM-Models
DEFF Research Database (Denmark)
Brorsen, Michael; Frigaard, Peter
1992-01-01
The boundary element method is applied to the computation of irregular gravity waves. The boundary conditions at the open boundaries are obtained by a digital filtering technique, where the surface elevations in front of the open boundary are filtered numerically yielding the velocity to be presc...... to be prescribed at the boundary. By numerical examples it is shown that well designed filters can reduce the wave reflection to a few per cent over a frequency range corresponding to a Jonswap spectrum....
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.
A Plant's Response to Gravity as a Wave Guide Phenomenon
Wagner, Orvin
1997-11-01
Plant experimental data provides a unifying wave theory (W-wave theory) for the growth and development of plants. A plant's response to gravity is an important aspect of this theory. It appears that a plant part is tuned to the angle with which it initially grew with respect to the gravitational field and changes produce correction responses. This is true because the velocity of W-waves (whose standing waves determine plant structure) within plant tissue is found to be different in different directions (angle a) with respect to the gravitational field. I found that there are preferred values of a, namely integral multiples of near 5 degrees for some plants. Conifers apparently are more sensitive to the gravitational field than deciduous trees, in the cases studied, so their structure is determined in more detail by the gravitational field. A plant's response to gravity appears to be a fundamental phenomenon and may provide a new model for gravity that can be experimentally verified in the laboratory. Along these same lines accelerometers placed in plant tissue indicate that plants produce gravity related forces that facilitate sap flow. See the
Field verification of ADCP surface gravity wave elevation spectra
Hoitink, A.J.F.; Peters, H.C.; Schroevers, M.
2007-01-01
Acoustic Doppler current profilers (ADCPs) can measure orbital velocities induced by surface gravity waves, yet the ADCP estimates of these velocities are subject to a relatively high noise level. The present paper introduces a linear filtration technique to significantly reduce the influence of
Atmospheric gravity waves in the Red Sea: a new hotspot
Magalhaes, J. M.; Araú jo, I. B.; da Silva, J. C. B.; Grimshaw, R. H. J.; Davis, K.; Pineda, J.
2011-01-01
The region of the Middle East around the Red Sea (between 32° E and 44° E longitude and 12° N and 28° N latitude) is a currently undocumented hotspot for atmospheric gravity waves (AGWs). Satellite imagery shows evidence that this region is prone
Atmospheric gravity waves due to the Tohoku-Oki tsunami observed in the thermosphere by GOCE
Garcia, R.F.; Doornbos, E.N.; Bruinsma, S.; Hebert, H.
2014-01-01
Oceanic tsunami waves couple with atmospheric gravity waves, as previously observed through ionospheric and airglow perturbations. Aerodynamic velocities and density variations are computed from Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) accelerometer and thruster data during
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
Directory of Open Access Journals (Sweden)
Baojun Zhao
2018-01-01
Full Text Available Envelope gravity solitary waves are an important research hot spot in the field of solitary wave. And the weakly nonlinear model equations system is a part of the research of envelope gravity solitary waves. Because of the lack of technology and theory, previous studies tried hard to reduce the variable numbers and constructed the two-dimensional model in barotropic atmosphere and could only describe the propagation feature in a direction. But for the propagation of envelope gravity solitary waves in real ocean ridges and atmospheric mountains, the three-dimensional model is more appropriate. Meanwhile, the baroclinic problem of atmosphere is also an inevitable topic. In the paper, the three-dimensional coupled nonlinear Schrödinger (CNLS equations are presented to describe the evolution of envelope gravity solitary waves in baroclinic atmosphere, which are derived from the basic dynamic equations by employing perturbation and multiscale methods. The model overcomes two disadvantages: (1 baroclinic problem and (2 propagation path problem. Then, based on trial function method, we deduce the solution of the CNLS equations. Finally, modulational instability of wave trains is also discussed.
Dynamics of flexural gravity waves: from sea ice to Hawking radiation and analogue gravity.
Das, S; Sahoo, T; Meylan, M H
2018-01-01
The propagation of flexural gravity waves, routinely used to model wave interaction with sea ice, is studied, including the effect of compression and current. A number of significant and surprising properties are shown to exist. The occurrence of blocking above a critical value of compression is illustrated. This is analogous to propagation of surface gravity waves in the presence of opposing current and light wave propagation in the curved space-time near a black hole, therefore providing a novel system for studying analogue gravity. Between the blocking and buckling limit of the compressive force, the dispersion relation possesses three positive real roots, contrary to an earlier observation of having a single positive real root. Negative energy waves, in which the phase and group velocity point in opposite directions, are also shown to exist. In the presence of an opposing current and certain critical ranges of compressive force, the second blocking point shifts from the positive to the negative branch of the dispersion relation. Such a shift is known as the Hawking effect from the analogous behaviour in the theory of relativity which leads to Hawking radiation. The theory we develop is illustrated with simulations of linear waves in the time domain.
Nonlinear drift waves in a dusty plasma with sheared flows
Energy Technology Data Exchange (ETDEWEB)
Vranjes, J. [K.U. Leuven (Belgium). Center for Plasma Astrophysics; Shukla, R.K. [Ruhr-Univ. Bochum (Germany). Inst. fuer Theoretische Physik IV
2002-01-01
Nonlinear properties of dust-modified drift waves and dust-drift waves in a dusty magnetoplasma with equilibrium sheared flows are examined. For this purpose, the relevant nonlinear equations for drift waves are analyzed for various profiles of the perpendicular and parallel plasma flows, and a variety of nonlinear solutions (viz. single and double vortex chains accompanied with zonal flows, tripolar and global vortices), which are driven by nommiform shear flows and nommiform dust density, is presented.
Nonlinear drift waves in a dusty plasma with sheared flows
International Nuclear Information System (INIS)
Vranjes, J.; Shukla, R.K.
2002-01-01
Nonlinear properties of dust-modified drift waves and dust-drift waves in a dusty magnetoplasma with equilibrium sheared flows are examined. For this purpose, the relevant nonlinear equations for drift waves are analyzed for various profiles of the perpendicular and parallel plasma flows, and a variety of nonlinear solutions (viz. single and double vortex chains accompanied with zonal flows, tripolar and global vortices), which are driven by nommiform shear flows and nommiform dust density, is presented
Nonlinear wave beams in a piezo semiconducting layer
International Nuclear Information System (INIS)
Bagdoev, A.G.; Shekoyan, A.V.; Danoyan, Z.N.
1997-01-01
The propagation of quasi-monochromatic nonlinear wave in a piezo semiconducting layer taking into account electron-concentration nonlinearity is considered. For such medium the evolution equations for incoming and reflected waves are derived. Nonlinear Schroedinger equations and solutions for narrow beams are obtained. It is shown that symmetry of incoming and reflected waves does not take place. The focusing of beams is investigated.18 refs
Gravity's shadow the search for gravitational waves
Collins, Harry
2004-01-01
According to the theory of relativity, we are constantly bathed in gravitational radiation. When stars explode or collide, a portion of their mass becomes energy that disturbs the very fabric of the space-time continuum like ripples in a pond. But proving the existence of these waves has been difficult; the cosmic shudders are so weak that only the most sensitive instruments can be expected to observe them directly. Fifteen times during the last thirty years scientists have claimed to have detected gravitational waves, but so far none of those claims have survived the scrutiny of the scie
Testing strong gravity with gravitational waves and Love numbers
International Nuclear Information System (INIS)
Franzin, E; Cardoso, V; Raposo, G; Pani, P
2017-01-01
The LIGO observation of GW150914 has inaugurated the gravitational-wave astronomy era and the possibility of testing gravity in extreme regimes. While distorted black holes are the most convincing sources of gravitational waves, similar signals might be produced also by other compact objects. In particular, we discuss what the gravitational-wave ringdown could tell us about the nature of the emitting object, and how measurements of the tidal Love numbers could help us in understanding the internal structure of compact dark objects. (paper)
The Binary Pulsar: Gravity Waves Exist.
Will, Clifford
1987-01-01
Reviews the history of pulsars generally and the 1974 discovery of the binary pulsar by Joe Taylor and Russell Hulse specifically. Details the data collection and analysis used by Taylor and Hulse. Uses this discussion as support for Albert Einstein's theory of gravitational waves. (CW)
A perturbative solution for gravitational waves in quadratic gravity
International Nuclear Information System (INIS)
Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de
2003-01-01
We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin
Modeling the SAR Signature of Nonlinear Internal Waves
National Research Council Canada - National Science Library
Lettvin, Ellen E
2008-01-01
Nonlinear Internal Waves are pervasive globally, particularly in coastal waters. The currents and displacements associated with internal waves influence acoustic propagation and underwater navigation, as well as ocean transport and mixing...
New travelling wave solutions for nonlinear stochastic evolution ...
Indian Academy of Sciences (India)
expansion method to look for travelling wave solutions of nonlinear partial differential equations. It is interesting to mention that, in this method the sign of the parameters can be used to judge the numbers and types of travelling wave solutions.
Nonlinear modulation of ion acoustic waves in a magnetized plasma
International Nuclear Information System (INIS)
Bharuthram, R.; Shukla, P.K.
1987-01-01
The quasistatic plasma slow response to coherent ion acoustic waves in a magnetized plasma is considered. A multidimensional cubic nonlinear Schroedinger equation is derived. It is found that the ion acoustic waves remain modulationally stable against oblique perturbations
Upper atmospheric gravity wave details revealed in nightglow satellite imagery
Miller, Steven D.; Straka, William C.; Yue, Jia; Smith, Steven M.; Alexander, M. Joan; Hoffmann, Lars; Setvák, Martin; Partain, Philip T.
2015-01-01
Gravity waves (disturbances to the density structure of the atmosphere whose restoring forces are gravity and buoyancy) comprise the principal form of energy exchange between the lower and upper atmosphere. Wave breaking drives the mean upper atmospheric circulation, determining boundary conditions to stratospheric processes, which in turn influence tropospheric weather and climate patterns on various spatial and temporal scales. Despite their recognized importance, very little is known about upper-level gravity wave characteristics. The knowledge gap is mainly due to lack of global, high-resolution observations from currently available satellite observing systems. Consequently, representations of wave-related processes in global models are crude, highly parameterized, and poorly constrained, limiting the description of various processes influenced by them. Here we highlight, through a series of examples, the unanticipated ability of the Day/Night Band (DNB) on the NOAA/NASA Suomi National Polar-orbiting Partnership environmental satellite to resolve gravity structures near the mesopause via nightglow emissions at unprecedented subkilometric detail. On moonless nights, the Day/Night Band observations provide all-weather viewing of waves as they modulate the nightglow layer located near the mesopause (∼90 km above mean sea level). These waves are launched by a variety of physical mechanisms, ranging from orography to convection, intensifying fronts, and even seismic and volcanic events. Cross-referencing the Day/Night Band imagery with conventional thermal infrared imagery also available helps to discern nightglow structures and in some cases to attribute their sources. The capability stands to advance our basic understanding of a critical yet poorly constrained driver of the atmospheric circulation. PMID:26630004
Manipulating acoustic wave reflection by a nonlinear elastic metasurface
Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent
2018-03-01
The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.
Nonlinear low frequency (LF) waves - Comets and foreshock phenomena
Tsurutani, Bruce T.
1991-01-01
A review is conducted of LF wave nonlinear properties at comets and in the earth's foreshock, engaging such compelling questions as why there are no cometary cyclotron waves, the physical mechanism responsible for 'dispersive whiskers', and the character of a general description of linear waves. Attention is given to the nonlinear properties of LF waves, whose development is illustrated by examples of waves and their features at different distances from the comet, as well as by computer simulation results. Also discussed is a curious wave mode detected from Comet Giacobini-Zinner, both at and upstream of the bow shock/wave.
f (T) Non-linear Massive Gravity and the Cosmic Acceleration
International Nuclear Information System (INIS)
Wu You; Chen Zu-Cheng; Wei Hao; Wang Jia-Xin
2015-01-01
Inspired by the f (R) non-linear massive gravity, we propose a new kind of modified gravity model, namely f (T) non-linear massive gravity, by adding the dRGT mass term reformulated in the vierbein formalism, to the f (T) theory. We then investigate the cosmological evolution of f (T) massive gravity, and constrain it by using the latest observational data. We find that it slightly favors a crossing of the phantom divide line from the quintessence-like phase (w_d_e > −1) to the phantom-like one (w_d_e < −1) as redshift decreases. (paper)
Propagation of inertial-gravity waves on an island shelf
Bondur, V. G.; Sabinin, K. D.; Grebenyuk, Yu. V.
2015-09-01
The propagation of inertial-gravity waves (IGV) at the boundary of the Pacific shelf near the island of Oahu (Hawaii), whose generation was studied in the first part of this work [1], is analyzed. It is shown that a significant role there is played by the plane oblique waves; whose characteristics were identified by the method of estimating 3D wave parameters for the cases when the measurements are available only for two verticals. It is established that along with the descending propagation of energy that is typical of IGVs, wave packets ascend from the bottom to the upper layers, which is caused by the emission of waves from intense jets of discharged waters flowing out of a diffusor located at the bottom.
Chen, Pengzhen; Wang, Xiaoqing; Liu, Li; Chong, Jinsong
2016-06-01
According to Bragg theory, capillary waves are the predominant scatterers of high-frequency band (such as Ka-band) microwave radiation from the surface of the ocean. Therefore, understanding the modulation mechanism of capillary waves is an important foundation for interpreting high-frequency microwave remote sensing images of the surface of the sea. In our experiments, we discovered that modulations of capillary waves are significantly larger than the values predicted by the classical theory. Further, analysis shows that the difference in restoring force results in an inflection point while the phase velocity changes from gravity waves region to capillary waves region, and this results in the capillary waves being able to resonate with gravity waves when the phase velocity of the gravity waves is equal to the group velocity of the capillary waves. Consequently, we propose a coupling modulation model in which the current modulates the capillary wave indirectly by modulating the resonant gravity waves, and the modulation of the former is approximated by that of the latter. This model very effectively explains the results discovered in our experiments. Further, based on Bragg scattering theory and this coupling modulation model, we simulate the modulation of normalized radar cross section (NRCS) of typical internal waves and show that the high-frequency bands are superior to the low-frequency bands because of their greater modulation of NRCS and better radiometric resolution. This result provides new support for choice of radar band for observation of wave-current modulation oceanic phenomena such as internal waves, fronts, and shears.
Temporal variability of gravity wave drag - vertical coupling and possible climate links
Miksovsky, Jiri; Sacha, Petr; Kuchar, Ales; Pisoft, Petr
2017-04-01
In the atmosphere, the internal gravity waves (IGW) are one of the fastest ways of natural information transfer in the vertical direction. Tropospheric changes that result in modification of sourcing, propagation or breaking conditions for IGWs almost immediately influence the distribution of gravity wave drag in the stratosphere. So far most of the related studies deal with IGW impacts higher in the upper stratospheric/mesospheric region and with the modulation of IGWs by planetary waves. This is most likely due to the fact that IGWs induce highest accelerations in the mesosphere and lower thermosphere region. However, the imposed drag force is much bigger in the stratosphere. In the presented analysis, we have assessed the relationship between the gravity wave activity in the stratosphere and other climatic phenomena through statistical techniques. Multivariable regression has been applied to investigate the IGW-related eastward and northward wind tendencies in the CMAM30-SD data, subject to the explanatory variables involving local circulation characteristics (derived from regional configuration of the thermobaric field) as well as the phases of the large-scale internal climate variability modes (ENSO, NAO, QBO). Our tests have highlighted several geographical areas with statistically significant responses of the orographic gravity waves effect to each of the variability modes under investigation; additional experiments have also indicated distinct signs of nonlinearity in some of the links uncovered. Furthermore, we have also applied composite analysis of displaced and split stratospheric polar vortex events (SPV) from CMAM30-SD to focus on how the strength and occurrence of the IGW hotspots can play a role in SPV occurrence and frequency.
Interaction between ionization and gravity waves in the upper atmosphere
International Nuclear Information System (INIS)
Balcioglu, O.
1982-10-01
It is known that travelling ionospheric disturbances are produced by gravity waves. During their movement from the F region downwards to the E region, gravity waves can produce thin layers called transients on ionograms and, if the wave motion persists, 'h-type Esub(S) can be produced. To investigate the problem, the continuity equations for both the E and F regions are solved for a perturbation, the motion of which is taken to be a gravity wave. Hitherto, N'/N 0 , the ratio of the disturbed to the undisturbed electron density, has been calculated by using only the Hall conductivity and ignoring the diffusion term for the F region. In the present calculations we have used Pedersan and Hall conductivities and calculated the N'/N 0 ratio for both the E and F regions. Using CIRA standard atmosphere data we find for the F region that N' can exceed N 0 by up to 4 percent, depending on the horizontal wind velocity. In the E region, N' reaches much higher values than in the F region. Thus at 120 km if we take a typical horizontal wind velocity of 80 m/sec (wavelength 150 km), N' is about twice as large as N 0 . From these results we see that the diffusion term is important for the E region. (author)
Conformal symmetry and nonlinear extensions of nonlocal gravity
Cusin, Giulia; Maggiore, Michele; Mancarella, Michele
2016-01-01
We study two nonlinear extensions of the nonlocal $R\\,\\Box^{-2}R$ gravity theory. We extend this theory in two different ways suggested by conformal symmetry, either replacing $\\Box^{-2}$ with $(-\\Box + R/6)^{-2}$, which is the operator that enters the action for a conformally-coupled scalar field, or replacing $\\Box^{-2}$ with the inverse of the Paneitz operator, which is a four-derivative operator that enters in the effective action induced by the conformal anomaly. We show that the former modification gives an interesting and viable cosmological model, with a dark energy equation of state today $w_{\\rm DE}\\simeq -1.01$, which very closely mimics $\\Lambda$CDM and evolves asymptotically into a de Sitter solution. The model based on the Paneitz operator seems instead excluded by the comparison with observations. We also review some issues about the causality of nonlocal theories, and we point out that these nonlocal models can be modified so to nicely interpolate between Starobinski inflation in the primordia...
Variational Boussinesq model for strongly nonlinear dispersive waves
Lawrence, C.; Adytia, D.; van Groesen, E.
2018-01-01
For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be
Nonlinear propagation of short wavelength drift-Alfven waves
DEFF Research Database (Denmark)
Shukla, P. K.; Pecseli, H. L.; Juul Rasmussen, Jens
1986-01-01
Making use of a kinetic ion and a hydrodynamic electron description together with the Maxwell equation, the authors derive a set of nonlinear equations which governs the dynamics of short wavelength ion drift-Alfven waves. It is shown that the nonlinear drift-Alfven waves can propagate as two-dim...
Stratospheric gravity wave activities inferred through the GPS radio occultation technique
International Nuclear Information System (INIS)
Wrasse, Cristiano Max; Takahashi, Hisao; Fechine, Joaquim; Denardini, Clezio Marcos; Wickert, Jens
2007-01-01
Stratospheric gravity wave activities were deduced from GPS radio occultation temperature profiles obtained by CHAMP satellite between 2001 and 2005. Potential energy profiles are used to analyze the gravity wave activity over South America. The results showed an inter-annual variation of the potential energy integrated between 24 and 34 km of altitude. The gravity wave activity is more concentrated around the equatorial region. In order to evaluate the seasonal variation of the gravity wave activity, a mean potential energy was determined over (10 deg N-10 deg S) and (100 deg W-20 deg W). The results showed a lower gravity wave activity during winter time, while during spring time the mean potential energy showed an increase in the wave activity. The results of the mean potential energy also showed that the gravity wave activity in the lower stratosphere exhibits a higher wave activity during 2002 and 2004 and a lower wave activity during 2003 and 2005. (author)
Transition from geostrophic turbulence to inertia–gravity waves in the atmospheric energy spectrum
Callies, Jörn; Ferrari, Raffaele; Bühler, Oliver
2014-01-01
Midlatitude fluctuations of the atmospheric winds on scales of thousands of kilometers, the most energetic of such fluctuations, are strongly constrained by the Earth’s rotation and the atmosphere’s stratification. As a result of these constraints, the flow is quasi-2D and energy is trapped at large scales—nonlinear turbulent interactions transfer energy to larger scales, but not to smaller scales. Aircraft observations of wind and temperature near the tropopause indicate that fluctuations at horizontal scales smaller than about 500 km are more energetic than expected from these quasi-2D dynamics. We present an analysis of the observations that indicates that these smaller-scale motions are due to approximately linear inertia–gravity waves, contrary to recent claims that these scales are strongly turbulent. Specifically, the aircraft velocity and temperature measurements are separated into two components: one due to the quasi-2D dynamics and one due to linear inertia–gravity waves. Quasi-2D dynamics dominate at scales larger than 500 km; inertia–gravity waves dominate at scales smaller than 500 km. PMID:25404349
Transition from geostrophic turbulence to inertia-gravity waves in the atmospheric energy spectrum.
Callies, Jörn; Ferrari, Raffaele; Bühler, Oliver
2014-12-02
Midlatitude fluctuations of the atmospheric winds on scales of thousands of kilometers, the most energetic of such fluctuations, are strongly constrained by the Earth's rotation and the atmosphere's stratification. As a result of these constraints, the flow is quasi-2D and energy is trapped at large scales—nonlinear turbulent interactions transfer energy to larger scales, but not to smaller scales. Aircraft observations of wind and temperature near the tropopause indicate that fluctuations at horizontal scales smaller than about 500 km are more energetic than expected from these quasi-2D dynamics. We present an analysis of the observations that indicates that these smaller-scale motions are due to approximately linear inertia-gravity waves, contrary to recent claims that these scales are strongly turbulent. Specifically, the aircraft velocity and temperature measurements are separated into two components: one due to the quasi-2D dynamics and one due to linear inertia-gravity waves. Quasi-2D dynamics dominate at scales larger than 500 km; inertia-gravity waves dominate at scales smaller than 500 km.
Nonlinear self-modulation of ion-acoustic waves
International Nuclear Information System (INIS)
Ikezi, H.; Schwarzenegger, K.; Simons, A.L.; Ohsawa, Y.; Kamimura, T.
1978-01-01
The nonlinear evolution of an ion-acoustic wave packet is studied. Experimentally, it is found that (i) nonlinear phase modulation develops in the wave packet; (ii) the phase modulation, together with the dispersion effect, causes expansion and breaking of the wave packet; (iii) the ions trapped in the troughs of the wave potential introduce self-phase modulation; and (iv) the ion-acoustic wave is stable with respect to the modulational instability. Computer simulations have reproduced the experimental results. The physical picture and the model equation describing the wave evolution are discussed
Acoustic-gravity waves in atmospheric and oceanic waveguides.
Godin, Oleg A
2012-08-01
A theory of guided propagation of sound in layered, moving fluids is extended to include acoustic-gravity waves (AGWs) in waveguides with piecewise continuous parameters. The orthogonality of AGW normal modes is established in moving and motionless media. A perturbation theory is developed to quantify the relative significance of the gravity and fluid compressibility as well as sensitivity of the normal modes to variations in sound speed, flow velocity, and density profiles and in boundary conditions. Phase and group speeds of the normal modes are found to have certain universal properties which are valid for waveguides with arbitrary stratification. The Lamb wave is shown to be the only AGW normal mode that can propagate without dispersion in a layered medium.
Nonlinear waves in bipolar complex viscous astroclouds
Karmakar, P. K.; Haloi, A.
2017-05-01
A theoretical evolutionary model to analyze the dynamics of strongly nonlinear waves in inhomogeneous complex astrophysical viscous clouds on the gravito-electrostatic scales of space and time is procedurally set up. It compositionally consists of warm lighter electrons and ions (Boltzmanian); and cold massive bi-polar dust grains (inertial fluids) alongside vigorous neutral dynamics in quasi-neutral hydrodynamic equilibrium. Application of the Sagdeev pseudo-potential method reduces the inter-coupled structure equations into a pair of intermixed forced Korteweg-de Vries-Burgers (f-KdVB) equations. The force-terms are self-consistently sourced by inhomogeneous gravito-electrostatic interplay. A numerical illustrative shape-analysis based on judicious astronomical parametric platform shows the electrostatic waves evolving as compressive dispersive shock-like eigen-modes. A unique transition from quasi-monotonic to non-monotonic oscillatory compressive shock-like patterns is found to exist. In contrast, the self-gravitational and effective perturbations grow purely as non-monotonic compressive oscillatory shock-like structures with no such transitory features. It is seen that the referral frame velocity acts as amplitude-reducing agent (stabilizing source) for the electrostatic fluctuations solely. A comparison in the prognostic light of various earlier satellite-based observations and in-situ measurements is presented. The paper ends up with synoptic highlights on the main implications and non-trivial applications in the interstellar space and cosmic plasma environments leading to bounded structure formation.
Holt, L A; Alexander, M J; Coy, L; Liu, C; Molod, A; Putman, W; Pawson, S
2017-07-01
In this study, gravity waves (GWs) in the high-resolution GEOS-5 Nature Run are first evaluated with respect to satellite and other model results. Southern Hemisphere winter sources of non-orographic GWs in the model are then investigated by linking measures of tropospheric non-orographic gravity wave generation tied to precipitation and frontogenesis with absolute gravity wave momentum flux in the lower stratosphere. Finally, non-orographic GW momentum flux is compared to orographic gravity wave momentum flux and compared to previous estimates. The results show that the global patterns in GW amplitude, horizontal wavelength, and propagation direction are realistic compared to observations. However, as in other global models, the amplitudes are weaker and horizontal wavelengths longer than observed. The global patterns in absolute GW momentum flux also agree well with previous model and observational estimates. The evaluation of model non-orographic GW sources in the Southern Hemisphere winter shows that strong intermittent precipitation (greater than 10 mm h -1 ) is associated with GW momentum flux over the South Pacific, whereas frontogenesis and less intermittent, lower precipitation rates (less than 10 mm h -1 ) are associated with GW momentum flux near 60°S. In the model, orographic GWs contribute almost exclusively to a peak in zonal mean momentum flux between 70 and 75°S, while non-orographic waves dominate at 60°S, and non-orographic GWs contribute a third to a peak in zonal mean momentum flux between 25 and 30°S.
Nonlinear VLF Wave Physics in the Radiation Belts
Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Mithaiwala, M.; Rudakov, L.; Hospodarsky, G. B.; Kletzing, C.
2014-12-01
Electromagnetic VLF waves, such as whistler mode waves, both control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering and are responsible for the energization of electrons during storms. Traditional approaches to understanding the influence of waves on trapped electrons have assumed that the wave characteristics (frequency spectrum, wave-normal angle distribution, etc.) were both stationary in time and amplitude independent from event to event. In situ data from modern satellite missions, such as the Van Allen probes, are showing that this assumption may not be justified. In addition, recent theoretical results [Crabtree et al. 2012] show that the threshold for nonlinear wave scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear wave scattering (Nonlinear Landau Damping) is an amplitude dependent mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Nonlinear scattering can alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al., 2012]. Such nonlinear wave effects can dramatically reduce electron lifetimes. Nonlinear wave dynamics such as these occur when there are more than one wave present, such a condition necessarily violates the assumption of traditional wave-normal analysis [Santolik et al., 2003] which rely on the plane wave assumption. To investigate nonlinear wave dynamics using modern in situ data we apply the maximum entropy method [Skilling and Bryan, 1984] to solve for the wave distribution function
Identification of nonlinear coupling in wave turbulence at the surface of water
Campagne, Antoine; Hassaini, Roumaissa; Redor, Ivan; Aubourg, Quentin; Sommeria, Joël; Mordant, Nicolas
2017-11-01
The Weak Turbulence Theory is a theory, in the limit of vanishing nonlinearity, that derive analytically statistical features of wave turbulence. The stationary spectrum for the surface elevation in the case of gravity waves, is predicted to E(k) k - 5 / 2 . This spectral exponent -5/2 remains elusive in all experiments. in which the measured exponent is systematically lower than the prediction. Furthermore in the experiments the weaker the nonlinearity the further the spectral exponent is from the prediction. In order to investigate the reason for this observation we developed an experiment in the CORIOLIS facility in Grenoble. It is a 13m-diameter circular pool filled with water with a 70 cm depth. We generate wave turbulence by using two wedge wavemakers. Surface elevation measurements are performed by a stereoscopic optical technique and by capacitive probes. The nonlinear coupling at work in this system are analyzed by computing 3- and 4-wave correlations of the Fourier wave amplitudes in frequency. Theory predicts that coupling should occur through 4-wave resonant interaction. In our data, strong 3-wave correlations are observed in addition to the 4-wave correlation. Most our observations are consistent with field observation in the Black Sea (Leckler et al. 2015). This project has received funding from the European Research Council (ERC, Grant Agreement No 647018-WATU).
Issues concerning gravity waves from first-order phase transitions
International Nuclear Information System (INIS)
Kosowsky, A.
1993-01-01
The stochastic background of gravitational radiation is a unique and potentially valuable source of information about the early universe. Photons thermally decoupled when the universe was around 100,000 years old; electromagnetic radiation cannot directly provide information about the epoch earlier than this. In contrast, gravitons presumably decoupled around the Planck time, when the universe was only 10 -44 seconds old. Since gravity wave propagate virtually unimpeded, any energetic event in the evolution of the universe will leave an imprint on the gravity wave background. Turner and Wilczek first suggested that first-order phase transitions, and particularly transitions which occur via the nucleation, expansion, and percolation of vacuum bubbles, will be a particularly efficient source of gravitational radiation. Detailed calculations with scalar-field vacuum bubbles confirm this conjecture and show that strongly first-order phase transitions are probably the strongest stochastic gravity-wave source yet conjectured. In this work the author first reviews the vacuum bubble calculations, stressing their physical assumptions. The author then discusses realistic scenarios for first-order phase transitions and describes how the calculations must be modified and extended to produce reliable results. 11 refs
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
International Nuclear Information System (INIS)
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-01-01
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.
Nonlinear evolution of the matter power spectrum in modified theories of gravity
International Nuclear Information System (INIS)
Koyama, Kazuya; Taruya, Atsushi; Hiramatsu, Takashi
2009-01-01
We present a formalism to calculate the nonlinear matter power spectrum in modified gravity models that explain the late-time acceleration of the Universe without dark energy. Any successful modified gravity models should contain a mechanism to recover general relativity (GR) on small scales in order to avoid the stringent constrains on deviations from GR at solar system scales. Based on our formalism, the quasi-nonlinear power spectrum in the Dvali-Gabadadze-Porratti braneworld models and f(R) gravity models are derived by taking into account the mechanism to recover GR properly. We also extrapolate our predictions to fully nonlinear scales using the parametrized post-Friedmann framework. In the Dvali-Gabadadze-Porratti and f(R) gravity models, the predicted nonlinear power spectrum is shown to reproduce N-body results. We find that the mechanism to recover GR suppresses the difference between the modified gravity models and dark energy models with the same expansion history, but the difference remains large at the weakly nonlinear regime in these models. Our formalism is applicable to a wide variety of modified gravity models and it is ready to use once consistent models for modified gravity are developed.
Nonlinear interaction of waves in an inhomogeneous plasma
International Nuclear Information System (INIS)
Istomin, Ya.N.
1988-01-01
Nonlinear wave processes in a weakly inhomogeneous plasma are considered. A quasilinear equation is derived which takes into account the effect of the waves on resonance particles, provided that the inhomogeneity appreciably affects the nature of the resonance interaction. Three-wave interaction is investigated under the same conditions. As an example, the nonlinear interaction in a relativistic plasma moving along a strong curvilinear magnetic field is considered
Nonlinear physics of shear Alfvén waves
International Nuclear Information System (INIS)
Zonca, Fulvio; Chen, Liu
2014-01-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results
Nonlinear physics of shear Alfvén waves
Zonca, Fulvio; Chen, Liu
2014-02-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These "nonlinear equilibria" or "phase-space zonal structures" dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
Nonlinear Whistler Wave Physics in the Radiation Belts
Crabtree, Chris
2016-10-01
Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data
On the unstable mode merging of gravity-inertial waves with Rossby waves
Directory of Open Access Journals (Sweden)
J. F. McKenzie
2011-08-01
Full Text Available We recapitulate the results of the combined theory of gravity-inertial-Rossby waves in a rotating, stratified atmosphere. The system is shown to exhibit a "local" (JWKB instability whenever the phase speed of the low-frequency-long wavelength westward propagating Rossby wave exceeds the phase speed ("Kelvin" speed of the high frequency-short wavelength gravity-inertial wave. This condition ensures that mode merging, leading to instability, takes place in some intermediate band of frequencies and wave numbers. The contention that such an instability is "spurious" is not convincing. The energy source of the instability resides in the background enthalpy which can be released by the action of the gravitational buoyancy force, through the combined wave modes.
Energy Technology Data Exchange (ETDEWEB)
Peralta, J.; López-Valverde, M. A. [Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Imamura, T. [Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan); Read, P. L. [Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford (United Kingdom); Luz, D. [Centro de Astronomia e Astrofísica da Universidade de Lisboa (CAAUL), Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa (Portugal); Piccialli, A., E-mail: peralta@iaa.es [LATMOS, UVSQ, 11 bd dAlembert, 78280 Guyancourt (France)
2014-07-01
This paper is the first of a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases when the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this first part, only waves that are direct solutions of the generic dispersion relation are studied—acoustic and inertia-gravity waves. Concerning inertia-gravity waves, we found that in the cases of short horizontal wavelengths, null background wind, or propagation in the equatorial region, only pure gravity waves are possible, while for the limit of large horizontal wavelengths and/or null static stability, the waves are inertial. The correspondence between classical atmospheric approximations and wave filtering has been examined too, and we carried out a classification of the mesoscale waves found in the clouds of Venus at different vertical levels of its atmosphere. Finally, the classification of waves in exoplanets is discussed and we provide a list of possible candidates with cyclostrophic regimes.
Nonlinear density waves in a marginally stable gravitating disk
International Nuclear Information System (INIS)
Korchagin, V.I.
1986-01-01
The evolution of short nonlinear density waves in a disk at the stability limit is studied for arbitrary values of the radial wave number k/sub r/. For waves with wave numbers that do not lie at the minimum of the dispersion curve, the behavior of the amplitude is described by a nonlinear parabolic equation; however, stationary soliton solutions cannot exist in such a system since there is no dispersion spreading of a packet. For wave numbers lying at the minimum of the dispersion curve, soliton structures with determined amplitude are possible. In stable gravitating disks and in a disk at the stability limit, two physically different types of soliton can exist
Nonlinear Alfvén Waves in a Vlasov Plasma
DEFF Research Database (Denmark)
Bell, T.F.
1965-01-01
Stationary solutions to the nonlinear Vlasov—Boltzmann equations are considered which represent one-dimensional electromagnetic waves in a hot magnetoplasma. These solutions appear in arbitrary reference frames as circularly polarized, sinusoidal waves of unlimited amplitude, i.e., as nonlinear...... Alfvén waves. Solutions are found implicitly by deriving a set of integral dispersion relations which link the wave characteristics with the particle distribution functions. A physical discussion is given of the way in which the Alfvén waves can trap particles, and it is shown that the presence...
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Propagation of 3D internal gravity wave beams in a slowly varying stratification
Fan, Boyu; Akylas, T. R.
2017-11-01
The time-mean flows induced by internal gravity wave beams (IGWB) with 3D variations have been shown to have dramatic implications for long-term IGWB dynamics. While uniform stratifications are convenient both theoretically and in the laboratory, stratifications in the ocean can vary by more than an order of magnitude over the ocean depth. Here, in view of this fact, we study the propagation of a 3D IGWB in a slowly varying stratification. We assume that the stratification varies slowly relative to the local variations in the wave profile. In the 2D case, the IGWB bends in response to the changing stratification, but nonlinear effects are minor even in the finite amplitude regime. For a 3D IGWB, in addition to bending, we find that nonlinearity results in the transfer of energy from waves to a large-scale time-mean flow associated with the mean potential vorticity, similar to IGWB behavior in a uniform stratification. In a weakly nonlinear setting, we derive coupled evolution equations that govern this process. We also use these equations to determine the stability properties of 2D IGWB to 3D perturbations. These findings indicate that 3D effects may be relevant and possibly fundamental to IGWB dynamics in nature. Supported by NSF Grant DMS-1512925.
Nonlinear interaction of the surface waves at a plasma boundary
International Nuclear Information System (INIS)
Dolgopolov, V.V.; El-Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.
1976-01-01
Amplitudes of electromagnetic waves with combination frequencies, radiating from the plasma boundary due to nonlinear interaction of the surface waves, have been found. Previous papers on this subject did not take into account that the tangential components of the electric field of waves with combination frequencies were discontinuous at the plasma boundary. (Auth.)
Nonlinear Scattering of VLF Waves in the Radiation Belts
Crabtree, Chris; Rudakov, Leonid; Ganguli, Guru; Mithaiwala, Manish
2014-10-01
Electromagnetic VLF waves, such as whistler mode waves, control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering. Since the pitch-angle scattering rate is a strong function of the wave properties, a solid understanding of VLF wave sources and propagation in the magnetosphere is critical to accurately calculate electron lifetimes. Nonlinear scattering (Nonlinear Landau Damping) is a mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation, and has not been accounted for in previous models of radiation belt dynamics. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Recent results show that the threshold for nonlinear scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear scattering can then dramatically alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al. 2012]. By considering these effects, the lifetimes of electrons can be dramatically reduced. This work is supported by the Naval Research Laboratory base program.
Generation of Caustics and Rogue Waves from Nonlinear Instability.
Safari, Akbar; Fickler, Robert; Padgett, Miles J; Boyd, Robert W
2017-11-17
Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.
Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves
Tobita, Miwa; Omura, Yoshiharu
2018-03-01
We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.
Sediment gravity flows triggered by remotely generated earthquake waves
Johnson, H. Paul; Gomberg, Joan S.; Hautala, Susan L.; Salmi, Marie S.
2017-06-01
Recent great earthquakes and tsunamis around the world have heightened awareness of the inevitability of similar events occurring within the Cascadia Subduction Zone of the Pacific Northwest. We analyzed seafloor temperature, pressure, and seismic signals, and video stills of sediment-enveloped instruments recorded during the 2011-2015 Cascadia Initiative experiment, and seafloor morphology. Our results led us to suggest that thick accretionary prism sediments amplified and extended seismic wave durations from the 11 April 2012 Mw8.6 Indian Ocean earthquake, located more than 13,500 km away. These waves triggered a sequence of small slope failures on the Cascadia margin that led to sediment gravity flows culminating in turbidity currents. Previous studies have related the triggering of sediment-laden gravity flows and turbidite deposition to local earthquakes, but this is the first study in which the originating seismic event is extremely distant (> 10,000 km). The possibility of remotely triggered slope failures that generate sediment-laden gravity flows should be considered in inferences of recurrence intervals of past great Cascadia earthquakes from turbidite sequences. Future similar studies may provide new understanding of submarine slope failures and turbidity currents and the hazards they pose to seafloor infrastructure and tsunami generation in regions both with and without local earthquakes.
On the Chemical Mixing Induced by Internal Gravity Waves
Energy Technology Data Exchange (ETDEWEB)
Rogers, T. M. [School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne (United Kingdom); McElwaine, J. N. [Planetary Science Institute, Tucson, AZ 85721 (United States)
2017-10-10
Detailed modeling of stellar evolution requires a better understanding of the (magneto)hydrodynamic processes that mix chemical elements and transport angular momentum. Understanding these processes is crucial if we are to accurately interpret observations of chemical abundance anomalies, surface rotation measurements, and asteroseismic data. Here, we use two-dimensional hydrodynamic simulations of the generation and propagation of internal gravity waves in an intermediate-mass star to measure the chemical mixing induced by these waves. We show that such mixing can generally be treated as a diffusive process. We then show that the local diffusion coefficient does not depend on the local fluid velocity, but rather on the wave amplitude. We then use these findings to provide a simple parameterization for this diffusion, which can be incorporated into stellar evolution codes and tested against observations.
Nonlinear acoustic waves in micro-inhomogeneous solids
Nazarov, Veniamin
2014-01-01
Nonlinear Acoustic Waves in Micro-inhomogeneous Solids covers the broad and dynamic branch of nonlinear acoustics, presenting a wide variety of different phenomena from both experimental and theoretical perspectives. The introductory chapters, written in the style of graduate-level textbook, present a review of the main achievements of classic nonlinear acoustics of homogeneous media. This enables readers to gain insight into nonlinear wave processes in homogeneous and micro-inhomogeneous solids and compare it within the framework of the book. The subsequent eight chapters covering: Physical m
Nonlinear wave breaking in self-gravitating viscoelastic quantum fluid
Energy Technology Data Exchange (ETDEWEB)
Mitra, Aniruddha, E-mail: anibabun@gmail.com [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India); Roychoudhury, Rajkumar, E-mail: rajdaju@rediffmail.com [Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata 700075 (India); Department of Mathematics, Bethune College, Kolkata 700006 (India); Bhar, Radhaballav [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India); Khan, Manoranjan, E-mail: mkhan.ju@gmail.com [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India)
2017-02-12
The stability of a viscoelastic self-gravitating quantum fluid has been studied. Symmetry breaking instability of solitary wave has been observed through ‘viscosity modified Ostrovsky equation’ in weak gravity limit. In presence of strong gravitational field, the solitary wave breaks into shock waves. Response to a Gaussian perturbation, the system produces quasi-periodic short waves, which in terns predicts the existence of gravito-acoustic quasi-periodic short waves in lower solar corona region. Stability analysis of this dynamical system predicts gravity has the most prominent effect on the phase portraits, therefore, on the stability of the system. The non-existence of chaotic solution has also been observed at long wavelength perturbation through index value theorem. - Highlights: • In weak gravitational field, viscoelastic quantum fluid exhibits symmetry breaking instability. • Gaussian perturbation produces quasi-periodic gravito-acoustic waves into the system. • There exists no chaotic state of the system against long wavelength perturbations.
Nonlinear evolution equations for waves in random media
International Nuclear Information System (INIS)
Pelinovsky, E.; Talipova, T.
1994-01-01
The scope of this paper is to highlight the main ideas of asymptotical methods applying in modern approaches of description of nonlinear wave propagation in random media. We start with the discussion of the classical conception of ''mean field''. Then an exactly solvable model describing nonlinear wave propagation in the medium with fluctuating parameters is considered in order to demonstrate that the ''mean field'' method is not correct. We develop new asymptotic procedures of obtaining the nonlinear evolution equations for the wave fields in random media. (author). 16 refs
Some remarks on coherent nonlinear coupling of waves in plasmas
International Nuclear Information System (INIS)
Wilhelmsson, H.
1976-01-01
The analysis of nonlinear processes in plasma physics has given rise to a basic set of coupled equations. These equations describe the coherent nonlinear evolution of plasma waves. In this paper various possibilities of analysing these equations are discussed and inherent difficulties in the description of nonlinear interactions between different types of waves are pointed out. Specific examples of stimulated excitation of waves are considered. These are the parametric excitation of hybrid resonances in hot magnetized multi-ion component plasma and laser-plasma interactions. (B.D.)
X. Liu; X. Liu; J. Xu; H.-L. Liu; J. Yue; W. Yuan
2014-01-01
Using a fully nonlinear two-dimensional (2-D) numerical model, we simulated gravity waves (GWs) breaking and their contributions to the formation of large winds and wind shears in the mesosphere and lower thermosphere (MLT). An eddy diffusion coefficient is used in the 2-D numerical model to parameterize realistic turbulent mixing. Our study shows that the momentum deposited by breaking GWs accelerates the mean wind. The resultant large background wind increases the GW's app...
Sensitivity of Gravity Wave Fluxes to Interannual Variations in Tropical Convection and Zonal Wind.
Alexander, M Joan; Ortland, David A; Grimsdell, Alison W; Kim, Ji-Eun
2017-09-01
Using an idealized model framework with high-frequency tropical latent heating variability derived from global satellite observations of precipitation and clouds, the authors examine the properties and effects of gravity waves in the lower stratosphere, contrasting conditions in an El Niño year and a La Niña year. The model generates a broad spectrum of tropical waves including planetary-scale waves through mesoscale gravity waves. The authors compare modeled monthly mean regional variations in wind and temperature with reanalyses and validate the modeled gravity waves using satellite- and balloon-based estimates of gravity wave momentum flux. Some interesting changes in the gravity spectrum of momentum flux are found in the model, which are discussed in terms of the interannual variations in clouds, precipitation, and large-scale winds. While regional variations in clouds, precipitation, and winds are dramatic, the mean gravity wave zonal momentum fluxes entering the stratosphere differ by only 11%. The modeled intermittency in gravity wave momentum flux is shown to be very realistic compared to observations, and the largest-amplitude waves are related to significant gravity wave drag forces in the lowermost stratosphere. This strong intermittency is generally absent or weak in climate models because of deficiencies in parameterizations of gravity wave intermittency. These results suggest a way forward to improve model representations of the lowermost stratospheric quasi-biennial oscillation winds and teleconnections.
Electron non-linearities in Langmuir waves with application to beat-wave experiments
International Nuclear Information System (INIS)
Bell, A.R.; Gibbon, P.
1988-01-01
Non-linear Langmuir waves are examined in the context of the beat-wave accelerator. With a background of immobile ions the waves in one dimension are subject to the relativistic non-linearity of Rosenbluth, M.N. and Liu, C.S., Phys. Rev. Lett., 1972, 29, 701. In two or three dimensions, other electron non-linearities occur which involve electric and magnetic fields. The quasi-linear equations for these non-linearities are developed and solved numerically in a geometry representative of laser-driven beat waves. (author)
Couston, Louis-Alexandre; Lecoanet, Daniel; Favier, Benjamin; Le Bars, Michael
2017-11-01
We investigate via direct numerical simulations the spontaneous generation and reversals of mean zonal flows in a stably-stratified fluid layer lying above a turbulent convective fluid. Contrary to the leading idealized theories of mean flow generation by self-interacting internal waves, the emergence of a mean flow in a convectively-generated internal gravity wave field is not always possible because nonlinear interactions of waves of different frequencies can disrupt the mean flow generation mechanism. Strong mean flows thus emerge when the divergence of the Reynolds stress resulting from the nonlinear interactions of internal waves produces a strong enough anti-diffusive acceleration for the mean flow, which, as we will demonstrate, is the case when the Prandtl number is sufficiently low, or when the energy input into the internal wavefield by the convection and density stratification are sufficiently large. Implications for mean zonal flow production as observed in the equatorial stratospheres of the Earth, Saturn and Jupiter, and possibly occurring in other geophysical systems such as planetary and stellar interiors will be briefly discussed. Funding provided by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program through Grant Agreement No. 681835-FLUDYCO-ERC-2015-CoG.
Rogue and shock waves in nonlinear dispersive media
Resitori, Stefania; Baronio, Fabio
2016-01-01
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists ...
Effect of Forcing Function on Nonlinear Acoustic Standing Waves
Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce
2003-01-01
Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.
Internal wave energy flux from density perturbations in nonlinear stratifications
Lee, Frank M.; Allshouse, Michael R.; Swinney, Harry L.; Morrison, P. J.
2017-11-01
Tidal flow over the topography at the bottom of the ocean, whose density varies with depth, generates internal gravity waves that have a significant impact on the energy budget of the ocean. Thus, understanding the energy flux (J = p v) is important, but it is difficult to measure simultaneously the pressure and velocity perturbation fields, p and v . In a previous work, a Green's-function-based method was developed to calculate the instantaneous p, v , and thus J , given a density perturbation field for a constant buoyancy frequency N. Here we extend the previous analytic Green's function work to include nonuniform N profiles, namely the tanh-shaped and linear cases, because background density stratifications that occur in the ocean and some experiments are nonlinear. In addition, we present a finite-difference method for the general case where N has an arbitrary profile. Each method is validated against numerical simulations. The methods we present can be applied to measured density perturbation data by using our MATLAB graphical user interface EnergyFlux. PJM was supported by the U.S. Department of Energy Contract DE-FG05-80ET-53088. HLS and MRA were supported by ONR Grant No. N000141110701.
Gravity wave vertical energy flux at 95 km
Jacob, P. G.; Jacka, F.
1985-01-01
A three-field photometer (3FP) located at Mt. Torrens near Adelaide, is capable of monitoring different airglow emissions from three spaced fields in the sky. A wheel containing up to six different narrow bandpass interference filters can be rotated, allowing each of the filters to be sequentially placed into each of the three fields. The airglow emission of interest is the 557.7 nm line which has an intensity maximum at 95 km. Each circular field of view is located at the apexes of an equilateral triangle centered on zenith with diameters of 5 km and field separations of 13 km when projected to the 95-km level. The sampling period was 30 seconds and typical data lengths were between 7 and 8 hours. The analysis and results from the interaction of gravity waves on the 557.7 nm emission layer are derived using an atmospheric model similar to that proposed by Hines (1960) where the atmosphere is assumed isothermal and perturbations caused by gravity waves are small and adiabatic, therefore, resulting in linearized equations of motion. In the absence of waves, the atmosphere is also considered stationary. Thirteen nights of quality data from January 1983 to October 1984, covering all seasons, are used in this analysis.
McWilliams, J. C.; Lane, E.; Melville, K.; Restrepo, J.; Sullivan, P.
2004-12-01
Oceanic surface gravity waves are approximately irrotational, weakly nonlinear, and conservative, and they have a much shorter time scale than oceanic currents and longer waves (e.g., infragravity waves) --- except where the primary surface waves break. This provides a framework for an asymptotic theory, based on separation of time (and space) scales, of wave-averaged effects associated with the conservative primary wave dynamics combined with a stochastic representation of the momentum transfer and induced mixing associated with non-conservative wave breaking. Such a theory requires only modest information about the primary wave field from measurements or operational model forecasts and thus avoids the enormous burden of calculating the waves on their intrinsically small space and time scales. For the conservative effects, the result is a vortex force associated with the primary wave's Stokes drift; a wave-averaged Bernoulli head and sea-level set-up; and an incremental material advection by the Stokes drift. This can be compared to the "radiation stress" formalism of Longuet-Higgins, Stewart, and Hasselmann; it is shown to be a preferable representation since the radiation stress is trivial at its apparent leading order. For the non-conservative breaking effects, a population of stochastic impulses is added to the current and infragravity momentum equations with distribution functions taken from measurements. In offshore wind-wave equilibria, these impulses replace the conventional surface wind stress and cause significant differences in the surface boundary layer currents and entrainment rate, particularly when acting in combination with the conservative vortex force. In the surf zone, where breaking associated with shoaling removes nearly all of the primary wave momentum and energy, the stochastic forcing plays an analogous role as the widely used nearshore radiation stress parameterizations. This talk describes the theoretical framework and presents some
Nonlinear periodic waves in dusty plasma with variable dust charge
International Nuclear Information System (INIS)
Yadav, Lakhan Lal; Bharuthram, R.
2002-01-01
Using the reductive perturbation method, we present a theory of nonlinear periodic waves, viz. the cnoidal waves, in a dusty plasma consisting of electrons, ions, and cold dust grains with charge fluctuations, which in the limiting case reduce to dust acoustic solitons. It is found that the frequency of the dust acoustic cnoidal wave increases with its amplitude. The dust charge fluctuations are found to affect the characteristics of the cnoidal waves
Gravity wave influence on NLC: experimental results from ALOMAR, 69° N
Directory of Open Access Journals (Sweden)
H. Wilms
2013-12-01
Full Text Available The influence of gravity waves on noctilucent clouds (NLC at ALOMAR (69° N is analysed by relating gravity wave activity to NLC occurrence from common-volume measurements. Gravity wave kinetic energies are derived from MF-radar wind data and filtered into different period ranges by wavelet transformation. From the dataset covering the years 1999–2011, a direct correlation between gravity wave kinetic energy and NLC occurrence is not found, i.e., NLC appear independently of the simultaneously measured gravity wave kinetic energy. In addition, gravity wave activity is divided into weak and strong activity as compared to a 13 yr mean. The NLC occurrence rates during strong and weak activity are calculated separately for a given wave period and compared to each other. Again, for the full dataset no dependence of NLC occurrence on relative gravity wave activity is found. However, concentrating on 12 h of NLC detections during 2008, we do find an NLC-amplification with strong long-period gravity wave occurrence. Our analysis hence confirms previous findings that in general NLC at ALOMAR are not predominantly driven by gravity waves while exceptions to this rule are at least possible.
Nonlinear electrostatic solitary waves in electron-positron plasmas
Lazarus, I. J.; Bharuthram, R.; Moolla, S.; Singh, S. V.; Lakhina, G. S.
2016-02-01
The generation of nonlinear electrostatic solitary waves (ESWs) is explored in a magnetized four component two-temperature electron-positron plasma. Fluid theory is used to derive a set of nonlinear equations for the ESWs, which propagate obliquely to an external magnetic field. The electric field structures are examined for various plasma parameters and are shown to yield sinusoidal, sawtooth and bipolar waveforms. It is found that an increase in the densities of the electrons and positrons strengthen the nonlinearity while the periodicity and nonlinearity of the wave increases as the cool-to-hot temperature ratio increases. Our results could be useful in understanding nonlinear propagation of waves in astrophysical environments and related laboratory experiments.
Nonlinear spin wave coupling in adjacent magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Nonlinear spin wave coupling in adjacent magnonic crystals
International Nuclear Information System (INIS)
Sadovnikov, A. V.; Nikitov, S. A.; Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E.
2016-01-01
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations
Zhang, Linghai
2017-10-01
The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 traveling wave front as well as the existence and instability of a standing pulse solution if 0 traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.
Qualitative aspects of nonlinear wave motion: Complexity and simplicity
International Nuclear Information System (INIS)
Engelbrecht, J.
1993-01-01
The nonlinear wave processes possess many qualitative properties which cannot be described by linear theories. In this presentation, an attempt is made to systematize the main aspects of this fascinating area. The sources of nonlinearities are analyzed in order to understand why and how the nonlinear mathematical models are formulated. The technique of evolution equations is discussed then as a main mathematical tool to separate multiwave processes into single waves. The evolution equations give concise but in many cases sufficient description of wave processes in solids permitting to analyze spectral changes, phase changes and velocities, coupling of waves, and interaction of nonlinearities with other physical effects of the same order. Several new problems are listed. Knowing the reasons, the seemingly complex problems can be effectively analyzed. 61 refs
Nonlinear surface waves at ferrite-metamaterial waveguide structure
Hissi, Nour El Houda; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Shabat, Mohammed Musa; Atangana, Jacques
2016-09-01
A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film-cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film-cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.
On The Implications of Atmospheric Gravity Waves on Wind Power
Norris, Luke
2011-01-01
In view of the rapidly rising cost of fossil fuels and concerns over climate change, there can be little doubt that renewable energy is to play a large role in the future of our economic development. The impact of Atmospheric Gravity Waves (AGWs) on wind power is, at best, unclear. In this research, AGWs are successfully modelled both in theoretical and real world environments using the WindSim software package which has revealed a potential 7.4% drop in annual power output as a direct ...
Can gravity waves significantly impact PSC occurrence in the Antarctic?
Directory of Open Access Journals (Sweden)
R. M. Woollands
2009-11-01
Full Text Available A combination of POAM III aerosol extinction and CHAMP RO temperature measurements are used to examine the role of atmospheric gravity waves in the formation of Antarctic Polar Stratospheric Clouds (PSCs. POAM III aerosol extinction observations and quality flag information are used to identify Polar Stratospheric Clouds using an unsupervised clustering algorithm.
A PSC proxy, derived by thresholding Met Office temperature analyses with the PSC Type Ia formation temperature (T_{NAT}, shows general agreement with the results of the POAM III analysis. However, in June the POAM III observations of PSC are more abundant than expected from temperature threshold crossings in five out of the eight years examined. In addition, September and October PSC identified using temperature thresholding is often significantly higher than that derived from POAM III; this observation probably being due to dehydration and denitrification. Comparison of the Met Office temperature analyses with corresponding CHAMP observations also suggests a small warm bias in the Met Office data in June. However, this bias cannot fully explain the differences observed.
Analysis of CHAMP data indicates that temperature perturbations associated with gravity waves may partially explain the enhanced PSC incidence observed in June (relative to the Met Office analyses. For this month, approximately 40% of the temperature threshold crossings observed using CHAMP RO data are associated with small-scale perturbations. Examination of the distribution of temperatures relative to T_{NAT} shows a large proportion of June data to be close to this threshold, potentially enhancing the importance of gravity wave induced temperature perturbations. Inspection of the longitudinal structure of PSC occurrence in June 2005 also shows that regions of enhancement are geographically associated with the Antarctic Peninsula; a known mountain wave "hotspot". The
Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas
Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.
1997-01-01
We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.
Optical rogue waves and soliton turbulence in nonlinear fibre optics
DEFF Research Database (Denmark)
Genty, G.; Dudley, J. M.; de Sterke, C. M.
2009-01-01
We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....
On Maximally Dissipative Shock Waves in Nonlinear Elasticity
Knowles, James K.
2010-01-01
Shock waves in nonlinearly elastic solids are, in general, dissipative. We study the following question: among all plane shock waves that can propagate with a given speed in a given one-dimensional nonlinearly elastic bar, which one—if any—maximizes the rate of dissipation? We find that the answer to this question depends strongly on the qualitative nature of the stress-strain relation characteristic of the given material. When maximally dissipative shocks do occur, they propagate according t...
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...
Green function formalism for nonlinear acoustic waves in layered media
International Nuclear Information System (INIS)
Lobo, A.; Tsoy, E.; De Sterke, C.M.
2000-01-01
Full text: The applications of acoustic waves in identifying defects in adhesive bonds between metallic plates have received little attention at high intensities where the media respond nonlinearly. However, the effects of reduced bond strength are more distinct in the nonlinear response of the structure. Here we assume a weak nonlinearity acting as a small perturbation, thereby reducing the problem to a linear one. This enables us to develop a specialized Green function formalism for calculating acoustic fields in layered media
Defocusing regimes of nonlinear waves in media with negative dispersion
DEFF Research Database (Denmark)
Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.
1996-01-01
Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schrodinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called critical dimension cannot collapse in finite time...
Exact travelling wave solutions for some important nonlinear
Indian Academy of Sciences (India)
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...
New travelling wave solutions for nonlinear stochastic evolution
Indian Academy of Sciences (India)
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic ...
Stability of nonlinear waves and patterns and related topics
Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn
2018-04-01
Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.
Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates
International Nuclear Information System (INIS)
Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young
2010-01-01
Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions: phase matching, non-zero power flux, group velocity matching, and non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter grew up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters
On the interaction of small-scale linear waves with nonlinear solitary waves
Xu, Chengzhu; Stastna, Marek
2017-04-01
In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow
Simulating nonlinear steady-state traveling waves on the falling liquid film entrained by a gas flow
Tsvelodub, O. Yu; Bocharov, A. A.
2017-09-01
The article is devoted to the simulation of nonlinear waves on a liquid film flowing under gravity in the known stress field at the interface. The paper studies nonlinear waves on a liquid film, flowing under the action of gravity in a known stress field at the interface. In the case of small Reynolds numbers the problem is reduced to the consideration of solutions of the nonlinear integral-differential equation for film thickness deviation from the undisturbed level. The periodic and soliton steady-state traveling solutions of this equation have been numerically found. The analysis of branching of new families of steady-state traveling solutions has been performed. In particular, it is shown that this model equation has solutions in the form of solitons-humps.
Propagation of nonlinear ion acoustic wave with generation of long-wavelength waves
International Nuclear Information System (INIS)
Ohsawa, Yukiharu; Kamimura, Tetsuo
1978-01-01
The nonlinear propagation of the wave packet of an ion acoustic wave with wavenumber k 0 asymptotically equals k sub(De) (the electron Debye wavenumber) is investigated by computer simulations. From the wave packet of the ion acoustic wave, waves with long wavelengths are observed to be produced within a few periods for the amplitude oscillation of the original wave packet. These waves are generated in the region where the original wave packet exists. Their characteristic wavelength is of the order of the length of the wave packet, and their propagation velocity is almost equal to the ion acoustic speed. The long-wavelength waves thus produced strongly affect the nonlinear evolution of the original wave packet. (auth.)
Atmosphere-ionosphere coupling from convectively generated gravity waves
Azeem, Irfan; Barlage, Michael
2018-04-01
Ionospheric variability impacts operational performances of a variety of technological systems, such as HF communication, Global Positioning System (GPS) navigation, and radar surveillance. The ionosphere is not only perturbed by geomagnetic inputs but is also influenced by atmospheric tides and other wave disturbances propagating from the troposphere to high altitudes. Atmospheric Gravity Waves (AGWs) excited by meteorological sources are one of the largest sources of mesoscale variability in the ionosphere. In this paper, Total Electron Content (TEC) data from networks of GPS receivers in the United States are analyzed to investigate AGWs in the ionosphere generated by convective thunderstorms. Two case studies of convectively generated gravity waves are presented. On April 4, 2014 two distinct large convective systems in Texas and Arkansas generated two sets of concentric AGWs that were observed in the ionosphere as Traveling Ionospheric Disturbances (TIDs). The period of the observed TIDs was 20.8 min, the horizontal wavelength was 182.4 km, and the horizontal phase speed was 146.4 m/s. The second case study shows TIDs generated from an extended squall line on December 23, 2015 stretching from the Gulf of Mexico to the Great Lakes in North America. Unlike the concentric wave features seen in the first case study, the extended squall line generated TIDs, which exhibited almost plane-parallel phase fronts. The TID period was 20.1 min, its horizontal wavelength was 209.6 km, and the horizontal phase speed was 180.1 m/s. The AGWs generated by both of these meteorological events have large vertical wavelength (>100 km), which are larger than the F2 layer thickness, thus allowing them to be discernible in the TEC dataset.
International Nuclear Information System (INIS)
Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong
2011-01-01
In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.
Gravitational wave echoes from macroscopic quantum gravity effects
Energy Technology Data Exchange (ETDEWEB)
Barceló, Carlos [Instituto de Astrofísica de Andalucía (IAA-CSIC),Glorieta de la Astronomía, 18008 Granada (Spain); Carballo-Rubio, Raúl [The Cosmology & Gravity Group and the Laboratory for Quantum Gravity & Strings,Department of Mathematics & Applied Mathematics, University of Cape Town,Private Bag, Rondebosch 7701 (South Africa); Garay, Luis J. [Departamento de Física Teórica II,Universidad Complutense de Madrid, 28040 Madrid (Spain); Instituto de Estructura de la Materia (IEM-CSIC),Serrano 121, 28006 Madrid (Spain)
2017-05-10
New theoretical approaches developed in the last years predict that macroscopic quantum gravity effects in black holes should lead to modifications of the gravitational wave signals expected in the framework of classical general relativity, with these modifications being characterized in certain scenarios by the existence of dampened repetitions of the primary signal. Here we use the fact that non-perturbative corrections to the near-horizon external geometry of black holes are necessary for these modifications to exist, in order to classify different proposals and paradigms with respect to this criterion and study in a neat and systematic way their phenomenology. Proposals that lead naturally to the existence of echoes in the late-time ringdown of gravitational wave signals from black hole mergers must share the replacement of black holes by horizonless configurations with a physical surface showing reflective properties in the relevant range of frequencies. On the other hand, proposals or paradigms that restrict quantum gravity effects on the external geometry to be perturbative, such as black hole complementarity or the closely related firewall proposal, do not display echoes. For the sake of completeness we exploit the interplay between the timescales associated with the formation of firewalls and the mechanism behind the existence of echoes in order to conclude that even unconventional distortions of the firewall concept (such as naked firewalls) do not lead to this phenomenon.
Symbolic computation of nonlinear wave interactions on MACSYMA
International Nuclear Information System (INIS)
Bers, A.; Kulp, J.L.; Karney, C.F.F.
1976-01-01
In this paper the use of a large symbolic computation system - MACSYMA - in determining approximate analytic expressions for the nonlinear coupling of waves in an anisotropic plasma is described. MACSYMA was used to implement the solutions of a fluid plasma model nonlinear partial differential equations by perturbation expansions and subsequent iterative analytic computations. By interacting with the details of the symbolic computation, the physical processes responsible for particular nonlinear wave interactions could be uncovered and appropriate approximations introduced so as to simplify the final analytic result. Details of the MACSYMA system and its use are discussed and illustrated. (Auth.)
Nonlinear pattern formation of Faraday waves
Binks, D.J.; Water, van de W.
1997-01-01
A cascade of surface wave patterns with increasing rotational symmetry ranging from simple square to tenfold quasiperiodic is observed for Faraday waves. The experiment concerns the excitation of subharmonic standing surface waves by oscillating vertical acceleration. Our observation agrees with the
Nonlinear waves in electron–positron–ion plasmas including charge ...
Indian Academy of Sciences (India)
2017-01-04
Jan 4, 2017 ... The introduction of the Poisson equation increased the Mach number required to generate the waveforms but the driving electric field E0 was reduced. The results are compared with satellite observations. Keywords. Nonlinear waves; low frequency; ion-acoustic waves. PACS Nos 52.35.Qz; 52.35.Fp; 52.35 ...
The response of superpressure balloons to gravity wave motions
Directory of Open Access Journals (Sweden)
R. A. Vincent
2014-04-01
Full Text Available Superpressure balloons (SPB, which float on constant density (isopycnic surfaces, provide a unique way of measuring the properties of atmospheric gravity waves (GW as a function of wave intrinsic frequency. Here we devise a quasi-analytic method of investigating the SPB response to GW motions. It is shown that the results agree well with more rigorous numerical simulations of balloon motions and provide a better understanding of the response of SPB to GW, especially at high frequencies. The methodology is applied to ascertain the accuracy of GW studies using 12 m diameter SPB deployed in the 2010 Concordiasi campaign in the Antarctic. In comparison with the situation in earlier campaigns, the vertical displacements of the SPB were measured directly using GPS. It is shown using a large number of Monte Carlo-type simulations with realistic instrumental noise that important wave parameters, such as momentum flux, phase speed and wavelengths, can be retrieved with good accuracy from SPB observations for intrinsic wave periods greater than ca. 10 min. The noise floor for momentum flux is estimated to be ca. 10−4 mPa.
Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao
2018-04-01
We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.
Directional nonlinear guided wave mixing: Case study of counter-propagating shear horizontal waves
Hasanian, Mostafa; Lissenden, Cliff J.
2018-04-01
While much nonlinear ultrasonics research has been conducted on higher harmonic generation, wave mixing provides the potential for sensitive measurements of incipient damage unencumbered by instrumentation nonlinearity. Studies of nonlinear ultrasonic wave mixing, both collinear and noncollinear, for bulk waves have shown the robust capability of wave mixing for early damage detection. One merit of bulk wave mixing lies in their non-dispersive nature, but guided waves enable inspection of otherwise inaccessible material and a variety of mixing options. Co-directional guided wave mixing was studied previously, but arbitrary direction guided wave mixing has not been addressed until recently. Wave vector analysis is applied to study variable mixing angles to find wave mode triplets (two primary waves and a secondary wave) resulting in the phase matching condition. As a case study, counter-propagating Shear Horizontal (SH) guided wave mixing is analyzed. SH wave interactions generate a secondary Lamb wave mode that is readily receivable. Reception of the secondary Lamb wave mode is compared for an angle beam transducer, an air coupled transducer, and a laser Doppler vibrometer (LDV). Results from the angle beam and air coupled transducers are quite consistent, while the LDV measurement is plagued by variability issues.
Nonlinear frequency shift of finite-amplitude electrostatic surface waves
International Nuclear Information System (INIS)
Stenflo, L.
1989-01-01
The problem concerning the appropriate form for the nonlinear frequency shift arising from slow density modulations of electrostatic surface waves in a semi-infinite unmagnetized plasma is reconsidered. The spatial dependence of the wave amplitude normal to the surface is kept general in order to allow for possible nonlinear attenuation behaviour of the surface waves. It is found that if the frequency shift is expressed as a function of the density and its gradient then the result is identical with that of Zhelyazkov, I. Proceedings International Conference on Plasma Physics, Kiev, 1987, Vol. 2, p. 694, who assumed a linear exponential attenuation behaviour. (author)
Characteristics of equatorial gravity waves derived from mesospheric airglow imaging observations
Directory of Open Access Journals (Sweden)
S. Suzuki
2009-04-01
Full Text Available We present the characteristics of small-scale (<100 km gravity waves in the equatorial mesopause region derived from OH airglow imaging observations at Kototabang (100.3° E, 0.2° S, Indonesia, from 2002 to 2005. We adopted a method that could automatically detect gravity waves in the airglow images using two-dimensional cross power spectra of gravity waves. The propagation directions of the waves were likely controlled by zonal filtering due to stratospheric mean winds that show a quasi-biennial oscillation (QBO and the presence of many wave sources in the troposphere.
Nonlinear periodic space-charge waves in plasma
International Nuclear Information System (INIS)
Kovalev, V. A.
2009-01-01
A solution is obtained in the form of coupled nonlinear periodic space-charge waves propagating in a magnetoactive plasma. The wave spectrum in the vicinity of the critical point, where the number of harmonics increases substantially, is found to fall with harmonic number as ∝ s -1/3 . Periodic space-charge waves are invoked to explain the zebra pattern in the radio emission from solar flares.
Nonlinear excitation of geodesic acoustic modes by drift waves
International Nuclear Information System (INIS)
Chakrabarti, N.; Singh, R.; Kaw, P. K.; Guzdar, P. N.
2007-01-01
In this paper, two mode-coupling analyses for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by drift waves are presented. The first approach is a coherent parametric process, which leads to a three-wave resonant interaction. This investigation allows for the drift waves and the GAMs to have comparable scales. The second approach uses the wave-kinetic equations for the drift waves, which then couples to the GAMs. This requires that the GAM scale length be large compared to the wave packet associated with the drift waves. The resonance conditions for these two cases lead to specific predictions of the radial wave number of the excited GAMs
Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia
Jung, P.; Cornell-Bell, A. H.
Astrocyte-signaling has been observed in cell cultures and brain slices in the form of Calcium waves. Their functional relevance for neuronal communication, brain functions and diseases is, however, not understood. In this paper, the propagation of intercellular calcium waves is modeled in terms of waves in excitable media on a stochastic support. We utilize a novel method to decompose the spatiotemporal patterns into space-time clusters (wave fragments). Based on this cluster decomposition, a statistical description of wave patterns is developed.
(abstract) Tropospheric Calibration for the Mars Observer Gravity Wave Experiment
Walter, Steven J.; Armstrong, John
1994-01-01
In spring 1993, microwave radiometer-based tropospheric calibration was provided for the Mars Observer gravitational wave search. The Doppler shifted X-band radio signals propagating between Earth and the Mars Observer satellite were precisely measured to determine path length variations that might signal passage of gravitational waves. Experimental sensitivity was restricted by competing sources of variability in signal transit time. Principally, fluctuations in the solar wind and ionospheric plasma density combined with fluctions in tropospheric refractivity determined the detection limit. Troposphere-induced path delay fluctions are dominated by refractive changes caused by water vapor inhomogeneities blowing through the signal path. Since passive microwave remote sensing techniques are able to determine atmospheric propagation delays, radiometer-based tropospheric calibration was provided at the Deep Space Network Uranus tracking site (DSS-15). Two microwave water vapor radiometers (WVRs), a microwave temperature profiler (MTP), and a ground based meterological station were deployed to determine line-of-sight vapor content and vertical temperature profile concurrently with Mars Observer tracking measurements. This calibration system provided the capability to correct Mars Observer Doppler data for troposphere-induced path variations. We present preliminary analysis of the Doppler and WVR data sets illustrating the utility of WVRs to calibrate Doppler data. This takes an important step toward realizing the ambitious system required to support future Ka-band Cassini satellite gravity wave tropospheric calibration system.
Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains
Przedborski, Michelle; Anco, Stephen C.
2017-09-01
A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.
Alfven wave resonances and flow induced by nonlinear Alfven waves in a stratified atmosphere
International Nuclear Information System (INIS)
Stark, B. A.; Musielak, Z. E.; Suess, S. T.
1996-01-01
A nonlinear, time-dependent, ideal MHD code has been developed and used to compute the flow induced by nonlinear Alfven waves propagating in an isothermal, stratified, plane-parallel atmosphere. The code is based on characteristic equations solved in a Lagrangian frame. Results show that resonance behavior of Alfven waves exists in the presence of a continuous density gradient and that the waves with periods corresponding to resonant peaks exert considerably more force on the medium than off-resonance periods. If only off-peak periods are considered, the relationship between the wave period and induced longitudinal velocity shows that short period WKB waves push more on the background medium than longer period, non-WKB, waves. The results also show the development of the longitudinal waves induced by finite amplitude Alfven waves. Wave energy transferred to the longitudinal mode may provide a source of localized heating
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
International Nuclear Information System (INIS)
Tataronis, J. A.
2004-01-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfven continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named ''accumulation continuum'' and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory
Constrained non-linear waves for offshore wind turbine design
International Nuclear Information System (INIS)
Rainey, P J; Camp, T R
2007-01-01
Advancements have been made in the modelling of extreme wave loading in the offshore environment. We give an overview of wave models used at present, and their relative merits. We describe a method for embedding existing non-linear solutions for large, regular wave kinematics into linear, irregular seas. Although similar methods have been used before, the new technique is shown to offer advances in computational practicality, repeatability, and accuracy. NewWave theory has been used to constrain the linear simulation, allowing best possible fit with the large non-linear wave. GH Bladed was used to compare the effect of these models on a generic 5 MW turbine mounted on a tripod support structure
International Nuclear Information System (INIS)
Bertel, L.; Bertin, F.; Testud, J.
1976-01-01
The interpretation of the measurements of the integrated electron content in terms of gravity wave requires (1) a gravity wave model at thermospheric altitudes; (2) a gravity wave-ionization interaction model in the F-region of the ionosphere; and (3) a computing program for the resulting perturbation on the integrated electron content between the satellite and the earth station used. The gravity wave model considered in this paper takes into account the dissipative effects (viscosity, thermal conduction) which become very importanr above 250 km altitude and the effect of the base wind which is capable of affecting deeply the propagation of the waves of medium scale. Starting with this model, the domains of frequencies and the wavelength of atmospheric waves which may exist in the upper atmosphere are considered. The interaction of such waves and the ionization is examined. The theoretical results give information particularly on the selectivity of the ionospheric response to the wave passage. The deduced selectivity of the models appears to be smaller than that given by other authors who used simplified gravity wave models. The method for computing the perturbation of the of the integrated electron content introduced by the wave passage is given for a geostationary satellite. Computational results are presented for application to the case of medium scale gravity waves. (author)
Holographic p-wave superfluid in Gauss–Bonnet gravity
International Nuclear Information System (INIS)
Liu, Shancheng; Pan, Qiyuan; Jing, Jiliang
2017-01-01
We construct the holographic p-wave superfluid in Gauss–Bonnet gravity via a Maxwell complex vector field model and investigate the effect of the curvature correction on the superfluid phase transition in the probe limit. We obtain the rich phase structure and find that the higher curvature correction hinders the condensate of the vector field but makes it easier for the appearance of translating point from the second-order transition to the first-order one or for the emergence of the Cave of Winds. Moreover, for the supercurrents versus the superfluid velocity, we observe that our results near the critical temperature are independent of the Gauss–Bonnet parameter and agree well with the Ginzburg–Landau prediction.
Holographic p-wave superfluid in Gauss–Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Liu, Shancheng [Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan 410081 (China); Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan 410081 (China); Pan, Qiyuan, E-mail: panqiyuan@126.com [Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan 410081 (China); Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan 410081 (China); Jing, Jiliang, E-mail: jljing@hunnu.edu.cn [Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan 410081 (China); Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan 410081 (China)
2017-02-10
We construct the holographic p-wave superfluid in Gauss–Bonnet gravity via a Maxwell complex vector field model and investigate the effect of the curvature correction on the superfluid phase transition in the probe limit. We obtain the rich phase structure and find that the higher curvature correction hinders the condensate of the vector field but makes it easier for the appearance of translating point from the second-order transition to the first-order one or for the emergence of the Cave of Winds. Moreover, for the supercurrents versus the superfluid velocity, we observe that our results near the critical temperature are independent of the Gauss–Bonnet parameter and agree well with the Ginzburg–Landau prediction.
Nonlinear response and bistability of driven ion acoustic waves
Akbari-Moghanjoughi, M.
2017-08-01
The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.
Energy Technology Data Exchange (ETDEWEB)
Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)
2015-03-31
This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.
Directory of Open Access Journals (Sweden)
M. Ern
2018-04-01
Full Text Available Gravity waves are one of the main drivers of atmospheric dynamics. The spatial resolution of most global atmospheric models, however, is too coarse to properly resolve the small scales of gravity waves, which range from tens to a few thousand kilometers horizontally, and from below 1 km to tens of kilometers vertically. Gravity wave source processes involve even smaller scales. Therefore, general circulation models (GCMs and chemistry climate models (CCMs usually parametrize the effect of gravity waves on the global circulation. These parametrizations are very simplified. For this reason, comparisons with global observations of gravity waves are needed for an improvement of parametrizations and an alleviation of model biases. We present a gravity wave climatology based on atmospheric infrared limb emissions observed by satellite (GRACILE. GRACILE is a global data set of gravity wave distributions observed in the stratosphere and the mesosphere by the infrared limb sounding satellite instruments High Resolution Dynamics Limb Sounder (HIRDLS and Sounding of the Atmosphere using Broadband Emission Radiometry (SABER. Typical distributions (zonal averages and global maps of gravity wave vertical wavelengths and along-track horizontal wavenumbers are provided, as well as gravity wave temperature variances, potential energies and absolute momentum fluxes. This global data set captures the typical seasonal variations of these parameters, as well as their spatial variations. The GRACILE data set is suitable for scientific studies, and it can serve for comparison with other instruments (ground-based, airborne, or other satellite instruments and for comparison with gravity wave distributions, both resolved and parametrized, in GCMs and CCMs. The GRACILE data set is available as supplementary data at https://doi.org/10.1594/PANGAEA.879658.
Ern, Manfred; Trinh, Quang Thai; Preusse, Peter; Gille, John C.; Mlynczak, Martin G.; Russell, James M., III; Riese, Martin
2018-04-01
Gravity waves are one of the main drivers of atmospheric dynamics. The spatial resolution of most global atmospheric models, however, is too coarse to properly resolve the small scales of gravity waves, which range from tens to a few thousand kilometers horizontally, and from below 1 km to tens of kilometers vertically. Gravity wave source processes involve even smaller scales. Therefore, general circulation models (GCMs) and chemistry climate models (CCMs) usually parametrize the effect of gravity waves on the global circulation. These parametrizations are very simplified. For this reason, comparisons with global observations of gravity waves are needed for an improvement of parametrizations and an alleviation of model biases. We present a gravity wave climatology based on atmospheric infrared limb emissions observed by satellite (GRACILE). GRACILE is a global data set of gravity wave distributions observed in the stratosphere and the mesosphere by the infrared limb sounding satellite instruments High Resolution Dynamics Limb Sounder (HIRDLS) and Sounding of the Atmosphere using Broadband Emission Radiometry (SABER). Typical distributions (zonal averages and global maps) of gravity wave vertical wavelengths and along-track horizontal wavenumbers are provided, as well as gravity wave temperature variances, potential energies and absolute momentum fluxes. This global data set captures the typical seasonal variations of these parameters, as well as their spatial variations. The GRACILE data set is suitable for scientific studies, and it can serve for comparison with other instruments (ground-based, airborne, or other satellite instruments) and for comparison with gravity wave distributions, both resolved and parametrized, in GCMs and CCMs. The GRACILE data set is available as supplementary data at https://doi.org/10.1594/PANGAEA.879658" target="_blank">https://doi.org/10.1594/PANGAEA.879658.
Nonlinear wave chaos: statistics of second harmonic fields.
Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M
2017-10-01
Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.
Computer simulations on the nonlinear frequency shift and nonlinear modulation of ion-acoustic waves
International Nuclear Information System (INIS)
Ohsawa, Yukiharu; Kamimura, Tetsuo.
1976-11-01
The nonlinear behavior of ion-acoustic waves with rather short wave-length, k lambda sub(De) asymptotically equals 1, is investigated by computer sumulations. It is observed that the nonlinear frequency shift is negative and is proportional to square root of the initial wave amplitude when the amplitude is not too large. This proportionality breaks down and the frequency shift can become positive (for large Te/Ti), when (n tilde sub(i)/n 0 )sup(1/2)>0.25, where n tilde sub(i) is the ion density perturbation and n 0 the average plasma density. Nonlinear modulation of the wave-packet is clearly seen; however, modulational instability was not observed. The importance of the effects of trapped ions to these phenomena is emphasized. (auth.)
Nonlinear wave particle interaction in the Earth's foreshock
Mazelle, C.; LeQueau, D.; Meziane, K.; Lin, R. P.; Parks, G.; Reme, H.; Sanderson, T.; Lepping, R. P.
1997-01-01
The possibility that ion beams could provide a free energy source for driving an ion/ion instability responsible for the ULF wave occurrence is investigated. For this, the wave dispersion relation with the observed parameters is solved. Secondly, it is shown that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered around a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions with the observations are compared.
Nonlinear transient waves in coupled phase oscillators with inertia.
Jörg, David J
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
Nonlinear modulation of torsional waves in elastic rod. [Instability
Energy Technology Data Exchange (ETDEWEB)
Hirao, M; Sugimoto, N [Osaka Univ., Toyonaka (Japan). Faculty of Engineering Science
1977-06-01
Nonlinear Schroedinger equation, which describes the nonlinear modulation of dispersive torsional waves in an elastic rod of circular cross-section, is derived by the derivative expansion method. It is found, for the lowest dispersive mode, that the modulational instability occurs except in the range of the carrier wavenumber, 2.799
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...
Thermodynamic instability of nonlinearly charged black holes in gravity's rainbow
Energy Technology Data Exchange (ETDEWEB)
Hendi, S.H. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Panahiyan, S. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Shahid Beheshti University, Physics Department, Tehran (Iran, Islamic Republic of); Panah, B.E.; Momennia, M. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)
2016-03-15
Motivated by the violation of Lorentz invariance in quantum gravity, we study black hole solutions in gravity's rainbow in the context of Einstein gravity coupled with various models of nonlinear electrodynamics. We regard an energy dependent spacetime and obtain the related metric functions and electric fields. We show that there is an essential singularity at the origin which is covered by an event horizon. We also compute the conserved and thermodynamical quantities and examine the validity of the first law of thermodynamics in the presence of rainbow functions. Finally, we investigate the thermal stability conditions for these black hole solutions in the context of canonical ensemble. We show that the thermodynamical structure of the solutions depends on the choices of nonlinearity parameters, charge, and energy functions. (orig.)
On the Stochastic Wave Equation with Nonlinear Damping
International Nuclear Information System (INIS)
Kim, Jong Uhn
2008-01-01
We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping
Wu, J. F.; Xue, X. H.; Hoffmann, L.; Dou, X. K.; Li, H. M.; Chen, T. D.
2015-01-01
Atmospheric gravity waves (GWs) significantly influence global circulation. Deep convection, particularly that associated with typhoons, is believed to be an important source of gravity waves. Stratospheric gravity waves induced by Typhoon Mindulle (2004) were detected by the Atmospheric Infrared Sounder (AIRS). Semicircular GWs with horizontal wavelengths of 100–400 km were found over Taiwan through an inspection of AIRS radiances at 4.3 μm. Characteristics of the stratospheric gravity waves...
Iterative analysis of concrete gravity dam-nonlinear foundation ...
African Journals Online (AJOL)
The solution of the coupled system is accomplished by solving the two systems separately and then considering the interaction effects at the soil–structure interface enforced by a developed iterative scheme. Emphasis has been laid on the study of material nonlinearity of the foundation material in the interaction analysis.
Ganguli, G.; Crabtree, C. E.; Rudakov, L.; Mithaiwala, M.
2014-12-01
Velocity ring instabilities are a common naturally occuring magnetospheric phenomenon that can also be generated by man made ionospheric experiments. These instabilities are known to generate lower-hybrid waves, which generally cannot propagte out of the source region. However, nonlinear wave physics can convert these linearly driven electrostatic lower-hybrid waves into electromagnetic waves that can escape the source region. These nonlinearly generated waves can be an important source of VLF turbulence that controls the trapped electron lifetime in the radiation belts. We develop numerical solutions to the wave-kinetic equation in a periodic box including the effects of nonlinear (NL) scattering (nonlinear Landau damping) of Lower-hybrid waves giving the evolution of the wave-spectra in wavenumber space. Simultaneously we solve the particle diffusion equation of both the background plasma particles and the ring ions, due to both linear and nonlinear Landau resonances. At initial times for cold ring ions, an electrostatic beam mode is excited, while the kinetic mode is stable. As the instability progresses the ring ions heat, the beam mode is stabilized, and the kinetic mode destabilizes. When the amplitude of the waves becomes sufficient the lower-hybrid waves are scattered (by either nearly unmagnetized ions or magnetized electrons) into electromagnetic magnetosonic waves [Ganguli et al 2010]. The effect of NL scattering is to limit the amplitude of the waves, slowing down the quasilinear relaxation time and ultimately allowing more energy from the ring to be liberated into waves [Mithaiwala et al. 2011]. The effects of convection out of the instability region are modeled, additionally limiting the amplitude of the waves, allowing further energy to be liberated from the ring [Scales et al., 2012]. Results are compared to recent 3D PIC simulations [Winske and Duaghton 2012].
Nonlinearly driven oscillations in the gyrotron traveling-wave amplifier
International Nuclear Information System (INIS)
Chiu, C. C.; Pao, K. F.; Yan, Y. C.; Chu, K. R.; Barnett, L. R.; Luhmann, N. C. Jr.
2008-01-01
By delivering unprecedented power and gain, the gyrotron traveling-wave amplifier (gyro-TWT) offers great promise for advanced millimeter wave radars. However, the underlying physics of this complex nonlinear system is yet to be fully elucidated. Here, we report a new phenomenon in the form of nonlinearly driven oscillations. A zero-drive stable gyro-TWT is shown to be susceptible to a considerably reduced dynamic range at the band edge, followed by a sudden transition into driven oscillations and then a hysteresis effect. An analysis of this unexpected behavior and its physical interpretation are presented.
Propagation of Quasi-plane Nonlinear Waves in Tubes
Directory of Open Access Journals (Sweden)
P. Koníček
2002-01-01
Full Text Available This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicability of the KZK equation and the GBE equation for describing nonlinear waves in tubes are discussed.
International Nuclear Information System (INIS)
El Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.
1992-09-01
Electromagnetic waves radiated with combination frequencies from a semi-bounded plasma due to nonlinear interaction of radiation with surface wave (both of P-polarization) has been investigated. Waves are radiated both into vacuum and plasma are found to be P-polarized. We take into consideration the continuity at the plasma boundary of the tangential components of the electric field of the waves. The case of normal incidence of radiation and rarefield plasma layer is also studied. (author). 7 refs
Nonlinear steady-state coupling of LH waves
International Nuclear Information System (INIS)
Ko, K.; Krapchev, V.B.
1981-02-01
The coupling of lower hybrid waves at the plasma edge by a two waveguide array with self-consistent density modulation is solved numerically. For a linear density profile, the governing nonlinear Klein-Gordon equation for the electric field can be written as a system of nonlinearly modified Airy equations in Fourier k/sub z/-space. Numerical solutions to the nonlinear system satisfying radiation condition are obtained. Spectra broadening and modifications to resonance cone trajectories are observed with increase of incident power
Nonlinear reflection of shock shear waves in soft elastic media.
Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël
2010-02-01
For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.
Instability of coupled gravity-inertial-Rossby waves on a β-plane in solar system atmospheres
Directory of Open Access Journals (Sweden)
J. F. McKenzie
2009-11-01
Full Text Available This paper provides an analysis of the combined theory of gravity-inertial-Rossby waves on a β-plane in the Boussinesq approximation. The wave equation for the system is fifth order in space and time and demonstrates how gravity-inertial waves on the one hand are coupled to Rossby waves on the other through the combined effects of β, the stratification characterized by the Väisälä-Brunt frequency N, the Coriolis frequency f at a given latitude, and vertical propagation which permits buoyancy modes to interact with westward propagating Rossby waves. The corresponding dispersion equation shows that the frequency of a westward propagating gravity-inertial wave is reduced by the coupling, whereas the frequency of a Rossby wave is increased. If the coupling is sufficiently strong these two modes coalesce giving rise to an instability. The instability condition translates into a curve of critical latitude Θc versus effective equatorial rotational Mach number M, with the region below this curve exhibiting instability. "Supersonic" fast rotators are unstable in a narrow band of latitudes around the equator. For example Θc~12° for Jupiter. On the other hand slow "subsonic" rotators (e.g. Mercury, Venus and the Sun's Corona are unstable at all latitudes except very close to the poles where the β effect vanishes. "Transonic" rotators, such as the Earth and Mars, exhibit instability within latitudes of 34° and 39°, respectively, around the Equator. Similar results pertain to Oceans. In the case of an Earth's Ocean of depth 4km say, purely westward propagating waves are unstable up to 26° about the Equator. The nonlinear evolution of this instability which feeds off rotational energy and gravitational buoyancy may play an important role in atmospheric dynamics.
Instability of coupled gravity-inertial-Rossby waves on a β-plane in solar system atmospheres
Directory of Open Access Journals (Sweden)
J. F. McKenzie
2009-11-01
Full Text Available This paper provides an analysis of the combined theory of gravity-inertial-Rossby waves on a β-plane in the Boussinesq approximation. The wave equation for the system is fifth order in space and time and demonstrates how gravity-inertial waves on the one hand are coupled to Rossby waves on the other through the combined effects of β, the stratification characterized by the Väisälä-Brunt frequency N, the Coriolis frequency f at a given latitude, and vertical propagation which permits buoyancy modes to interact with westward propagating Rossby waves. The corresponding dispersion equation shows that the frequency of a westward propagating gravity-inertial wave is reduced by the coupling, whereas the frequency of a Rossby wave is increased. If the coupling is sufficiently strong these two modes coalesce giving rise to an instability. The instability condition translates into a curve of critical latitude Θ_{c} versus effective equatorial rotational Mach number M, with the region below this curve exhibiting instability. "Supersonic" fast rotators are unstable in a narrow band of latitudes around the equator. For example Θ_{c}~12° for Jupiter. On the other hand slow "subsonic" rotators (e.g. Mercury, Venus and the Sun's Corona are unstable at all latitudes except very close to the poles where the β effect vanishes. "Transonic" rotators, such as the Earth and Mars, exhibit instability within latitudes of 34° and 39°, respectively, around the Equator. Similar results pertain to Oceans. In the case of an Earth's Ocean of depth 4km say, purely westward propagating waves are unstable up to 26° about the Equator. The nonlinear evolution of this instability which feeds off rotational energy and gravitational buoyancy may play an important role in atmospheric dynamics.
Nonlinear Wave Mixing Technique for Nondestructive Assessment of Infrastructure Materials
Ju, Taeho
To operate safely, structures and components need to be inspected or monitored either periodically or in real time for potential failure. For this purpose, ultrasonic nondestructive evaluation (NDE) techniques have been used extensively. Most of these ultrasonic NDE techniques utilize only the linear behavior of the ultrasound. These linear techniques are effective in detecting discontinuities in materials such as cracks, voids, interfaces, inclusions, etc. However, in many engineering materials, it is the accumulation of microdamage that leads to degradation and eventual failure of a component. Unfortunately, it is difficult for linear ultrasonic NDE techniques to characterize or quantify such damage. On the other hand, the acoustic nonlinearity parameter (ANLP) of a material is often positively correlated with such damage in a material. Thus, nonlinear ultrasonic NDE methods have been used in recently years to characterize cumulative damage such as fatigue in metallic materials, aging in polymeric materials, and degradation of cement-based materials due to chemical reactions. In this thesis, we focus on developing a suit of novel nonlinear ultrasonic NDE techniques based on the interactions of nonlinear ultrasonic waves, namely wave mixing. First, a noncollinear wave mixing technique is developed to detect localized damage in a homogeneous material by using a pair of noncollinear a longitudinal wave (L-wave) and a shear wave (S-wave). This pair of incident waves make it possible to conduct NDE from a single side of the component, a condition that is often encountered in practical applications. The proposed noncollinear wave mixing technique is verified experimentally by carrying out measurements on aluminum alloy (AA 6061) samples. Numerical simulations using the Finite Element Method (FEM) are also conducted to further demonstrate the potential of the proposed technique to detect localized damage in structural components. Second, the aforementioned nonlinear
Nonlinear wave equations, formation of singularities
John, Fritz
1990-01-01
This is the second volume in the University Lecture Series, designed to make more widely available some of the outstanding lectures presented in various institutions around the country. Each year at Lehigh University, a distinguished mathematical scientist presents the Pitcher Lectures in the Mathematical Sciences. This volume contains the Pitcher lectures presented by Fritz John in April 1989. The lectures deal with existence in the large of solutions of initial value problems for nonlinear hyperbolic partial differential equations. As is typical with nonlinear problems, there are many results and few general conclusions in this extensive subject, so the author restricts himself to a small portion of the field, in which it is possible to discern some general patterns. Presenting an exposition of recent research in this area, the author examines the way in which solutions can, even with small and very smooth initial data, "blow up" after a finite time. For various types of quasi-linear equations, this time de...
Slope wavenumber spectrum models of capillary and capillary-gravity waves
Institute of Scientific and Technical Information of China (English)
贾永君; 张杰; 王岩峰
2010-01-01
Capillary and capillary-gravity waves possess a random character, and the slope wavenumber spectra of them can be used to represent mean distributions of wave energy with respect to spatial scale of variability. But simple and practical models of the slope wavenumber spectra have not been put forward so far. In this article, we address the accurate definition of the slope wavenumber spectra of water surface capillary and capillary-gravity waves. By combining the existing slope wavenumber models and using th...
A general theory of two-wave mixing in nonlinear media
DEFF Research Database (Denmark)
Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael
2009-01-01
A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...
Closed form solutions of two time fractional nonlinear wave equations
Directory of Open Access Journals (Sweden)
M. Ali Akbar
2018-06-01
Full Text Available In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G′/G-expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics. Keywords: Traveling wave solution, Soliton, Generalized (G′/G-expansion method, Time fractional Duffing equation, Time fractional Riccati equation
Experimental observation of azimuthal shock waves on nonlinear acoustical vortices
International Nuclear Information System (INIS)
Brunet, Thomas; Thomas, Jean-Louis; Marchiano, Regis; Coulouvrat, Francois
2009-01-01
Thanks to a new focused array of piezoelectric transducers, experimental results are reported here to evidence helical acoustical shock waves resulting from the nonlinear propagation of acoustical vortices (AVs). These shock waves have a three-dimensional spiral shape, from which both the longitudinal and azimuthal components are studied. The inverse filter technique used to synthesize AVs allows various parameters to be varied, especially the topological charge which is the key parameter describing screw dislocations. Firstly, an analysis of the longitudinal modes in the frequency domain reveals a wide cascade of harmonics (up to the 60th order) leading to the formation of the shock waves. Then, an original measurement in the transverse plane exhibits azimuthal behaviour which has never been observed until now for acoustical shock waves. Finally, these new experimental results suggest interesting potential applications of nonlinear effects in terms of acoustics spanners in order to manipulate small objects.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
On the pressure field of nonlinear standing water waves
Schwartz, L. W.
1980-01-01
The pressure field produced by two dimensional nonlinear time and space periodic standing waves was calculated as a series expansion in the wave height. The high order series was summed by the use of Pade approximants. Calculations included the pressure variation at great depth, which was considered to be a likely cause of microseismic activity, and the pressure distribution on a vertical barrier or breakwater.
Testing universal relations of neutron stars with a nonlinear matter-gravity coupling theory
International Nuclear Information System (INIS)
Sham, Y.-H.; Lin, L.-M.; Leung, P. T.
2014-01-01
Due to our ignorance of the equation of state (EOS) beyond nuclear density, there is still no unique theoretical model for neutron stars (NSs). It is therefore surprising that universal EOS-independent relations connecting different physical quantities of NSs can exist. Lau et al. found that the frequency of the f-mode oscillation, the mass, and the moment of inertia are connected by universal relations. More recently, Yagi and Yunes discovered the I-Love-Q universal relations among the mass, the moment of inertia, the Love number, and the quadrupole moment. In this paper, we study these universal relations in the Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general relativity (GR) significantly only at high densities due to the nonlinear coupling between matter and gravity. It thus provides us an ideal case to test how robust the universal relations of NSs are with respect to the change of the gravity theory. Due to the apparent EOS formulation of EiBI gravity developed recently by Delsate and Steinhoff, we are able to study the universal relations in EiBI gravity using the same techniques as those in GR. We find that the universal relations in EiBI gravity are essentially the same as those in GR. Our work shows that, within the currently viable coupling constant, there exists at least one modified gravity theory that is indistinguishable from GR in view of the unexpected universal relations.
Testing Universal Relations of Neutron Stars with a Nonlinear Matter-Gravity Coupling Theory
Sham, Y.-H.; Lin, L.-M.; Leung, P. T.
2014-02-01
Due to our ignorance of the equation of state (EOS) beyond nuclear density, there is still no unique theoretical model for neutron stars (NSs). It is therefore surprising that universal EOS-independent relations connecting different physical quantities of NSs can exist. Lau et al. found that the frequency of the f-mode oscillation, the mass, and the moment of inertia are connected by universal relations. More recently, Yagi and Yunes discovered the I-Love-Q universal relations among the mass, the moment of inertia, the Love number, and the quadrupole moment. In this paper, we study these universal relations in the Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general relativity (GR) significantly only at high densities due to the nonlinear coupling between matter and gravity. It thus provides us an ideal case to test how robust the universal relations of NSs are with respect to the change of the gravity theory. Due to the apparent EOS formulation of EiBI gravity developed recently by Delsate and Steinhoff, we are able to study the universal relations in EiBI gravity using the same techniques as those in GR. We find that the universal relations in EiBI gravity are essentially the same as those in GR. Our work shows that, within the currently viable coupling constant, there exists at least one modified gravity theory that is indistinguishable from GR in view of the unexpected universal relations.
Some nonlinear processes relevant to the beat wave accelerator
International Nuclear Information System (INIS)
Bingham, R.; Mori, W.B.
1985-03-01
The beat wave accelerator depends on the generation of a large amplitude plasma wave with a phase velocity close to the velocity of light c. The plasma wave (ωsub(p), ksub(p)) is generated by beating colinear laser beams (ω 1 , k 1 ) and (ω 2 ,k 2 ) with ωsub(p) = ω 1 -ω 2 , ksub(p) = k 1 -k 2 . Since the process involves both large amplitude transverse and longitudinal waves, various nonlinear instabilities associated with either wave may occur. The object of the article is to discuss some of the processes that may compete with the beat wave generation listing their threshold and growth rate. (author)
On the so called rogue waves in nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Y. Charles Li
2016-04-01
Full Text Available The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial period limit to the homoclinic solutions. In this article, from the perspective of the phase space structure of these homoclinic orbits in the infinite dimensional phase space where the NLS defines a dynamical system, we examine the observability of these homoclinic orbits (and their approximations. Our conclusion is that these approximate homoclinic orbits are the most observable solutions, and they should correspond to the most common deep ocean waves rather than the rare rogue waves. We also discuss other possibilities for the mechanism of a rogue wave: rough dependence on initial data or finite time blow up.
Wave propagation in non-linear media
Broer, L.J.F.
1965-01-01
The problem of the propagation of electromagnetic waves through solids is essentially one of interaction between light quanta and matter. The most fundamental and general treatment of this subject is therefore undoubtedly based on the quantummechanical theory of this interaction. Nevertheless, a
Periodic solutions for one dimensional wave equation with bounded nonlinearity
Ji, Shuguan
2018-05-01
This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.
Parameter spaces for linear and nonlinear whistler-mode waves
International Nuclear Information System (INIS)
Summers, Danny; Tang, Rongxin; Omura, Yoshiharu; Lee, Dong-Hun
2013-01-01
We examine the growth of magnetospheric whistler-mode waves which comprises a linear growth phase followed by a nonlinear growth phase. We construct time-profiles for the wave amplitude that smoothly match at the transition between linear and nonlinear wave growth. This matching procedure can only take place over a limited “matching region” in (N h /N 0 ,A T )-space, where A T is the electron thermal anisotropy, N h is the hot (energetic) electron number density, and N 0 is the cold (background) electron number density. We construct this matching region and determine how the matching wave amplitude varies throughout the region. Further, we specify a boundary in (N h /N 0 ,A T )-space that separates a region where only linear chorus wave growth can occur from the region in which fully nonlinear chorus growth is possible. We expect that this boundary should prove of practical use in performing computationally expensive full-scale particle simulations, and in interpreting experimental wave data
Particle dispersion and mixing induced by breaking internal gravity waves
Bouruet-Aubertot, Pascale; Koudella, C.; Staquet, C.; Winters, K. B.
2001-01-01
The purpose of this paper is to analyze diapycnal mixing induced by the breaking of an internal gravity wave — the primary wave — either standing or propagating. To achieve this aim we apply two different methods. The first method consists of a direct estimate of vertical eddy diffusion from particle dispersion while the second method relies upon potential energy budgets [Winters, K.B., Lombard, P.N., Riley, J.J., D'Asaro, E.A., 1995. J. Fluid Mech. 289, 115-128; Winters, K.B., D'Asaro, E.A., 1996. J. Fluid Mech. 317, 179-193]. The primary wave we consider is of small amplitude and is statically stable, a case for which the breaking process involves two-dimensional instabilities. The dynamics of the waves have been previously analyzed by means of two-dimensional direct numerical simulations [Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1995. J. Fluid Mech. 285, 265-301; Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1996. Dyn. Atmos. Oceans 29, 41-63; Koudella, C., Staquet, C., 1998. In: Davis, P. (Ed.), Proceedings of the IMA Conference on Mixing and Dispersion on Stably-stratified Flows, Dundee, September 1996. IMA Publication]. High resolution three-dimensional calculations of the same wave are also reported here [Koudella, C., 1999]. A local estimate of mixing is first inferred from the time evolution of sets of particles released in the flow during the breaking regime. We show that, after an early evolution dominated by shear effects, a diffusion law is reached and the dispersion coefficient is fairly independent of the initial seeding location of the particles in the flow. The eddy diffusion coefficient, K, is then estimated from the diapycnal diffusive flux. A good agreement with the value inferred from particle dispersion is obtained. This finding is of particular interest regarding the interpretation of in situ estimates of K inferred either from tracer dispersion or from microstructure measurements. Computation of the Cox number, equal to the
Optical rogue waves generation in a nonlinear metamaterial
Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin
2014-11-01
We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.
Nonlinear Bloch waves in metallic photonic band-gap filaments
International Nuclear Information System (INIS)
Kaso, Artan; John, Sajeev
2007-01-01
We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10-50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell's equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament
Nonlinear Bloch waves in metallic photonic band-gap filaments
Kaso, Artan; John, Sajeev
2007-11-01
We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10 50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell’s equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament.
Simulations of nonlinear continuous wave pressure fields in FOCUS
Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.
2017-03-01
The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.
Waves in nonlinear pre-stressed materials
Schneider, Wilhelm; Saccomandi, G
2007-01-01
The papers in this book provide a unique state-of-the-art multidisciplinary overview on the subject of waves in pre-stressed materials through the interaction of several topics, ranging from the mathematical modelling of incremental material response (elastic and inelastic), to the analysis of the governing differential equations and boundary-value problems, and to computational methods for the solution to these problems, with particular reference to industrial, geophysical, and biomechanical applications. A complete view on the title subject is proposed, including: The basic and fundamental theoretical issues (mechanical modelling, exact solutions, asymptotic methods, numerical treatment); A unified introduction to wave propagation (small on large and large on large); A look toward classical (such as geophysics and the mechanics of rubber-like solids) and emergent (such as biomechanics) applications.
Nonlinear wave mechanics from classical dynamics and scale covariance
International Nuclear Information System (INIS)
Hammad, F.
2007-01-01
Nonlinear Schroedinger equations proposed by Kostin and by Doebner and Goldin are rederived from Nottale's prescription for obtaining quantum mechanics from classical mechanics in nondifferentiable spaces; i.e., from hydrodynamical concepts and scale covariance. Some soliton and plane wave solutions are discussed
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 86; Issue 6. Periodic and solitary wave solutions of cubic–quintic nonlinear reaction-diffusion equation with variable convection coefficients. BHARDWAJ S B SINGH RAM MEHAR SHARMA KUSHAL MISHRA S C. Regular Volume 86 Issue 6 June 2016 pp 1253-1258 ...
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations
Directory of Open Access Journals (Sweden)
Waheed A. Ahmed
2017-11-01
Full Text Available Approximate symmetries of a class of perturbed nonlinear wave equations are computed using two newly-developed methods. Invariant solutions associated with the approximate symmetries are constructed for both methods. Symmetries and solutions are compared through discussing the advantages and disadvantages of each method.
Travelling wave solutions to nonlinear physical models by means
Indian Academy of Sciences (India)
This paper presents the ﬁrst integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established ﬁrst integrals, exact solutions are successfully ...
An inhomogeneous wave equation and non-linear Diophantine approximation
DEFF Research Database (Denmark)
Beresnevich, V.; Dodson, M. M.; Kristensen, S.
2008-01-01
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...
Nonlinear wave propagation studies, dispersion modeling, and signal parameters correction
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
..: ..., 2004, 00. [European Workshop on FP6-AERONEWS /1./. Naples (IT), 13.09.2004-16.09.2004] EU Projects: European Commission(XE) 502927 - AERO-NEWS Institutional research plan: CEZ:AV0Z2076919 Keywords : nodestructive testing * nonlinear elastic wave spectroscopy Subject RIV: BI - Acoustics
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In...
Controlling nonlinear waves in excitable media
International Nuclear Information System (INIS)
Puebla, Hector; Martin, Roland; Alvarez-Ramirez, Jose; Aguilar-Lopez, Ricardo
2009-01-01
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
Controlling nonlinear waves in excitable media
Energy Technology Data Exchange (ETDEWEB)
Puebla, Hector [Departamento de Energia, Universidad Autonoma Metropolitana, Av. San Pablo No. 180, Reynosa-Tamaulipas, Azcapotzalco 02200, DF, Mexico (Mexico)], E-mail: hpuebla@correo.azc.uam.mx; Martin, Roland [Laboratoire de Modelisation et d' Imagerie en Geosciences, CNRS UMR and INRIA Futurs Magique-3D, Universite de Pau (France); Alvarez-Ramirez, Jose [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa (Mexico); Aguilar-Lopez, Ricardo [Departamento de Biotecnologia y Bioingenieria, CINVESTAV-IPN (Mexico)
2009-01-30
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
Dispersive shock waves in nonlinear and atomic optics
Directory of Open Access Journals (Sweden)
Kamchatnov Anatoly
2017-01-01
Full Text Available A brief review is given of dispersive shock waves observed in nonlinear optics and dynamics of Bose-Einstein condensates. The theory of dispersive shock waves is developed on the basis of Whitham modulation theory for various situations taking place in these two fields. In particular, the full classification is established for types of wave structures evolving from initial discontinuities for propagation of long light pulses in fibers with account of steepening effect and for dynamics of the polarization mode in two-component Bose-Einstein condensates.
Preusse, Peter; Eckermann, Stephen D.; Offermann, Dirk; Jackman, Charles H. (Technical Monitor)
2000-01-01
Gravity wave temperature fluctuations acquired by the CRISTA instrument are compared to previous estimates of zonal-mean gravity wave temperature variance inferred from the LIMS, MLS and GPS/MET satellite instruments during northern winter. Careful attention is paid to the range of vertical wavelengths resolved by each instrument. Good agreement between CRISTA data and previously published results from LIMS, MLS and GPS/MET are found. Key latitudinal features in these variances are consistent with previous findings from ground-based measurements and some simple models. We conclude that all four satellite instruments provide reliable global data on zonal-mean gravity wave temperature fluctuations throughout the middle atmosphere.
Gravity waves as a probe of the Hubble expansion rate during an electroweak scale phase transition
International Nuclear Information System (INIS)
Chung, Daniel J. H.; Zhou Peng
2010-01-01
Just as big bang nucleosynthesis allows us to probe the expansion rate when the temperature of the Universe was around 1 MeV, the measurement of gravity waves from electroweak scale first order phase transitions may allow us to probe the expansion rate when the temperature of the Universe was at the electroweak scale. We compute the simple transformation rule for the gravity wave spectrum under the scaling transformation of the Hubble expansion rate. We then apply this directly to the scenario of quintessence kination domination and show how gravity wave spectra would shift relative to Laser Interferometer Space Antenna and Big Bang Observer projected sensitivities.
Nonlinear acoustic/seismic waves in earthquake processes
International Nuclear Information System (INIS)
Johnson, Paul A.
2012-01-01
Nonlinear dynamics induced by seismic sources and seismic waves are common in Earth. Observations range from seismic strong ground motion (the most damaging aspect of earthquakes), intense near-source effects, and distant nonlinear effects from the source that have important consequences. The distant effects include dynamic earthquake triggering—one of the most fascinating topics in seismology today—which may be elastically nonlinearly driven. Dynamic earthquake triggering is the phenomenon whereby seismic waves generated from one earthquake trigger slip events on a nearby or distant fault. Dynamic triggering may take place at distances thousands of kilometers from the triggering earthquake, and includes triggering of the entire spectrum of slip behaviors currently identified. These include triggered earthquakes and triggered slow, silent-slip during which little seismic energy is radiated. It appears that the elasticity of the fault gouge—the granular material located between the fault blocks—is key to the triggering phenomenon.
Fatigue crack localization using laser nonlinear wave modulation spectroscopy (LNWMS)
Energy Technology Data Exchange (ETDEWEB)
Liu, Peipei; Sohn, Hoon [Dept. of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Kundu, Tribikram [Dept. of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson (United States)
2014-12-15
Nonlinear features of ultrasonic waves are more sensitive to the presence of a fatigue crack than their linear counterparts are. For this reason, the use of nonlinear ultrasonic techniques to detect a fatigue crack at its early stage has been widely investigated. Of the different proposed techniques, laser nonlinear wave modulation spectroscopy (LNWMS) is unique because a pulse laser is used to exert a single broadband input and a noncontact measurement can be performed. Broadband excitation causes a nonlinear source to exhibit modulation at multiple spectral peaks owing to interactions among various input frequency components. A feature called maximum sideband peak count difference (MSPCD), which is extracted from the spectral plot, measures the degree of crack-induced material nonlinearity. First, the ratios of spectral peaks whose amplitudes are above a moving threshold to the total number of peaks are computed for spectral signals obtained from the pristine and the current state of a target structure. Then, the difference of these ratios are computed as a function of the moving threshold. Finally, the MSPCD is defined as the maximum difference between these ratios. The basic premise is that the MSPCD will increase as the nonlinearity of the material increases. This technique has been used successfully for localizing fatigue cracks in metallic plates.
Initial-value problem for the Gardner equation applied to nonlinear internal waves
Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim
2017-04-01
., Talipova T. Internal solitary waves // Chapter 4 in the book ``Solitary Waves in Fluids''. WIT Press. Southampton, Boston. 2007. P. 85 - 110. Rouvinskaya E., Kurkina O., Kurkin A. Dynamics of nonlinear internal gravity waves in layered fluids // NNSTU n.a. R.E. Alekseev Press - Nizhny Novgorod, 2014 - 160 p. [In Russian] Trillo S., Klein M., Clauss G., Onorato M. Observation of dispersive shock waves developing from initial depressions in shallow water // Physica D, 2016. - http://dx.doi.org/10.1016/j.physd.2016.01.007.
Baumgarten, Kathrin; Gerding, Michael; Baumgarten, Gerd; Lübken, Franz-Josef
2018-01-01
Gravity waves (GWs) as well as solar tides are a key driving mechanism for the circulation in the Earth's atmosphere. The propagation of gravity waves is strongly affected by tidal waves as they modulate the mean background wind field and vice versa, which is not yet fully understood and not adequately implemented in many circulation models. The daylight-capable Rayleigh-Mie-Raman (RMR) lidar at Kühlungsborn (54° N, 12° E) typically provides temperature data to investigate both wave phenomena during one full day or several consecutive days in the middle atmosphere between 30 and 75 km altitude. Outstanding weather conditions in May 2016 allowed for an unprecedented 10-day continuous lidar measurement, which shows a large variability of gravity waves and tides on timescales of days. Using a one-dimensional spectral filtering technique, gravity and tidal waves are separated according to their specific periods or vertical wavelengths, and their temporal evolution is studied. During the measurement period a strong 24 h wave occurs only between 40 and 60 km and vanishes after a few days. The disappearance is related to an enhancement of gravity waves with periods of 4-8 h. Wind data provided by ECMWF are used to analyze the meteorological situation at our site. The local wind structure changes during the observation period, which leads to different propagation conditions for gravity waves in the last days of the measurement period and therefore a strong GW activity. The analysis indicates a further change in wave-wave interaction resulting in a minimum of the 24 h tide. The observed variability of tides and gravity waves on timescales of a few days clearly demonstrates the importance of continuous measurements with high temporal and spatial resolution to detect interaction phenomena, which can help to improve parametrization schemes of GWs in general circulation models.
Spherically symmetric analysis on open FLRW solution in non-linear massive gravity
Energy Technology Data Exchange (ETDEWEB)
Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)
2012-12-01
We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.
Energy Technology Data Exchange (ETDEWEB)
Liu, X. [Chinese Academy of Sciences, Beijing (China). State Key Lab. of Space Weather; Henan Normal Univ., Xinxiang (China). College of Mathematics and Information Science; Xu, J. [Chinese Academy of Sciences, Beijing (China). State Key Lab. of Space Weather; Yue, J. [National Center for Atmospheric Research, Boulder, CO (United States). High Altitude Observatory; Hampton Univ., VA (United States). Atmospheric and Planetary Sciences; Vadas, S.L. [North West Research Associates, Inc., Boulder, CO (United States)
2013-03-01
We study the momentum deposition in the thermosphere from the dissipation of small amplitude gravity waves (GWs) within a wave packet using a fully nonlinear two-dimensional compressible numerical model. The model solves the nonlinear propagation and dissipation of a GW packet from the stratosphere into the thermosphere with realistic molecular viscosity and thermal diffusivity for various Prandtl numbers. The numerical simulations are performed for GW packets with initial vertical wavelengths ({lambda}{sub z}) ranging from 5 to 50 km. We show that {lambda}{sub z} decreases in time as a GW packet dissipates in the thermosphere, in agreement with the ray trace results of Vadas and Fritts (2005) (VF05). We also find good agreement for the peak height of the momentum flux (z{sub diss}) between our simulations and VF05 for GWs with initial {lambda}{sub z} {<=} 2{pi}H in an isothermal, windless background, where H is the density scale height.We also confirm that z{sub diss} increases with increasing Prandtl number. We include eddy diffusion in the model, and find that the momentum deposition occurs at lower altitudes and has two separate peaks for GW packets with small initial {lambda}{sub z}. We also simulate GW packets in a non-isothermal atmosphere. The net {lambda}{sub z} profile is a competition between its decrease from viscosity and its increase from the increasing background temperature. We find that the wave packet disperses more in the non-isothermal atmosphere, and causes changes to the momentum flux and {lambda}{sub z} spectra at both early and late times for GW packets with initial {lambda}{sub z} {>=} 10 km. These effects are caused by the increase in T in the thermosphere, and the decrease in T near the mesopause. (orig.)
Typology of nonlinear activity waves in a layered neural continuum.
Koch, Paul; Leisman, Gerry
2006-04-01
Neural tissue, a medium containing electro-chemical energy, can amplify small increments in cellular activity. The growing disturbance, measured as the fraction of active cells, manifests as propagating waves. In a layered geometry with a time delay in synaptic signals between the layers, the delay is instrumental in determining the amplified wavelengths. The growth of the waves is limited by the finite number of neural cells in a given region of the continuum. As wave growth saturates, the resulting activity patterns in space and time show a variety of forms, ranging from regular monochromatic waves to highly irregular mixtures of different spatial frequencies. The type of wave configuration is determined by a number of parameters, including alertness and synaptic conditioning as well as delay. For all cases studied, using numerical solution of the nonlinear Wilson-Cowan (1973) equations, there is an interval in delay in which the wave mixing occurs. As delay increases through this interval, during a series of consecutive waves propagating through a continuum region, the activity within that region changes from a single-frequency to a multiple-frequency pattern and back again. The diverse spatio-temporal patterns give a more concrete form to several metaphors advanced over the years to attempt an explanation of cognitive phenomena: Activity waves embody the "holographic memory" (Pribram, 1991); wave mixing provides a plausible cause of the competition called "neural Darwinism" (Edelman, 1988); finally the consecutive generation of growing neural waves can explain the discontinuousness of "psychological time" (Stroud, 1955).
Numerical simulation of convective generated gravity waves in the stratosphere and MLT regions.
Heale, C. J.; Snively, J. B.
2017-12-01
Convection is an important source of gravity wave generation, especially in the summer tropics and midlatitudes, and coherent wave fields above convection are now routinely measured in the stratosphere and mesosphere [e.g. Hoffmann et al., JGR, 118, 2013; Gong et al., JGR, 120, 2015; Perwitasari et al., GRL, 42, 22, 2016]. Numerical studies have been performed to investigate the generation mechanisms, source spectra, and their effects on the middle and upper atmosphere [e.g. Fovell et al., AMS, 49,16, 1992; Alexander and Holton, Atmos. Chem. Phys., 4 2004; Vincent et al., JGR, 1118, 2013], however there is still considerable work needed to fully describe these parameters. GCMs currently lack the resolution to explicitly simulate convection generation and rely on simplified parameterizations while full cloud resolving models are computationally expensive and often only extend into the stratosphere. More recent studies have improved the realism of these simulations by using radar derived precipitation rates to drive latent heating in models that simulate convection [Grimsdell et al., AMS, 67, 2010; Stephan and Alexander., J. Adv. Model. Earth. Syst, 7, 2015], however they too only consider wave propagation in the troposphere and stratosphere. We use a 2D nonlinear, fully compressible model [Snively and Pasko., JGR, 113, 2008] to excite convectively generated waves, based on NEXRAD radar data, using the Stephan and Alexander [2015] algorithms. We study the propagation, and spectral evolution of the generated waves up into the MLT region. Ambient atmosphere parameters are derived from observations and MERRA-2 reanalysis data, and stratospheric (AIRS) and mesospheric (Lidar, OH airglow) observations enable comparisons with simulation results.
Nonlinear low-frequency wave aspect of foreshock density holes
Directory of Open Access Journals (Sweden)
N. Lin
2008-11-01
Full Text Available Recent observations have uncovered short-duration density holes in the Earth's foreshock region. There is evidence that the formation of density holes involves non-linear growth of fluctuations in the magnetic field and plasma density, which results in shock-like boundaries followed by a decrease in both density and magnetic field. In this study we examine in detail a few such events focusing on their low frequency wave characteristics. The propagation properties of the waves are studied using Cluster's four point observations. We found that while these density hole-structures were convected with the solar wind, in the plasma rest frame they propagated obliquely and mostly sunward. The wave amplitude grows non-linearly in the process, and the waves are circularly or elliptically polarized in the left hand sense. The phase velocities calculated from four spacecraft timing analysis are compared with the velocity estimated from δE/δB. Their agreement justifies the plane electromagnetic wave nature of the structures. Plasma conditions are found to favor firehose instabilities. Oblique Alfvén firehose instability is suggested as a possible energy source for the wave growth. Resonant interaction between ions at certain energy and the waves could reduce the ion temperature anisotropy and thus the free energy, thereby playing a stabilizing role.
Nonlinear low-frequency wave aspect of foreshock density holes
Directory of Open Access Journals (Sweden)
N. Lin
2008-11-01
Full Text Available Recent observations have uncovered short-duration density holes in the Earth's foreshock region. There is evidence that the formation of density holes involves non-linear growth of fluctuations in the magnetic field and plasma density, which results in shock-like boundaries followed by a decrease in both density and magnetic field. In this study we examine in detail a few such events focusing on their low frequency wave characteristics. The propagation properties of the waves are studied using Cluster's four point observations. We found that while these density hole-structures were convected with the solar wind, in the plasma rest frame they propagated obliquely and mostly sunward. The wave amplitude grows non-linearly in the process, and the waves are circularly or elliptically polarized in the left hand sense. The phase velocities calculated from four spacecraft timing analysis are compared with the velocity estimated from δE/δB. Their agreement justifies the plane electromagnetic wave nature of the structures. Plasma conditions are found to favor firehose instabilities. Oblique Alfvén firehose instability is suggested as a possible energy source for the wave growth. Resonant interaction between ions at certain energy and the waves could reduce the ion temperature anisotropy and thus the free energy, thereby playing a stabilizing role.
Lagrangian analysis of nonlinear wave-wave interactions in bounded plasmas
International Nuclear Information System (INIS)
Carr, A.R.
1979-01-01
In a weakly turbulent nonlinear wave-supporting medium, one of the important nonlinear processes which may occur is resonant three-wave interaction. Whitham's averaged Lagrangian method provides a general formulation of wave evolution laws which is easily adapted to nonlinear dispersive media. In this thesis, the strength of nonlinear interactions between three coherent, axisymmetric, low frequency, magnetohydrodynamic (Alfven) waves propagating in resonance along a cold cylindrical magnetized plasma column is calculated. Both a uniform and a parabolic density distribution have been considered. To account for a non-zero plasma temperature, pressure effects have been included. Distinctive features of the work are the use of cylindrical geometry, the presence of a finite rather than an infinite axial magnetic field, the treatment of a parabolic density distribution, and the inclusion of both ion and electron contributions in all expressions. Two astrophysical applications of the presented theory have been considered. In the first, the possibility of resonant three-wave coupling between geomagnetic micropulsations, which propagate as Alfven or magnetosonic waves along the Earth's magnetic field lines, has been investigated. The second case is the theory of energy transport through the solar chromosphere by upward propagating magnetohydrodynamic waves, which may then couple to heavily damped waves in the corona, causing the observed excess heating in that region
Acoustic nonlinear periodic waves in pair-ion plasmas
Mahmood, Shahzad; Kaladze, Tamaz; Ur-Rehman, Hafeez
2013-09-01
Electrostatic acoustic nonlinear periodic (cnoidal) waves and solitons are investigated in unmagnetized pair-ion plasmas consisting of same mass and oppositely charged ion species with different temperatures. Using reductive perturbation method and appropriate boundary conditions, the Korteweg-de Vries (KdV) equation is derived. The analytical solutions of both cnoidal wave and soliton solutions are discussed in detail. The phase plane plots of cnoidal and soliton structures are shown. It is found that both compressive and rarefactive cnoidal wave and soliton structures are formed depending on the temperature ratio of positive and negative ions in pair-ion plasmas. In the special case, it is revealed that the amplitude of soliton may become larger than it is allowed by the nonlinear stationary wave theory which is equal to the quantum tunneling by particle through a potential barrier effect. The serious flaws in the earlier published results by Yadav et al., [PRE 52, 3045 (1995)] and Chawla and Misra [Phys. Plasmas 17, 102315 (2010)] of studying ion acoustic nonlinear periodic waves are also pointed out.
Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua
2015-08-01
Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. Copyright © 2015 Elsevier B.V. All rights reserved.
Closed form solutions of two time fractional nonlinear wave equations
Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan
2018-06-01
In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.
Ulysses Observations of Nonlinear Wave-wave Interactions in the ...
Indian Academy of Sciences (India)
tribpo
The Ulysses Unified Radio and Plasma Wave Experiment. (URAP) has observed Langmuir, ... gesting that strong turbulence processes, such as modulational instability and soliton formation, often coexist ... Solar and interplanetary type III radio bursts, which occur at the fundamental and the second harmonic of the electron ...
CISM Course on Nonlinear Waves in Real Fluids
1991-01-01
The study of materials which exhibit new and unconventional properties is of central importance for the devel- opment of advanced and refined technologies in many fields of engineering science. In this connection there has been a rapidly growing interest in real fluid effects on wave phenomena in the past few years. A prominent example is provided by Bethe-Zel'dovich-Thompson (BZT) fluids which have the distinguishing feature that they exhibit negative nonlinearity over a finite range of temperature and pressures in the pure vapour phase. However, two phase flows with and without phase change are an even richer source of new unexpected and previously thought impossible phenomena. Topics covered by this volume include waves in gases near the critical point, waves in retrograde fluids, temperature waves in superfluid helium and density waves in suspensions of particles in liquids. Clearly, the aim of the various contributions is twofold. First, they are intended to provide scientists and engineers working in th...
Venkat Ratnam, Madineni; Karanam, Kishore Kumar; Sunkara, Eswaraiah; Vijaya Bhaskara Rao, S.; Subrahmanyam, K. V.; Ramanjaneyulu, L.
2016-07-01
Mesosphere and Lower Thermosphere (MLT) mean winds, gravity waves, tidal and planetary wave characteristics are investigated using two years (2013-2015) of advanced meteor radar installed at Tirupathi (13.63oN, 79.4oE), India. The observations reveal the presence of high frequency gravity waves (30-120 minutes), atmospheric tides (diurnal, semi-diurnal and terr-diurnal) along with long period oscillations in both zonal and meridional winds. Background mean zonal winds show clear semi-annual oscillation in the mesosphere, whereas meridional winds are characterized by annual oscillation as expected. Diurnal tide amplitudes are significantly larger (60-80 m/s) than semi-diurnal (10-20 m/s) and terr-diurnal (5-8 m/s) tides and larger in meridional than zonal winds. The measured meridional components are in good agreement with Global Scale Wave Model (GSWM-09) predictions than zonal up to ~90 km in all the seasons, except fall equinox. Diurnal tidal phase matches well than the amplitudes between observations and model predictions. However, no similarity is being found in the semi-diurnal tides between observations and model. The measurements are further compared with nearby Thumba meteor radar (8.5oN, 77oE) observations. Some differences do exist between the measurements from Tirupati and Thumba meteor radar and model outputs at greater heights and the possible reasons are discussed. SVU meteor radar observations clearly showed the dominance of well-known ultra-fast kelvin waves (3.5 days), 5-8 day, 16 day, 27 day, and 30-40 day oscillations. Due to higher meteor count extending up to 110 km, we could investigate the variability of these PWs and oscillations covering wider range (70-110 km) for the first time. Significant change above 100 km is noticed in all the above mentioned PW activity and oscillations. We also used ERA-Interim reanalysis data sets available at 0.125x0.125 degree grids for investigating the characteristics of these PW right from surface to 1 h
Canonical formulations of full nonlinear topologically massive gravity
International Nuclear Information System (INIS)
Deser, S.; Xiang, X.
1991-01-01
First-order forms of the complete nonlinear Einstein plus Chern-Simons third-derivative-order action are exhibited in both metric and dreibein forms. The 'hamiltonians' are combinations of diffeomorphism and tangent space rotation generators as expected of generally covariant systems; the pure Chern-Simons hamiltonian has an additional, conformal transformation, term. These constraints reduce the apparent number of degrees of freedom to 1 and 0 respectively. The constraint algebras close, as required by this counting, without second-class constraints. The nature of the noninvariant terms in the Chern-Simons lagrangian density is discussed. For comparison, the linearized limit and the corresponding nonabelian vector action's canonical form are also given. (orig.)
Nonlinear Passive Control of a Wave Energy Converter Subject to Constraints in Irregular Waves
Directory of Open Access Journals (Sweden)
Liguo Wang
2015-06-01
Full Text Available This paper investigates a passive control method of a point absorbing wave energy converter by considering the displacement and velocity constraints under irregular waves in the time domain. A linear generator is used as a power take-off unit, and the equivalent damping force is optimized to improve the power production of the wave energy converter. The results from nonlinear and linear passive control methods are compared, and indicate that the nonlinear passive control method leads to the excitation force in phase with the velocity of the converter that can significantly improve the energy production of the converter.
Mesospheric gravity wave momentum flux estimation using hybrid Doppler interferometry
Directory of Open Access Journals (Sweden)
A. J. Spargo
2017-06-01
Full Text Available Mesospheric gravity wave (GW momentum flux estimates using data from multibeam Buckland Park MF radar (34.6° S, 138.5° E experiments (conducted from July 1997 to June 1998 are presented. On transmission, five Doppler beams were symmetrically steered about the zenith (one zenith beam and four off-zenith beams in the cardinal directions. The received beams were analysed with hybrid Doppler interferometry (HDI (Holdsworth and Reid, 1998, principally to determine the radial velocities of the effective scattering centres illuminated by the radar. The methodology of Thorsen et al. (1997, later re-introduced by Hocking (2005 and since extensively applied to meteor radar returns, was used to estimate components of Reynolds stress due to propagating GWs and/or turbulence in the radar resolution volume. Physically reasonable momentum flux estimates are derived from the Reynolds stress components, which are also verified using a simple radar model incorporating GW-induced wind perturbations. On the basis of these results, we recommend the intercomparison of momentum flux estimates between co-located meteor radars and vertical-beam interferometric MF radars. It is envisaged that such intercomparisons will assist with the clarification of recent concerns (e.g. Vincent et al., 2010 of the accuracy of the meteor radar technique.
Mesospheric gravity wave momentum flux estimation using hybrid Doppler interferometry
Spargo, Andrew J.; Reid, Iain M.; MacKinnon, Andrew D.; Holdsworth, David A.
2017-06-01
Mesospheric gravity wave (GW) momentum flux estimates using data from multibeam Buckland Park MF radar (34.6° S, 138.5° E) experiments (conducted from July 1997 to June 1998) are presented. On transmission, five Doppler beams were symmetrically steered about the zenith (one zenith beam and four off-zenith beams in the cardinal directions). The received beams were analysed with hybrid Doppler interferometry (HDI) (Holdsworth and Reid, 1998), principally to determine the radial velocities of the effective scattering centres illuminated by the radar. The methodology of Thorsen et al. (1997), later re-introduced by Hocking (2005) and since extensively applied to meteor radar returns, was used to estimate components of Reynolds stress due to propagating GWs and/or turbulence in the radar resolution volume. Physically reasonable momentum flux estimates are derived from the Reynolds stress components, which are also verified using a simple radar model incorporating GW-induced wind perturbations. On the basis of these results, we recommend the intercomparison of momentum flux estimates between co-located meteor radars and vertical-beam interferometric MF radars. It is envisaged that such intercomparisons will assist with the clarification of recent concerns (e.g. Vincent et al., 2010) of the accuracy of the meteor radar technique.
Tropical Gravity Wave Momentum Fluxes and Latent Heating Distributions
Geller, Marvin A.; Zhou, Tiehan; Love, Peter T.
2015-01-01
Recent satellite determinations of global distributions of absolute gravity wave (GW) momentum fluxes in the lower stratosphere show maxima over the summer subtropical continents and little evidence of GW momentum fluxes associated with the intertropical convergence zone (ITCZ). This seems to be at odds with parameterizations forGWmomentum fluxes, where the source is a function of latent heating rates, which are largest in the region of the ITCZ in terms of monthly averages. The authors have examined global distributions of atmospheric latent heating, cloud-top-pressure altitudes, and lower-stratosphere absolute GW momentum fluxes and have found that monthly averages of the lower-stratosphere GW momentum fluxes more closely resemble the monthly mean cloud-top altitudes rather than the monthly mean rates of latent heating. These regions of highest cloud-top altitudes occur when rates of latent heating are largest on the time scale of cloud growth. This, plus previously published studies, suggests that convective sources for stratospheric GW momentum fluxes, being a function of the rate of latent heating, will require either a climate model to correctly model this rate of latent heating or some ad hoc adjustments to account for shortcomings in a climate model's land-sea differences in convective latent heating.
Simulation of non-hydrostatic gravity wave propagation in the upper atmosphere
Directory of Open Access Journals (Sweden)
Y. Deng
2014-04-01
Full Text Available The high-frequency and small horizontal scale gravity waves may be reflected and ducted in non-hydrostatic simulations, but usually propagate vertically in hydrostatic models. To examine gravity wave propagation, a preliminary study has been conducted with a global ionosphere–thermosphere model (GITM, which is a non-hydrostatic general circulation model for the upper atmosphere. GITM has been run regionally with a horizontal resolution of 0.2° long × 0.2° lat to resolve the gravity wave with wavelength of 250 km. A cosine wave oscillation with amplitude of 30 m s−1 has been applied to the zonal wind at the low boundary, and both high-frequency and low-frequency waves have been tested. In the high-frequency case, the gravity wave stays below 200 km, which indicates that the wave is reflected or ducted in propagation. The results are consistent with the theoretical analysis from the dispersion relationship when the wavelength is larger than the cutoff wavelength for the non-hydrostatic situation. However, the low-frequency wave propagates to the high altitudes during the whole simulation period, and the amplitude increases with height. This study shows that the non-hydrostatic model successfully reproduces the high-frequency gravity wave dissipation.
A global climatology of stratospheric gravity waves from Atmospheric Infrared Sounder observations
Hoffmann, Lars; Xue, Xianghui; Alexander, M. Joan
2014-05-01
We present the results of a new study that aims on the detection and classification of `hotspots' of stratospheric gravity waves on a global scale. The analysis is based on a nine-year record (2003 to 2011) of radiance measurements by the Atmospheric Infrared Sounder (AIRS) aboard NASA's Aqua satellite. We detect the presence of stratospheric gravity waves based on 4.3 micron brightness temperature variances. Our method is optimized for peak events, i.e., strong gravity wave events for which the local variance considerably exceeds background levels. We estimated the occurrence frequencies of these peak events for different seasons and time of day and used the results to find local maxima of gravity wave activity. In addition, we use AIRS radiances at 8.1 micron to simultaneously detect convective events, including deep convection in the tropics and mesoscale convective systems at mid latitudes. We classified the gravity waves according to their sources, based on seasonal occurrence frequencies for convection and by means of topographic data. Our study reproduces well-known hotspots of gravity waves, e.g., the mountain wave hotspots at the Andes and the Antarctic Peninsula or the convective hotspot during the thunderstorm season over the North American Great Plains. However, the high horizontal resolution of the AIRS observations also helped us to locate several smaller hotspots, which were partly unknown or poorly studied so far. Most of these smaller hotspots are found near orographic features like small mountain ranges, in coastal regions, in desert areas, or near isolated islands. This new study will help to select the most promising regions and seasons for future observational studies of gravity waves. Reference: Hoffmann, L., X. Xue, and M. J. Alexander, A global view of stratospheric gravity wave hotspots located with Atmospheric Infrared Sounder observations, J. Geophys. Res., 118, 416-434, doi:10.1029/2012JD018658, 2013.
Christodoulou's nonlinear gravitational-wave memory: Evaluation in the quadrupole approximation
International Nuclear Information System (INIS)
Wiseman, A.G.; Will, C.M.
1991-01-01
Christodoulou has found a new nonlinear contribution to the net change in the wave form caused by the passage of a burst of gravity waves (''memory of the burst''). We argue that this effect is nothing but the gravitational wave form generated by the stress energy in the burst itself. We derive an explicit formula for this effect in terms of a retarded-time integral of products of time derivatives of wave-zone gravitational wave forms. The resulting effect corresponds in size to a correction 2.5 post-Newtonian orders [O((Gm/rc 2 ) 5/2 ) =(O(v/c) 5 )] beyond the quadrupole approximation, and is therefore negligible for all but the most relativistic of systems. For gravitational bremsstrahlung from two stars moving at 300 km s -1 , the effect is much less than 10 -10 of the usual linear quadrupole wave form, while for a system of coalescing binary compact objects we estimate that the effect is of order 10 -1 for two neutron stars
Bassiri, Sassan; Hajj, George A.
1993-01-01
Natural and man-made events like earthquakes and nuclear explosions launch atmospheric gravity waves (AGW) into the atmosphere. Since the particle density decreases exponentially with height, the gravity waves increase exponentially in amplitude as they propagate toward the upper atmosphere and ionosphere. As atmospheric gravity waves approach the ionospheric heights, the neutral particles carried by gravity waves collide with electrons and ions, setting these particles in motion. This motion of charged particles manifests itself by wave-like fluctuations and disturbances that are known as traveling ionospheric disturbances (TID). The perturbation in the total electron content due to TID's is derived analytically from first principles. Using the tilted dipole magnetic field approximation and a Chapman layer distribution for the electron density, the variations of the total electron content versus the line-of-sight direction are numerically analyzed. The temporal variation associated with the total electron content measurements due to AGW's can be used as a means of detecting characteristics of the gravity waves. As an example, detection of tsunami generated earthquakes from their associated atmospheric gravity waves using the Global Positioning System is simulated.
Thermal effect on gravity waves in a compressible liquid layer over a ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. This paper deals with the effect of temperature on gravity waves in a compressible liquid layer over a solid half-space. It has been assumed that the liquid layer is under the action of gravity, while the solid half-space is under the influence of initial compressive hydrostatic stress. When the temperature of the.
Thermal effect on gravity waves in a compressible liquid layer over a ...
Indian Academy of Sciences (India)
This paper deals with the effect of temperature on gravity waves in a compressible liquid layer over a solid half-space. It has been assumed that the liquid layer is under the action of gravity, while the solid half-space is under the inﬂuence of initial compressive hydrostatic stress. When the temperature of the half-space is ...
Numerical Simulation of a Breaking Gravity Wave Event Over Greenland Observed During Fastex
National Research Council Canada - National Science Library
Doyle, James
1997-01-01
Measurements from the NOAA G4 research aircraft and high-resolution numerical simulations are used to study the evolution and dynamics of a large-amplitude gravity wave event over Greenland that took...
National Aeronautics and Space Administration — Gravity wave detection using space-based long-baseline laser interferometric sensors imposes stringent noise requirements on the system components, including the...
A nonlinear scenario for development of vortex layer instability in gravity field
International Nuclear Information System (INIS)
Goncharov, V. P.
2007-01-01
A Hamiltonian version of contour dynamics is formulated for models of constant-vorticity plane flows with interfaces. The proposed approach is used as a framework for a nonlinear scenario for instability development. Localized vortex blobs are analyzed as structural elements of a strongly perturbed wall layer of a vorticity-carrying fluid with free boundary in gravity field. Gravity and vorticity effects on the geometry and velocity of vortex structures are examined. It is shown that compactly supported nonlinear solutions (compactons) are candidates for the role of particle-like vortex structures in models of flow breakdown. An analysis of the instability mechanism demonstrates the possibility of a self-similar collapse. It is found that the vortex shape stabilizes at the final stage of the collapse, while the vortex sheet strength on its boundary increases as (t 0 - t) -1 , where t 0 is the collapse time
Seasonal variation and sources of atmospheric gravity waves in the Antarctic
Directory of Open Access Journals (Sweden)
Kaoru Sato
2010-12-01
Full Text Available In the last recent ten years, our knowledge of gravity waves in the Antarctic has been significantly improved through numerous studies using balloon and satellite observations and high-resolution model simulations. In this report, we introduce results from two studies which were performed as a part of the NIPR project "Integrated analysis of the material circulation in the Antarctic atmosphere-cryosphere-ocean" (2004-2009, i.e., Yoshiki et al. (2004 and Sato and Yoshiki (2008. These two studies focused on the seasonal variation and sources of the gravity waves in the Antarctic, because horizontal wavelengths and phase velocities depend largely on the wave sources. The former study used original high-resolution data from operational radiosonde observations at Syowa Station. In the lowermost stratosphere, gravity waves do not exhibit characteristic seasonal variation; instead, the wave energy is intensified when lower latitude air intrudes into the area near Syowa Station in the upper troposphere. This intrusion is associated with blocking events or developed synoptic-scale waves. In the lower and middle stratosphere, the gravity wave energy is maximized in spring and particularly intensified when the axis of the polar night jet approaches Syowa Station. The latter study is based on intensive radiosonde observation campaigns that were performed in 2002 at Syowa Station as an activity of JARE-43. Gravity wave propagation was statistically examined using two dimensional (i.e., vertical wavenumber versus frequency spectra in each season. It was shown that the gravity waves are radiated upward and downward from an unbalanced region of the polar night jet. This feature is consistent with the gravity-wave resolving GCM simulation.
Nonlinear damping of drift waves by strong flow curvature
International Nuclear Information System (INIS)
Sidikman, K.L.; Carreras, B.A.; Garcia, L.; Diamond, P.H.
1993-01-01
A single-equation model has been used to study the effect of a fixed poloidal flow (V 0 ) on turbulent drift waves. The electron dynamics come from a laminar kinetic equation in the dissipative trapped-electron regime. In the past, the authors have assumed that the mode frequency is close to the drift-wave frequency. Trapped-electron density fluctuations are then related to potential fluctuations by an open-quotes iδclose quotes term. Flow shear (V 0 ') and curvature (V 0 double-prime) both have a stabilizing effect on linear modes for this open-quotes iδclose quotes model. However, in the nonlinear regime, single-helicity effects inhibit the flow damping. Neither V 0 ' nor V 0 double-prime produces a nonlinear damping effect. The above assumption on the frequency can be relaxed by including the electron time-response in the linear part of the evolution. In this time-dependent model, instability drive due to trapped electrons is reduced when mode frequency is greater than drift-wave frequency. Since V 0 double-prime produces such a frequency shift, its linear effect is enhanced. There is also nonlinear damping, since single-helicity effects do not eliminate the shift. Renormalized theory for this model predicts nonlinear stability for sufficiently large curvature. Single-helicity calculations have already shown nonlinear damping, and this strong V 0 double-prime regime is being explored. In the theory, the Gaussian shape of the nonlinear diffusivity is expanded to obtain a quadratic potential. The implications of this assumption will be tested by solving the full renormalized equation using a shooting method
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
Nonlinear bounce resonances between magnetosonic waves and equatorially mirroring electrons
Chen, Lunjin; Maldonado, Armando; Bortnik, Jacob; Thorne, Richard M.; Li, Jinxing; Dai, Lei; Zhan, Xiaoya
2015-08-01
Equatorially mirroring energetic electrons pose an interesting scientific problem, since they generally cannot resonate with any known plasma waves and hence cannot be scattered down to lower pitch angles. Observationally it is well known that the flux of these equatorial particles does not simply continue to build up indefinitely, and so a mechanism must necessarily exist that transports these particles from an equatorial pitch angle of 90° down to lower values. However, this mechanism has not been uniquely identified yet. Here we investigate the mechanism of bounce resonance with equatorial noise (or fast magnetosonic waves). A test particle simulation is used to examine the effects of monochromatic magnetosonic waves on the equatorially mirroring energetic electrons, with a special interest in characterizing the effectiveness of bounce resonances. Our analysis shows that bounce resonances can occur at the first three harmonics of the bounce frequency (nωb, n = 1, 2, and 3) and can effectively reduce the equatorial pitch angle to values where resonant scattering by whistler mode waves becomes possible. We demonstrate that the nature of bounce resonance is nonlinear, and we propose a nonlinear oscillation model for characterizing bounce resonances using two key parameters, effective wave amplitude Ã and normalized wave number k~z. The threshold for higher harmonic resonance is more strict, favoring higher Ã and k~z, and the change in equatorial pitch angle is strongly controlled by k~z. We also investigate the dependence of bounce resonance effects on various physical parameters, including wave amplitude, frequency, wave normal angle and initial phase, plasma density, and electron energy. It is found that the effect of bounce resonance is sensitive to the wave normal angle. We suggest that the bounce resonant interaction might lead to an observed pitch angle distribution with a minimum at 90°.
A new type of surface acoustic waves in solids due to nonlinear elasticity
International Nuclear Information System (INIS)
Mozhaev, V.G.
1988-12-01
It is shown that in nonlinear elastic semi-infinite medium possessing a property of self focusing of shear waves, besides bulk non-linear shear waves, new surface acoustic waves exist, localization of which near the boundary is entirely due to nonlinear effects. (author). 8 refs
A Comparison Between Gravity Wave Momentum Fluxes in Observations and Climate Models
Geller, Marvin A.; Alexadner, M. Joan; Love, Peter T.; Bacmeister, Julio; Ern, Manfred; Hertzog, Albert; Manzini, Elisa; Preusse, Peter; Sato, Kaoru; Scaife, Adam A.;
2013-01-01
For the first time, a formal comparison is made between gravity wave momentum fluxes in models and those derived from observations. Although gravity waves occur over a wide range of spatial and temporal scales, the focus of this paper is on scales that are being parameterized in present climate models, sub-1000-km scales. Only observational methods that permit derivation of gravity wave momentum fluxes over large geographical areas are discussed, and these are from satellite temperature measurements, constant-density long-duration balloons, and high-vertical-resolution radiosonde data. The models discussed include two high-resolution models in which gravity waves are explicitly modeled, Kanto and the Community Atmosphere Model, version 5 (CAM5), and three climate models containing gravity wave parameterizations,MAECHAM5, Hadley Centre Global Environmental Model 3 (HadGEM3), and the Goddard Institute for Space Studies (GISS) model. Measurements generally show similar flux magnitudes as in models, except that the fluxes derived from satellite measurements fall off more rapidly with height. This is likely due to limitations on the observable range of wavelengths, although other factors may contribute. When one accounts for this more rapid fall off, the geographical distribution of the fluxes from observations and models compare reasonably well, except for certain features that depend on the specification of the nonorographic gravity wave source functions in the climate models. For instance, both the observed fluxes and those in the high-resolution models are very small at summer high latitudes, but this is not the case for some of the climate models. This comparison between gravity wave fluxes from climate models, high-resolution models, and fluxes derived from observations indicates that such efforts offer a promising path toward improving specifications of gravity wave sources in climate models.
F region manifestation of atmospheric gravity waves at a high magnetic dip station
International Nuclear Information System (INIS)
Yeh, K.C.; Dubroff, R.E.; Nagpal, O.P.
1976-01-01
An average power spectrum of the observed fluctuations in electron content at Urbana has been computed. Several features of the experimental results can be explained in terms of theoretical models of the ionospheric response to internal gravity waves. An extension of an earlier theory to include the effect of dissipation provides additional justification for the relation between the observed electron content fluctuations and internal gravity waves
Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering
Ablowitz, Mark J.
1994-12-01
Research investigations involving the fundamental understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical computation have been carried out and a number of significant results have been obtained. A class of nonlinear wave equations which can be solved by the inverse scattering transform (IST) have been studied, including the Kadaomtsev-Petviashvili (KP) equation, the Davey-Stewartson equation, and the 2+1 Toda system. The solutions obtained by IST correspond to the Cauchy initial value problem with decaying initial data. We have also solved two important systems via the IST method: a 'Volterra' system in 2+1 dimensions and a new one dimensional nonlinear equation which we refer to as the Toda differential-delay equation. Research in computational chaos in moderate to long time numerical simulations continues.
Uieda, Leonardo; Barbosa, Valéria C. F.
2017-01-01
Estimating the relief of the Moho from gravity data is a computationally intensive nonlinear inverse problem. What is more, the modelling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized nonlinear gravity inversion method that has a low computational footprint and employs a spherical Earth approximation. To achieve this, we combine the highly efficient Bott's method with smoothness regularization and a discretization of the anomalous Moho into tesseroids (spherical prisms). The computational efficiency of our method is attained by harnessing the fact that all matrices involved are sparse. The inversion results are controlled by three hyperparameters: the regularization parameter, the anomalous Moho density-contrast, and the reference Moho depth. We estimate the regularization parameter using the method of hold-out cross-validation. Additionally, we estimate the density-contrast and the reference depth using knowledge of the Moho depth at certain points. We apply the proposed method to estimate the Moho depth for the South American continent using satellite gravity data and seismological data. The final Moho model is in accordance with previous gravity-derived models and seismological data. The misfit to the gravity and seismological data is worse in the Andes and best in oceanic areas, central Brazil and Patagonia, and along the Atlantic coast. Similarly to previous results, the model suggests a thinner crust of 30-35 km under the Andean foreland basins. Discrepancies with the seismological data are greatest in the Guyana Shield, the central Solimões and Amazonas Basins, the Paraná Basin, and the Borborema province. These differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing.
Gravitational Wave Polarizations in f (R Gravity and Scalar-Tensor Theory
Directory of Open Access Journals (Sweden)
Gong Yungui
2018-01-01
Full Text Available The detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory opens a new era to use gravitational waves to test alternative theories of gravity. We investigate the polarizations of gravitational waves in f (R gravity and Horndeski theory, both containing scalar modes. These theories predict that in addition to the familiar + and × polarizations, there are transverse breathing and longitudinal polarizations excited by the massive scalar mode and the new polarization is a single mixed state. It would be very difficult to detect the longitudinal polarization by interferometers, while pulsar timing array may be the better tool to detect the longitudinal polarization.
Nonlinear damping of oblique whistler mode waves through Landau resonance
Hsieh, Y.; Omura, Y.
2017-12-01
Nonlinear trapping of electrons through Landau resonance is a characteristic dynamics in oblique whistler-mode wave particle interactions. The resonance velocity of the Landau resonance at quasi-parallel propagation becomes very close to the parallel group velocity of whistler-mode wave at frequency around 0.5 Ωe, causing a long distance of resonant interaction and strong acceleration of resonant electrons [1]. We demonstrate these effective accelerations for electrons with high equatorial pitch angle ( > 60°) by test particle simulations with parameters for the Earth's inner magnetosphere at L=5. In the simulations, we focus on slightly oblique whistler mode waves with wave normal angle 10.1002/2016JA023255.
Controlling wave propagation through nonlinear engineered granular systems
Leonard, Andrea
We study the fundamental dynamic behavior of a special class of ordered granular systems in order to design new, structured materials with unique physical properties. The dynamic properties of granular systems are dictated by the nonlinear, Hertzian, potential in compression and zero tensile strength resulting from the discrete material structure. Engineering the underlying particle arrangement of granular systems allows for unique dynamic properties, not observed in natural, disordered granular media. While extensive studies on 1D granular crystals have suggested their usefulness for a variety of engineering applications, considerably less attention has been given to higher-dimensional systems. The extension of these studies in higher dimensions could enable the discovery of richer physical phenomena not possible in 1D, such as spatial redirection and anisotropic energy trapping. We present experiments, numerical simulation (based on a discrete particle model), and in some cases theoretical predictions for several engineered granular systems, studying the effects of particle arrangement on the highly nonlinear transient wave propagation to develop means for controlling the wave propagation pathways. The first component of this thesis studies the stress wave propagation resulting from a localized impulsive loading for three different 2D particle lattice structures: square, centered square, and hexagonal granular crystals. By varying the lattice structure, we observe a wide range of properties for the propagating stress waves: quasi-1D solitary wave propagation, fully 2D wave propagation with tunable wave front shapes, and 2D pulsed wave propagation. Additionally the effects of weak disorder, inevitably present in real granular systems, are investigated. The second half of this thesis studies the solitary wave propagation through 2D and 3D ordered networks of granular chains, reducing the effective density compared to granular crystals by selectively placing wave
Asymptotic approach for the nonlinear equatorial long wave interactions
International Nuclear Information System (INIS)
Ramirez Gutierrez, Enver; Silva Dias, Pedro L; Raupp, Carlos
2011-01-01
In the present work we use an asymptotic approach to obtain the long wave equations. The shallow water equation is put as a function of an external parameter that is a measure of both the spatial scales anisotropy and the fast to slow time ratio. The values given to the external parameters are consistent with those computed using typical values of the perturbations in tropical dynamics. Asymptotically, the model converge toward the long wave model. Thus, it is possible to go toward the long wave approximation through intermediate realizable states. With this approach, the resonant nonlinear wave interactions are studied. To simplify, the reduced dynamics of a single resonant triad is used for some selected equatorial trios. It was verified by both theoretical and numerical results that the nonlinear energy exchange period increases smoothly as we move toward the long wave approach. The magnitude of the energy exchanges is also modified, but in this case depends on the particular triad used and also on the initial energy partition among the triad components. Some implications of the results for the tropical dynamics are discussed. In particular, we discuss the implications of the results for El Nino and the Madden-Julian in connection with other scales of time and spatial variability.
A nonlinear wave equation in nonadiabatic flame propagation
International Nuclear Information System (INIS)
Booty, M.R.; Matalon, M.; Matkowsky, B.J.
1988-01-01
The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time
Nonlinear dynamics and chaotic behaviour of spin wave instabilities
Energy Technology Data Exchange (ETDEWEB)
Rezende, S M; Aguiar, F.M. de.
1986-09-01
Recent experiments revealed that spin wave instabilities driven by microwave fields, either parallel or transverse to the static magnetic field, display chaotic dynamics similar to other physical systems. A theory based on the coupled nonlinear equations of motion for two spin wave modes is presented which explains most features of the experimental observations. The model predicts subharmonic routes to chaos that depend on the parameter values. For certain parameters the system exhibits a Feigenbaum scenario characteristic of one-dimensional maps. Other parameters lead to different subharmonic routes indicative of multidimensional behavior, as observed in some experiments.
Stochastic Background of Relic Scalar Gravitational Waves tuned by Extended Gravity
International Nuclear Information System (INIS)
De Laurentis, Mariafelicia; Capozziello, Salvatore
2009-01-01
A stochastic background of relic gravitational waves is achieved by the so called adiabatically-amplified zero-point fluctuations process derived from early inflation. It provides a distinctive spectrum of relic gravitational waves. In the framework of scalar-tensor gravity, we discuss the scalar modes of gravitational waves and the primordial production of this scalar component which is generated beside tensorial one. Then analyze seven different viable f(R)-gravities towards the Solar System tests and stochastic gravitational waves background. It is demonstrated that seven viable f(R)-gravities under consideration not only satisfy the local tests, but additionally, pass the above PPN-and stochastic gravitational waves bounds for large classes of parameters.
Nonlinear electrostatic wave equations for magnetized plasmas - II
DEFF Research Database (Denmark)
Dysthe, K. B.; Mjølhus, E.; Pécseli, H. L.
1985-01-01
For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrosta......For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent...... (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases....
Hidden regularity for a strongly nonlinear wave equation
International Nuclear Information System (INIS)
Rivera, J.E.M.
1988-08-01
The nonlinear wave equation u''-Δu+f(u)=v in Q=Ωx]0,T[;u(0)=u 0 ,u'(0)=u 1 in Ω; u(x,t)=0 on Σ= Γx]0,T[ where f is a continuous function satisfying, lim |s| sup →+∞ f(s)/s>-∞, and Ω is a bounded domain of R n with smooth boundary Γ, is analysed. It is shown that there exist a solution for the presented nonlinear wave equation that satisfies the regularity condition: |∂u/∂ η|ε L 2 (Σ). Moreover, it is shown that there exist a constant C>0 such that, |∂u/∂ η|≤c{ E(0)+|v| 2 Q }. (author) [pt
Atmospheric gravity waves observed by an international network of micro-barographs
International Nuclear Information System (INIS)
Marty, Julien
2010-01-01
The Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) manages an international network of forty-two operational infra-sound stations recording the pressure fluctuations produced at the ground surface by infrasonic waves. This thesis demonstrates that most of these stations also accurately detect the pressure fluctuations in the entire gravity wave band. This work includes carrying out and analyzing several metrological laboratory experiments and a field campaign (M2008) in Mongolia in 2008. The layout of the experiments as well as the interpretation of their results gave rise to the development of a new linear spectral numerical model able to simulate the generation and propagation of gravity waves. This model was used to quantify the gravity waves produced by the atmospheric cooling that occurs during solar eclipses. The pressure fluctuations expected at ground level were estimated and compared to the data recorded during the 1 August 2008 solar eclipse by the CTBTO and M2008 stations. A detailed data analysis reveals two waves with similar time-frequency characteristics to those simulated for a stratospheric and tropospheric cooling. This constitutes, to our knowledge, a unique result. The validation of worldwide and pluri-annual pressure measurements in the entire gravity wave band allowed the statistical study of gravity wave spectra and atmospheric tides. The work presented throughout this thesis has led to the publication of two articles. A third one is in the drafting process. (author)
Nonlinear propagation of Alfven waves in cometary plasmas
International Nuclear Information System (INIS)
Lakhina, G.S.; Shukla, P.K.
1987-07-01
Large amplitude Alfven waves propagating along the guide magnetic field in a three-component plasma are shown to be modulationally unstable due to their nonlinear interaction with nonresonant electrostatic density fluctuations. A new class of subsonic Alfven soliton solutions are found to exist in the three-component plasma. The Alfven solitons can be relevant in explaining the properties of hydromagnetic turbulence near the comets. (author). 15 refs
Propagation of Quasi-plane Nonlinear Waves in Tubes
P. Koníček; M. Bednařík; M. Červenka
2002-01-01
This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicabi...
Nonlinear effects in Pulsations of Compact Stars and Gravitational Waves
International Nuclear Information System (INIS)
Passamonti, A
2007-01-01
Nonlinear stellar oscillations can be studied by using a multiparameter perturbative approach, which is appropriate for investigating the low and mild nonlinear dynamical regimes. We present the main properties of our perturbative framework for describing, in the time domain, the nonlinear coupling between the radial and nonradial perturbations of spherically symmetric and perfect fluid compact stars. This particular coupling can be described by gauge invariant quantities that obeys a system of partial differential equations with source terms, which are made up of product of first order radial and nonradial perturbations. We report the results of numerical simulations for both the axial and polar coupling perturbations, that exhibit in the stellar dynamics and in the associated gravitational wave signal some interesting nonlinear effects, such as combination harmonics and resonances. In particular, we concentrate on the axial case, where the linear axial perturbations describe a harmonic component of a differentially rotating neutron star. The gravitational wave signal of this stellar configuration mirrors at second perturbative order the spectral features of the linear radial normal modes. In addition, a signal amplification appears when one of the radial frequencies is close to the axial w-mode frequencies of the star
Nonlinear ultrasonic wave modulation for online fatigue crack detection
Sohn, Hoon; Lim, Hyung Jin; DeSimio, Martin P.; Brown, Kevin; Derriso, Mark
2014-02-01
This study presents a fatigue crack detection technique using nonlinear ultrasonic wave modulation. Ultrasonic waves at two distinctive driving frequencies are generated and corresponding ultrasonic responses are measured using permanently installed lead zirconate titanate (PZT) transducers with a potential for continuous monitoring. Here, the input signal at the lower driving frequency is often referred to as a 'pumping' signal, and the higher frequency input is referred to as a 'probing' signal. The presence of a system nonlinearity, such as a crack formation, can provide a mechanism for nonlinear wave modulation, and create spectral sidebands around the frequency of the probing signal. A signal processing technique combining linear response subtraction (LRS) and synchronous demodulation (SD) is developed specifically to extract the crack-induced spectral sidebands. The proposed crack detection method is successfully applied to identify actual fatigue cracks grown in metallic plate and complex fitting-lug specimens. Finally, the effect of pumping and probing frequencies on the amplitude of the first spectral sideband is investigated using the first sideband spectrogram (FSS) obtained by sweeping both pumping and probing signals over specified frequency ranges.
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, Abhik; Janaki, M. S. [Saha Institute of Nuclear Physics, Calcutta (India); Bose, Anirban [Serampore College, West Bengal (India)
2014-07-15
Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.
Nonlinear interaction and wave breaking with a submerged porous structure
Hsieh, Chih-Min; Sau, Amalendu; Hwang, Robert R.; Yang, W. C.
2016-12-01
Numerical simulations are performed to investigate interactive velocity, streamline, turbulent kinetic energy, and vorticity perturbations in the near-field of a submerged offshore porous triangular structure, as Stokes waves of different heights pass through. The wave-structure interaction and free-surface breaking for the investigated flow situations are established based on solutions of 2D Reynolds Averaged Navier-Stokes equations in a Cartesian grid in combination with K-ɛ turbulent closure and the volume of fluid methodology. The accuracy and stability of the adopted model are ascertained by extensive comparisons of computed data with the existing experimental and theoretical findings and through efficient predictions of the internal physical kinetics. Simulations unfold "clockwise" and "anticlockwise" rotation of fluid below the trough and the crest of the viscous waves, and the penetrated wave energy creates systematic flow perturbation in the porous body. The interfacial growths of the turbulent kinetic energy and the vorticity appear phenomenal, around the apex of the immersed structure, and enhanced significantly following wave breaking. Different values of porosity parameter and two non-porous cases have been examined in combination with varied incident wave height to reveal/analyze the nonlinear flow behavior in regard to local spectral amplification and phase-plane signatures. The evolution of leading harmonics of the undulating free-surface and the vertical velocity exhibits dominating roles of the first and the second modes in inducing the nonlinearity in the post-breaking near-field that penetrates well below the surface layer. The study further suggests the existence of a critical porosity that can substantially enhance the wave-shoaling and interface breaking.
Energy Technology Data Exchange (ETDEWEB)
Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg [School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Zhou, Yu [Advanced Remanufacturing and Technology Center (ARTC), 3 Clean Tech Loop, CleanTech Two, Singapore 637143 (Singapore)
2016-07-15
Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonant frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.
Vorotnikov, K.; Starosvetsky, Y.
2018-01-01
The present study concerns two-dimensional nonlinear mechanisms of bidirectional and unidirectional channeling of longitudinal and shear waves emerging in the locally resonant acoustic structure. The system under consideration comprises an oscillatory chain of the axially coupled masses. Each mass of the chain is subject to the local linear potential along the lateral direction and incorporates the lightweight internal rotator. In the present work, we demonstrate the emergence of special resonant regimes of complete bi- and unidirectional transitions between the longitudinal and the shear waves of the locally resonant chain. These regimes are manifested by the two-dimensional energy channeling between the longitudinal and the shear traveling waves in the recurrent as well as the irreversible fashion. We show that the spatial control of the two dimensional energy flow between the longitudinal and the shear waves is solely governed by the motion of the internal rotators. Nonlinear analysis of the regimes of a bidirectional wave channeling unveils their global bifurcation structure and predicts the zones of their spontaneous transitions from a complete bi-directional wave channeling to the one-directional entrapment. An additional regime of a complete irreversible resonant transformation of the longitudinal wave into a shear wave is analyzed in the study. The intrinsic mechanism governing the unidirectional wave reorientation is described analytically. The results of the analysis of both mechanisms are substantiated by the numerical simulations of the full model and are found to be in a good agreement.
Universal power law of the gravity wave manifestation in the AIM CIPS polar mesospheric cloud images
Rong, Pingping; Yue, Jia; Russell, James M., III; Siskind, David E.; Randall, Cora E.
2018-01-01
We aim to extract a universal law that governs the gravity wave manifestation in polar mesospheric clouds (PMCs). Gravity wave morphology and the clarity level of display vary throughout the wave population manifested by the PMC albedo data. Higher clarity refers to more distinct exhibition of the features, which often correspond to larger variances and a better-organized nature. A gravity wave tracking algorithm based on the continuous Morlet wavelet transform is applied to the PMC albedo data at 83 km altitude taken by the Aeronomy of Ice in the Mesosphere (AIM) Cloud Imaging and Particle Size (CIPS) instrument to obtain a large ensemble of the gravity wave detections. The horizontal wavelengths in the range of ˜ 20-60 km are the focus of the study. It shows that the albedo (wave) power statistically increases as the background gets brighter. We resample the wave detections to conform to a normal distribution to examine the wave morphology and display clarity beyond the cloud brightness impact. Sample cases are selected at the two tails and the peak of the normal distribution to represent the full set of wave detections. For these cases the albedo power spectra follow exponential decay toward smaller scales. The high-albedo-power category has the most rapid decay (i.e., exponent = -3.2) and corresponds to the most distinct wave display. The wave display becomes increasingly blurrier for the medium- and low-power categories, which hold the monotonically decreasing spectral exponents of -2.9 and -2.5, respectively. The majority of waves are straight waves whose clarity levels can collapse between the different brightness levels, but in the brighter background the wave signatures seem to exhibit mildly turbulent-like behavior.
Nonlinear ion-acoustic waves and solitons in a magnetized plasma
International Nuclear Information System (INIS)
Lee, L.C.; Kan, J.R.
1981-01-01
A unified formulation is presented to study the nonlinear low-frequency electrostatic waves in a magnetized low-β plasma. It is found that there exist three types of nonlinear waves; (1) nonlinear ion-cyclotron periodic waves with a wave speed V/sub p/ > C/sub s/ (ion-acoustic velocity); (2) nonlinear ion-acoustic periodic waves with V/sub p/ < C/sub s/ costheta; and (3) ion-acoustic solitons with C/sub s/ costheta < V/sub p/ < C/sub s/, where theta is the angle between the wave vector and the magnetic field
Nonlinear Time-Reversal in a Wave Chaotic System
Frazier, Matthew; Taddese, Biniyam; Ott, Edward; Antonsen, Thomas; Anlage, Steven
2012-02-01
Time reversal mirrors are particularly simple to implement in wave chaotic systems and form the basis for a new class of sensors [1-3]. These sensors work by applying the quantum mechanical concepts of Loschmidt echo and fidelity decay to classical waves. The sensors make explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to remotely measure the presence of small perturbations to the system. The underlying ray chaos increases the sensitivity to small perturbations throughout the volume explored by the waves. We extend our time-reversal mirror to include a discrete element with a nonlinear dynamical response. The initially injected pulse interacts with the nonlinear element, generating new frequency components originating at the element. By selectively filtering for and applying the time-reversal mirror to the new frequency components, we focus a pulse only onto the element, without knowledge of its location. Furthermore, we demonstrate transmission of arbitrary patterns of pulses to the element, creating a targeted communication channel to the exclusion of 'eavesdroppers' at other locations in the system. [1] Appl. Phys. Lett. 95, 114103 (2009) [2] J. Appl. Phys. 108, 1 (2010) [3] Acta Physica Polonica A 112, 569 (2007)
Identification and determination of solitary wave structures in nonlinear wave propagation
International Nuclear Information System (INIS)
Newman, W.I.; Campbell, D.K.; Hyman, J.M.
1991-01-01
Nonlinear wave phenomena are characterized by the appearance of ''solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that these structures are briefly noninteracting, we propose a method for the identification of the number of independent features and their respective speeds. Using data generated from an exact two-soliton solution to the Korteweg-de-Vries equation, we test the method and discuss its strengths and limitations. 41 refs., 2 figs
La, I.; Yum, S. S.; Yeom, J. M.; Gultepe, I.
2017-12-01
Since microphysical and dynamical processes of fog are not well-known and have non-linear relationships among processes that are related to fog formation, improving the accuracy of the fog forecasting/nowcasting system is challenging. For these reasons, understanding the fog mechanism is needed to develop the fog forecasting system. So, we focus on understanding fog-turbulence interactions and fog-gravity wave interactions. Many studies noted that turbulence plays important roles in fog. However, a discrepancy between arguments for the effect of turbulent mixing on fog formation exists. Several studies suggested that turbulent mixing suppresses fog formation. Some other studies reported that turbulent mixing contributes to fog formation. On the other hand, several quasi-periodic oscillations of temperature, visibility, and vertical velocity, which have period of 10-20 minutes, were observed to be related to gravity waves in fog; because gravity waves play significant dynamic roles in the atmosphere. Furthermore, a numerical study suggested that gravity waves, simulated near the top of the fog layer, may affect fog microphysics. Thus, we investigate the effects of turbulent mixing on fog formation and the influences of gravity waves on fog microphysics to understand fog structure in Pyeongchang. In these studies, we analyze the data that are obtained from doppler lidar and 3.5 m meteorological observation tower including 3D-ultrasonic anemometer, IR sensor, and fog monitor during ICE-POP (International Collaborative Experiments for Pyeongchang 2018 Olympic and Paralympic winter games) campaign. In these instruments, doppler lidar is a good instrument to observe the gravity waves near the fog top, while in situ measurements have small spatial coverage. The instruments are installed at the mountainous terrain of Pyeongchang, Korea. More details will be presented at the conference.
Nonlinear time-dependent simulation of helix traveling wave tubes
International Nuclear Information System (INIS)
Peng Wei-Feng; Yang Zhong-Hai; Hu Yu-Lu; Li Jian-Qing; Lu Qi-Ru; Li Bin
2011-01-01
A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of the high frequency structure, such as the pitch taper and the effect of harmonics, the spatial average over a wavelength is substituted by a time average over a wave period in the equation of the radio frequency field. Under this assumption, the space charge field of the electron beam can be treated by a space charge wave model along with the space charge coefficient. The effects of the radio frequency and the space charge fields on the electrons are presented by the equations of the electron energy and the electron phase. The time-dependent simulation is compared with the frequency-domain simulation for a helix TWT, which validates the availability of this theory. (interdisciplinary physics and related areas of science and technology)
Dynamics of nonlinear waves in the tubes filled with aerosol
Directory of Open Access Journals (Sweden)
Gubaidullin Damir
2018-01-01
Full Text Available The results of experimental investigations of nonlinear oscillations of finely dispersed aerosol in the tube with various geometry on the end in the shock-wave, the shock-free wave modes and in the mode of transition to shock waves near the resonance frequency are presented. The time dependences of the numerical concentration of the oscillating aerosol droplets are presented. The effect of the frequency and amplitude of the piston displacement and the influence of the diaphragm internal diameter on the time coagulation and sedimentation of aerosol were studied. An increase in the amplitude of the piston displacement in all modes results in acceleration of the process of coagulation and sedimentation of aerosol. The dependence of time of coagulation and sedimentation of aerosol on the excitation frequency was found to be of a nonmonotonic character with the minimum value upon the resonance frequency.
Nonlinear electromagnetic waves in a degenerate electron-positron plasma
Energy Technology Data Exchange (ETDEWEB)
El-Labany, S.K., E-mail: skellabany@hotmail.com [Department of Physics, Faculty of Science, Damietta University, New Damietta (Egypt); El-Taibany, W.F., E-mail: eltaibany@hotmail.com [Department of Physics, College of Science for Girls in Abha, King Khalid University, Abha (Saudi Arabia); El-Samahy, A.E.; Hafez, A.M.; Atteya, A., E-mail: ahmedsamahy@yahoo.com, E-mail: am.hafez@sci.alex.edu.eg, E-mail: ahmed_ateya2002@yahoo.com [Department of Physics, Faculty of Science, Alexandria University, Alexandria (Egypt)
2015-08-15
Using the reductive perturbation technique (RPT), the nonlinear propagation of magnetosonic solitary waves in an ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing ultracold, degenerate electron, and positron fluids) is investigated. The set of basic equations is reduced to a Korteweg-de Vries (KdV) equation for the lowest-order perturbed magnetic field and to a KdV type equation for the higher-order perturbed magnetic field. The solutions of these evolution equations are obtained. For better accuracy and searching on new features, the new solutions are analyzed numerically based on compact objects (white dwarf) parameters. It is found that including the higher-order corrections results as a reduction (increment) of the fast (slow) electromagnetic wave amplitude but the wave width is increased in both cases. The ranges where the RPT can describe adequately the total magnetic field including different conditions are discussed. (author)
Nonlinear acoustic waves in partially ionized collisional plasmas
International Nuclear Information System (INIS)
Rao, N.N.; Kaup, D.J.; Shukla, P.K.
1991-01-01
Nonlinear propagation of acoustic-type waves in a partially ionized three-component collisional plasma consisting of electrons, ions and neutral particles is investigated. For bidirectional propagation, it is shown that the small- but finite-amplitude waves are governed by the Boussinesq equation, which for unidirectional propagation near the acoustic speed reduces to the usual Korteweg-de Vries equation. For large-amplitude waves, it is demonstrated that the relevant fluid equations are integrable in a stationary frame, and the parameter values for the existence of finite-amplitude solutions are explicitly obtained. In both cases, the different temperatures of the individual species, are taken into account. The relevance of the results to the earth's ionospheric plasma in the lower altitude ranges is pointed out. (author)
Current structure of strongly nonlinear interfacial solitary waves
Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor
2015-04-01
The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr
Surface gravity waves and their acoustic signatures, 1-30 Hz, on the mid-Pacific sea floor.
Farrell, W E; Munk, Walter
2013-10-01
In 1999, Duennebier et al. deployed a hydrophone and geophone below the conjugate depth in the abyssal Pacific, midway between Hawaii and California. Real time data were transmitted for 3 yr over an abandoned ATT cable. These data have been analyzed in the frequency band 1 to 30 Hz. Between 1 and 6 Hz, the bottom data are interpreted as acoustic radiation from surface gravity waves, an extension to higher frequencies of a non-linear mechanism proposed by Longuet-Higgins in 1950 to explain microseisms. The inferred surface wave spectrum for wave lengths between 6 m and 17 cm is saturated (wind-independent) and roughly consistent with the traditional Phillips κ(-4) wave number spectrum. Shorter ocean waves have a strong wind dependence and a less steep wave number dependence. Similar features are found in the bottom record between 6 and 30 Hz. But this leads to an enigma: The derived surface spectrum inferred from the Longuet-Higgins mechanism with conventional assumptions for the dispersion relation is associated with mean square slopes that greatly exceed those derived from glitter. Regardless of the generation mechanism, the measured bottom intensities between 10 and 30 Hz are well below minimum noise standards reported in the literature.
Nonlinear instability and chaos in plasma wave-wave interactions, I., Introduction
International Nuclear Information System (INIS)
Kueny, C.S.; Morrison, P.J.
1994-11-01
Conventional linear stability analyses may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper [submitted to Physics of Plasmas], this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various (integrable) systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper
Nonlinear instability and chaos in plasma wave--wave interactions. I. Introduction
International Nuclear Information System (INIS)
Kueny, C.S.; Morrison, P.J.
1995-01-01
Conventional linear stability analyses may fail for fluid systems with an indefinite free-energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave--wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper (submitted to Phys. Plasmas), this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various integrable systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper. copyright 1995 American Institute of Physics
Propagation of nonlinear waves over submerged step: wave separation and subharmonic generation
Monsalve, Eduardo; Maurel, Agnes; Pagneux, Vincent; Petitjeans, Philippe
2015-11-01
Water waves can be described in simplified cases by the Helmholtz equation. However, even in these cases, they present a high complexity, among which their dispersive character and their nonlinearities are the subject of the present study. Using Fourier Transform Profilometry, we study experimentally the propagation of waves passing over a submerged step. Because of the small water depth after the step, the wave enters in a nonlinear regime. In the shallow water region, the second harmonic leads to two types of waves: bound waves which are slaves of the fundamental frequency with wavenumber 2 k (ω) , and free waves which propagate according to the usual dispersion relation with wavenumber k (2 ω) . Because of the presence of these two waves, beats are produced at the second harmonic with characteristic beat length. In this work, for the first time we extended this analysis to the third and higher harmonics. Next, the region after the step is limited to a finite size L with a reflecting wall. For certain frequencies and L- values, the spectral component becomes involved, with the appearance of sub harmonics. This regime is analyzed in more details, suggesting a transition to a chaotic and quasi-periodic wave behavior.
Qin, Yan-Hong; Zhao, Li-Chen; Yang, Zhan-Ying; Yang, Wen-Li
2018-01-01
We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by a pair-transition coupled two-component Bose-Einstein condensate. We demonstrate that the interference effects can induce several localized waves possessing distinctive wave structures, mainly including anti-dark solitons, W-shaped solitons, multi-peak solitons, Kuznetsov-Ma like breathers, and multi-peak breathers. Specifically, the explicit conditions for them are clarified by a phase diagram based on the linear interference properties. Furthermore, the interactions between these localized waves are discussed. The detailed analysis indicates that the soliton-soliton interaction induced phase shift brings the collision between these localized waves which can be inelastic for solitons involving collision and can be elastic for breathers. These characters come from the fact that the profile of solitons depends on the relative phase between bright solitons and a plane wave, and the profile of breathers does not depend on the relative phase. These results would motivate more discussions on linear interference between other nonlinear waves. Specifically, the solitons or breathers obtained here are not related to modulational instability. The underlying reasons are discussed in detail. In addition, possibilities to observe these localized waves are discussed in a two species Bose-Einstein condensate.
Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface
Energy Technology Data Exchange (ETDEWEB)
Kim, No Hyu; Yang, Seung Yong [Korea University of Technology and Education, Cheonan (Korea, Republic of)
2007-12-15
Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness
Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface
International Nuclear Information System (INIS)
Kim, No Hyu; Yang, Seung Yong
2007-01-01
Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness
Zhao, J.; Geraghty, I.; Chu, X.; Vadas, S.; Becker, E.; Harvey, V. L.; Jones, R. M.; Chen, C.; Lu, X.
2017-12-01
After Antarctic persistent gravity waves (GWs) in the Mesosphere and Lower Thermosphere (MLT) were discovered from lidar observations [Chen et al., 2013, 2016], secondary wave generation theory was proposed to explain the source. Here we perform a source investigation of such persistent GWs through analyzing both stratospheric and MLT GWs at McMurdo using temperature measurements (30 - 50 km, year 2011 - 2015) obtained by Fe Boltzmann lidar. In the stratosphere, GW vertical wavelengths (λ) and periods exhibit seasonal cycles with winter maxima and summer minima, which linearly correlated with mean zonal wind velocities. GWs dissipate more in winter than in summer due to larger wave amplitudes. The potential energy density (Ep) are anti-correlated with wind rotation angles but positively correlated with surface and stratospheric winds. Critical level filtering, in-situ generation of GWs, and wave saturation changes play roles in Ep seasonal variations (winter maxima and summer minima). The large increase of Ep from summer to winter possibly results from the decrease in critical level filtering. The gradual variations of Ep from Mar to Oct are likely related both to the increased λ towards winter, allowing larger wave amplitudes before saturation, and to in-situ GW generation via geostrophic adjustment, secondary GW generation. Large Ep occur when McMurdo is inside the jet stream core 5-24º poleward from vortex edge. In winter MLT, the persistent GWs cause larger temperature perturbations (± 30 K, compared to ± 10 K in the stratosphere) with longer λ (23.5 km) and larger vertical phase speeds (1.8 m/s). More waves (95.4%) show downward phase progression compared to the stratospheric GWs (70.4%). Since the inferred horizontal wavelength of stratospheric GWs (350 - 450 km) are much shorter than those of the persistent GWs in the MLT (1000 - 2000 km), the dominant stratospheric GWs are not the direct source of the MLT persistent GWs. Secondary wave generation
Observation of gravity waves during the extreme tornado outbreak of 3 April 1974
Hung, R. J.; Phan, T.; Smith, R. E.
1978-01-01
A continuous wave-spectrum high-frequency radiowave Doppler sounder array was used to observe upper-atmospheric disturbances during an extreme tornado outbreak. The observations indicated that gravity waves with two harmonic wave periods were detected at the F-region ionospheric height. Using a group ray path computational technique, the observed gravity waves were traced in order to locate potential sources. The signals were apparently excited 1-3 hours before tornado touchdown. Reverse ray tracing indicated that the wave source was located at the aurora zone with a Kp index of 6 at the time of wave excitation. The summation of the 24-hour Kp index for the day was 36. The results agree with existing theories (Testud, 1970; Titheridge, 1971; Kato, 1976) for the excitation of large-scale traveling ionospheric disturbances associated with geomagnetic activity in the aurora zone.
Vals, M.
2017-09-01
We use MAVEN/NGIMS CO2 density measurements to analyse gravity waves in the thermosphere of Mars. In particular the seasonal/latitudinal variability of their amplitude is studied and interpreted. Key background parameters controlling the activity of gravity waves are analysed with the help of the Mars Climate Database (MCD). Gravity waves activity presents a good anti-correlation to the temperature variability retrieved from the MCD. An analysis at pressure levels is ongoing.
Ardhuin, Fabrice; Lavanant, Thibaut; Obrebski, Mathias; Marié, Louis; Royer, Jean-Yves; d'Eu, Jean-François; Howe, Bruce M; Lukas, Roger; Aucan, Jerome
2013-10-01
The generation of ultra-low frequency acoustic noise (0.1 to 1 Hz) by the nonlinear interaction of ocean surface gravity waves is well established. More controversial are the quantitative theories that attempt to predict the recorded noise levels and their variability. Here a single theoretical framework is used to predict the noise level associated with propagating pseudo-Rayleigh modes and evanescent acoustic-gravity modes. The latter are dominant only within 200 m from the sea surface, in shallow or deep water. At depths larger than 500 m, the comparison of a numerical noise model with hydrophone records from two open-ocean sites near Hawaii and the Kerguelen islands reveal: (a) Deep ocean acoustic noise at frequencies 0.1 to 1 Hz is consistent with the Rayleigh wave theory, in which the presence of the ocean bottom amplifies the noise by 10 to 20 dB; (b) in agreement with previous results, the local maxima in the noise spectrum support the theoretical prediction for the vertical structure of acoustic modes; and (c) noise level and variability are well predicted for frequencies up to 0.4 Hz. Above 0.6 Hz, the model results are less accurate, probably due to the poor estimation of the directional properties of wind-waves with frequencies higher than 0.3 Hz.
Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
Luna, Manuel
2011-05-01
Solitary wave formation is a well studied nonlinear phenomenon arising in propagation of dispersive nonlinear waves under suitable conditions. In non-homogeneous materials, dispersion may happen due to effective reflections between the material interfaces. This dispersion has been used along with nonlinearities to find solitary wave formation using the one-dimensional p-system. These solitary waves are called stegotons. The main goal in this work is to find two-dimensional stegoton formation. To do so we consider the nonlinear two-dimensional p-system with variable coefficients and solve it using finite volume methods. The second goal is to obtain effective equations that describe the macroscopic behavior of the variable coefficient system by a constant coefficient one. This is done through a homogenization process based on multiple-scale asymptotic expansions. We compare the solution of the effective equations with the finite volume results and find a good agreement. Finally, we study some stability properties of the homogenized equations and find they and one-dimensional versions of them are unstable in general.
Nonlinear particle-wave kinetics in weakly unstable plasmas
International Nuclear Information System (INIS)
Breizman, B.N.; Berk, H.L.; Pekker, M.S.
1996-01-01
With the motivation to address the behavior of the fusion produced alpha particles in a thermonuclear reactor, a theory is developed for predicting the wave saturation levels and particle transport in weakly unstable systems with a discrete number of modes in the presence of energetic particle sources and sinks. Conditions are established for either steady state or bursting nonlinear scenarios when several modes are excited for cases where there is and there is not resonance overlap. Depending on parameters, the particles can undergo benign relaxation, with only a small fraction of the available free energy released to waves and with no global transport, or the particles can experience rapid global transport caused by a substantial conversion of their free energy into wave energy. When the resonance condition of the particle-wave interaction is varied adiabatically, the particles trapped in a wave are found to form phase space holes or clumps that enhance the particle-wave energy exchange. This mechanism, which has been experimentally observed when there is frequency chirping, causes increased saturation levels of instabilities. If resonance sweeping is imposed externally, the particle free energy can even be tapped in stable systems where background dissipation suppresses linear instability. Externally applied resonance sweeping can be important for alpha particle energy channeling, as well as for understanding fishbone and some Alfven wave instability experiments. Near instability threshold, that is when the destabilizing drive just exceeds the background dissipation, a more sophisticated analysis is developed to predict the correct saturation. To leading order, this problem reduces to an integral equation for the wave amplitude with a temporally non local cubic term. This equation has a self-similar solution that blows-up in a finite time
Gravity Waves and Wind-Farm Efficiency in Neutral and Stable Conditions
Allaerts, Dries; Meyers, Johan
2018-02-01
We use large-eddy simulations (LES) to investigate the impact of stable stratification on gravity-wave excitation and energy extraction in a large wind farm. To this end, the development of an equilibrium conventionally neutral boundary layer into a stable boundary layer over a period of 8 h is considered, using two different cooling rates. We find that turbulence decay has considerable influence on the energy extraction at the beginning of the boundary-layer transition, but afterwards, energy extraction is dominated by geometrical and jet effects induced by an inertial oscillation. It is further shown that the inertial oscillation enhances gravity-wave excitation. By comparing LES results with a simple one-dimensional model, we show that this is related to an interplay between wind-farm drag, variations in the Froude number and the dispersive effects of vertically-propagating gravity waves. We further find that the pressure gradients induced by gravity waves lead to significant upstream flow deceleration, reducing the average turbine output compared to a turbine in isolated operation. This leads us to the definition of a non-local wind-farm efficiency, next to a more standard wind-farm wake efficiency, and we show that both can be of the same order of magnitude. Finally, an energy flux analysis is performed to further elucidate the effect of gravity waves on the flow in the wind farm.
Improved analysis of all-sky meteor radar measurements of gravity wave variances and momentum fluxes
Directory of Open Access Journals (Sweden)
V. F. Andrioli
2013-05-01
Full Text Available The advantages of using a composite day analysis for all-sky interferometric meteor radars when measuring mean winds and tides are widely known. On the other hand, problems arise if this technique is applied to Hocking's (2005 gravity wave analysis for all-sky meteor radars. In this paper we describe how a simple change in the procedure makes it possible to use a composite day in Hocking's analysis. Also, we explain how a modified composite day can be constructed to test its ability to measure gravity wave momentum fluxes. Test results for specified mean, tidal, and gravity wave fields, including tidal amplitudes and gravity wave momentum fluxes varying strongly with altitude and/or time, suggest that the modified composite day allows characterization of monthly mean profiles of the gravity wave momentum fluxes, with good accuracy at least at the altitudes where the meteor counts are large (from 89 to 92.5 km. In the present work we also show that the variances measured with Hocking's method are often contaminated by the tidal fields and suggest a method of empirical correction derived from a simple simulation model. The results presented here greatly increase our confidence because they show that our technique is able to remove the tide-induced false variances from Hocking's analysis.
New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation
International Nuclear Information System (INIS)
Yang Qin; Dai Chaoqing; Zhang Jiefang
2005-01-01
Some new exact travelling wave and period solutions of discrete nonlinear Schroedinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.
Frequency variations of gravity waves interacting with a time-varying tide
Energy Technology Data Exchange (ETDEWEB)
Huang, C.M.; Zhang, S.D.; Yi, F.; Huang, K.M.; Gan, Q.; Gong, Y. [Wuhan Univ., Hubei (China). School of Electronic Information; Ministry of Education, Wuhan, Hubei (China). Key Lab. of Geospace Environment and Geodesy; State Observatory for Atmospheric Remote Sensing, Wuhan, Hubei (China); Zhang, Y.H. [Nanjing Univ. of Information Science and Technology (China). College of Hydrometeorolgy
2013-11-01
Using a nonlinear, 2-D time-dependent numerical model, we simulate the propagation of gravity waves (GWs) in a time-varying tide. Our simulations show that when aGW packet propagates in a time-varying tidal-wind environment, not only its intrinsic frequency but also its ground-based frequency would change significantly. The tidal horizontal-wind acceleration dominates the GW frequency variation. Positive (negative) accelerations induce frequency increases (decreases) with time. More interestingly, tidal-wind acceleration near the critical layers always causes the GW frequency to increase, which may partially explain the observations that high-frequency GW components are more dominant in the middle and upper atmosphere than in the lower atmosphere. The combination of the increased ground-based frequency of propagating GWs in a time-varying tidal-wind field and the transient nature of the critical layer induced by a time-varying tidal zonal wind creates favorable conditions for GWs to penetrate their originally expected critical layers. Consequently, GWs have an impact on the background atmosphere at much higher altitudes than expected, which indicates that the dynamical effects of tidal-GW interactions are more complicated than usually taken into account by GW parameterizations in global models.
Linear and non-linear Modified Gravity forecasts with future surveys
Casas, Santiago; Kunz, Martin; Martinelli, Matteo; Pettorino, Valeria
2017-12-01
Modified Gravity theories generally affect the Poisson equation and the gravitational slip in an observable way, that can be parameterized by two generic functions (η and μ) of time and space. We bin their time dependence in redshift and present forecasts on each bin for future surveys like Euclid. We consider both Galaxy Clustering and Weak Lensing surveys, showing the impact of the non-linear regime, with two different semi-analytical approximations. In addition to these future observables, we use a prior covariance matrix derived from the Planck observations of the Cosmic Microwave Background. In this work we neglect the information from the cross correlation of these observables, and treat them as independent. Our results show that η and μ in different redshift bins are significantly correlated, but including non-linear scales reduces or even eliminates the correlation, breaking the degeneracy between Modified Gravity parameters and the overall amplitude of the matter power spectrum. We further apply a Zero-phase Component Analysis and identify which combinations of the Modified Gravity parameter amplitudes, in different redshift bins, are best constrained by future surveys. We extend the analysis to two particular parameterizations of μ and η and consider, in addition to Euclid, also SKA1, SKA2, DESI: we find in this case that future surveys will be able to constrain the current values of η and μ at the 2-5% level when using only linear scales (wavevector k < 0 . 15 h/Mpc), depending on the specific time parameterization; sensitivity improves to about 1% when non-linearities are included.
Relativistic harmonic content of nonlinear electromagnetic waves in underdense plasmas
International Nuclear Information System (INIS)
Mori, W.B.; Decker, C.D.; Leemans, W.P.
1993-01-01
The relativistic harmonic content of large amplitude electromagnetic waves propagating in underdense plasmas is investigated. The steady state harmonic content of nonlinear linearly polarized waves is calculated for both the very underdense (w p /w o ) much-lt 1 and critical density (w p /w o ) ≅ 1 limits. For weak nonlinearities, eE o /mcw o p /w o . Arguments are given for extending these results for arbitrary wave amplitudes. The authors also show that the use of the variable x-ct and the quasi-static approximation leads to errors in both magnitude and sign when calculating the third harmonic. In the absence of damping or density gradients the third harmonic's amplitude is found to oscillate between zero and twice the steady state value. Preliminary PIC simulation results are presented. The simulation results are in basic agreement with the uniform plasma predictions for the third harmonic amplitude. However, the higher harmonics are orders of magnitude larger than expected and the presence of density ramps significantly modifies the results
Phase velocity of nonlinear plasma waves in the laser beat-wave accelerator
International Nuclear Information System (INIS)
Spence, W.L.
1985-01-01
The suggested plasma-laser accelerator is an attempt to achieve a very high energy gradient by resonantly exciting a longitudinal wave traveling at close to the speed of light in cold plasma by means of the beat-wave generated by the transverse fields in two laser beams. Previous calculations to all orders in v/sub z/ have been done essentially from the laboratory frame point of view and have treated the plasma wave as having sharply defined phase velocity equal to the speed of light. However a high energy particle beam undergoing acceleration sees the plasma wave from a nearly light-like frame of reference and hence is very sensitive to small deviations in its phase velocity. Here the authors introduce a calculational scheme that includes all orders in v/sub z/ and in the plasma density, and additionally takes into account the influence of plasma nonlinearities on the wave's phase velocity. The main assumption is that the laser frequencies are very large compared to the plasma frequency - under which they are able to in essence formally sum up all orders of forward Raman scattering. They find that the nonlinear plasma wave does not have simply a single phase velocity - it is really a superposition of many - but that the beat-wave which drives it is usefully described by a non-local effective phase velocity function
Dynamics of Nearshore Sand Bars and Infra-gravity Waves: The Optimal Theory Point of View
Bouchette, F.; Mohammadi, B.
2016-12-01
It is well known that the dynamics of near-shore sand bars are partly controlled by the features (location of nodes, amplitude, length, period) of the so-called infra-gravity waves. Reciprocally, changes in the location, size and shape of near-shore sand bars can control wave/wave interactions which in their turn alter the infra-gravity content of the near-shore wave energy spectrum. The coupling infra-gravity / near-shore bar is thus definitely two ways. Regarding numerical modelling, several approaches have already been considered to analyze such coupled dynamics. Most of them are based on the following strategy: 1) define an energy spectrum including infra-gravity, 2) tentatively compute the radiation stresses driven by this energy spectrum, 3) compute sediment transport and changes in the seabottom elevation including sand bars, 4) loop on the computation of infra-gravity taking into account the morphological changes. In this work, we consider an alternative approach named Nearshore Optimal Theory, which is a kind of breakdown point of view for the modeling of near-shore hydro-morphodynamics and wave/ wave/ seabottom interactions. Optimal theory applied to near-shore hydro-morphodynamics arose with the design of solid coastal defense structures by shape optimization methods, and is being now extended in order to model dynamics of any near-shore system combining waves and sand. The basics are the following: the near-shore system state is through a functional J representative of the energy of the system in some way. This J is computed from a model embedding the physics to be studied only (here hydrodynamics forced by simple infra-gravity). Then the paradigm is to say that the system will evolve so that the energy J tends to minimize. No really matter the complexity of wave propagation nor wave/bottom interactions. As soon as J embeds the physics to be explored, the method does not require a comprehensive modeling. Near-shore Optimal Theory has already given
Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains
Energy Technology Data Exchange (ETDEWEB)
Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M., E-mail: D.J.Pascoe@warwick.ac.uk [Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)
2017-10-01
Quasi-periodic rapidly propagating wave trains are frequently observed in extreme ultraviolet observations of the solar corona, or are inferred by the quasi-periodic modulation of radio emission. The dispersive nature of fast magnetohydrodynamic waves in coronal structures provides a robust mechanism to explain the detected quasi-periodic patterns. We perform 2D numerical simulations of impulsively generated wave trains in coronal plasma slabs and investigate how the behavior of the trapped and leaky components depend on the properties of the initial perturbation. For large amplitude compressive perturbations, the geometrical dispersion associated with the waveguide suppresses the nonlinear steepening for the trapped wave train. The wave train formed by the leaky components does not experience dispersion once it leaves the waveguide and so can steepen and form shocks. The mechanism we consider can lead to the formation of multiple shock fronts by a single, large amplitude, impulsive event and so can account for quasi-periodic features observed in radio spectra.
Nonlinear Electron Acoustic Waves in Dissipative Plasma with Superthermal Electrons
El-Hanbaly, A. M.; El-Shewy, E. K.; Kassem, A. I.; Darweesh, H. F.
2016-01-01
The nonlinear properties of small amplitude electron-acoustic ( EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and superthermal hot electrons obeying superthermal distribution, and stationary ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili-Burgers (KP-Brugers) equation. Some solutions of physical interest are obtained. These solutions are related to soliton, monotonic and oscillatory shock waves and their behaviour are shown graphically. The formation of these solutions depends crucially on the value of the Burgers term and the plasma parameters as well. By using the tangent hyperbolic (tanh) method, another interesting type of solution which is a combination between shock and soliton waves is obtained. The topology of phase portrait and potential diagram of the KP-Brugers equation is investigated.The advantage of using this method is that one can predict different classes of the travelling wave solutions according to different phase orbits. The obtained results may be helpful in better understanding of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.
Experimental study of the propgation and dispersion of internal atmospheric gravity waves
International Nuclear Information System (INIS)
Ballard, K.A.
1981-01-01
Traveling ionospheric disturbances (TID's) appear as large-scale transverse waves in the F-region (150 to 1000 km altitude), with frequencies on the order of 0.005 to 0.005 cycles per minute, which propagate horizontally over hundreds or even thousands of kilometers. These disturbances have been observed by various radiowave techniques over the past thirty-five years and are now generally accepted as being the manifestation, in the ionized medium, of internal atmospheric gravity waves. A model describing the propagation of gravity waves in an isothermal atmosphere is presented here. The dispersion relation is derived from fundamental principles, and the relation between phase velocity and group velocity is examined. The effects of the Coriolis force and horizontally stratified winds on wave propagation are also analyzed. Conservation of energy in the gravity wave requires increasing amplitude with increasing altitude, inasmuch as the atmospheric density decreases with height. However, this is counteracted by dissipation of wave energy by ion drag, thermal conductivity, and viscous damping. The production of TID's (in the ionized medium) by gravity waves (in the neutral medium) is discussed in quantitative terms, and the vertical predictive function is derived. Dartmouth College has operated a three-station ionosonde network in northern New Hampshire and Vermont on an intermittent basis since 1968. Seven large TID's, found in the 1969 data, are reexamined here in an exhaustive and successful comparison with the gravity wave model. Iso-true-height contours of electron density are used to determine several pertinent TID wave parameters as a function of height
Nonlinear wave-mixing processes in the extreme ultraviolet
International Nuclear Information System (INIS)
Misoguti, L.; Christov, I. P.; Backus, S.; Murnane, M. M.; Kapteyn, H. C.
2005-01-01
We present data from two-color high-order harmonic generation in a hollow waveguide, that suggest the presence of a nonlinear-optical frequency conversion process driven by extreme ultraviolet light. By combining the fundamental and second harmonic of an 800 nm laser in a hollow-core fiber, with varying relative polarizations, and by observing the pressure and power scaling of the various harmonic orders, we show that the data are consistent with a picture where we drive the process of high-harmonic generation, which in turn drives four-wave frequency mixing processes in the extreme EUV. This work promises a method for extending nonlinear optics into the extreme ultraviolet region of the spectrum using an approach that has not previously been considered, and has compelling implications for generating tunable light at short wavelengths
Nonlinear attenuation of S-waves and Love waves within ambient rock
Sleep, Norman H.; Erickson, Brittany A.
2014-04-01
obtain scaling relationships for nonlinear attenuation of S-waves and Love waves within sedimentary basins to assist numerical modeling. These relationships constrain the past peak ground velocity (PGV) of strong 3-4 s Love waves from San Andreas events within Greater Los Angeles, as well as the maximum PGV of future waves that can propagate without strong nonlinear attenuation. During each event, the shaking episode cracks the stiff, shallow rock. Over multiple events, this repeated damage in the upper few hundred meters leads to self-organization of the shear modulus. Dynamic strain is PGV divided by phase velocity, and dynamic stress is strain times the shear modulus. The frictional yield stress is proportional to depth times the effective coefficient of friction. At the eventual quasi-steady self-organized state, the shear modulus increases linearly with depth allowing inference of past typical PGV where rock over the damaged depth range barely reaches frictional failure. Still greater future PGV would cause frictional failure throughout the damaged zone, nonlinearly attenuating the wave. Assuming self-organization has taken place, estimated maximum past PGV within Greater Los Angeles Basins is 0.4-2.6 m s-1. The upper part of this range includes regions of accumulating sediments with low S-wave velocity that may have not yet compacted, rather than having been damaged by strong shaking. Published numerical models indicate that strong Love waves from the San Andreas Fault pass through Whittier Narrows. Within this corridor, deep drawdown of the water table from its currently shallow and preindustrial levels would nearly double PGV of Love waves reaching Downtown Los Angeles.
The Role of Gravity Waves in the Formation and Organization of Clouds during TWPICE
Energy Technology Data Exchange (ETDEWEB)
Reeder, Michael J. [Monash University; Lane, Todd P. [University of Melbourne; Hankinson, Mai Chi Nguyen [Monash University
2013-09-27
All convective clouds emit gravity waves. While it is certain that convectively-generated waves play important parts in determining the climate, their precise roles remain uncertain and their effects are not (generally) represented in climate models. The work described here focuses mostly on observations and modeling of convectively-generated gravity waves, using the intensive observations from the DoE-sponsored Tropical Warm Pool International Cloud Experiment (TWP-ICE), which took place in Darwin, from 17 January to 13 February 2006. Among other things, the research has implications the part played by convectively-generated gravity waves in the formation of cirrus, in the initiation and organization of further convection, and in the subgrid-scale momentum transport and associated large-scale stresses imposed on the troposphere and stratosphere. The analysis shows two groups of inertia-gravity waves are detected: group L in the middle stratosphere during the suppressed monsoon period, and group S in the lower stratosphere during the monsoon break period. Waves belonging to group L propagate to the south-east with a mean intrinsic period of 35 h, and have vertical and horizontal wavelengths of about 5-6 km and 3000-6000 km, respectively. Ray tracing calculations indicate that these waves originate from a deep convective region near Indonesia. Waves belonging to group S propagate to the south-south-east with an intrinsic period, vertical wavelength and horizontal wavelength of about 45 h, 2 km and 2000-4000 km, respectively. These waves are shown to be associated with shallow convection in the oceanic area within about 1000 km of Darwin. The intrinsic periods of high-frequency waves are estimated to be between 20-40 minutes. The high-frequency wave activity in the stratosphere, defined by mass-weighted variance of the vertical motion of the sonde, has a maximum following the afternoon local convection indicating that these waves are generated by local convection
Relic gravitational wave spectrum, the trans-Planckian physics and Horava-Lifshitz gravity
International Nuclear Information System (INIS)
Koh, Seoktae
2010-01-01
We calculate the spectrum of the relic gravitational wave due to the trans-Planckian effect in which the standard linear dispersion relations may be modified. Of the modified dispersion relations suggested in the literature which has investigated the trans-Planckian effect, we especially use the Corley-Jacobson dispersion relations. The Corley-Jacobson-type modified dispersion relations can be obtained from Horava-Lifshitz gravity which is non-relativistic and UV complete. Although it is not clear how the transitions from Horava-Lifshitz gravity in the UV regime to Einstein gravity in the IR limit occur, we assume that the Horava-Lifshitz gravity regime is followed by the inflationary phase in Einstein gravity.
Stoneley waves in a non-homogeneous orthotropic granular medium under the influence of gravity
Directory of Open Access Journals (Sweden)
S. M. Ahmed
2005-01-01
Full Text Available The aim of this paper is to investigate the Stoneley waves in a non-homogeneous orthotropic granular medium under the influence of a gravity field. The frequency equation obtained, in the form of a sixth-order determinantal expression, is in agreement with the corresponding result when both media are elastic. The frequency equation when the gravity field is neglected has been deduced as a particular case.
Wallen, Samuel P.
Granular media are one of the most common, yet least understood forms of matter on earth. The difficulties in understanding the physics of granular media stem from the fact that they are typically heterogeneous and highly disordered, and the grains interact via nonlinear contact forces. Historically, one approach to reducing these complexities and gaining new insight has been the study of granular crystals, which are ordered arrays of similarly-shaped particles (typically spheres) in Hertzian contact. Using this setting, past works explored the rich nonlinear dynamics stemming from contact forces, and proposed avenues where such granular crystals could form designer, dynamically responsive materials, which yield beneficial functionality in dynamic regimes. In recent years, the combination of self-assembly fabrication methods and laser ultrasonic experimental characterization have enabled the study of granular crystals at microscale. While our intuition may suggest that these microscale granular crystals are simply scaled-down versions of their macroscale counterparts, in fact, the relevant physics change drastically; for example, short-range adhesive forces between particles, which are negligible at macroscale, are several orders of magnitude stronger than gravity at microscale. In this thesis, we present recent advances in analytical and computational modeling of microscale granular crystals, in particular concerning the interplay of nonlinearity, shear interactions, and particle rotations, which have previously been either absent, or included separately at macroscale. Drawing inspiration from past works on phononic crystals and nonlinear lattices, we explore problems involving locally-resonant metamaterials, nonlinear localized modes, amplitude-dependent energy partition, and other rich dynamical phenomena. This work enhances our understanding of microscale granular media, which may find applicability in fields such as ultrasonic wave tailoring, signal processing
The Effect of Surface Topography on the Nonlinear Dynamics of Rossby Waves
Abarzhi, S. I.; Desjardins, O.; Pitsch, H.
2003-01-01
Boussinesq convection in rotating systems attracts a sustained attention of the fluid dynamics community, because it has intricate non-linear dynamics (Cross & Hohenberg 1993) and plays an important role in geophysical and astrophysical applications, such as the motion of the liquid outer core of Earth, the Red Spot in Jupiter, the giant cells in the Sun etc. (Alridge et al. 1990). A fundamental distinction between the real geo- and astrophysical problems and the idealized laboratory studies is that natural systems are inhomogeneous (Alridge et al. 1990). Heterogeneities modulate the flow and influence significantly the dynamics of convective patterns (Alridge et al. 1990; Hide 1971). The effect of modulations on pattern formation and transition to turbulence in Boussinesq convection is far from being completely understood (Cross & Hohenberg 1993; Aranson & Kramer 2002). It is generally accepted that in the liquid outer core of the Earth the transport of the angular momentum and internal heat occurs via thermal Rossby waves (Zhang et al. 2001; Kuang & Bloxham 1999). These waves been visualized in laboratory experiments in rotating liquid-filled spheres and concentric spherical shells (Zhang et al. 2001; Kuang & Bloxham 1999). The basic dynamical features of Rossby waves have been reproduced in a cylindrical annulus, a system much simpler than the spherical ones (Busse & Or 1986; Or & Busse 1987). For convection in a cylindrical annulus, the fluid motion is two-dimensional, and gravity is replaced by a centrifugal force, (Busse & Or 1986; Or & Busse 1987). Hide (1971) has suggested that the momentum and heat transport in the core might be influenced significantly by so-called bumps, which are heterogeneities on the mantle-core boundary. To model the effect of surface topography on the transport of momentum and energy in the liquid outer core of the Earth, Bell & Soward (1996), Herrmann & Busse (1998) and Westerburg & Busse (2001) have studied the nonlinear dynamics
Czech Academy of Sciences Publication Activity Database
Laštovička, Jan
2001-01-01
Roč. 26, 6, Part C (2001), s. 381-386 ISSN 1464-1917 R&D Projects: GA AV ČR IBS3012007; GA AV ČR IAA3042102; GA MŠk OC 271.10 Institutional research plan: CEZ:AV0Z3042911 Keywords : planetary wave * gravity wave * lower ionosphere Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 0.399, year: 2001
Beach steepness effects on nonlinear infragravity-wave interactions : A numerical study
De Bakker, A. T M; Tissier, M.F.S.; Ruessink, B. G.
2016-01-01
The numerical model SWASH is used to investigate nonlinear energy transfers between waves for a diverse set of beach profiles and wave conditions, with a specific focus on infragravity waves. We use bispectral analysis to study the nonlinear triad interactions, and estimate energy transfers to
Beach steepness effects on nonlinear infragravity-wave interactions : A numerical study
de Bakker, A. T M; Tissier, M. F S; Ruessink, B. G.
2016-01-01
The numerical model SWASH is used to investigate nonlinear energy transfers between waves for a diverse set of beach profiles and wave conditions, with a specific focus on infragravity waves. We use bispectral analysis to study the nonlinear triad interactions, and estimate energy transfers to
Linear and nonlinear analysis of density wave instability phenomena
International Nuclear Information System (INIS)
Ambrosini, Walter
1999-01-01
In this paper the mechanism of density-wave oscillations in a boiling channel with uniform and constant heat flux is analysed by linear and nonlinear analytical tools. A model developed on the basis of a semi-implicit numerical discretization of governing partial differential equations is used to provide information on the transient distribution of relevant variables along the channel during instabilities. Furthermore, a lumped parameter model and a distributed parameter model developed in previous activities are also adopted for independent confirmation of the observed trends. The obtained results are finally put in relation with the picture of the phenomenon proposed in classical descriptions. (author)
Hitting probabilities for nonlinear systems of stochastic waves
Dalang, Robert C
2015-01-01
The authors consider a d-dimensional random field u = \\{u(t,x)\\} that solves a non-linear system of stochastic wave equations in spatial dimensions k \\in \\{1,2,3\\}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent \\beta. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of \\mathbb{R}^d, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that ap
The Atmospheric Waves Experiment (AWE): Quantifying the Impact of Gravity Waves on the Edge of Space
Taylor, M. J.; Forbes, J. M.; Fritts, D. C.; Eckermann, S. D.; Snively, J. B.; Liu, H.; Janches, D.; Syrstad, E. A.; Esplin, R. W.; Pautet, P. D.; Zhao, Y.; Pendleton, W. R.
2017-12-01
New theory and modeling now indicate that upward-propagating gravity waves (GWs) originating in the lower atmosphere have profound effects on the variability and mean state of the ionosphere-thermosphere-mesosphere (ITM) system. A major unknown is the spectrum of small-scale ( 30-300 km) GWs entering this system from below. Yet, this part of the spectrum contains most of the waves that will produce the greatest ITM effects. To address this knowledge gap, the Atmospheric Waves Experiment (AWE) plans to deploy a high-resolution imager (based on the successful Utah State University Advanced Mesospheric Temperature Mapper) on the International Space Station (ISS) to gain a transformative set of GW-resolving temperature measurements using the OH nightglow emission (altitude 87 km). The ISS provides the ideal combination of altitude, geographic and local time coverage to accomplish our proposed science objectives, which seeks not only near-global measurements of GW characteristics in the mesopause region, but also quantification of GW momentum and energy fluxes driving the IT from below. Combined with state-of-the-art high-resolution models, the AWE mission will also assess the relative importance of sources versus propagation conditions in explaining the observed spatial and temporal variability of the GWs. The AWE mission was recently selected for a "Phase A" study as part of the NASA 2016 Heliophysics Explorers Mission of Opportunity (MO) Program. In this presentation, we describe the primary goals of this program and introduce our proposed research methods using proven IR instrument technology. AWE's exceptional capabilities are illustrated with recent discoveries in observing GWs from the ground and from aircraft during the NSF DEEPWAVE campaign, promising a major step forward in understanding how troposphere weather translates to space weather.
Quintessential inflation on the brane and the relic gravity wave background
International Nuclear Information System (INIS)
Sami, M.; Sahni, V.
2004-01-01
Quintessential inflation describes a scenario in which both inflation and dark energy (quintessence) are described by the same scalar field. In conventional braneworld models of quintessential inflation gravitational particle-production is used to reheat the universe. This reheating mechanism is very inefficient and results in an excessive production of gravity waves which violate nucleosynthesis constraints and invalidate the model. We describe a new method of realizing quintessential inflation on the brane in which inflation is followed by 'instant preheating' (Felder, Kofman and Linde 1999). The larger reheating temperature in this model results in a smaller amplitude of relic gravity waves which is consistent with nucleosynthesis bounds. The relic gravity wave background has a 'blue' spectrum at high frequencies and is a generic byproduct of successful quintessential inflation on the brane
Hart, V. P.; Taylor, M. J.; Doyle, T. E.; Zhao, Y.; Pautet, P.-D.; Carruth, B. L.; Rusch, D. W.; Russell, J. M.
2018-01-01
This research presents the first application of tomographic techniques for investigating gravity wave structures in polar mesospheric clouds (PMCs) imaged by the Cloud Imaging and Particle Size instrument on the NASA AIM satellite. Albedo data comprising consecutive PMC scenes were used to tomographically reconstruct a 3-D layer using the Partially Constrained Algebraic Reconstruction Technique algorithm and a previously developed "fanning" technique. For this pilot study, a large region (760 × 148 km) of the PMC layer (altitude 83 km) was sampled with a 2 km horizontal resolution, and an intensity weighted centroid technique was developed to create novel 2-D surface maps, characterizing the individual gravity waves as well as their altitude variability. Spectral analysis of seven selected wave events observed during the Northern Hemisphere 2007 PMC season exhibited dominant horizontal wavelengths of 60-90 km, consistent with previous studies. These tomographic analyses have enabled a broad range of new investigations. For example, a clear spatial anticorrelation was observed between the PMC albedo and wave-induced altitude changes, with higher-albedo structures aligning well with wave troughs, while low-intensity regions aligned with wave crests. This result appears to be consistent with current theories of PMC development in the mesopause region. This new tomographic imaging technique also provides valuable wave amplitude information enabling further mesospheric gravity wave investigations, including quantitative analysis of their hemispheric and interannual characteristics and variations.
Directory of Open Access Journals (Sweden)
Yu-Hua Zhang
2017-01-01
Full Text Available Residual stress has significant influence on the performance of mechanical components, and the nondestructive estimation of residual stress is always a difficult problem. This study applies the relative nonlinear coefficient of critical refraction longitudinal (LCR wave to nondestructively characterize the stress state of materials; the feasibility of residual stress estimation using the nonlinear property of LCR wave is verified. The nonlinear ultrasonic measurements based on LCR wave are conducted on components with known stress state to calculate the relative nonlinear coefficient. Experimental results indicate that the relative nonlinear coefficient monotonically increases with prestress and the increment of relative nonlinear coefficient is about 80%, while the wave velocity only decreases about 0.2%. The sensitivity of the relative nonlinear coefficient for stress is much higher than wave velocity. Furthermore, the dependence between the relative nonlinear coefficient and deformation state of components is found. The stress detection resolution based on the nonlinear property of LCR wave is 10 MPa, which has higher resolution than wave velocity. These results demonstrate that the nonlinear property of LCR wave is more suitable for stress characterization than wave velocity, and this quantitative information could be used for residual stress estimation.
Nonlinear travelling waves in rotating Hagen–Poiseuille flow
Pier, Benoît; Govindarajan, Rama
2018-03-01
The dynamics of viscous flow through a rotating pipe is considered. Small-amplitude stability characteristics are obtained by linearizing the Navier–Stokes equations around the base flow and solving the resulting eigenvalue problems. For linearly unstable configurations, the dynamics leads to fully developed finite-amplitude perturbations that are computed by direct numerical simulations of the complete Navier–Stokes equations. By systematically investigating all linearly unstable combinations of streamwise wave number k and azimuthal mode number m, for streamwise Reynolds numbers {{Re}}z ≤slant 500 and rotational Reynolds numbers {{Re}}{{Ω }} ≤slant 500, the complete range of nonlinear travelling waves is obtained and the associated flow fields are characterized.
Nonlinear wave propagation in discrete and continuous systems
Rothos, V. M.
2016-09-01
In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.
Nonlinear wave-beam kinetic equilibrium in decelerating systems
International Nuclear Information System (INIS)
Grishin, V.K.; Shaposhnikova, E.N.
1981-01-01
The equilibrium state of the wave-beam system arising during the interaction of a particle beam and excited electromagnetic wave has been investigated on the basis of the analysis of the exact polution of a non-linear self-consistent linear equation using the complete system of conservation laws. A waveguide with a dielectric filler, into which a monoenergetic particle beam magnetized in a transverse plane is continuously injected, is used as a model of an decelerating system. A dispersion equation describing the system state and expression for the evaluation of efficiency of the beam energy conversion to the field energy have been obtained. It is concluded that larae fields and high efficiency of energy conversion are achieved during the marked beam reconstruction. States with different values of current and beam velocity but similar amplitudes of a longitudinal field are possible in the system considered [ru
Nonlinear beat excitation of low frequency wave in degenerate plasmas
Mir, Zahid; Shahid, M.; Jamil, M.; Rasheed, A.; Shahbaz, A.
2018-03-01
The beat phenomenon due to the coupling of two signals at slightly different frequencies that generates the low frequency signal is studied. The linear dispersive properties of the pump and sideband are analyzed. The modified nonlinear dispersion relation through the field coupling of linear modes against the beat frequency is derived in the homogeneous quantum dusty magnetoplasmas. The dispersion relation is used to derive the modified growth rate of three wave parametric instability. Moreover, significant quantum effects of electrons through the exchange-correlation potential, the Bohm potential, and the Fermi pressure evolved in macroscopic three wave interaction are presented. The analytical results are interpreted graphically describing the significance of the work. The applications of this study are pointed out at the end of introduction.
Directory of Open Access Journals (Sweden)
V. Deepa
2006-10-01
Full Text Available The altitude profiles of temperature fluctuations in the stratosphere and mesosphere observed with the Rayleigh Lidar at Gadanki (13.5° N, 79.2° E on 30 nights during January to March 1999 and 21 nights during February to April 2000 were analysed to bring out the temporal and vertical propagation characteristics of gravity wave perturbations. The gravity wave perturbations showed periodicities in the 0.5–3-h range and attained large amplitudes (4–5 K in the mesosphere. The phase propagation characteristics of gravity waves with different periods showed upward wave propagation with a vertical wavelength of 5–7 km. The mean flow acceleration computed from the divergence of momentum flux of gravity waves is compared with that calculated from monthly values of zonal wind obtained from RH-200 rockets flights. Thus, the contribution of gravity waves towards the generation of Stratospheric Semi Annual Oscillation (SSAO is estimated.
Rakshit, G.; Jana, S.; Maitra, A.
2017-12-01
The perturbations of temperature profile over a location give an estimate of the potential energy of gravity waves propagating through the atmosphere. Disturbances in the lower atmosphere due to tropical deep convection, orographic effects and various atmospheric disturbances generates of gravity waves. The present study investigates the gravity wave energy estimated from fluctuations in temperature profiles over the tropical location Kolkata (22°34' N, 88°22' E). Gravity waves are most intense during the pre-monsoon period (March-June) at the present location, the potential energy having high values above the boundary layer (2-4 km) as observed from radiosonde profiles. An increase in temperature perturbation, due to high ambient temperature in the presence of heat absorbing aerosols, causes an enhancement in potential energy. As the present study location is an urban metropolitan city experiencing high level of pollution, pollutant aerosols can go much above the normal boundary layer during daytime due to convection causing an extended boundary layer. The Aerosol Index (AAI) obtained from Global Ozone Monitoring Experiment-2 (GOME-2) on MetOp-A platform at 340 nm and 380 nm confirms the presence of absorbing aerosol particles over the present location. The Hysplit back trajectory analysis shows that the aerosol particles at those heights are of local origin and are responsible for depleting liquid water content due to cloud burning. The aerosol extinction coefficient obtained from CALIPSO data exhibits an increasing trend during 2006-2016 accompanied by a similar pattern of gravity wave energy. Thus the absorbing aerosols have a significant role in increasing the potential energy of gravity wave at an urban location in the tropical region.
Nonlinear interactions of electromagnetic waves with the auroral ionosphere
Wong, Alfred Y.
1999-09-01
The ionosphere provides us with an opportunity to perform plasma experiments in an environment with long confinement times, very large-scale lengths, and no confining walls. The auroral ionosphere with its nearly vertical magnetic field geometry is uniquely endowed with large amount of free energy from electron and ion precipitation along the magnetic field and mega-ampere current across the magnetic field. To take advantage of this giant outdoor laboratory, two facilities HAARP and HIPAS, with frequencies ranging from the radio to optical bands, are now available for active probing of and interaction with this interesting region. The ponderomotive pressures from the self-consistent wave fields have produced significant local perturbations of density and particle distributions at heights where the incident EM frequency matches a plasma resonance. This paper will review theory and experiments covering the nonlinear phenomena of parametric decay instability to wave collapse processes. At HF frequencies plasma lenses can be created by preconditioning pulses to focus what is a normally divergent beam into a high-intensity spot to further enhance nonlinear phenomena. At optical wavelengths a large rotating liquid metal mirror is used to focus laser pulses up to a given height. Such laser pulses are tuned to the same wavelengths of selected atomic and molecular resonances, with resulting large scattering cross sections. Ongoing experiments on dual-site experiments and excitation of ELF waves will be presented. The connection of such basic studies to environmental applications will be discussed. Such applications include the global communication using ELF waves, the ozone depletion and remediation and the control of atmospheric CO2 through the use of ion cyclotron resonant heating.
International Nuclear Information System (INIS)
Omura, Yoshiharu; Matsumoto, Hiroshi.
1989-01-01
Past theoretical and numerical studies of the nonlinear evolution of electromagnetic cyclotron waves are reviewed. Such waves are commonly observed in space plasmas such as Alfven waves in the solar wind or VLF whistler mode waves in the magnetosphere. The use of an electromagnetic full-particle code to study an electron cyclotron wave and of an electromagnetic hybrid code to study an ion cyclotron wave is demonstrated. Recent achievements in the simulations of nonlinear revolution of electromagnetic cyclotron waves are discussed. The inverse cascading processes of finite-amplitude whistler and Alfven waves is interpreted in terms of physical elementary processes. 65 refs
Yan, X.; Tao, Y.; Xia, C.; Qi, Y.; Zuo, X.
2017-12-01
Several studies have reported the earthquake-induced atmospheric gravity waves detected by some new technologies such as airglow (Makela et al., 2011), GOCE (Garcia et al., 2013), GRACE (Yang et al., 2014), F3/C radio occultation sounding (Coïsson et al., 2015). In this work, we collected all occultation events on 11 March, and selected four events to analyze at last. The original and filtered podTEC is represented as function of the altitude of the impact parameter and UT of the four events. Then, the travel time diagrams of filtered podTEC derived from the events were analyzed. The occultation signal from one event (marked as No.73) is consistent with the previous results reported by Coïsson. 2015, which is corresponds to the ionospheric signal induced from tsunami gravity wave. What is noticeable, in this work, is that three occultation events of No.403, 77 and 118 revealed a disturbance of atmospheric gravity wave with velocity 300m/s, preceding the tsunami. It would probably be correspond to the gravity waves caused by seismic rupture but not tsunami. In addition, it can be seen that the perturbation height of occultation observation TEC is concentrated at 200-400km, corresponding ionosphere F region. The signals detected above are compared with GPS measurements of TEC from GEONET and IGS. From GPS data, traveling ionospheric disturbances were observed spreading out from the epicenter as a quasi-circular propagation pattern with the time. Exactly, we observed an acoustic wave coupled with Rayleigh wave starting from the epicenter with a speed of 3.0km/s and a superimposed acoustic-gravity wave moving with a speed of 800m/s. The acoustic-gravity wave generated at the epicenter and gradually attenuated 800km away, then it is replaced by a gravity wave coupled with the tsunami that moves with a speed of between 100 and 300m/s. It is necessary to confirm the propagation process of the waves if we attempt to evaluate the use of ionospheric seismology as a
Wu, Dong L.; Zhang, Fuqing
2004-01-01
Satellite microwave data are used to study gravity wave properties and variabilities over the northeastern United States and the North Atlantic in the December-January periods. The gravity waves in this region, found in many winters, can reach the stratopause with growing amplitude. The Advanced Microwave Sounding Unit-A (AMSU-A) observations show that the wave occurrences are correlated well with the intensity and location of the tropospheric baroclinic jet front systems. To further investigate the cause(s) and properties of the North Atlantic gravity waves, we focus on a series of wave events during 19-21 January 2003 and compare AMSU-A observations to simulations from a mesoscale model (MM5). The simulated gravity waves compare qualitatively well with the satellite observations in terms of wave structures, timing, and overall morphology. Excitation mechanisms of these large-amplitude waves in the troposphere are complex and subject to further investigations.
Energy Technology Data Exchange (ETDEWEB)
Tsuchiya, T [Dia Consultants Company, Tokyo (Japan)
1996-10-01
Nonlinear full-wave tomography (FWT) is under investigation to improve the estimation accuracy of Vp/Vs distributions. Full-wave tomography is one of the underground structure exploration methods mainly using Tarantola`s nonlinear local optimization method (LOM). Numerical experiment for FWT was carried out assuming relatively weak nonlinear underground structure. In the case of inversion by local optimization method, adequate preconditioning is important. Utilization of geological information is also effective in estimating low-frequency components of a model. As far as data are obtained under proper observation arrangement, even in actual field, precise estimation of Vp/Vs distributions is possible by FWT using explosion in a hole as wave source. In full-wave tomography, selection of observation arrangement is essential for both Vp and Vs. However, the proper arrangement is different between Vp and Vs. Approach to different analyses for Vp and Vs is also necessary by using only proper data for Vp and Vs among obtained data sets. 4 figs.
Wave propagation in a strongly nonlinear locally resonant granular crystal
Vorotnikov, K.; Starosvetsky, Y.; Theocharis, G.; Kevrekidis, P. G.
2018-02-01
In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment.
Tidal and gravity waves study from the airglow measurements at ...
Indian Academy of Sciences (India)
E) during the period 2004–2007 are analyzed to study the dominant waves present in the 80–100 km altitude region of the atmosphere. The nocturnal intensity variations of different airglow emissions are observed using scanning temperature controlled filter photometers. Waves having period lying between 2 and 12 hours ...
Geometric controls of the flexural gravity waves on the Ross Ice Shelf
Sergienko, O. V.
2017-12-01
Long-period ocean waves, formed locally or at distant sources, can reach sub-ice-shelf cavities and excite coupled motion in the cavity and the ice shelf - flexural gravity waves. Three-dimensional numerical simulations of the flexural gravity waves on the Ross Ice Shelf show that propagation of these waves is strongly controlled by the geometry of the system - the cavity shape, its water-column thickness and the ice-shelf thickness. The results of numerical simulations demonstrate that propagation of the waves is spatially organized in beams, whose orientation is determined by the direction of the of the open ocean waves incident on the ice-shelf front. As a result, depending on the beams orientation, parts of the Ross Ice Shelf experience significantly larger flexural stresses compared to other parts where the flexural gravity beams do not propagate. Very long-period waves can propagate farther away from the ice-shelf front exciting flexural stresses in the vicinity of the grounding line.
Computational study of nonlinear plasma waves. I. Simulation model and monochromatic wave propagtion
International Nuclear Information System (INIS)
Matda, Y.; Crawford, F.W.
1974-12-01
An economical low noise plasma simulation model is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation, to establish the low noise features and to verify the theoretical linear dispersion relation at wave energy levels as low as 0.000,001 of the plasma thermal energy. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories. The additional phenomena of sideband instability and satellite growth, stimulated by large amplitude wave propagation and the resulting particle trapping, are described. (auth)
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich
2011-01-01
A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hami...... is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation. © 2010 Springer Science+Business Media B.V.......A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...... the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions...
On the Dynamics of Two-Dimensional Capillary-Gravity Solitary Waves with a Linear Shear Current
Directory of Open Access Journals (Sweden)
Dali Guo
2014-01-01
Full Text Available The numerical study of the dynamics of two-dimensional capillary-gravity solitary waves on a linear shear current is presented in this paper. The numerical method is based on the time-dependent conformal mapping. The stability of different kinds of solitary waves is considered. Both depression wave and large amplitude elevation wave are found to be stable, while small amplitude elevation wave is unstable to the small perturbation, and it finally evolves to be a depression wave with tails, which is similar to the irrotational capillary-gravity waves.
Observations of linear and nonlinear processes in the foreshock wave evolution
Directory of Open Access Journals (Sweden)
Y. Narita
2007-07-01
Full Text Available Waves in the foreshock region are studied on the basis of a hypothesis that the linear process first excites the waves and further wave-wave nonlinearities distribute scatter the energy of the primary waves into a number of daughter waves. To examine this wave evolution scenario, the dispersion relations, the wave number spectra of the magnetic field energy, and the dimensionless cross helicity are determined from the observations made by the four Cluster spacecraft. The results confirm that the linear process is the ion/ion right-hand resonant instability, but the wave-wave interactions are not clearly identified. We discuss various reasons why the test for the wave-wave nonlinearities fails, and conclude that the higher order statistics would provide a direct evidence for the wave coupling phenomena.
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
Gritto, Roland [Univ. of California, Berkeley, CA (United States)
1995-12-01
Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of -100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k_{p}R = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.
Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions
International Nuclear Information System (INIS)
Ablowitz, M J; Haut, T S
2010-01-01
High-order asymptotic series are obtained for gravity-capillary solitary waves, where the first term in the series is the well-known sech 2 solution of the KdV equation. The asymptotic series is used, with nine terms included, to investigate the effects of surface tension on the height and energy of large amplitude waves, and waves close to the solitary version of Stokes' extreme wave. In particular, for surface tension below a critical value, the solitary wave with the maximum energy is obtained. For large surface tension, the series is also used to study the energy related to the solitary waves of depression. Energy considerations suggest that, for large enough surface tension, there are solitary waves that can get close to the fluid bottom. Comparisons are also made with recent experiments.
Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order
International Nuclear Information System (INIS)
Feng Qing-Hua; Zhang Yao-Ming; Meng Fan-Wei
2011-01-01
In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin—Bona—Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method. (general)
Garfinkel, C. I.; Oman, L. D.
2018-01-01
The effect of small islands in the Southern Ocean on the atmospheric circulation in the Southern Hemisphere is considered with a series of simulations using the NASA Goddard Earth Observing System Chemistry-Climate Model in which the gravity wave stress generated by these islands is increased to resemble observed values. The enhanced gravity wave drag leads to a 2 K warming of the springtime polar stratosphere, partially ameliorating biases in this region. Resolved wave drag declines in the stratospheric region in which the added orographic gravity waves deposit their momentum, such that changes in gravity waves are partially compensated by changes in resolved waves, though resolved wave drag increases further poleward. The orographic drag from these islands has impacts for surface climate, as biases in tropospheric jet position are also partially ameliorated. These results suggest that these small islands are likely contributing to the missing drag near 60 degrees S in the upper stratosphere evident in many data assimilation products.
Capillary-gravity waves and the Navier-Stokes equation
International Nuclear Information System (INIS)
Behroozi, F.; Podolefsky, N.
2001-01-01
Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation. (author)
Raju, Thokala Soloman; Pal, Ritu
2018-05-01
We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.
Locating the Tohoku-Oki 2011 tsunami source using acoustic-gravity waves
Andriamiranto Raveloson; Rainer Kind; Xiaohui Yuan; L. Cerana
2012-01-01
The giant Tohoku-Oki earthquake of 11 March 2011 in offshore Japan did not only generate tsunami waves in the ocean but also infrasound (or acoustic-gravity) waves in the atmosphere. We indentified ultra-long-period signals (>500s) in the recordings of infrasound stations in northeast Asia, the northwest Pacific, and Alaska. Their source was fond close to the earthquake epicenter. Therefore, we conclude that in general, infrasound observations after a large offshore earthquake are evidence th...
Czech Academy of Sciences Publication Activity Database
Chum, Jaroslav; Šindelářová, Tereza; Laštovička, Jan; Hruška, František; Burešová, Dalia; Baše, Jiří
2010-01-01
Roč. 115, - (2010), A11322/1-A11322/13 ISSN 0148-0227 R&D Projects: GA ČR GA205/07/1367; GA ČR GA205/09/1253 Grant - others:AV ČR(CZ) M100420901 Institutional research plan: CEZ:AV0Z30420517 Keywords : Ionosphere * gravity waves * wave propagation * remote sensing Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 3.303, year: 2010
Czech Academy of Sciences Publication Activity Database
Šauli, Petra; Roux, S. G.; Abry, P.; Boška, Josef
2007-01-01
Roč. 69, 17-18 (2007), s. 2465-2484 ISSN 1364-6826 R&D Projects: GA ČR GA205/06/1619; GA AV ČR IAA300420504 Grant - others:CNRS(FR) 18098 Institutional research plan: CEZ:AV0Z30420517 Keywords : Acoustic–gravity wave * Vertical ionospheric sounding * F-layer * Wavelet transform * Wave-packet characterization Subject RIV: DG - Athmosphere Sciences, Meteorology Impact factor: 1.566, year: 2007
Dynamics of electron wave packet in a disordered chain with delayed nonlinear response
International Nuclear Information System (INIS)
Zhu Hongjun; Xiong Shijie
2010-01-01
We investigate the dynamics of one electron wave packet in a linear chain with random on-site energies and a nonadiabatic electron-phonon interaction which is described by a delayed cubic nonlinear term in the time-dependent Schroedinger equation. We show that in the regime where the wave packet is delocalized in the case with only the delayed nonlinearity, the wave packet becomes localized when the disorder is added and the localization is enhanced by increasing the disorder. In the regime where the self-trapping phenomenon occurs in the case with only the delayed nonlinearity, by adding the disorder the general dynamical features of the wave packet do not change if the nonlinearity parameter is small, but the dynamics shows the subdiffusive behavior if the nonlinearity parameter is large. The numerical results demonstrate complicated wave packet dynamics of systems with both the disorder and nonlinearity.
Cnoidal waves as solutions of the nonlinear liquid drop model
International Nuclear Information System (INIS)
Ludu, Andrei; Sandulescu, Aureliu; Greiner Walter
1997-01-01
By introducing in the hydrodynamic model, i.e. in the hydrodynamic equation and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equations (KdV). The same equation is obtained by introducing in the liquid drop model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms in the second order. The KdV equation has the cnoidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary waves. The solitons could describe the preformation of clusters on the nuclear surface. We apply this nonlinear liquid drop model to the alpha formation in heavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear surface. By introducing the shell effects we choose this minimum to be degenerated with the ground state. The spectroscopic factor is given by ratio of the square amplitudes in the two minima. (authors)
Pimenova, Anastasiya V.; Goldobin, Denis S.; Lyubimova, Tatyana P.
2018-02-01
We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and arbitrary ratio of layer thicknesses. The derivation is performed within the framework of the long-wavelength approximation, which is relevant as the linear instability of a thin-layers system is long-wavelength. The dynamics of equations is integrable and the equations themselves can be compared to the Boussinesq equation for the gravity waves in shallow water, which allows one to compare the action of the vibrational field to the action of the gravity and its possible effective inversion.
Quantum spreading of a self-gravitating wave-packet in singularity free gravity
Energy Technology Data Exchange (ETDEWEB)
Buoninfante, Luca [Universita di Salerno, Dipartimento di Fisica ' ' E.R. Caianiello' ' , Fisciano (Italy); INFN-Sezione di Napoli, Gruppo Collegato di Salerno, Fisciano (Italy); University of Groningen, Van Swinderen Institute, Groningen (Netherlands); Lambiase, Gaetano [Universita di Salerno, Dipartimento di Fisica ' ' E.R. Caianiello' ' , Fisciano (Italy); INFN-Sezione di Napoli, Gruppo Collegato di Salerno, Fisciano (Italy); Mazumdar, Anupam [University of Groningen, Van Swinderen Institute, Groningen (Netherlands); University of Groningen, Kapteyn Astronomical Institute, Groningen (Netherlands)
2018-01-15
In this paper we will study for the first time how the wave-packet of a self-gravitating meso-scopic system spreads in theories beyond Einstein's general relativity. In particular, we will consider a ghost-free infinite derivative gravity, which resolves the 1/r singularity in the potential - such that the gradient of the potential vanishes within the scale of non-locality. We will show that a quantum wave-packet spreads faster for a ghost-free and singularity-free gravity as compared to the Newtonian case, therefore providing us a unique scenario for testing classical and quantum properties of short-distance gravity in a laboratory in the near future. (orig.)
Cosmic Tsunamis in Modified Gravity: Disruption of Screening Mechanisms from Scalar Waves.
Hagala, R; Llinares, C; Mota, D F
2017-03-10
Extending general relativity by adding extra degrees of freedom is a popular approach for explaining the accelerated expansion of the Universe and to build high energy completions of the theory of gravity. The presence of such new degrees of freedom is, however, tightly constrained from several observations and experiments that aim to test general relativity in a wide range of scales. The viability of a given modified theory of gravity, therefore, strongly depends on the existence of a screening mechanism that suppresses the extra degrees of freedom. We perform simulations, and find that waves propagating in the new degrees of freedom can significantly impact the efficiency of some screening mechanisms, thereby threatening the viability of these modified gravity theories. Specifically, we show that the waves produced in the symmetron model can increase the amplitude of the fifth force and the parametrized post Newtonian parameters by several orders of magnitude.
Quantum spreading of a self-gravitating wave-packet in singularity free gravity
Buoninfante, Luca; Lambiase, Gaetano; Mazumdar, Anupam
2018-01-01
In this paper we will study for the first time how the wave-packet of a self-gravitating meso-scopic system spreads in theories beyond Einstein's general relativity. In particular, we will consider a ghost-free infinite derivative gravity, which resolves the 1 / r singularity in the potential - such that the gradient of the potential vanishes within the scale of non-locality. We will show that a quantum wave-packet spreads faster for a ghost-free and singularity-free gravity as compared to the Newtonian case, therefore providing us a unique scenario for testing classical and quantum properties of short-distance gravity in a laboratory in the near future.
Computation of 3D steady Navier-Stokes flow with free-surface gravity waves
Lewis, M.R.; Koren, B.; Raven, H.C.; Armfield, S.; Morgan, P.; Srinivas, K,
2003-01-01
In this paper an iterative method for the computation of stationary gravity-wave solutions is investigated, using a novel formulation of the free-surface (FS) boundary-value problem. This method requires the solution of a sequence of stationary Reynolds-Averaged Navier-Stokes subproblems employing
Computation of 3D steady Navier-Stokes flow with free-surface gravity waves
M.R. Lewis; B. Koren (Barry); H.C. Raven
2003-01-01
textabstractIn this paper an iterative method for the computation of stationary gravity-wave solutions is investigated, using a novel formulation of the free-surface (FS) boundary-value problem. This method requires the solution of a sequence of stationary Reynolds-Averaged Navier-Stokes subproblems
Investigation of Gravity Waves VIA the Rotational Temperature of Hydroxyl Nightglow
National Research Council Canada - National Science Library
Willingham, Erin
2001-01-01
... monochrometer optimized for the visible and near infrared. Quantifying gravity wave activity was the ultimate objective of this experiment. No spectrum of OH nightglow was recorded. The instrumentation was not sensitive enough to pick up the weak signal. This thesis is primarily a characterization of the equipment, its capabilities, and its limitations.
Quantum spreading of a self-gravitating wave-packet in singularity free gravity
Buoninfante, Luca; Lambiase, Gaetano; Mazumdar, Anupam
In this paper we will study for the first time how the wave-packet of a self-gravitating meso-scopic system spreads in theories beyond Einstein’s general relativity. In particular, we will consider a ghost-free infinite derivative gravity, which resolves the 1 / r singularity in the potential – such
A statistical study of variations of internal gravity wave energy characteristics in meteor zone
Gavrilov, N. M.; Kalov, E. D.
1987-01-01
Internal gravity wave (IGW) parameters obtained by the radiometer method have been considered by many other researchers. The results of the processing of regular radiometeor measurements taken during 1979 to 1980 in Obninsk (55.1 deg N, 36.6 deg E) are presented.
International Nuclear Information System (INIS)
Wright, J.W.; Pitteway, M.L.V.
1982-01-01
A sequence of digital ionograms is processed by dopplionogram and gonionogram methods. Together, these disclose a disturbance in the F region which descends in altitude with time. Two wavelike periods of the disturbance are evident. The Doppler and angle-of-arrival behavior are consistent with a semiquantitative model of the plasma perturbations caused by an internal atmospheric gravity wave
Numerical simulation of the nonlinear dynamics of packets of spiral density waves
International Nuclear Information System (INIS)
Korchagin, V.I.
1987-01-01
In a numerical experiment, the behavior of nonlinear packets of spiral density waves in a gas disk has been investigated for different initial wave amplitudes. If the amplitude of the density perturbations is small (<5%), the wave packet is drawn toward the center or toward the periphery of the disk in accordance with the linear theory. The behavior of linear packets of waves with wavelength comparable to the disk radius (R/sub d//lambda = 4) exhibits good agreement with the conclusions of the linear theory of tightly wound spiral waves. The dynamics of wave packets with initial density amplitudes 16, 30, 50% demonstrates the nonlinear nature of the behavior. THe behavior is governed by whether or not the nonlinear effects of higher than third order in the wave amplitude play a part. If the wave packet dynamics is determined by the cubic nonlinearity, the results of the numerical experiment are in qualitative and quantitative agreement with the nonlinear theory of short waves, although the characteristic scale of the packet and the wavelength are of the order of the disk radius. In the cases when the nonlinear effects of higher orders in the amplitude play an important part, the behavior of a packet does not differ qualitatively from the behavior predicted by the theory of cubic nonlinearity, but the nonlinear spreading of the packet takes place more rapidly
Theory for stationary nonlinear wave propagation in complex magnetic geometry
International Nuclear Information System (INIS)
Watanabe, T.; Hojo, H.; Nishikawa, Kyoji.
1977-08-01
We present our recent efforts to derive a systematic calculation scheme for nonlinear wave propagation in the self-consistent plasma profile in complex magnetic-field geometry. Basic assumptions and/or approximations are i) use of the collisionless two-fluid model with an equation of state; ii) restriction to a steady state propagation and iii) existence of modified magnetic surface, modification due to Coriolis' force. We discuss four situations: i) weak-field propagation without static flow, ii) arbitrary field strength with flow in axisymmetric system, iii) weak field limit of case ii) and iv) arbitrary field strength in nonaxisymmetric torus. Except for case iii), we derive a simple variation principle, similar to that of Seligar and Whitham, by introducing appropriate coordinates. In cases i) and iii), we derive explicit results for quasilinear profile modification. (auth.)
Lipschitz Metrics for a Class of Nonlinear Wave Equations
Bressan, Alberto; Chen, Geng
2017-12-01
The nonlinear wave equation {u_{tt}-c(u)(c(u)u_x)_x=0} determines a flow of conservative solutions taking values in the space {H^1(R)}. However, this flow is not continuous with respect to the natural H 1 distance. The aim of this paper is to construct a new metric which renders the flow uniformly Lipschitz continuous on bounded subsets of {H^1(R)}. For this purpose, H 1 is given the structure of a Finsler manifold, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, one can carefully estimate how the weighted length grows in time. By the generic regularity result proved in [7], these piecewise regular paths are dense and can be used to construct a geodesic distance with the desired Lipschitz property.
International Nuclear Information System (INIS)
Matsuda, Y.; Crawford, F.W.
1975-01-01
An economical low-noise plasma simulation model originated by Denavit is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation. These tests serve to establish the low-noise features of the model, and to verify the theoretical linear dispersion relation at wave energy levels as low as 10 -6 of the plasma thermal energy: Better quantitative results are obtained, for comparable computing time, than can be obtained by conventional particle simulation models, or direct solution of the Vlasov equation. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories
Gravity wave generation from jets and fronts: idealized and real-case simulations
Plougonven, Riwal; Arsac, Antonin; Hertzog, Albert; Guez, Lionel; Vial, François
2010-05-01
The generation of gravity waves from jets and fronts remains an outstanding issue in the dynamics of the atmosphere. It is important to explain and quantify this emission because of the several impacts of these waves, in particular the induced momentum fluxes towards the middle atmosphere, and their contribution to turbulence and mixing, e.g. in the region of the tropopause. Yet, the mechanisms at the origin of these waves have been difficult to identify, the fundamental reason for this being the separation between the time scales of balanced motions and gravity waves. Recent simulations of idealized baroclinic life cycles and of dipoles have provided insights into the mechanisms determining the characteristics and the amplitude of gravity waves emitted by jets. It has been shown in particular that the environmental strain and shear play a crucial role in determining the characteristics and location of the emitted waves, emphasizing jet exit regions for the appearance of coherent low-frequency waves. It has also been shown how advection of relatively small-scales allow to overcome the separation of time scales alluded to above. Recent results, remaining open questions and ongoing work on these idealized simulations will be briefly summarized. Nevertheless, unavoidable shortcomings of such idealized simulations include the sensitivity of the emitted waves to model setup (resolution, diffusion, parameterizations) and uncertainty regarding the realism of this aspect of the simulations. Hence, it is necessary to compare simulations with observations in order to assess their relevance. Such comparison has been undertaken using the dataset from the Vorcore campaign (Sept. 2005 - Feb. 2006, Hertzog, J. Atmos. Ocean. Techno. 2007) during which 27 superpressure balloons drifted as quasi-Lagrangian tracers in the lower stratosphere above Antarctica and the Southern Ocean. High-resolution simulations (dx = 20 km) have been carried out using the Weather Research and Forecast
Nonlinear mechanisms for drift wave saturation and induced particle transport
International Nuclear Information System (INIS)
Dimits, A.M.; Lee, W.W.
1989-12-01
A detailed theoretical study of the nonlinear dynamics of gyrokinetic particle simulations of electrostatic collisionless and weakly collisional drift waves is presented. In previous studies it was shown that, in the nonlinearly saturated phase of the evolution, the saturation levels and especially the particle fluxes have an unexpected dependence on collisionality. In this paper, the explanations for these collisionality dependences are found to be as follows: The saturation level is determined by a balance between the electron and ion fluxes. The ion flux is small for levels of the potential below an E x B-trapping threshold and increases sharply once this threshold is crossed. Due to the presence of resonant electrons, the electron flux has a much smoother dependence on the potential. In the 2-1/2-dimensional (''pseudo-3D'') geometry, the electrons are accelerated away from the resonance as they diffuse spatially, resulting in an inhibition of their diffusion. Collisions and three-dimensional effects can repopulate the resonance thereby increasing the value of the particle flux. 30 refs., 32 figs., 2 tabs
Robust Numerical Methods for Nonlinear Wave-Structure Interaction in a Moving Frame of Reference
DEFF Research Database (Denmark)
Kontos, Stavros; Lindberg, Ole
This project is focused on improving the state of the art for predicting the interaction between nonlinear ocean waves and marine structures. To achieve this goal, a flexible order finite difference potential flow solver has been extended to calculate for fully nonlinear wave-structure interaction...
Quantum X waves with orbital angular momentum in nonlinear dispersive media
Ornigotti, Marco; Conti, Claudio; Szameit, Alexander
2018-06-01
We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.
Validation of the CUTLASS HF radar gravity wave observing capability using EISCAT CP-1 data
Directory of Open Access Journals (Sweden)
N. F. Arnold
1998-10-01
Full Text Available Quasi-periodic fluctuations in the returned ground-scatter power from the SuperDARN HF radars have been linked to the passage of medium-scale gravity waves. We have applied a technique that extracts the first radar range returns from the F-region to study the spatial extent and characteristics of these waves in the CUTLASS field-of-view. Some ray tracing was carried out to test the applicability of this method. The EISCAT radar facility at Tromsø is well within the CUTLASS field-of-view for these waves and provides a unique opportunity to assess independently the ability of the HF radars to derive gravity wave information. Results from 1st March, 1995, where the EISCAT UHF radar was operating in its CP-1 mode, demonstrate that the radars were in good agreement, especially if one selects the electron density variations measured by EISCAT at around 235 km. CUTLASS and EISCAT gravity wave observations complement each other; the former extends the spatial field of view considerably, whilst the latter provides detailed vertical information about a range of ionospheric parameters.Key words. Ionosphere (ionosphere – atmosphere interactions · Meteorology and atmospheric dynamics (thermospheric dynamics · Radio science (ionospheric propagations
Validation of the CUTLASS HF radar gravity wave observing capability using EISCAT CP-1 data
Directory of Open Access Journals (Sweden)
N. F. Arnold
Full Text Available Quasi-periodic fluctuations in the returned ground-scatter power from the SuperDARN HF radars have been linked to the passage of medium-scale gravity waves. We have applied a technique that extracts the first radar range returns from the F-region to study the spatial extent and characteristics of these waves in the CUTLASS field-of-view. Some ray tracing was carried out to test the applicability of this method. The EISCAT radar facility at Tromsø is well within the CUTLASS field-of-view for these waves and provides a unique opportunity to assess independently the ability of the HF radars to derive gravity wave information. Results from 1st March, 1995, where the EISCAT UHF radar was operating in its CP-1 mode, demonstrate that the radars were in good agreement, especially if one selects the electron density variations measured by EISCAT at around 235 km. CUTLASS and EISCAT gravity wave observations complement each other; the former extends the spatial field of view considerably, whilst the latter provides detailed vertical information about a range of ionospheric parameters.
Key words. Ionosphere (ionosphere – atmosphere interactions · Meteorology and atmospheric dynamics (thermospheric dynamics · Radio science (ionospheric propagations
Gravity induced corrections to quantum mechanical wave functions
International Nuclear Information System (INIS)
Singh, T.P.
1990-03-01
We perform a semiclassical expansion in the Wheeler-DeWitt equation, in powers of the gravitational constant. We then show that quantum gravitational fluctuations can provide a correction to the wave-functions which are solutions of the Schroedinger equation for matter. This also implies a correction to the expectation values of quantum mechanical observables. (author). 6 refs
An efficient flexible-order model for 3D nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bingham, Harry B.; Lindberg, Ole
2009-01-01
The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal......, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental...
Initial boundary value problems of nonlinear wave equations in an exterior domain
International Nuclear Information System (INIS)
Chen Yunmei.
1987-06-01
In this paper, we investigate the existence and uniqueness of the global solutions to the initial boundary value problems of nonlinear wave equations in an exterior domain. When the space dimension n >= 3, the unique global solution of the above problem is obtained for small initial data, even if the nonlinear term is fully nonlinear and contains the unknown function itself. (author). 10 refs
Heavens, N. G.
2017-12-01
It has been recognized for over two decades that the mesoscale statistical variance observed by Earth-observing satellites at temperature-sensitive frequencies above the instrumental noise floor is a measure of gravity wave activity. These types of observation have been made by a variety of satellite instruments have been an important validation tool for gravity wave parameterizations in global and mesoscale models. At Mars, the importance of topographic and non-topographic sources of gravity waves for the general circulation is now widely recognized and the target of recent modeling efforts. However, despite several ingenious studies, gravity wave activity near hypothetical lower atmospheric sources has been poorly and unsystematically characterized, partly because of the difficulty of separating the gravity wave activity from baroclinic wave activity and the thermal tides. Here will be presented a preliminary analysis of calibrated radiance variance at 15.4 microns (635-665 cm-1) from nadir, off-nadir, and limb observations by the Mars Climate Sounder on board Mars Reconnaissance Orbiter. The overarching methodology follows Wu and Waters (1996, 1997). Nadir, off-nadir, and lowest detector limb observations should sample variability with vertical weighting functions centered high in the lower atmosphere (20-30 km altitude) and full width half maximum (FWHM) 20 km but be sensitive to gravity waves with different horizontal wavelengths and slightly different vertical wavelengths. This work is supported by NASA's Mars Data Analysis Program (NNX14AM32G). References Wu, D.L. and J.W. Waters, 1996, Satellite observations of atmospheric variances: A possible indication of gravity waves, GRL, 23, 3631-3634. Wu D.L. and J.W. Waters, 1997, Observations of Gravity Waves with the UARS Microwave Limb Sounder. In: Hamilton K. (eds) Gravity Wave Processes. NATO ASI Series (Series I: Environmental Change), vol 50. Springer, Berlin, Heidelberg.
Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei
2016-07-01
Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.
Excitation of nonlinear wave patterns in flowing complex plasmas
Jaiswal, S.; Bandyopadhyay, P.; Sen, A.
2018-01-01
We describe experimental observations of nonlinear wave structures excited by a supersonic mass flow of dust particles over an electrostatic potential hill in a dusty plasma medium. The experiments have been carried out in a Π- shaped experimental (DPEx) device in which micron sized Kaolin particles are embedded in a DC glow discharge Argon plasma. An equilibrium dust cloud is formed by maintaining the pumping speed and gas flow rate and the dust flow is induced either by suddenly reducing the height of a potential hill or by suddenly reducing the gas flow rate. For a supersonic flow of the dust fluid precursor solitons are seen to propagate in the upstream direction while wake structures propagate in the downstream direction. For flow speeds with a Mach number greater than 2 the dust particles flowing over the potential hill give rise to dispersive dust acoustic shock waves. The experimental results compare favorably with model theories based on forced K-dV and K-dV Burger's equations.
Gamow, George
2003-01-01
A distinguished physicist and teacher, George Gamow also possessed a special gift for making the intricacies of science accessible to a wide audience. In Gravity, he takes an enlightening look at three of the towering figures of science who unlocked many of the mysteries behind the laws of physics: Galileo, the first to take a close look at the process of free and restricted fall; Newton, originator of the concept of gravity as a universal force; and Einstein, who proposed that gravity is no more than the curvature of the four-dimensional space-time continuum.Graced with the author's own draw
Statistical comparisons of gravity wave features derived from OH airglow and SABER data
Gelinas, L. J.; Hecht, J. H.; Walterscheid, R. L.
2017-12-01
The Aerospace Corporation's near-IR camera (ANI), deployed at Andes Lidar Observatory (ALO), Cerro Pachon Chile (30S,70W) since 2010, images the bright OH Meinel (4,2) airglow band. The imager provides detailed observations of gravity waves and instability dynamics, as described by Hecht et al. (2014). The camera employs a wide-angle lens that views a 73 by 73 degree region of the sky, approximately 120 km x 120 km at 85 km altitude. Image cadence of 30s allows for detailed spectral analysis of the horizontal components of wave features, including the evolution and decay of instability features. The SABER instrument on NASA's TIMED spacecraft provides remote soundings of kinetic temperature profiles from the lower stratosphere to the lower thermosphere. Horizontal and vertical filtering techniques allow SABER temperatures to be analyzed for gravity wave variances [Walterscheid and Christensen, 2016]. Here we compare the statistical characteristics of horizontal wave spectra, derived from airglow imagery, with vertical wave variances derived from SABER temperature profiles. The analysis is performed for a period of strong mountain wave activity over the Andes spanning the period between June and September 2012. Hecht, J. H., et al. (2014), The life cycle of instability features measured from the Andes Lidar Observatory over Cerro Pachon on March 24, 2012, J. Geophys. Res. Atmos., 119, 8872-8898, doi:10.1002/2014JD021726. Walterscheid, R. L., and A. B. Christensen (2016), Low-latitude gravity wave variances in the mesosphere and lower thermosphere derived from SABER temperature observation and compared with model simulation of waves generated by deep tropical convection, J. Geophys. Res. Atmos., 121, 11,900-11,912, doi:10.1002/2016JD024843.
Directory of Open Access Journals (Sweden)
E. A. K. Ford
2008-02-01
Full Text Available Data from the Fabry-Perot Interferometers at KEOPS (Sweden, Sodankylä (Finland, and Svalbard (Norway, have been analysed for gravity wave activity on all the clear nights from 2000 to 2006. A total of 249 nights were available from KEOPS, 133 from Sodankylä and 185 from the Svalbard FPI. A Lomb-Scargle analysis was performed on each of these nights to identify the periods of any wave activity during the night. Comparisons between many nights of data allow the general characteristics of the waves that are present in the high latitude upper thermosphere to be determined. Comparisons were made between the different parameters: the atomic oxygen intensities, the thermospheric winds and temperatures, and for each parameter the distribution of frequencies of the waves was determined. No dependence on the number of waves on geomagnetic activity levels, or position in the solar cycle, was found. All the FPIs have had different detectors at various times, producing different time resolutions of the data, so comparisons between the different years, and between data from different sites, showed how the time resolution determines which waves are observed. In addition to the cutoff due to the Nyquist frequency, poor resolution observations significantly reduce the number of short-period waves (<1 h period that may be detected with confidence. The length of the dataset, which is usually determined by the length of the night, was the main factor influencing the number of long period waves (>5 h detected. Comparisons between the number of gravity waves detected at KEOPS and Sodankylä over all the seasons showed a similar proportion of waves to the number of nights used for both sites, as expected since the two sites are at similar latitudes and therefore locations with respect to the auroral oval, confirming this as a likely source region. Svalbard showed fewer waves with short periods than KEOPS data for a season when both had the same time resolution data
Propagation and Breaking at High Altitudes of Gravity Waves Excited by Tropospheric Forcing
Prusa, Joseph M.; Smolarkiewicz, Piotr K.; Garcia, Rolando R.
1996-01-01
An anelastic approximation is used with a time-variable coordinate transformation to formulate a two-dimensional numerical model that describes the evolution of gravity waves. The model is solved using a semi-Lagrangian method with monotone (nonoscillatory) interpolation of all advected fields. The time-variable transformation is used to generate disturbances at the lower boundary that approximate the effect of a traveling line of thunderstorms (a squall line) or of flow over a broad topographic obstacle. The vertical propagation and breaking of the gravity wave field (under conditions typical of summer solstice) is illustrated for each of these cases. It is shown that the wave field at high altitudes is dominated by a single horizontal wavelength; which is not always related simply to the horizontal dimension of the source. The morphology of wave breaking depends on the horizontal wavelength; for sufficiently short waves, breaking involves roughly one half of the wavelength. In common with other studies, it is found that the breaking waves undergo "self-acceleration," such that the zonal-mean intrinsic frequency remains approximately constant in spite of large changes in the background wind. It is also shown that many of the features obtained in the calculations can be understood in terms of linear wave theory. In particular, linear theory provides insights into the wavelength of the waves that break at high altitudes, the onset and evolution of breaking. the horizontal extent of the breaking region and its position relative to the forcing, and the minimum and maximum altitudes where breaking occurs. Wave breaking ceases at the altitude where the background dissipation rate (which in our model is a proxy for molecular diffusion) becomes greater than the rate of dissipation due to wave breaking, This altitude, in effect, the model turbopause, is shown to depend on a relatively small number of parameters that characterize the waves and the background state.
Controllable behaviours of rogue wave triplets in the nonautonomous nonlinear and dispersive system
International Nuclear Information System (INIS)
Dai Chaoqing; Tian Qing; Zhu Shiqun
2012-01-01
A similarity transformation connecting the variable coefficient nonlinear Schrödinger equation with the standard nonlinear Schrödinger equation is constructed. The self-similar rogue wave triplet solutions (rational solutions) are analytically obtained for the nonautonomous nonlinear and dispersive system. The controllable behaviours of rogue wave triplets in two typical soliton management systems are discussed. In the exponential dispersion decreasing fibre, three kinds of rogue wave triplets with controllable behaviours are analysed. In the periodic distributed system, the rogue wave triplets recur periodically in the form of a cluster. (paper)
Energy Technology Data Exchange (ETDEWEB)
Ruderman, M S
1988-08-01
Nonlinear Alfven surface wave propagation at a magnetic interface in a compressible fluid is considered. It is supposed that the magnetic field directions at both sides of the interface and the direction of wave propagation coincide. The equation governing time-evolution of nonlinear small-amplitude waves is derived by the method of multiscale expansions. This equation is similar to the equation for nonlinear Alfven surface waves in an incompressible fluid derived previously. The numerical solution of the equation shows that a sinusoidal disturbance overturns, i.e. infinite gradients arise.
Mesoscale variations in acoustic signals induced by atmospheric gravity waves.
Chunchuzov, Igor; Kulichkov, Sergey; Perepelkin, Vitaly; Ziemann, Astrid; Arnold, Klaus; Kniffka, Anke
2009-02-01
The results of acoustic tomographic monitoring of the coherent structures in the lower atmosphere and the effects of these structures on acoustic signal parameters are analyzed in the present study. From the measurements of acoustic travel time fluctuations (periods 1 min-1 h) with distant receivers, the temporal fluctuations of the effective sound speed and wind speed are retrieved along different ray paths connecting an acoustic pulse source and several receivers. By using a coherence analysis of the fluctuations near spatially distanced ray turning points, the internal wave-associated fluctuations are filtered and their spatial characteristics (coherences, horizontal phase velocities, and spatial scales) are estimated. The capability of acoustic tomography in estimating wind shear near ground is shown. A possible mechanism describing the temporal modulation of the near-ground wind field by ducted internal waves in the troposphere is proposed.
Global Gravity Wave Variances from Aura MLS: Characteristics and Interpretation
2008-12-01
slight longitudinal variations, with secondary high- latitude peaks occurring over Greenland and Europe . As the QBO changes to the westerly phase, the...equatorial GW temperature variances from suborbital data (e.g., Eck- ermann et al. 1995). The extratropical wave variances are generally larger in the...emanating from tropopause altitudes, presumably radiated from tropospheric jet stream in- stabilities associated with baroclinic storm systems that
Propagation of acoustic-gravity waves in arctic zones with elastic ice-sheets
Kadri, Usama; Abdolali, Ali; Kirby, James T.
2017-04-01
We present an analytical solution of the boundary value problem of propagating acoustic-gravity waves generated in the ocean by earthquakes or ice-quakes in arctic zones. At the surface, we assume elastic ice-sheets of a variable thickness, and show that the propagating acoustic-gravity modes have different mode shape than originally derived by Ref. [1] for a rigid ice-sheet settings. Computationally, we couple the ice-sheet problem with the free surface model by Ref. [2] representing shrinking ice blocks in realistic sea state, where the randomly oriented ice-sheets cause inter modal transition at the edges and multidirectional reflections. We then derive a depth-integrated equation valid for spatially slowly varying thickness of ice-sheet and water depth. Surprisingly, and unlike the free-surface setting, here it is found that the higher acoustic-gravity modes exhibit a larger contribution. These modes travel at the speed of sound in water carrying information on their source, e.g. ice-sheet motion or submarine earthquake, providing various implications for ocean monitoring and detection of quakes. In addition, we found that the propagating acoustic-gravity modes can result in orbital displacements of fluid parcels sufficiently high that may contribute to deep ocean currents and circulation, as postulated by Refs. [1, 3]. References [1] U. Kadri, 2016. Generation of Hydroacoustic Waves by an Oscillating Ice Block in Arctic Zones. Advances in Acoustics and Vibration, 2016, Article ID 8076108, 7 pages http://dx.doi.org/10.1155/2016/8076108 [2] A. Abdolali, J. T. Kirby and G. Bellotti, 2015, Depth-integrated equation for hydro-acoustic waves with bottom damping, J. Fluid Mech., 766, R1 doi:10.1017/jfm.2015.37 [3] U. Kadri, 2014. Deep ocean water transportation by acoustic?gravity waves. J. Geophys. Res. Oceans, 119, doi:10.1002/ 2014JC010234
A statistical study of gravity waves from radiosonde observations at Wuhan (30° N, 114° E China
Directory of Open Access Journals (Sweden)
S. D. Zhang
2005-03-01
Full Text Available Several works concerning the dynamical and thermal structures and inertial gravity wave activities in the troposphere and lower stratosphere (TLS from the radiosonde observation have been reported before, but these works were concentrated on either equatorial or polar regions. In this paper, background atmosphere and gravity wave activities in the TLS over Wuhan (30° N, 114° E (a medium latitudinal region were statistically studied by using the data from radiosonde observations on a twice daily basis at 08:00 and 20:00 LT in the period between 2000 and 2002. The monthly-averaged temperature and horizontal winds exhibit the essential dynamic and thermal structures of the background atmosphere. For avoiding the extreme values of background winds and temperature in the height range of 11-18km, we studied gravity waves, respectively, in two separate height regions, one is from ground surface to 10km (lower part, and the other is within 18-25km (upper part. In total, 791 and 1165 quasi-monochromatic inertial gravity waves were extracted from our data set for the lower and upper parts, respectively. The gravity wave parameters (intrinsic frequencies, amplitudes, wavelengths, intrinsic phase velocities and wave energies are calculated and statistically studied. The statistical results revealed that in the lower part, there were 49.4% of gravity waves propagating upward, and the percentage was 76.4% in the upper part. Moreover, the average wave amplitudes and energies are less than those at the lower latitudinal regions, which indicates that the gravity wave parameters have a latitudinal dependence. The correlated temporal evolution of the monthly-averaged wave energies in the lower and upper parts and a subsequent quantitative analysis strongly suggested that at the observation site, dynamical instability (strong wind shear induced by the tropospheric jet is the main excitation source of inertial gravity waves in the TLS.
Nonlinear propagation of intense electromagnetic waves in weakly-ionized plasmas
International Nuclear Information System (INIS)
Shukla, P.K.
1993-01-01
The nonlinear propagation of intense electromagnetic waves in weakly-ionized plasmas is considered. Stimulated scattering mechanisms involving electromagnetic and acoustic waves in an unmagnetized plasma are investigated. The growth rate and threshold for three-wave decay interactions as well as modulational and filamentation instabilities are presented. Furthermore, the electromagnetic wave modulation theory is generalized for weakly ionized collisional magnetoplasmas. Here, the radiation envelope is generally governed by a nonlinear Schroedinger equation. Accounting for the dependence of the attachment frequency on the radiation intensity, ponderomotive force, as well as the differential Joule heating nonlinearity, the authors derive the equations for the nonthermal electron density and temperature perturbations. The various nonlinear terms in the electron motion are compared. The problems of self-focusing and wave localization are discussed. The relevance of the investigation to ionospheric modification by powerful electromagnetic waves is pointed out
Tsuda, Toshitaka
2014-01-01
The wind velocity and temperature profiles observed in the middle atmosphere (altitude: 10-100 km) show perturbations resulting from superposition of various atmospheric waves, including atmospheric gravity waves. Atmospheric gravity waves are known to play an important role in determining the general circulation in the middle atmosphere by dynamical stresses caused by gravity wave breaking. In this paper, we summarize the characteristics of atmospheric gravity waves observed using the middle and upper atmosphere (MU) radar in Japan, as well as novel satellite data obtained from global positioning system radio occultation (GPS RO) measurements. In particular, we focus on the behavior of gravity waves in the mesosphere (50-90 km), where considerable gravity wave attenuation occurs. We also report on the global distribution of gravity wave activity in the stratosphere (10-50 km), highlighting various excitation mechanisms such as orographic effects, convection in the tropics, meteorological disturbances, the subtropical jet and the polar night jet.
Effect of small floating disks on the propagation of gravity waves
Energy Technology Data Exchange (ETDEWEB)
Santi, F De; Olla, P, E-mail: olla@dsf.unica.it [ISAC-CNR, Sez. Cagliari, I-09042 Monserrato (Italy)
2017-04-15
A dispersion relation for gravity waves in water covered by disk-like impurities embedded in a viscous matrix is derived. The macroscopic equations are obtained by ensemble-averaging the fluid equations at the disk scale in the asymptotic limit of long waves and low disk surface fraction. Various regimes are identified depending on the disk radii and the thickness and viscosity of the top layer. Semi-quantitative analysis in the close-packing regime suggests dramatic modification of the dynamics, with orders of magnitude increase in wave damping and wave dispersion. A simplified model working in this regime is proposed. Possible applications to wave propagation in an ice-covered ocean are discussed and comparison with field data is provided. (paper)
Observation of mesospheric gravity waves at Comandante Ferraz Antarctica Station (62° S
Directory of Open Access Journals (Sweden)
P. B. Souza
2009-06-01
Full Text Available An airglow all-sky imager was operated at Comandante Ferraz Antarctica Station (62.1° S, 58.4° W, between April and October of 2007. Mesospheric gravity waves were observed using the OH airglow layer during 43 nights with good weather conditions. The waves presented horizontal wavelengths between 10 and 60 km and observed periods mainly distributed between 5 and 20 min. The observed phase speeds range between 5 m/s and 115 m/s; the majority of the wave velocities were between 10 and 60 m/s. The waves showed a preferential propagation direction towards the southwest in winter (May to July, while during spring (August to October there was an anisotropy with a preferential propagation direction towards the northwest. Unusual mesospheric fronts were also observed. The most probable wave source could be associated to orographic forcing, cold fronts or strong cyclonic activity in the Antarctica Peninsula.