Analysis of Laminar Boundary Layer Equations
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R. Yesman
2012-01-01
Full Text Available The paper proposes methodology for analysis and calculation of laminar fluid flow processes in a boundary layer.The presented dependences can be used for practical calculations while power carriers of various application are moving in the channels of heat and power devices.
Loitsianskii. L. G.
1956-01-01
The fundamental, practically the most important branch of the modern mechanics of a viscous fluid or a gas, is that branch which concerns itself with the study of the boundary layer. The presence of a boundary layer accounts for the origin of the resistance and lift force, the breakdown of the smooth flow about bodies, and other phenomena that are associated with the motion of a body in a real fluid. The concept of boundary layer was clearly formulated by the founder of aerodynamics, N. E. Joukowsky, in his well-known work "On the Form of Ships" published as early as 1890. In his book "Theoretical Foundations of Air Navigation," Joukowsky gave an account of the most important properties of the boundary layer and pointed out the part played by it in the production of the resistance of bodies to motion. The fundamental differential equations of the motion of a fluid in a laminar boundary layer were given by Prandtl in 1904; the first solutions of these equations date from 1907 to 1910. As regards the turbulent boundary layer, there does not exist even to this day any rigorous formulation of this problem because there is no closed system of equations for the turbulent motion of a fluid. Soviet scientists have done much toward developing a general theory of the boundary layer, and in that branch of the theory which is of greatest practical importance at the present time, namely the study of the boundary layer at large velocities of the body in a compressed gas, the efforts of the scientists of our country have borne fruit in the creation of a new theory which leaves far behind all that has been done previously in this direction. We shall herein enumerate the most important results by Soviet scientists in the development of the theory of the boundary layer.
Ardema, M. D.; Yang, L.
1985-01-01
A method of solving the boundary-layer equations that arise in singular-perturbation analysis of flightpath optimization problems is presented. The method is based on Picard iterations of the integrated form of the equations and does not require iteration to find unknown boundary conditions. As an example, the method is used to develop a solution algorithm for the zero-order boundary-layer equations of the aircraft minimum-time-to-climb problem.
Tetervin, Neal; Lin, Chia Chiao
1951-01-01
A general integral form of the boundary-layer equation, valid for either laminar or turbulent incompressible boundary-layer flow, is derived. By using the experimental finding that all velocity profiles of the turbulent boundary layer form essentially a single-parameter family, the general equation is changed to an equation for the space rate of change of the velocity-profile shape parameter. The lack of precise knowledge concerning the surface shear and the distribution of the shearing stress across turbulent boundary layers prevented the attainment of a reliable method for calculating the behavior of turbulent boundary layers.
Boundary Layer Equations and Lie Group Analysis of a Sisko Fluid
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Gözde Sarı
2012-01-01
Full Text Available Boundary layer equations are derived for the Sisko fluid. Using Lie group theory, a symmetry analysis of the equations is performed. A partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved. Effects of non-Newtonian parameters on the solutions are discussed.
On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation
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Mohammed Guedda
2007-05-01
Full Text Available This paper concerns the singular solutions of the equation $$ f''' +kappa ff''-eta {f'}^2 = 0, $$ where $eta < 0$ and $kappa = 0$ or 1. This equation arises when modelling heat transfer past a vertical flat plate embedded in a saturated porous medium with an applied magnetic field. After suitable normalization, $f'$ represents the velocity parallel to the surface or the non-dimensional fluid temperature. Our interest is in solutions which develop a singularity at some point (the blow-up point. In particular, we shall examine in detail the behavior of $f$ near the blow-up point.
Non-perturbative solution of free-convective boundary-layer equation by Adomian decomposition method
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Kechil, Seripah Awang [Department of Mathematics, Universiti Teknologi MARA, 40450 Shah Alam Selangor (Malaysia); Hashim, Ishak [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)]. E-mail: ishak_h@ukm.my
2007-03-19
A free-convective boundary layer flow modeled by a system of nonlinear ordinary differential equations is considered. The system is solved using the Adomian decomposition method (ADM) which yields an analytic solution in the form of a rapidly convergent infinite series with easily computable terms. The analytical solutions and the pertinent features of the illustrations show the efficiency of the method.
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Boričić Zoran
2009-01-01
Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.
Roman-Miller, Lance Arthur
2011-01-01
This paper provides the first known exact general solutions of Painlev\\'e's sixth equation (PVI) and the exact general solutions of the Navier Stokes equations and Prandtl's boundary layer equations.
Stability analysis of Boundary Layer in Poiseuille Flow Through A Modified Orr-Sommerfeld Equation
Monwanou, A V; Orou, J B Chabi; 10.5539/apr.v4n4p138
2013-01-01
For applications regarding transition prediction, wing design and control of boundary layers, the fundamental understanding of disturbance growth in the flat-plate boundary layer is an important issue. In the present work we investigate the stability of boundary layer in Poiseuille flow. We normalize pressure and time by inertial and viscous effects. The disturbances are taken to be periodic in the spanwise direction and time. We present a set of linear governing equations for the parabolic evolution of wavelike disturbances. Then, we derive modified Orr-Sommerfeld equations that can be applied in the layer. Contrary to what one might think, we find that Squire's theorem is not applicable for the boundary layer. We find also that normalization by inertial or viscous effects leads to the same order of stability or instability. For the 2D disturbances flow ($\\theta=0$), we found the same critical Reynolds number for our two normalizations. This value coincides with the one we know for neutral stability of the k...
Transient Growth Analysis of Compressible Boundary Layers with Parabolized Stability Equations
Paredes, Pedro; Choudhari, Meelan M.; Li, Fei; Chang, Chau-Lyan
2016-01-01
The linear form of parabolized linear stability equations (PSE) is used in a variational approach to extend the previous body of results for the optimal, non-modal disturbance growth in boundary layer flows. This methodology includes the non-parallel effects associated with the spatial development of boundary layer flows. As noted in literature, the optimal initial disturbances correspond to steady counter-rotating stream-wise vortices, which subsequently lead to the formation of stream-wise-elongated structures, i.e., streaks, via a lift-up effect. The parameter space for optimal growth is extended to the hypersonic Mach number regime without any high enthalpy effects, and the effect of wall cooling is studied with particular emphasis on the role of the initial disturbance location and the value of the span-wise wavenumber that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary layer equations, mean flow solutions based on the full Navier-Stokes (NS) equations are used in select cases to help account for the viscous-inviscid interaction near the leading edge of the plate and also for the weak shock wave emanating from that region. These differences in the base flow lead to an increasing reduction with Mach number in the magnitude of optimal growth relative to the predictions based on self-similar mean-flow approximation. Finally, the maximum optimal energy gain for the favorable pressure gradient boundary layer near a planar stagnation point is found to be substantially weaker than that in a zero pressure gradient Blasius boundary layer.
About potential of double layer and boundary value problems for Laplace equation
International Nuclear Information System (INIS)
An integral operator raisen by a kernel of the double layer's potential is investigated. The kernel is defined on S (S - two-digit variety of C2 class presented by a boundary of the finite domain in R3). The operator is considered on C(S). Following results are received: the operator's spectrum belongs to [-1,1]; it's eigenvalues and eigenfunctions may be found by Kellog's method; knowledge of the operator's spectrum is enough to construct it's resolvent. These properties permit to point out the determined interation processes, solving boundary value problems for Laplace equation. One of such processes - solving of Roben problem - is generalized on electrostatic problems. 6 refs
On energy boundary layer equations in power law non-Newtonian fluids
Institute of Scientific and Technical Information of China (English)
郑连存; 张欣欣
2008-01-01
The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.
International Nuclear Information System (INIS)
A novel methodology is presented for the numerical treatment of multi-dimensional pdf (probability density function) models used to study particle transport in turbulent boundary layers. A system of coupled Fokker–Planck type equations is constructed to describe the transport of phase-space conditioned moments of particle and fluid velocities, both streamwise and wall-normal. This system, unlike conventional moment-based transport equations, allows for an exact treatment of particle deposition at the flow boundary and provides an efficient way to handle the 5-dimensional phase-space domain. Moreover, the equations in the system are linear and can be solved in a sequential fashion; there is no closure problem to address. A hybrid Hermite-Discontinuous Galerkin scheme is developed to treat the system. The choice of Hermite basis functions in combination with an iterative scaling approach permits the efficient computation of solutions to high accuracy. Results demonstrate the effectiveness of the methodology in resolving the extreme gradients characteristic of distributions near an absorbing boundary.
Analysis of turbulent boundary layers
Cebeci, Tuncer
2012-01-01
Analysis of Turbulent Boundary Layers focuses on turbulent flows meeting the requirements for the boundary-layer or thin-shear-layer approximations. Its approach is devising relatively fundamental, and often subtle, empirical engineering correlations, which are then introduced into various forms of describing equations for final solution. After introducing the topic on turbulence, the book examines the conservation equations for compressible turbulent flows, boundary-layer equations, and general behavior of turbulent boundary layers. The latter chapters describe the CS method for calculati
Institute of Scientific and Technical Information of China (English)
Muhammet Y(u)r(u)soy
2004-01-01
Two dimensional equations of steady motion for third order fluids are expressed in a special coordinate system generated by the potential flow corresponding to an inviscid fluid. For the inviscid flow around an arbitrary object, the streamlines are the phicoordinates and velocity potential lines are psi-coordinates which form an orthogonal curvilinear set of coordinates. The outcome, boundary layer equations, is then shown to be independent of the body shape immersed into the flow. As a first approximation, assumption that second grade terms are negligible compared to viscous and third grade terms. Second grade terms spoil scaling transformation which is only transformation leading to similarity solutions for third grade fluid. By using Lie group methods, infinitesimal generators of boundary layer equations are calculated. The equations are transformed into an ordinary differential system. Numerical solutions of outcoming nonlinear differential equations are found by using combination of a Runge-Kutta algorithm and shooting technique.
Solutions of atmospheric dispersion equation and parameters in the boundary layer
International Nuclear Information System (INIS)
There is an increasing interest in studies of atmospheric aerosols in the context of their impact and atmospheric chemistry associated. In this work attention was paid to mathematical relationship to evaluate air dispersion concentrations under different conditions.The material in the present thesis is organized in three chapters in the following way:In chapter (1), we describe as. In section 1-1, General introduction. In section 1-2. Study atmosphere boundary layer, in section 1-3.Study atmospheric diffusion, In section 1-4, defined the concentration, In section 1-5, Defined the dispersion and diffusion .In section 6.Characterization of Turbulent Diffusion.In chapter (2), we derive a simple solution of the steady state, dimensional diffusion equation that describes advection in the direction of the wind and diffusion in the vertical direction using separation method. The separation method has been found to give solution, which agrees well with observed concentration of sulfur dioxide. In section 1, we study the mathematically analogous problem of dispersal pollution over area sources. In section 2-2, we give a description of the analytical method, In section 2-3, we give a description of the numerical method while in section 2-4 and 2-5, we give an application of the method to the calculation of dispersal of sulfur dioxide in a 2-h, steady state period in the atmosphere of Nashville. Tennessee.In chapter (3), we estimated the concentration of PM10 (where it is the portion of particulate matter in the air having an aerodynamic equivalent diameter (AED) less than or equal to 10 μm) and compare horizontal flux calculations presented by (Veranth et al. (2003)) with emissions measured from a dispersion model applied to the same data. The next section is used to study the system of computing Horizontal fluxes. In section 3-2, using the mathematical techniques to derived the parameters such as the expressions and the mean plume velocity (where the mathematical
Boundary Layer under Oscillatory Wave
Mohammad Bagus Adityawan; Hitoshi Tanaka
2011-01-01
Turbulence due to wave motion and propagation is a very important aspect in sediment transport modeling. The boundary layer characteristic during the process will highly influence the sediment transport mechanism at the bottom. 1D model approach has been widely used to assess the turbulent boundary layer. However, the need for a more detailed model leads to the development of a more sophisticated models. This study presents a 2D turbulent model using k-ω equation to approach the turbulent bou...
Three-dimensional layerwise modeling of layered media with boundary integral equations
Kokkinos, Filis-Triantaphyllos T.
1995-01-01
A hybrid method is presented for the analysis of layers, plates, and multi-layered systems consisting of isotropic and linear elastic materials. The problem is formulated for the general case of a multi-layered system using a total potential energy formulation and employing the layerwise laminate theory of Reddy. A one-dimensional finite element model is used for the analysis of the multi-layered system through its thickness, and integral Fourier transforms are used to obtai...
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D. Diederen
2015-06-01
Full Text Available We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.
Approximate Analytical Solutions for a Class of Laminar Boundary-Layer Equations
Institute of Scientific and Technical Information of China (English)
Seripah Awang Kechil; Ishak Hashim; Sim Siaw Jiet
2007-01-01
A simple and efficient approximate analytical technique is presented to obtain solutions to a class of two-point boundary value similarity problems in fluid mechanics. This technique is based on the decomposition method which yields a general analytic solution in the form of a convergent infinite series with easily computable terms. Comparative study is carried out to show the accuracy and effectiveness of the technique.
Bertolotti, F. P.; Herbert, TH.
1991-01-01
The application of linearized parabolic stability equations (PSE) to compressible flow is considered. The effect of mean-flow nonparallelism is found to be weak on 2D waves and strong on 3D waves. Results for a single choice of free-stream parameters that corresponds to the atmospheric conditions at 15,000 m above sea level are presented.
International Nuclear Information System (INIS)
The γ-Reθ transition model of Menter et al. [Menter, F.R., Langtry, R.B., Volker, S., Huang, P.G., 2005. Transition modelling for general purpose CFD codes. ERCOFTAC International Symposium Engineering Turbulence Modelling and Measurements] is a highly generalized transport equation model in which it has been developed based on the concept of local variables compatible with modern CFD methods where the unstructured grid and the parallel computing technique are usually integrated in. To perform the prediction with this model, two essential parameters, Flength which is used to control the length of the transition region and Reθc which is used to control the onset of the transition location, must be specified to close the model. At present, both parameters are proprietary and their formulations are unpublished. For the first time here, the relations for both parameters are formulated by means of numerical experiments and analysis under the assumption of Reθc = Reθt corresponding with the bypass transition behavior. Based on this analysis, the optimized values of the parameters are found and their relations can be constructed as follows: Reθc = 803.73(Tu∞,le + 0.6067)-1.027 and Flength = 163 ln(Tu∞,le) + 3.625. The performance of this transition model is assessed by testing with the experimental cases of T3AM, T3A, and T3B. Detailed comparisons with the predicted results by the transition models of Suzen and Huang [Suzen, Y.B., Huang, P.G., 2000. Modeling of flow transition using an intermittency transport equation. J. Fluids Eng. 122, 273-284] and Lodefier et al. [Lodefier, K., Merci, B., De Langhe, C., Dick, E., 2003. Transition modelling with the SST turbulence model and intermittency transport equation. ASME Turbo Expo, Atlanta, GA, USA, June 16-19], and also with the predicted results by the k-ε model of Launder and Sharma [Launder, B.E., Sharma, B., 1974. Application of the energy dissipation model of turbulence to the calculation of flow near a
Jiang, Ning; Masmoudi, Nader
2015-01-01
We establish the incompressible Navier-Stokes-Fourier limit for solutions to the Boltzmann equation with a general cut-off collision kernel in a bounded domain. Appropriately scaled families of DiPerna-Lions-(Mischler) renormalized solutions with Maxwell reflection boundary conditions are shown to have fluctuations that converge as the Knudsen number goes to zero. Every limit point is a weak solution to the Navier-Stokes-Fourier system with different types of boundary conditions depending on ...
Institute of Scientific and Technical Information of China (English)
LU Chang-gen; CAO Wei-dong; QIAN Jian-hua
2006-01-01
A new method for direct numerical simulation of incompressible Navier-Stokes equations is studied in the paper. The compact finite difference and the non-linear terms upwind compact finite difference schemes on non-uniform meshes in x and y directions are developed respectively. With the Fourier spectral expansion in the spanwise direction, three-dimensional N-S equation are converted to a system of two-dimensional equations. The third-order mixed explicit-implicit scheme is employed for time integration. The treatment of the three-dimensional non-reflecting outflow boundary conditions is presented, which is important for the numerical simulations of the problem of transition in boundary layers, jets, and mixing layer. The numerical results indicate that high accuracy, stabilization and efficiency are achieved by the proposed numerical method. In addition, a theory model for the coherent structure in a laminar boundary layer is also proposed, based on which the numerical method is implemented to the non-linear evolution of coherent structure. It is found that the numerical results of the distribution of Reynolds stress, the formation of high shear layer, and the event of ejection and sweeping, match well with the observed characteristics of the coherent structures in a turbulence boundary layer.
Magnetohydrodynamic cross-field boundary layer flow
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D. B. Ingham
1982-01-01
Full Text Available The Blasius boundary layer on a flat plate in the presence of a constant ambient magnetic field is examined. A numerical integration of the MHD boundary layer equations from the leading edge is presented showing how the asymptotic solution described by Sears is approached.
International Nuclear Information System (INIS)
In this work is shown the solution of the advection-diffusion equation to simulate a pollutant dispersion in the Planetary Boundary Layer. The solution is obtained through of the GILTT (Generalized Integral Laplace Transform Technique) analytic method and of the numerical inversion Gauss Quadrature. The validity of the solution is proved using concentration obtained from the model with concentration obtained for Copenhagen experiment. In this comparison was utilized potential and logarithmic wind profile and eddy diffusivity derived by Degrazia et al (1997) [17] and (2002) [19]. The best results was using the potential wind profile and the eddy diffusivity derived by Degrazia et al (1997). The vertical velocity influence is shown in the plume behavior of the pollutant concentration. Moreover, the vertical and longitudinal velocity provided by Large Eddy Simulation (LES) was stood in the model to simulate the turbulent boundary layer more realistic, the result was satisfactory when compared with contained in the literature. (author)
Costigliola, V.
2010-09-01
It has long been known that specific atmospheric processes, such as weather and longer-term climatic fluctuations, affect human health. The biometeorological literature refers to this relationship as meteorotropism, defined as a change in an organism that is correlated with a change in atmospheric conditions. Plenty of (patho)physiological functions are affected by those conditions - like the respiratory diseases - and currently it is difficult to put any limits for pathologies developed in reply. Nowadays the importance of atmospheric boundary layer and health is increasingly recognised. A number of epidemiologic studies have reported associations between ambient concentrations of air pollution, specifically particulate pollution, and adverse health effects, even at the relatively low concentrations of pollution found. Since 1995 there have been over twenty-one studies from four continents that have explicitly examined the association between ambient air pollutant mixes and daily mortality. Statistically significant and positive associations have been reported in data from various locations around the world, all with varying air pollutant concentrations, weather conditions, population characteristics and public health policies. Particular role has been given to atmospheric boundary layer processes, the impact of which for specific patient-cohort is, however, not well understood till now. Assessing and monitoring air quality are thus fundamental to improve Europe's welfare. One of current projects run by the "European Medical Association" - PASODOBLE will develop and demonstrate user-driven downstream information services for the regional and local air quality sectors by combining space-based and in-situ data with models in 4 thematic service lines: - Health community support for hospitals, pharmacies, doctors and people at risk - Public information for regions, cities, tourist industry and sporting event organizers - Compliance monitoring support on particulate
Modeling the urban boundary layer
Bergstrom, R. W., Jr.
1976-01-01
A summary and evaluation is given of the Workshop on Modeling the Urban Boundary Layer; held in Las Vegas on May 5, 1975. Edited summaries from each of the session chairpersons are also given. The sessions were: (1) formulation and solution techniques, (2) K-theory versus higher order closure, (3) surface heat and moisture balance, (4) initialization and boundary problems, (5) nocturnal boundary layer, and (6) verification of models.
International Nuclear Information System (INIS)
We study the symmetries, conservation laws and reduction of third-order equations that evolve from a prior reduction of models that arise in fluid phenomena. These could be the ordinary differential equations (ODEs) that are reductions of partial differential equations (PDEs) or, alternatively, PDEs related to given ODEs. In this class, the analysis includes the well-known Blasius, Chazy, and other associated third-order ODEs. (general)
Nonlinear streak computation using boundary region equations
International Nuclear Information System (INIS)
The boundary region equations (BREs) are applied for the simulation of the nonlinear evolution of a spanwise periodic array of streaks in a flat plate boundary layer. The well-known BRE formulation is obtained from the complete Navier–Stokes equations in the high Reynolds number limit, and provides the correct asymptotic description of three-dimensional boundary layer streaks. In this paper, a fast and robust streamwise marching scheme is introduced to perform their numerical integration. Typical streak computations present in the literature correspond to linear streaks or to small-amplitude nonlinear streaks computed using direct numerical simulation (DNS) or the nonlinear parabolized stability equations (PSEs). We use the BREs to numerically compute high-amplitude streaks, a method which requires much lower computational effort than DNS and does not have the consistency and convergence problems of the PSE. It is found that the flow configuration changes substantially as the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, which end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results. (paper)
Boundary-layer linear stability theory
Mack, L. M.
1984-06-01
reached a stage of development which permit the direct solution of the primary differential equations, numerical results were obtained from the linear theory during the next 10 years for many different boundary layer flows: three dimensional boundary layers; free convention boundary layers; compressible boundary layers; boundary layers on compliant walls; a recomputation of Falkner-Skan flows; unsteady boundary layers; and heated wall boundary layers.
Boundary-layer linear stability theory
Mack, L. M.
1984-01-01
reached a stage of development which permit the direct solution of the primary differential equations, numerical results were obtained from the linear theory during the next 10 years for many different boundary layer flows: three dimensional boundary layers; free convention boundary layers; compressible boundary layers; boundary layers on compliant walls; a recomputation of Falkner-Skan flows; unsteady boundary layers; and heated wall boundary layers.
Boundary transfer matrices and boundary quantum KZ equations
Energy Technology Data Exchange (ETDEWEB)
Vlaar, Bart, E-mail: Bart.Vlaar@nottingham.ac.uk [School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD (United Kingdom)
2015-07-15
A simple relation between inhomogeneous transfer matrices and boundary quantum Knizhnik-Zamolodchikov (KZ) equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus, the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin’s boundary transfer matrices by merely imposing appropriate reflection equations, in particular without using the conditions of crossing symmetry and unitarity of the R-matrix.
Boundary-layer theory for blast waves
Kim, K. B.; Berger, S. A.; Kamel, M. M.; Korobeinikov, V. P.; Oppenheim, A. K.
1975-01-01
It is profitable to consider the blast wave as a flow field consisting of two regions: the outer, which retains the properties of the inviscid solution, and the inner, which is governed by flow equations including terms expressing the effects of heat transfer and, concomitantly, viscosity. The latter region thus plays the role of a boundary layer. Reported here is an analytical method developed for the study of such layers, based on the matched asymptotic expansion technique combined with patched solutions.
A Boundary Integral Equation Approach for Boundary Problem of Laplace Equation
Institute of Scientific and Technical Information of China (English)
SUNJian-she; YELiu-qing
2003-01-01
Using the second Green formula, the boundary problem of Laplace equation satisfied by potential function of static electric field is transformed to the problem of the boundary integral equation,and then a boundary integral equation approach is established by partitioning boundary using linear boundary element.
Byatt-Smith, J. G.
2000-01-01
Nekrasov's integral equation describing water waves of permanent form, determines the angle phi that the wave surface makes with the horizontal. The independent variable s is a suitably scaled velocity potential, evaluated at the free surface, with the origin corresponding to the crest of the wave. For all waves, except for amplitudes near the maximum, phi satisfies the inequality mod(phi) is less than pi/6. It has been shown numerically and analytically, that as the wave amplitude approaches...
Global stability analysis of axisymmetric boundary layers
Vinod, N
2016-01-01
This paper presents the linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inlet. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes(LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes are nega...
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Reaction diffusion equations with boundary degeneracy
Directory of Open Access Journals (Sweden)
Huashui Zhan
2016-03-01
Full Text Available In this article, we consider the reaction diffusion equation $$ \\frac{\\partial u}{\\partial t} = \\Delta A(u,\\quad (x,t\\in \\Omega \\times (0,T, $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.
Numerical simulation of turbulent atmospheric boundary layer flows
Energy Technology Data Exchange (ETDEWEB)
Bennes, L.; Bodnar, T.; Kozel, K.; Sladek, I. [Czech Technical Univ., Prague (Czech Republic). Dept. of Technical Mathematics; Fraunie, P. [Universite Toulon et du Var, La Garde (France). Lab. de Sondages Electromagnetiques de l' Environment Terrestre
2001-07-01
The work deals with the numerical solution of viscous turbulent steady flows in the atmospheric boundary layer including pollution propagation. For its description we use two different mathematical models: - a model based on the Reynolds averaged Navier-Stokes equations for incompressible flows - a model based on a system of boundary layer equations. These systems are completed by two transport equations for the concentration of passive pollutants and the potential temperature in conservative form, respectively, and by an algebraic turbulence model. (orig.)
Soliton equations solved by the boundary CFT
SAITO, Satoru; Sato, Ryuichi
2003-01-01
Soliton equations are derived which characterize the boundary CFT a la Callan et al. Soliton fields of classical soliton equations are shown to appear as a neutral bound state of a pair of soliton fields of BCFT. One soliton amplitude under the influence of the boundary is calculated explicitly and is shown that it is frozen at the Dirichlet limit.
Green House Gases Flux Model in Boundary Layer
Nurgaliev, Ildus
Analytical dynamic model of the turbulent flux in the three-layer boundary system is presented. Turbulence is described as a presence of the non-zero vorticity. The generalized advection-diffusion-reaction equation is derived for an arbitrary number of components in the flux. The fluxes in the layers are objects for matching requirements on the boundaries between the layers. Different types of transport mechanisms are dominant on the different levels of the layers.
BOUNDARY CONTROL OF MKDV-BURGERS EQUATION
Institute of Scientific and Technical Information of China (English)
TIAN Li-xin; ZHAO Zhi-feng; WANG Jing-feng
2006-01-01
The boundary control of MKdV-Burgers equation was considered by feedback control on the domain [0,1]. The existence of the solution of MKdV-Burgers equation with the feedback control law was proved. On the base, priori estimates for the solution was given. At last, the existence of the weak solution of MKdV-Burgers equation was proved and the global-exponential and asymptotic stability of the solution of MKdV-Burgers equation was given.
Absorbing layers for the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Pinaud, Olivier, E-mail: pinaud@math.colostate.edu
2015-05-15
This work is devoted to the construction of perfectly matched layers (PML) for the Dirac equation, that not only arises in relativistic quantum mechanics but also in the dynamics of electrons in graphene or in topological insulators. While the resulting equations are stable at the continuous level, some care is necessary in order to obtain a stable scheme at the discrete level. This is related to the so-called fermion doubling problem. For this matter, we consider the numerical scheme introduced by Hammer et al. [19], and combine it with the discretized PML equations. We state some arguments for the stability of the resulting scheme, and perform simulations in two dimensions. The perfectly matched layers are shown to exhibit, in various configurations, superior absorption than the absorbing potential method and the so-called transport-like boundary conditions.
Boundary Layer Heights from CALIOP
Kuehn, R.; Ackerman, S. A.; Holz, R.; Roubert, L.
2012-12-01
This work is focused on the development of a planetary boundary layer (PBL) height retrieval algorithm for CALIOP and validation studies. Our current approach uses a wavelet covariance transform analysis technique to find the top of the boundary layer. We use the methodology similar to that found in Davis et. al. 2000, ours has been developed to work with the lower SNR data provided by CALIOP, and is intended to work autonomously. Concurrently developed with the CALIOP algorithm we will show results from a PBL height retrieval algorithm from profiles of potential temperature, these are derived from Aircraft Meteorological DAta Relay (AMDAR) observations. Results from 5 years of collocated AMDAR - CALIOP retrievals near O'Hare airport demonstrate good agreement between the CALIOP - AMDAR retrievals. In addition, because we are able to make daily retrievals from the AMDAR measurements, we are able to observe the seasonal and annual variation in the PBL height at airports that have sufficient instrumented-aircraft traffic. Also, a comparison has been done between the CALIOP retrievals and the NASA Langley airborne High Spectral Resolution Lidar (HSRL) PBL height retrievals acquired during the GoMACCS experiment. Results of this comparison, like the AMDAR comparison are favorable. Our current work also involves the analysis and verification of the CALIOP PBL height retrieval from the 6 year CALIOP global data set. Results from this analysis will also be presented.
Two Dimensional Boundary Layer Growth with Suction
Directory of Open Access Journals (Sweden)
Krishna Lal
1970-07-01
Full Text Available The boundary layer equations for the unsteady fluid flow with constant suction velocity have been worked out for the impulsive motion of a circular cylinder in the form V(t=A exp (Ct where A and C are certain constants. The stream function has been expanded in terms of some functions X/sub 0/(s where s is a function of y coordinate. The phase angles for various terms have been calculated, and variations shown graphically for large and small frequency of oscillations, where the oscillatory motion is obtained on replacing C by iw.
Iterative solution of Hermite boundary integral equations
Energy Technology Data Exchange (ETDEWEB)
Gray, Leonard J [ORNL; Nintcheu Fata, Sylvain [ORNL; Ma, Ding [ORNL
2008-01-01
An efficient iterative method for the solution of the linear equations arising from a Hermite boundary integral approximation has been developed. Along with equations for the boundary unknowns, the Hermite system incorporates equations for the first-order surface derivatives (gradient) of the potential, and is therefore substantially larger than the matrix for a corresponding linear approximation. However, by exploiting the structure of the Hermite matrix, a two-level iterative algorithm has been shown to provide a very efficient solution algorithm. In this approach, the boundary function unknowns are treated separately from the gradient, taking advantage of the sparsity and near-positive definiteness of the gradient equations. In test problems, the new algorithm significantly reduced computation time compared to iterative solution applied to the full matrix. This approach should prove to be even more effective for the larger systems encountered in three-dimensional analysis, and increased efficiency should come from pre-conditioning of the non-sparse matrix component.
Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells
Nemeth, Michael P.; Smeltzer, Stanley S., III
2000-01-01
A study of the attenuation of bending boundary layers in balanced and unbalanced, symmetrically and unsymmetrically laminated cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize the effects of laminate orthotropy and anisotropy on the bending boundary-layer decay length in a very general manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all laminates considered, the results show that the differences between results obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that, in some cases, neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and, in other cases, results in an overestimation.
Ouwersloot, H.G.; Arellano, de J.V.G.
2013-01-01
In Ouwersloot and Vila-Guerau de Arellano (Boundary-Layer Meteorol. doi: 10. 1007/s10546-013-9816-z, 2013, this issue), the analytical solutions for the boundary-layer height and scalar evolutions are derived for the convective boundary layer, based on the prognostic equations of mixed-layer slab mo
On Cauchy conditions for asymmetric mixed convection boundary layer flows
Energy Technology Data Exchange (ETDEWEB)
Amaouche, Mustapha [Laboratoire de Physique Theorique, Universite de Bejaia (Algeria); Kessal, Mohand [Departement Transport et Equipement Petrolier, Faculte des Hydrocarbures et de la Chimie, Universite de Boumerdes, 35000, Boumerdes (Algeria)
2003-06-01
The fundamental question of how and where does an asymmetric mixed convection boundary layer flow around a heated horizontal circular cylinder begin to develop is raised. We first transform the classical boundary layer equations by using an integral method of Karman-Pohlhausen type and obtain two coupled equations governing the evolutions of the dynamic and thermal boundary layers. Because of its global character, the implemented method allows to bypass the difficulty of downstream-upstream interactions. Cauchy conditions characterizing the starting of the boundary layers are found; they are obtained in a surprisingly simple manner for the limiting cases corresponding to Pr=1, Pr{yields}0 and Pr{yields}{infinity}. Otherwise, these conditions can be found by using a prediction correction algorithm. Some numerical experiments are finally performed in order to illustrate the theory. (authors)
Microgravity Effects on Plant Boundary Layers
Stutte, Gary; Monje, Oscar
2005-01-01
The goal of these series of experiment was to determine the effects of microgravity conditions on the developmental boundary layers in roots and leaves and to determine the effects of air flow on boundary layer development. It is hypothesized that microgravity induces larger boundary layers around plant organs because of the absence of buoyancy-driven convection. These larger boundary layers may affect normal metabolic function because they may reduce the fluxes of heat and metabolically active gases (e.g., oxygen, water vapor, and carbon dioxide. These experiments are to test whether there is a change in boundary layer associated with microgravity, quantify the change if it exists, and determine influence of air velocity on boundary layer thickness under different gravity conditions.
Linear Stability of the boundary layer under a solitary wave
Verschaeve, Joris C. G.; Pedersen, Geir K.
2013-01-01
A theoretical and numerical analysis of the linear stability of the boundary layer flow under a solitary wave is presented. In the present work, the nonlinear boundary layer equations are solved. The result is compared to the linear boundary layer solution in Liu et al. (2007) reveal- ing that both profiles are disagreeing more than has been found before. A change of frame of reference has been used to allow for a classical linear stability analysis without the need to redefine the notion of ...
Boundary value problems and partial differential equations
Powers, David L
2005-01-01
Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions* Nearly 900 exercises ranging in difficulty* Many fully worked examples
Brüning, J.; Dobrokhotov, S. Yu.; Minenkov, D. S.
2011-12-01
The aim of this paper is to construct solutions of the Dirichlet problem for the 3D Laplace equation in a layer with highly oscillating boundary. The boundary simulates the surface of a nanotube array, and the solutions are applied to compute the cold field electron emission. We suggest a family of exact solutions that solve the problem for a boundary with appropriate geometry. These solutions, along with the Fowler-Nordheim formula, allow one to present explicit asymptotic formulas for the electric field and the emission current. In this part of the paper, we consider the main mathematical aspects, restricting ourselves to the analysis of properties of the potential created by a single tube and a regular array of tubes. In the next part, we shall consider some cases corresponding to nonregular arrays of tubes and concrete physical examples.
Near continuum boundary layer flows at a flat plate
Directory of Open Access Journals (Sweden)
Chunpei Cai
2015-05-01
Full Text Available The problem of boundary layer flows at a flat plate surface with velocity-slip and temperature-jump boundary conditions is analyzed. With the velocity slip conditions, there are multiple physical factors lumped together, and the boundary layer solutions significantly change their behaviors. The self-similarity in the solutions degenerates, however, the problem is still an ordinary differential equation which can be solved. Shooting methods are applied to solve the flowfield. The results include velocity and temperature for both the surface and flowfield. Unlike the traditional Blasius flat plate boundary layer solutions which are self-similar through all the plate boundary layer, the new solutions indicate that the front tip is actually a singularity point, especially at locations within one mean free path from the leading edge.
THE INTERIOR LAYER SOLUTION TO NONLOCAL REACTION DIFFUSION EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
An initial boundary value problem of semilinear nonlocal reaction diffusion equations is considered.Under some suitable conditions,using the asymptotic theory,the existence and asymptotic behavior of the interior layer solution to the initial boundary value problem are studied.
Theoretical skin-friction law in a turbulent boundary layer
International Nuclear Information System (INIS)
We study transitional and turbulent boundary layers using a turbulent velocity profile equation recently derived from the Navier-Stokes-alpha and Leray-alpha models. From this equation we obtain a theoretical prediction of the skin-friction coefficient in a wide range of Reynolds numbers based on momentum thickness, and deduce the maximal value of cfmax=0.0063 for turbulent velocity profiles. A two-parameter family of solutions to the equation matches experimental data in the transitional boundary layers with different free-stream turbulence intensity, while one-parameter family of solutions, obtained using our skin-friction coefficient law, matches experimental data in the turbulent boundary layer for moderately large Reynolds numbers
Boundary layer for non-newtonian fluids on curved surfaces
International Nuclear Information System (INIS)
By using the basic equation of fluid motion (conservation of mass and momentum) the boundary layer parameters for a Non-Newtonian, incompressible and laminar fluid flow, has been evaluated. As a test, the flat plate boundary layer is first analized and afterwards, a case with pressure gradient, allowing separation, is studied. In the case of curved surfaces, the problem is first developed in general and afterwards particularized to a circular cylinder. Finally suction and slip in the flow interface are examined. The power law model is used to represent the stress strain relationship in Non-Newtonian flow. By varying the fluid exponent one can then, have an idea of how the Non-Newtonian behavior of the flow influences the parameters of the boundary layer. Two equations, in an appropriate coordinate system have been obtained after an order of magnitude analysis of the terms in the equations of motion is performed. (Author)
BUBBLE - an urban boundary layer meteorology project
DEFF Research Database (Denmark)
Rotach, M.W.; Vogt, R.; Bernhofer, C.;
2005-01-01
The Basel urban Boundary Layer Experiment (BUBBLE) was a year-long experimental effort to investigate in detail the boundary layer structure in the City of Basel, Switzerland. At several sites over different surface types (urban, sub-urban and rural reference) towers up to at least twice the main...
Cyclone separator having boundary layer turbulence control
International Nuclear Information System (INIS)
A cyclone separator including boundary layer turbulence control that is operable to prevent undue build-up of particulate material at selected critical areas on the separator walls, by selectively varying the fluid pressure at those areas to maintain the momentum of the vortex, thereby preventing particulate material from inducing turbulence in the boundary layer of the vortical fluid flow through the separator
Experimental investigation of wave boundary layer
DEFF Research Database (Denmark)
Sumer, B. Mutlu
2003-01-01
A review is presented of experimental investigation of wave boundary layer. The review is organized in six main sections. The first section describes the wave boundary layer in a real-life environment and its simulation in the laboratory in an oscillating water tunnel and in a water tank with an ...
Cyclone separator having boundary layer turbulence control
Krishna, Coimbatore R.; Milau, Julius S.
1985-01-01
A cyclone separator including boundary layer turbulence control that is operable to prevent undue build-up of particulate material at selected critical areas on the separator walls, by selectively varying the fluid pressure at those areas to maintain the momentum of the vortex, thereby preventing particulate material from inducing turbulence in the boundary layer of the vortical fluid flow through the separator.
Atmospheric boundary layer over steep surface waves
Troitskaya, Yuliya; Sergeev, Daniil A.; Druzhinin, Oleg; Kandaurov, Alexander A.; Ermakova, Olga S.; Ezhova, Ekaterina V.; Esau, Igor; Zilitinkevich, Sergej
2014-08-01
Turbulent air-sea interactions coupled with the surface wave dynamics remain a challenging problem. The needs to include this kind of interaction into the coupled environmental, weather and climate models motivate the development of a simplified approximation of the complex and strongly nonlinear interaction processes. This study proposes a quasi-linear model of wind-wave coupling. It formulates the approach and derives the model equations. The model is verified through a set of laboratory (direct measurements of an airflow by the particle image velocimetry (PIV) technique) and numerical (a direct numerical simulation (DNS) technique) experiments. The experiments support the central model assumption that the flow velocity field averaged over an ensemble of turbulent fluctuations is smooth and does not demonstrate flow separation from the crests of the waves. The proposed quasi-linear model correctly recovers the measured characteristics of the turbulent boundary layer over the waved water surface.
LDV measurements of turbulent baroclinic boundary layers
Energy Technology Data Exchange (ETDEWEB)
Neuwald, P.; Reichenbach, H. [Fraunhofer-Institut fuer Kurzzeitdynamik - Ernst-Mach-Institut (EMI), Freiburg im Breisgau (Germany); Kuhl, A.L. [Lawrence Livermore National Lab., El Segundo, CA (United States)
1993-07-01
Described here are shock tube experiments of nonsteady, turbulent boundary layers with large density variations. A dense-gas layer was created by injecting Freon through the porous floor of the shock tube. As the shock front propagated along the layer, vorticity was created at the air-Freon interface by an inviscid, baroclinic mechanism. Shadow-schlieren photography was used to visualize the turbulent mixing in this baroclinic boundary layer. Laser-Doppler-Velocimetry (LDV) was used to measure the streamwise velocity histories at 14 heights. After transition, the boundary layer profiles may be approximated by a power-law function u {approximately} u{sup {alpha}} where {alpha} {approx_equal} 3/8. This value lies between the clean flat plate value ({alpha} = 1/7) and the dusty boundary layer value ({alpha} {approx_equal} 0.7), and is controlled by the gas density near the wall.
A NOVEL BOUNDARY INTEGRAL EQUATION METHOD FOR LINEAR ELASTICITY--NATURAL BOUNDARY INTEGRAL EQUATION
Institute of Scientific and Technical Information of China (English)
Niu Zhongrong; Wang Xiuxi; Zhou Huanlin; Zhang Chenli
2001-01-01
The boundary integral equation (BIE) of displacement derivatives is put at a disadvantage for the difficulty involved in the evaluation of the hypersingular integrals. In this paper, the operators δij and εij are used to act on the derivative BIE. The boundary displacements, tractions and displacement derivatives are transformed into a set of new boundary tensors as boundary variables. A new BIE formulation termed natural boundary integral equation (NBIE) is obtained. The NBIE is applied to solving two-dimensional elasticity problems. In the NBIE only the strongly singular integrals are contained. The Cauchy principal value integrals occurring in the NBIE are evaluated. A combination of the NBIE and displacement BIE can be used to directly calculate the boundary stresses. The numerical results of several examples demonstrate the accuracy of the NBIE.
Plasma boundary layer and magnetopause layer of the earth's magnetosphere
International Nuclear Information System (INIS)
IMP 6 observations of the plasma boundary layer (PBL) and magnetopause layer (MPL) of the earth's magnetosphere indicate that plasma in the low-latitude portion of the PBL is supplied primarily by direct transport of magnetosheath plasma across the MPL and that this transport process is relatively widespread over the entire sunward magnetospheric boundary
Joslin, Ronald D.; Streett, Craig L.; Chang, Chau-Lyan
1992-01-01
Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.
Boundary Layer on a Moving Wall with Suction and Injection
Institute of Scientific and Technical Information of China (English)
Anuar Ishak; Roslinda Nazar; Ioan Pop
2007-01-01
@@ We investigate the boundary-layer flow on a moving permeable plate parallel to a moving stream. The governing equations are solved numerically by a finite-difference method. Dual solutions are found to exist when the plate and the free stream move in the opposite directions.
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
The BIE (boundary integral equation) method is based on the numerical solution of a set of integral constraint equations which couple boundary tractions (stresses) to boundary displacements. Thus the dimensionality of the problem is reduced by one; only boundary geometry and data are discretized. Stresses at any set of selected interior points are computed following the boundary solution without any further numerical approximations. Thus, the BIE method has inherently greater resolution capability for stress gradients than does the finite element method. Conversely, the BIE method is not efficient for problems involving significant inhomogeneity such as in multi-thin-layered materials, or in elastoplasticity. Some progress in applyiing the BIE method to the latter problem has been made but much more work remains. Further, the BIE method is only optional for problems with significant stress risers, and only when boundary stresses are most important. Interior stress calculations are expensive, per point, and can drive the solution costs up rapidly. The current report summarizes some of the advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referencing some of the much broader developmental effort. Future emphasis is needed to exploit the BIE method in conjunction with other techniques such as the finite element method through the creation of hybrid stress analysis methods
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
Numerical analysis has become the basic tool for both design and research problems in solid mechanics. The boundary-integral equation (BIE) method is based on classical mathematical techniques but is finding new life as a basic stress analysis tool for engineering applications. The BIE method is based on the numerical solution of a set of integral constraint equations which couple boundary tractions (stresses) to boundary displacements. Thus the dimensionality of the problem is reduced by one; only boundary geometry and data are discretized. Stresses at any set of selected interior points are computed following the boundary solution without any further numerical approximations. Thus, the BIE method has inherently greater resolution capability for stress gradients than does the finite element method. Conversely, the BIE method is not efficient for problems involving significant inhomogeneity such as in multi-thin-layered materials, or in elastoplasticity. Some progress in applying the BIE method to the latter problem has been made but much more work remains. Further, the BIE method is only optional for problems with significant stress risers, and only when boundary stresses are more important. Interior stress calculations are expensive, per point, and can drive the solution costs up rapidly. The current report summarizes some of the advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referring some of the much broader developmental effort. (Auth.)
Boundary layer physics over snow and ice
Directory of Open Access Journals (Sweden)
P. S. Anderson
2008-07-01
Full Text Available Observations of the unique chemical environment over snow and ice in recent decades, particularly in the polar regions, have stimulated increasing interest in the boundary layer processes that mediate exchanges between the ice/snow interface and the atmosphere. This paper provides a review of the underlying concepts and examples from recent field studies in polar boundary layer meteorology, which will generally apply to atmospheric flow over snow and ice surfaces. It forms a companion paper to the chemistry review papers in this special issue of ACP that focus on processes linking halogens to the depletion of boundary layer ozone in coastal environments, mercury transport and deposition, snow photochemistry, and related snow physics. In this context, observational approaches, stable boundary layer behavior, the effects of a weak or absent diurnal cycle, and transport and mixing over the heterogeneous surfaces characteristic of coastal ocean environments are of particular relevance.
Boundary Layer Flow Over a Moving Wavy Surface
Hendin, Gali; Toledo, Yaron
2016-04-01
Boundary Layer Flow Over a Moving Wavy Surface Gali Hendin(1), Yaron Toledo(1) January 13, 2016 (1)School of Mechanical Engineering, Tel-Aviv University, Israel Understanding the boundary layer flow over surface gravity waves is of great importance as various atmosphere-ocean processes are essentially coupled through these waves. Nevertheless, there are still significant gaps in our understanding of this complex flow behaviour. The present work investigates the fundamentals of the boundary layer air flow over progressive, small-amplitude waves. It aims to extend the well-known Blasius solution for a boundary layer over a flat plate to one over a moving wavy surface. The current analysis pro- claims the importance of the small curvature and the time-dependency as second order effects, with a meaningful impact on the similarity pattern in the first order. The air flow over the ocean surface is modelled using an outer, inviscid half-infinite flow, overlaying the viscous boundary layer above the wavy surface. The assumption of a uniform flow in the outer layer, used in former studies, is now replaced with a precise analytical solution of the potential flow over a moving wavy surface with a known celerity, wavelength and amplitude. This results in a conceptual change from former models as it shows that the pressure variations within the boundary layer cannot be neglected. In the boundary layer, time-dependent Navier-Stokes equations are formulated in a curvilinear, orthogonal coordinate system. The formulation is done in an elaborate way that presents additional, formerly neglected first-order effects, resulting from the time-varying coordinate system. The suggested time-dependent curvilinear orthogonal coordinate system introduces a platform that can also support the formulation of turbulent problems for any surface shape. In order to produce a self-similar Blasius-type solution, a small wave-steepness is assumed and a perturbation method is applied. Consequently, a
Boundary differentiability for inhomogeneous infinity Laplace equations
Directory of Open Access Journals (Sweden)
Guanghao Hong
2014-03-01
Full Text Available We study the boundary regularity of the solutions to inhomogeneous infinity Laplace equations. We prove that if $u\\in C(\\bar{\\Omega}$ is a viscosity solution to $\\Delta_{\\infty}u:=\\sum_{i,j=1}^n u_{x_i}u_{x_j}u_{x_ix_j}=f$ with $f\\in C(\\Omega\\cap L^{\\infty}(\\Omega$ and for $x_0\\in \\partial\\Omega$ both $\\partial\\Omega$ and $g:=u|_{\\partial\\Omega}$ are differentiable at $x_0$, then u is differentiable at $x_0$.
Characterization of internal boundary layer capacitors
International Nuclear Information System (INIS)
Internal boundary layer capacitors were characterized by scanning transmission electron microscopy and by microscale electrical measurements. Data are given for the chemical and physical characteristics of the individual grains and boundaries, and their associated electric and dielectric properties. Segregated internal boundary layers were identified with resistivities of 1012-1013 Ω-cm. Bulk apparent dielectric constants were 10,000-60,000. A model is proposed to explain the dielectric behavior in terms of an equivalent n-c-i-c-n representation of ceramic microstructure, which is substantiated by capacitance-voltage analysis
Boundary conditions for hyperbolic formulations of the Einstein equations
Frittelli, Simonetta; Gomez, Roberto
2003-01-01
In regards to the initial-boundary value problem of the Einstein equations, we argue that the projection of the Einstein equations along the normal to the boundary yields necessary and appropriate boundary conditions for a wide class of equivalent formulations. We explicitly show that this is so for the Einstein-Christoffel formulation of the Einstein equations in the case of spherical symmetry.
Studies of stability of blade cascade suction surface boundary layer
Institute of Scientific and Technical Information of China (English)
DONG Xue-zhi; YAN Pei-gang; HAN Wan-jin
2007-01-01
Compressible boundary layers stability on blade cascade suction surface was discussed by wind tunnel experiment and numerical solution. Three dimensional disturbance wave Parabolized Stability Equations(PSE) of orthogonal Curvilinear Coordinates in compressible flow was deducted. The surface pressure of blade in wind tunnel experiment was measured. The Falkner-Skan equation was solved under the boundary conditions of experiment result, and velocity, pressure and temperature of average flow were obtained. Substituted this result for discretization of the PSE Eigenvalue Problem, the stability problem can be solved.
Modeling the summertime Arctic cloudy boundary layer
Energy Technology Data Exchange (ETDEWEB)
Curry, J.A.; Pinto, J.O. [Univ. of Colorado, Boulder, CO (United States); McInnes, K.L. [CSIRO Division of Atmospheric Research, Mordialloc (Australia)
1996-04-01
Global climate models have particular difficulty in simulating the low-level clouds during the Arctic summer. Model problems are exacerbated in the polar regions by the complicated vertical structure of the Arctic boundary layer. The presence of multiple cloud layers, a humidity inversion above cloud top, and vertical fluxes in the cloud that are decoupled from the surface fluxes, identified in Curry et al. (1988), suggest that models containing sophisticated physical parameterizations would be required to accurately model this region. Accurate modeling of the vertical structure of multiple cloud layers in climate models is important for determination of the surface radiative fluxes. This study focuses on the problem of modeling the layered structure of the Arctic summertime boundary-layer clouds and in particular, the representation of the more complex boundary layer type consisting of a stable foggy surface layer surmounted by a cloud-topped mixed layer. A hierarchical modeling/diagnosis approach is used. A case study from the summertime Arctic Stratus Experiment is examined. A high-resolution, one-dimensional model of turbulence and radiation is tested against the observations and is then used in sensitivity studies to infer the optimal conditions for maintaining two separate layers in the Arctic summertime boundary layer. A three-dimensional mesoscale atmospheric model is then used to simulate the interaction of this cloud deck with the large-scale atmospheric dynamics. An assessment of the improvements needed to the parameterizations of the boundary layer, cloud microphysics, and radiation in the 3-D model is made.
DEFF Research Database (Denmark)
Chivaee, Hamid Sarlak; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming
2012-01-01
simulation and the boundary layer shape will be modified due to the interaction of the turbine wakes and buoyancy contributions. The implemented method is capable of capturing the most important features of wakes of wind farms [1] while having the advantage of resolving the wall layer with a coarser grid......Large eddy simulation (LES) of flow in a wind farm is studied in neutral as well as thermally stratified atmospheric boundary layer (ABL). An approach has been practiced to simulate the flow in a fully developed wind farm boundary layer. The approach is based on the Immersed Boundary Method (IBM...
Lagrangian analysis of the laminar flat plate boundary layer
Gabr, Mohammad
2016-01-01
The leading edge flow properties has been a singularity to the Blasius laminar boundary layer equations, by applying the Lagrangian approach the leading edge velocity profiles of the laminar boundary layer over a flat plate are studied. Experimental observations as well as the theoretical analysis show an exact Gaussian distribution curve as the original starting profile of the laminar flow. Comparisons between the Blasius solution and the Gaussian curve solution are carried out providing a new insight into the physics of the laminar flow.
THE CORNER LAYER SOLUTION TO ROBIN PROBLEM FOR REACTION DIFFUSION EQUATION
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
A class of Robin boundary value problem for reaction diffusion equation is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the corner layer solution to the initial boundary value problem are studied.
International Nuclear Information System (INIS)
The system of partial differential equation for the description of the laminar, steady, axisymmetric flow of an incompressible fluid on a flat horizontal bottom has been derived. The impermeability condition and full slipping condition on the bottom have been used. The reduction of the initial system to an ordinary differential equation for the steam function has been obtained. It has been shown that this equation is reduced under certain conditions to two Chazy equations. The exact solution expressed in terms of Airy functions has been obtained at one value of the parameter in the equation. Three types of the flow of the fluid depending on the values of two arbitrary constants in the solution have been discovered by analyzing this solution
Linear Stability of the boundary layer under a solitary wave
Verschaeve, Joris C G
2013-01-01
A theoretical and numerical analysis of the linear stability of the boundary layer flow under a solitary wave is presented. In the present work, the nonlinear boundary layer equations are solved. The result is compared to the linear boundary layer solution in Liu et al. (2007) reveal- ing that both profiles are disagreeing more than has been found before. A change of frame of reference has been used to allow for a classical linear stability analysis without the need to redefine the notion of stability for this otherwise unsteady flow. For the linear stability the Orr-Sommerfeld equation and the parabolic stability equation were used. The results are compared to key results of inviscid stability theory and validated by means of a direct numerical simulation using a Legendre-Galerkin spectral ele- ment Navier-Stokes solver. Special care has been taken to ensure that the numerical results are valid. Linear stability predicts that the boundary layer flow is unstable for the entire parameter range considered, conf...
Problems of matter-antimatter boundary layers
International Nuclear Information System (INIS)
This paper outlines the problems of the quasi-steady matter-antimatter boundary layers discussed in Klein-Alfven's cosmological theory, and a crude model of the corresponding ambiplasma balance is presented: (i) at interstellar particle densities, no well-defined boundary layer can exist in presence of neutral gas, nor can such a layer be sustained in an unmagnetized fully ionized ambiplasma. (ii) Within the limits of applicability of the present model, sharply defined boundary layers are under certain conditions found to exist in a magnetized ambiplasma. Thus, at beta values less than unity, a steep pressure drop of the low-energy components of matter and antimatter can be balanced by a magnetic field and the electric currents in the ambiplasma. (iii) The boundary layer thickness is of the order of 2x0 approximately 10/BT0sup(1/4) meters, where B is the magnetic field strength in MKS units and T0 the characteristic temperature of the low-energy components in the layer. (Auth.)
Calculation of Turbulent Boundary Layers Using the Dissipation Integral Method
Institute of Scientific and Technical Information of China (English)
MatthiasBuschmann
1999-01-01
This paper gives an introduction into the dissipation integral method.The general integral equations for the three-dimensional case are derved.It is found that for a practical calculation algorithm the integral monentum equation and the integral energy equation are msot useful.Using Two different sets of mean velocity profiles the hyperbolical character of a dissipation integral method is shown.Test cases for two-and three-dimensional boundary layers are analysed and discussed.The paper concludes with a discussion of the advantages and limits of dissipation integral methods.
Boundary layer physics over snow and ice
Directory of Open Access Journals (Sweden)
P. S. Anderson
2007-06-01
Full Text Available A general understanding of the physics of advection and turbulent mixing within the near surface atmosphere assists the interpretation and predictive power of air chemistry theory. The theory of the physical processes involved in diffusion of trace gas reactants in the near surface atmosphere is still incomplete. Such boundary layer theory is least understood over snow and ice covered surfaces, due in part to the thermo-optical properties of the surface. Polar boundary layers have additional aspects to consider, due to the possibility of long periods without diurnal forcing and enhanced Coriolis effects.
This paper provides a review of present concepts in polar boundary layer meteorology, which will generally apply to atmospheric flow over snow and ice surfaces. It forms a companion paper to the chemistry review papers in this special issue of ACP.
Boundary layer heights derived from velocity spectra
Energy Technology Data Exchange (ETDEWEB)
Hoejstrup, J.; Barthelmie, R.J. [Risoe National Lab., Roskilde (Denmark); Kaellstrand, B. [Univ. of Uppsala, Uppsala (Sweden)
1997-10-01
It is a well-known fact that the height of the mixed layer determines the size of the largest and most energetic eddies that can be observed in the unstable boundary layer, and consequently a peak can be observed in the power spectra of the along-wind velocity component at scales comparable to the mixed layer depth. We will now show how the mixed layer depth can be derived from the u-specta and the results will be compared with direct measurements using pibal and tethersonde measurements. (au)
Self-similar magnetohydrodynamic boundary layers
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel; Lastra, Alberto, E-mail: mnjmhd@am.uva.e [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)
2010-10-15
The boundary layer created by parallel flow in a magnetized fluid of high conductivity is considered in this paper. Under appropriate boundary conditions, self-similar solutions analogous to the ones studied by Blasius for the hydrodynamic problem may be found. It is proved that for these to be stable, the size of the Alfven velocity at the outer flow must be smaller than the flow velocity, a fact that has a ready physical explanation. The process by which the transverse velocity and the thickness of the layer grow with the size of the Alfven velocity is detailed.
Free Boundary Value Problems for Abstract Elliptic Equations and Applications
Institute of Scientific and Technical Information of China (English)
Veli SHAKHMUROV
2011-01-01
The free boundary value problems for elliptic differential-operator equations are studied.Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract Lp-spaces are given.In application,the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic type equations are studied.
A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
Energy Technology Data Exchange (ETDEWEB)
Kupiainen, M; Sjogreen, B
2008-03-21
We here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in [6] and for the Euler equations of compressible fluid flow in [11], to the compressible Navier-Stokes equations. We describe the method and we implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.
Thick diffusion limit boundary layer test problems
International Nuclear Information System (INIS)
We develop two simple test problems that quantify the behavior of computational transport solutions in the presence of boundary layers that are not resolved by the spatial grid. In particular we study the quantitative effects of 'contamination' terms that, according to previous asymptotic analyses, may have a detrimental effect on the solutions obtained by both discontinuous finite element (DFEM) and characteristic-method (CM) spatial discretizations, at least for boundary layers caused by azimuthally asymmetric incident intensities. Few numerical results have illustrated the effects of this contamination, and none have quantified it to our knowledge. Our test problems use leading-order analytic solutions that should be equal to zero in the problem interior, which means the observed interior solution is the error introduced by the contamination terms. Results from DFEM solutions demonstrate that the contamination terms can cause error propagation into the problem interior for both orthogonal and non-orthogonal grids, and that this error is much worse for non-orthogonal grids. This behavior is consistent with the predictions of previous analyses. We conclude that these boundary layer test problems and their variants are useful tools for the study of errors that are introduced by unresolved boundary layers in diffusive transport problems. (authors)
DYNAMICS OF A BOUNDARY LAYER SEPARATION
Czech Academy of Sciences Publication Activity Database
Uruba, Václav; Knob, Martin
2009-01-01
Roč. 16, č. 1 (2009), s. 29-38. ISSN 1802-1484 R&D Projects: GA ČR GA101/08/1112 Institutional research plan: CEZ:AV0Z20760514 Keywords : boundary layer * triple-deck theory * Time-Resolved PIV Subject RIV: BK - Fluid Dynamics
Computation of 2D stratified flows in atmospheric boundary layer
Czech Academy of Sciences Publication Activity Database
Tauer, M.; Šimonek, J.; Kozel, Karel; Jaňour, Zbyněk
Praha : Ústav termomechaniky AV ČR, v. v. i., 2009 - (Jonáš, P.; Uruba, V.), s. 47-48 ISBN 978-80-87012-21-5. [Colloquium Fluid Dynamics 2009. Praha (CZ), 21.10.2009-23.10.2009] R&D Projects: GA ČR GA103/09/0977 Institutional research plan: CEZ:AV0Z20760514 Keywords : computation stratified flows * Navier-Stokes equations * atmospheric boundary layer Subject RIV: DG - Athmosphere Sciences, Meteorology
Nature, theory and modelling of geophysical convective planetary boundary layers
Zilitinkevich, Sergej
2015-04-01
Geophysical convective planetary boundary layers (CPBLs) are still poorly reproduced in oceanographic, hydrological and meteorological models. Besides the mean flow and usual shear-generated turbulence, CPBLs involve two types of motion disregarded in conventional theories: 'anarchy turbulence' comprised of the buoyancy-driven plumes, merging to form larger plumes instead of breaking down, as postulated in conventional theory (Zilitinkevich, 1973), large-scale organised structures fed by the potential energy of unstable stratification through inverse energy transfer in convective turbulence (and performing non-local transports irrespective of mean gradients of transporting properties). C-PBLs are strongly mixed and go on growing as long as the boundary layer remains unstable. Penetration of the mixed layer into the weakly turbulent, stably stratified free flow causes turbulent transports through the CPBL outer boundary. The proposed theory, taking into account the above listed features of CPBL, is based on the following recent developments: prognostic CPBL-depth equation in combination with diagnostic algorithm for turbulence fluxes at the CPBL inner and outer boundaries (Zilitinkevich, 1991, 2012, 2013; Zilitinkevich et al., 2006, 2012), deterministic model of self-organised convective structures combined with statistical turbulence-closure model of turbulence in the CPBL core (Zilitinkevich, 2013). It is demonstrated that the overall vertical transports are performed mostly by turbulence in the surface layer and entrainment layer (at the CPBL inner and outer boundaries) and mostly by organised structures in the CPBL core (Hellsten and Zilitinkevich, 2013). Principal difference between structural and turbulent mixing plays an important role in a number of practical problems: transport and dispersion of admixtures, microphysics of fogs and clouds, etc. The surface-layer turbulence in atmospheric and marine CPBLs is strongly enhanced by the velocity shears in
The free boundary Euler equations with large surface tension
Disconzi, Marcelo M.; Ebin, David G.
2015-01-01
We study the free boundary Euler equations with surface tension in three spatial dimensions, showing that the equations are well-posed if the coefficient of surface tension is positive. Then we prove that under natural assumptions, the solutions of the free boundary motion converge to solutions of the Euler equations in a domain with fixed boundary when the coefficient of surface tension tends to infinity.
The free boundary Euler equations with large surface tension
Disconzi, Marcelo M.; Ebin, David G.
2016-07-01
We study the free boundary Euler equations with surface tension in three spatial dimensions, showing that the equations are well-posed if the coefficient of surface tension is positive. Then we prove that under natural assumptions, the solutions of the free boundary motion converge to solutions of the Euler equations in a domain with fixed boundary when the coefficient of surface tension tends to infinity.
Energy Technology Data Exchange (ETDEWEB)
Ishak, Anuar; Nazar, Roslinda [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia); Pop, Ioan [Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253 (Romania)
2008-07-01
The steady mixed convection boundary layer flow through a stable stratified medium adjacent to a vertical surface is investigated. The velocity outside the boundary layer and the surface temperature are assumed to vary linearly from the leading edge of the surface. The transformed ordinary differential equations are solved numerically by the Keller-box method. It is found that dual solutions exist, and the thermal stratification delays the boundary layer separation. (author)
SOLVABILITY FOR NONLINEAR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The solvability of nonlinear elliptic equation with boundary perturbation is considered. The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.
Energy Technology Data Exchange (ETDEWEB)
Vlahostergios, Z. [Laboratory of Fluid Mechanics and Turbomachinery, Department of Mechanical Engineering, Aristotle University of Thessaloniki, Karamanli str., Thessaloniki 54124 (Greece); Yakinthos, K. [Laboratory of Fluid Mechanics and Turbomachinery, Department of Mechanical Engineering, Aristotle University of Thessaloniki, Karamanli str., Thessaloniki 54124 (Greece)], E-mail: kyros@eng.auth.gr; Goulas, A. [Laboratory of Fluid Mechanics and Turbomachinery, Department of Mechanical Engineering, Aristotle University of Thessaloniki, Karamanli str., Thessaloniki 54124 (Greece)
2009-08-15
We present an effort to model the separation-induced transition on a flat plate with a semi-circular leading edge, using a cubic non-linear eddy-viscosity model combined with the laminar kinetic energy. A non-linear model, compared to a linear one, has the advantage to resolve the anisotropic behavior of the Reynolds-stresses in the near-wall region and it provides a more accurate expression for the generation of turbulence in the transport equation of the turbulence kinetic energy. Although in its original formulation the model is not able to accurately predict the separation-induced transition, the inclusion of the laminar kinetic energy increases its accuracy. The adoption of the laminar kinetic energy by the non-linear model is presented in detail, together with some additional modifications required for the adaption of the laminar kinetic energy into the basic concepts of the non-linear eddy-viscosity model. The computational results using the proposed combined model are shown together with the ones obtained using an isotropic linear eddy-viscosity model, which adopts also the laminar kinetic energy concept and in comparison with the existing experimental data.
Governing equations for vibrating constrained-layer damping sandwich plates and beams.
Yan, M.-J.; Dowell, E. H.
1972-01-01
A simple differential equation is derived to describe constrained-layer damping in nonsymmetric sandwich plates and beams composed of isotropic and homogeneous layers. The natural boundary conditions related to this equation are determined and some typical numerical results obtained by this equation are given. The equation is valid within the linear theories of elasticity and viscoelasticity in the absence of any constraints on thicknesses, positions, symmetries, and densities of the layers.
MHD Boundary Layer Slip Flow and Heat Transfer over a Flat Plate
Institute of Scientific and Technical Information of China (English)
Krishnendu Bhattacharyya; Swati Mukhopadhyay; G.C.Layek
2011-01-01
An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented. A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method. In the boundary slip condition no local similarity occurs. Velocity and temperature distributions within the boundary layer are presented. Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate.%@@ An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented.A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method.In the boundary slip condition no local similarity occurs.Velocity and temperature distributions within the boundary layer are presented.Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate.
DNS of compressible turbulent boundary layer around a sharp cone
Institute of Scientific and Technical Information of China (English)
2008-01-01
Direct numerical simulation of the turbulent boundary layer over a sharp cone with 20° cone angle (or 10° half-cone angle) is performed by using the mixed seventh- order up-wind biased finite difference scheme and sixth-order central difference scheme. The free stream Mach number is 0.7 and free stream unit Reynolds number is 250000/inch. The characteristics of transition and turbulence of the sharp cone boundary layer are compared with those of the flat plate boundary layer. Statistics of fully developed turbulent flow agree well with the experimental and theoretical data for the turbulent flat-plate boundary layer flow. The near wall streak-like structure is shown and the average space between streaks (normalized by the local wall unit) keeps approximately invariable at different streamwise locations. The turbulent energy equation in the cylindrical coordinate is given and turbulent en-ergy budget is studied. The computed results show that the effect of circumferen-tial curvature on turbulence characteristics is not obvious.
DNS of compressible turbulent boundary layer around a sharp cone
Institute of Scientific and Technical Information of China (English)
LI XinLiang; FU DeXun; MA YanWen
2008-01-01
Direct numerical simulation of the turbulent boundary layer over a sharp cone with 20° cone angle (or 10° half-cone angle) is performed by using the mixed seventh-order up-wind biased finite difference scheme and sixth-order central difference scheme.The free stream Mach number is 0.7 and free stream unit Reynolds number is 250000/inch.The characteristics of transition and turbulence of the sharp cone boundary layer are compared with those of the flat plate boundary layer,Statistics of fully developed turbulent flow agree well with the experimental and theoretical data for the turbulent flat-plate boundary layer flow.The near wall streak-like structure is shown and the average space between streaks (normalized by the local wall unit) keeps approximately invariable at different streamwise locations,The turbulent energy equation in the cylindrical coordinate is given and turbulent en-ergy budget is studied.The computed results show that the effect of circumferen-tial curvature on turbulence characteristics is not obvious.
Active control of ionized boundary layers
Mendes, R V
1997-01-01
The challenging problems, in the field of control of chaos or of transition to chaos, lie in the domain of infinite-dimensional systems. Access to all variables being impossible in this case and the controlling action being limited to a few collective variables, it will not in general be possible to drive the whole system to the desired behaviour. A paradigmatic problem of this type is the control of the transition to turbulence in the boundary layer of fluid motion. By analysing a boundary layer flow for an ionized fluid near an airfoil, one concludes that active control of the transition amounts to the resolution of an generalized integro-differential eigenvalue problem. To cope with the required response times and phase accuracy, electromagnetic control, whenever possible, seems more appropriate than mechanical control by microactuators.
Magnetic activity in accretion disc boundary layers
Armitage, Philip J.
2002-03-01
We use three-dimensional magnetohydrodynamic simulations to study the structure of the boundary layer between an accretion disc and a non-rotating, unmagnetized star. Under the assumption that cooling is efficient, we obtain a narrow but highly variable transition region in which the radial velocity is only a small fraction of the sound speed. A large fraction of the energy dissipation occurs in high-density gas adjacent to the hydrostatic stellar envelope, and may therefore be reprocessed and largely hidden from view of the observer. As suggested by Pringle, the magnetic field energy in the boundary layer is strongly amplified by shear, and exceeds that in the disc by an order of magnitude. These fields may play a role in generating the magnetic activity, X-ray emission and outflows in disc systems where the accretion rate is high enough to overwhelm the stellar magnetosphere.
Analytic prediction for planar turbulent boundary layers
Chen, Xi
2016-01-01
Analytic predictions of mean velocity profile (MVP) and streamwise ($x$) development of related integral quantities are presented for flows in channel and turbulent boundary layer (TBL), based on a symmetry analysis of eddy length and total stress. Specific predictions are the friction velocity $u_\\tau$: ${ U_e/u_\\tau }\\approx 2.22\\ln Re_x+2.86-3.83\\ln(\\ln Re_x)$; the boundary layer thickness $\\delta_e$: $x/\\delta_e \\approx 7.27\\ln Re_x-5.18-12.52\\ln(\\ln Re_x)$; the momentum thickness Reynolds number: $Re_x/Re_\\theta=4.94[{(\\ln {{\\mathop{\\rm Re}\
DYNAMICS OF A BOUNDARY LAYER SEPARATION
Czech Academy of Sciences Publication Activity Database
Uruba, Václav
Budapest : University of Technology and Economics , 2009, s. 268-275. ISBN 978-963-420-985-0. [Conference on Modelling Fluid Flow CMFF'09. Budapest (HU), 09.09.2009-12.09.2009] R&D Projects: GA ČR GA101/08/1112 Institutional research plan: CEZ:AV0Z20760514 Keywords : boundary layer * dynamics * separation * POPs Subject RIV: BK - Fluid Dynamics
Numerical Simulation of the Atmospheric Boundary Layer
Czech Academy of Sciences Publication Activity Database
Bauer, Petr
Praha : Česká technika - nakladatelství ČVUT, 2006 - (Ambrož, P.; Masáková, Z.), s. 11-18 [Doktorandské dny 2006. Katedra matematiky FJFI ČVUT, Praha (CZ), 10.11.2006-24.11.2006] Institutional research plan: CEZ:AV0Z20760514 Keywords : atmospheric boundary layer * numerical simulation * finite element method Subject RIV: DI - Air Pollution ; Quality
Instabilities and transition in boundary layers
Indian Academy of Sciences (India)
N Vinod; Rama Govindarajan
2005-03-01
Some recent developments in boundary layer instabilities and transition are reviewed. Background disturbance levels determine the instability mechanism that ultimately leads to turbulence. At low noise levels, the traditional Tollmien–Schlichting route is followed, while at high levels, a `by-pass' route is more likely. Our recent work shows that spot birth is related to the pattern of secondary instability in either route.
Dynamical analysis of separated boundary layer flow
Czech Academy of Sciences Publication Activity Database
Uruba, Václav
Berlin : Technische Universität Berlin, 2009. s. 1-2 ISBN N. [Nonlinear Normal Modes, Dimension Reduction and Localization in Vibrating Systems. 27.09.2009-02.10.2009, Frascati (Rome)] R&D Projects: GA ČR GA101/08/1112 Institutional research plan: CEZ:AV0Z20760514 Keywords : boundary layer * separation * dynamics Subject RIV: BK - Fluid Dynamics
Submarine design optimization using boundary layer control
Christopher L Warren
1997-01-01
Several hull designs are studied with parametric based volume and area estimates to obtain preliminary hull forms. The volume and area study includes the effects of technologies which manifest themselves in the parametric study through stack length requirements. Subsequently, the hull forms are studied using a Reynolds Averaged Navier Stokes analysis coupled with a vortex lattice propeller design code. Optimization is done through boundary layer control analysis and through studies on the eff...
Coupled wake boundary layer model of windfarms
Stevens, Richard; Gayme, Dennice; Meneveau, Charles
2014-11-01
We present a coupled wake boundary layer (CWBL) model that describes the distribution of the power output in a windfarm. The model couples the traditional, industry-standard wake expansion/superposition approach with a top-down model for the overall windfarm boundary layer structure. Wake models capture the effect of turbine positioning, while the top-down approach represents the interaction between the windturbine wakes and the atmospheric boundary layer. Each portion of the CWBL model requires specification of a parameter that is unknown a-priori. The wake model requires the wake expansion rate, whereas the top-down model requires the effective spanwise turbine spacing within which the model's momentum balance is relevant. The wake expansion rate is obtained by matching the mean velocity at the turbine from both approaches, while the effective spanwise turbine spacing is determined from the wake model. Coupling of the constitutive components of the CWBL model is achieved by iterating these parameters until convergence is reached. We show that the CWBL model predictions compare more favorably with large eddy simulation results than those made with either the wake or top-down model in isolation and that the model can be applied successfully to the Horns Rev and Nysted windfarms. The `Fellowships for Young Energy Scientists' (YES!) of the Foundation for Fundamental Research on Matter supported by NWO, and NSF Grant #1243482.
The Pauli equation with complex boundary conditions
Kochan, D; Novak, R; Siegl, P
2012-01-01
We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. A special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T.
Uddin, Mohammed J.; Khan, Waqar A.; Ahmed I Ismail
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first convert...
Absorbing boundary conditions for second-order hyperbolic equations
Jiang, Hong; Wong, Yau Shu
1990-01-01
A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.
RADIATION BOUNDARY CONDITIONS FOR MAXWELL'S EQUATIONS: A REVIEW OF ACCURATE TIME-DOMAIN FORMULATIONS
Institute of Scientific and Technical Information of China (English)
Thomas Hagstrom; Stephen Lau
2007-01-01
We review time-domain formulations of radiation boundary conditions for Maxwell's equations, focusing on methods which can deliver arbitrary accuracy at acceptable computational cost. Examples include fast evaluations of nonlocal conditions on symmetric and general boundaries, methods based on identifying and evaluating equivalent sources, and local approximations such as the perfectly matched layer and sequences of local boundary conditions. Complexity estimates are derived to assess work and storage requirements as a function of wavelength and simulation time.
A global boundary-layer height climatology
Energy Technology Data Exchange (ETDEWEB)
Dop, H. van; Krol, M.; Holtslag, B. [Inst. for Marine and Atmospheric Research Utrecht, IMAU, Utrecht (Netherlands)
1997-10-01
In principle the ABL (atmospheric boundary layer) height can be retrieved from atmospheric global circulation models since they contain algorithms which determine the intensity of the turbulence as a function of height. However, these data are not routinely available, or on a (vertical) resolution which is too crude in view of the application. This justifies the development of a separate algorithm in order to define the ABL. The algorithm should include the generation of turbulence by both shear and buoyancy and should be based on readily available atmospheric parameters. There is obviously a wide application for boundary heights in off-line global and regional chemistry and transport modelling. It is also a much used parameter in air pollution meteorology. In this article we shall present a theory which is based on current insights in ABL dynamics. The theory is applicable over land and sea surfaces in all seasons. The theory is (for various reasons) not valid in mountainous areas. In areas where boundary-layer clouds or deep cumulus convection are present the theory does not apply. However, the same global atmospheric circulation models contain parameterizations for shallow and deep convection from which separate estimates can be obtained for the extent of vertical mixing. (au)
Magnetohydrodynamic Boundary Layer Slip Flow and Heat Transfer of Power Law Fluid over a Flat Plate
Directory of Open Access Journals (Sweden)
Jacob Hirschhorn
2016-01-01
Full Text Available In this paper, we consider the magnetohydrodynamic (MHD boundary layer flow and heat transfer of power law fluid over a flat plate with slip boundary conditions. We use a similarity transformation to convert the governing nonlinear partial differential equations into a system of ordinary differential equations and solve the resulting system numerically using MATLAB’s boundary value solver, bvp4c, and the shooting method. We present velocity and temperature profiles within the boundary layer and demonstrate the effect of changing the magnetic parameter, Prandtl number, and slip parameters.
The Pauli equation with complex boundary conditions
International Nuclear Information System (INIS)
We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin–magnetic interaction on the interplay between the type of boundary conditions and the spectrum. Special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)
The Pauli equation with complex boundary conditions
Kochan, D.; Krejčiřík, D.; Novák, R.; Siegl, P.
2012-11-01
We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. Special attention is paid to {PT}-symmetric boundary conditions with the physical choice of the time-reversal operator {T}. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Integral method for the calculation of three-dimensional, laminar and turbulent boundary layers
Stock, H. W.
1978-01-01
The method for turbulent flows is a further development of an existing method; profile families with two parameters and a lag entrainment method replace the simple entrainment method and power profiles with one parameter. The method for laminar flows is a new development. Moment of momentum equations were used for the solution of the problem, the profile families were derived from similar solutions of boundary layer equations. Laminar and turbulent flows at the wings were calculated. The influence of wing tapering on the boundary layer development was shown. The turbulent boundary layer for a revolution ellipsoid is calculated for 0 deg and 10 deg incidence angles.
Boundary-layer effects in composite laminates: Free-edge stress singularities, part 6
Wanag, S. S.; Choi, I.
1981-01-01
A rigorous mathematical model was obtained for the boundary-layer free-edge stress singularity in angleplied and crossplied fiber composite laminates. The solution was obtained using a method consisting of complex-variable stress function potentials and eigenfunction expansions. The required order of the boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution of the partial differential equations. Numerical results obtained show that the boundary-layer stress singularity depends only upon material elastic constants and fiber orientation of the adjacent plies. For angleplied and crossplied laminates the order of the singularity is weak in general.
Modelling turbulent spots in swept boundary layers
International Nuclear Information System (INIS)
Highlights: • A linear perturbation method can capture the important flow features within a turbulent spot. • The horseshoe vortex in the perturbed velocity field is the dominant flow feature. • Sweep leads to skewing of the turbulent spot and calmed region. • The effects of pressure gradient are generally reduced by sweep. -- Abstract: A computational technique is presented for determining the fully 3-d viscid unsteady perturbation to a non-developing laminar swept boundary layer. For zero pressure gradient, unswept boundary layers, the perturbation method reveals a strongly three dimensional flow within the turbulent spot and its associated calmed region which is very similar to that observed in experiments and full DNS calculations. The perturbation method cannot predict turbulent motion but nevertheless provides a simple yet accurate means of studying and understanding the development of turbulent spot geometry. The most influential flow feature is the horseshoe vortex observed in the fluctuation velocity field, which is responsible for delivering the fluid found in the calmed region between its trailing legs. The upwards flow around the outer periphery of the vortex is also responsible for delivering low momentum fluid to the spot, but additional high momentum fluid also enters the spot from its rear through the downward sweeping motion of fluid between the vortex legs. The effect of an adverse streamwise pressure gradient is to increase the size of the spot and calmed region whereas a favourable pressure gradient has the opposite effect. When sweep is introduced to the boundary layer the spot is skewed for all non-zero pressure gradients, but the changes in size of the spot and calmed region due to pressure gradient are reduced. For favourable pressure gradients the skew increases monotonically with sweep, but this is not the case for adverse pressure gradients where the effect of sweep is more complex
The open boundary equation (discussion paper)
Diederen, D.; Savenije, H.H.G.; Toffolon, M.
2015-01-01
We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection) under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave
Multilevel Model of Planetary Boundary-layer Suitable for use with Mesoscale Dynamic Models
DEFF Research Database (Denmark)
Busch, N. E.; Chang, S. W.; Anthes, R. A.
1976-01-01
In this paper a simple model of the planetary boundary layer (PBL) is proposed. The surface layer is modeled according to established similarity theory. Above the surface layer a prognostic equation for the mixing length is introduced. The time-dependent mixing length is a function of the PBL...
The large Reynolds number - Asymptotic theory of turbulent boundary layers.
Mellor, G. L.
1972-01-01
A self-consistent, asymptotic expansion of the one-point, mean turbulent equations of motion is obtained. Results such as the velocity defect law and the law of the wall evolve in a relatively rigorous manner, and a systematic ordering of the mean velocity boundary layer equations and their interaction with the main stream flow are obtained. The analysis is extended to the turbulent energy equation and to a treatment of the small scale equilibrium range of Kolmogoroff; in velocity correlation space the two-thirds power law is obtained. Thus, the two well-known 'laws' of turbulent flow are imbedded in an analysis which provides a great deal of other information.
Thin-Layer Solutions of the Helmholtz and Related Equations
Ockendon, J. R.
2012-01-01
This paper concerns a certain class of two-dimensional solutions to four generic partial differential equations-the Helmholtz, modified Helmholtz, and convection-diffusion equations, and the heat conduction equation in the frequency domain-and the connections between these equations for this particular class of solutions.S pecifically, we consider thin-layer solutions, valid in narrow regions across which there is rapid variation, in the singularly perturbed limit as the coefficient of the Laplacian tends to zero.F or the wellstudied Helmholtz equation, this is the high-frequency limit and the solutions in question underpin the conventional ray theory/WKB approach in that they provide descriptions valid in some of the regions where these classical techniques fail.E xamples are caustics, shadow boundaries, whispering gallery, and creeping waves and focusing and bouncing ball modes.It transpires that virtually all such thin-layer models reduce to a class of generalized parabolic wave equations, of which the heat conduction equation is a special case. Moreover, in most situations, we will find that the appropriate parabolic wave equation solutions can be derived as limits of exact solutions of the Helmholtz equation.W e also show how reasonably well-understood thin-layer phenomena associated with any one of the four generic equations may translate into less well-known effects associated with the others.In addition, our considerations also shed some light on the relationship between the methods of matched asymptotic, WKB, and multiple-scales expansions. © 2012 Society for Industrial and Applied Mathematics.
Direct numerical simulation of supersonic turbulent boundary layers
Guarini, Stephen
The objectives of this research were to develop a method by which the spatially developing compressible turbulent boundary layer could be simulated using a temporally developing numerical simulation and to study the physics of the compressible turbulent boundary layer. We take advantage of the technique developed by Spalart (1987, 1988) for the incompressible case. In this technique, it is recognized that the boundary layer exhibits slow growth in the streamwise direction, so the turbulence can be treated as approximately homogeneous in this direction. The slow growth is accounted for with a coordinate transformation and a multiple scale analysis. The result is a modified system of equations (Navier-Stokes plus some extra terms, which we call "slow growth terms") that are homogeneous in both the streamwise and spanwise directions and represent the state of the boundary layer at a given streamwise location (or, equivalently, a given thickness). The compressible Navier-Stokes equations are solved using a mixed Fourier and B-spline "spectral" method. The dependent variables are expanded in terms of a Fourier representation in the horizontal directions and a B-spline representation in the wall-normal direction. In the wall-normal direction non-reflecting boundary conditions are used at the freestream boundary, and zero-heat-flux no-slip boundary conditions are used at the wall. This combination of splines and Fourier methods produces a very accurate numerical method. Mixed implicit/explicit time discretization is used. Results are presented for a case with a Mach number of 2.5, and a Reynolds number, based on momentum integral thickness and wall viscosity, of Rsb{thetasp'} = 840. The results show that the van Driest transformed velocity satisfies the incompressible scalings and a narrow logarithmic region is obtained. The results for the turbulence intensities compare well with the incompressible simulations of Spalart. Pressure fluctuations are found to be higher than
Computing the Casimir force using regularized boundary integral equations
Kilen, Isak; Jakobsen, Per Kristen
2014-11-01
In this paper we use a novel regularization procedure to reduce the calculation of the Casimir force for 2D scalar fields between compact objects to the solution of a classical integral equation defined on the boundaries of the objects. The scalar fields are subject to Dirichlet boundary conditions on the object boundaries. We test the integral equation by comparing with what we get for parallel plates, concentric circles and adjacent circles using mode summation and the functional integral method. We show how symmetries in the shapes and configuration of boundaries can easily be incorporated into our method and that it leads to fast evaluation of the Casimir force for symmetric situations.
From the Boltzmann Equation to the Euler Equations in the Presence of Boundaries
Golse, François
2011-01-01
The fluid dynamic limit of the Boltzmann equation leading to the Euler equations for an incompressible fluid with constant density in the presence of material boundaries shares some important features with the better known inviscid limit of the Navier-Stokes equations. The present paper slightly extends recent results from [C. Bardos, F. Golse, L. Paillard, Comm. Math. Sci., 10 (2012), 159--190] to the case of boundary conditions for the Boltzmann equation more general than Maxwell's accomodation condition.
From the Boltzmann Equation to the Euler Equations in the Presence of Boundaries
Golse, François
2011-01-01
The fluid dynamic limit of the Boltzmann equation leading to the Euler equations for an incompressible fluid with constant density in the presence of material boundaries shares some important features with the better known inviscid limit of the Navier-Stokes equations. The present paper slightly extends recent results from [C. Bardos, F. Golse, L. Paillard, Comm. Math. Sci., 10 (2012), 159--190] to the case of boundary conditions for the Boltzmann equation more general than Maxwell's accomoda...
Cebeci, Tuncer
2005-01-01
This second edition of our book extends the modeling and calculation of boundary-layer flows to include compressible flows. The subjects cover laminar, transitional and turbulent boundary layers for two- and three-dimensional incompressible and compressible flows. The viscous-inviscid coupling between the boundary layer and the inviscid flow is also addressed. The book has a large number of homework problems.
Wave phenomena in a high Reynolds number compressible boundary layer
Bayliss, A.; Maestrello, L.; Parikh, P.; Turkel, E.
1987-01-01
The behavior of spatially unstable waves in a high Reynolds number compressible laminar boundary layer is investigated by solution of the laminar two-dimensional compressible Navier-Stokes equations (solved to fourth-order accuracy) over a flat plate with a fluctuating disturbance generated at the inflow. A significant nonlinear distortion is produced, in qualitative agreement with experimental data. It is shown that increasing compressibility can significantly stabilize the flow over a flat plate, and that the mechanism of phase cancellation is a viable mechanism for the control of growing disturbances.
Numerical simulation of 3D flows in atmospheric boundary layer
Czech Academy of Sciences Publication Activity Database
Šimonek, Jiří; Kozel, K.; Jaňour, Zbyněk
Praha : Ústav termomechaniky AV ČR, v. v. i, 2012 - (Šimurda, D.; Kozel, K.), s. 93-96 ISBN 978-80-87012-40-6. [Topical Problems of Fluid Mechanics 2012 . Praha (CZ), 15.02. 2012 -17.02. 2012 ] R&D Projects: GA ČR GAP101/12/1271 Institutional research plan: CEZ:AV0Z20760514 Keywords : numerical solution * atmospheric boundary layer * Navier-Stokes equation s Subject RIV: DG - Athmosphere Sciences, Meteorology
On the Implementation of 3D Galerkin Boundary Integral Equations
Energy Technology Data Exchange (ETDEWEB)
Nintcheu Fata, Sylvain [ORNL; Gray, Leonard J [ORNL
2010-01-01
In this article, a reverse contribution technique is proposed to accelerate the construction of the dense influence matrices associated with a Galerkin approximation of singular and hypersingular boundary integral equations of mixed-type in potential theory. In addition, a general-purpose sparse preconditioner for boundary element methods has also been developed to successfully deal with ill-conditioned linear systems arising from the discretization of mixed boundary-value problems on non-smooth surfaces. The proposed preconditioner, which originates from the precorrected-FFT method, is sparse, easy to generate and apply in a Krylov subspace iterative solution of discretized boundary integral equations. Moreover, an approximate inverse of the preconditioner is implicitly built by employing an incomplete LU factorization. Numerical experiments involving mixed boundary-value problems for the Laplace equation are included to illustrate the performance and validity of the proposed techniques.
APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS
Vorona Yu.V.; Kara I.D.
2015-01-01
Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.
APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS
Directory of Open Access Journals (Sweden)
Vorona Yu.V.
2015-12-01
Full Text Available Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.
Boundary value problems of discrete generalized Emden-Fowler equation
Institute of Scientific and Technical Information of China (English)
YU; Jianshe; GUO; Zhiming
2006-01-01
By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established.
Boundary Integral Equations and A Posteriori Error Estimates
Institute of Scientific and Technical Information of China (English)
YU Dehao; ZHAO Longhua
2005-01-01
Adaptive methods have been rapidly developed and applied in many fields of scientific and engineering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori error estimates based on the hyper-singular integral equations. Three kinds of residuals are used as the estimates for boundary element errors. The theoretical analysis and numerical examples show that the hyper-singular residuals are good a posteriori error indicators in many adaptive boundary element computations.
Numerical studies on laminar-turbulent transition in boundary layers
International Nuclear Information System (INIS)
Laminar-turbulent transition in flat-plate boundary layers is investigated by direct numerical solution of the full Navier-Stokes equations. Both forced transition (in parallel Blasius flow excited by a vibrating ribbon) and natural transition (in a decelerating boundary layer) are studied. In both cases, an initial state containing random noise is employed to eliminate bias in selecting unstable waves. In the simulations of ribbon-induced transition, close agreement with experiments (Saric et al. (1984)) is obtained for low-amplitude two-dimensional Tollmien-Schlichting waves-producing subharmonic breakdown (C- or H-type). For high amplitudes, a mixture of subharmonic and fundamental structures is observed. Clear-cut fundamental breakdown (K-type) is never obtained. In the simulation of the early stages of natural transition in a decelerating boundary layer, two-dimensional and/or slightly oblique waves initially grow due to the inflectional instability. When they become strong enough, they initiate a secondary instability leading to three dimensional distortion and Λ vortices, in good agreement with experiments (Gad-el-Hak et al. (1984)). The tips of the Λ vortices are rarely aligned with the flow direction, and that they appear locally in apace. A simple wave-interference model accounting for these features of natural transition has been developed. It suggests that multiple waves are active in the secondary instability, and that they are determined by unpredictable initial disturbances. The later stages of transition in a decelerating boundary layer were also studied with higher numerical resolution. The naturally-born Λ vortices undergo breakdown processes similar to those of ribbon-induced Λ vortices. Conversely, this justifies the conventional approach to study laminar-turbulent transition-the vibrating-ribbon technique
Froessling, Nils
1958-01-01
The fundamental boundary layer equations for the flow, temperature and concentration fields are presented. Two dimensional symmetrical and unsymmetrical and rotationally symmetrical steady boundary layer flows are treated as well as the transfer boundary layer. Approximation methods for the calculation of the transfer layer are discussed and a brief survey of an investigation into the validity of the law that the Nusselt number is proportional to the cube root of the Prandtl number is presented.
Modelling of the Evolving Stable Boundary Layer
Sorbjan, Zbigniew
2014-06-01
A single-column model of the evolving stable boundary layer (SBL) is tested for self-similar properties of the flow and effects of ambient forcing. The turbulence closure of the model is diagnostic, based on the K-theory approach, with a semi-empirical form of the mixing length, and empirical stability functions of the Richardson number. The model results, expressed in terms of local similarity scales, are universal functions, satisfied in the entire SBL. Based on similarity expression, a realizability condition is derived for the minimum allowable turbulent heat flux in the SBL. Numerical experiments show that the development of "horse-shoe" shaped, fixed-elevation hodographs in the interior of the SBL around sunrise is controlled by effects imposed by surface thermal forcing.
Geometric invariance of compressible turbulent boundary layers
Bi, Wei-Tao; Wu, Bin; She, Zhen-Su; Hussain, Fazle
2015-11-01
A symmetry based approach is applied to analyze the mean velocity and temperature fields of compressible, flat plate turbulent boundary layers (CTBL). A Reynolds stress length scale and a turbulent heat flux length scale are identified to possess the same defect scaling law in the CTBL bulk, which is solely owing to the constraint of the wall to the geometry of the wall-attached eddies, but invariant to compressibility and wall heat transfer. This invariance is called the geometric invariance of CTBL eddies and is likely the origin of the Mach number invariance of Morkovin's hypothesis, as well as the similarity of energy and momentum transports. A closure for the turbulent transport by using the invariant lengths is attainted to predict the mean velocity and temperature profiles in the CTBL bulk- superior to the van Driest transformation and the Reynolds analogy based relations for its sound physics and higher accuracy. Additionally, our approach offers a new understanding of turbulent Prandtl number.
Boundary stabilization of wave equations with variable coefficients
Institute of Scientific and Technical Information of China (English)
FENG; Shaoji
2001-01-01
［1］Chen, G., Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain, J. Math. Pures. & Appl., 1979, 58: 249.［2］Komornik, V., Exact controllability and stabilization, Research in Applied Mathematics (Series Editors: Ciarlet, P. G., Lions, J.), New York: Masson/John Wiley copublication, 1994.［3］Komornik, V., Zuazua, E., A direct method for the boundary stabilization of the wave equation, J. Math. Pures. & Appl., 1990, 69: 33.［4］Lagnese, J., Decay of solutions of wave equations in a bounded region with boundary dissipation, J. Differential Equations, 1983, 50: 163.［5］Lasiecka, I., Triggiani, R., Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions, Appl. Math. & Optim., 1992, 25: 189.［6］Wyler, A., Stability of wave equations with dissipative boundary conditions in a bounded domain, Differential and Integral Equations,1994, 7: 345.［7］Yao, P. F., On the observability inequality for exact controllability of wave equations with variable coefficients, SIAM J. Control & Optimization, 1999, 37, 5: 1568.［8］Wu, H., Shen, C. L., Yu, Y. L., Introduction to Riemannian Geometry (in Chinese), Beijing: Peking University Press, 1989.
On a stochastic Burgers equation with Dirichlet boundary conditions
Directory of Open Access Journals (Sweden)
Ekaterina T. Kolkovska
2003-01-01
Full Text Available We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.
Plasma boundary layer with active surface. Pt. 1
International Nuclear Information System (INIS)
The space-charge boundary layer between plasma and wall which is normally (almost) homogeneous may become instable and may decay into largely independent spots of plasma-induced unipolar-like discharges. In Tokamaks the existence of such highly inhomogeneous boundary plasmas often has been found by observation of arc tracks and of ''hot spots'' a.s.o. In this way wall erosion and production rates of plasma impurities will be enhanced, and several special phenomena of intense wall erosion (like ''carbon blooming'') may be traced back to such effects. In this paper the influence of electron emission from the wall (i.e. of an ''active'' surface) on the parameter of the space charge sheath is investigated, applying simple balance equations, as a first step towards an explanation of the transition from a homogeneous into an inhomogeneous boundary layer. Several variations of such models are calculated, using typical plasma parameters. Essential result is the dependence of the sheath potential and of the surface power density on the emission yield and on the net current density. Irrespective of the chosen constants the potential drop between plasma and wall turns out to become the higher the lower is the electron emission and the higher is the net current. Opposite is the dependence of the energy flux to the wall which, however, passes a minimum and increases rapidly again near the maximum net current jmax (with jmax∼jis(γ-1), where jis=ion saturation current, and γ=emission yield per ion). As a consequence, the wall loading is strongly enhanced as well in case of high negative net currents and intense electron emission, as near the maximum net current. This will be infavour of an instability of the boundary layer, resulting - with high probability - in the decay of the layer into plasma-induced arc spots. As a next step in this investigation of such plasma boundary layers a careful analysis of this transition is provided for, taking the specified conditions of the
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
International Nuclear Information System (INIS)
A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump, and thermal creep coefficients with linearized Boltzmann solutions for Maxwell’s accommodation model for different values of the accommodation coefficient. For this, the linearized R13 equations are solved for viscous slip, thermal creep, and temperature jump problems and the results are compared to the solutions of the linearized Boltzmann equation. The influence of different collision models (hard-sphere, Bhatnagar–Gross–Krook, and Maxwell molecules) and accommodation coefficients on the phenomenological coefficients is studied
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
Rana, Anirudh Singh; Struchtrup, Henning
2016-02-01
A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump, and thermal creep coefficients with linearized Boltzmann solutions for Maxwell's accommodation model for different values of the accommodation coefficient. For this, the linearized R13 equations are solved for viscous slip, thermal creep, and temperature jump problems and the results are compared to the solutions of the linearized Boltzmann equation. The influence of different collision models (hard-sphere, Bhatnagar-Gross-Krook, and Maxwell molecules) and accommodation coefficients on the phenomenological coefficients is studied.
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
Energy Technology Data Exchange (ETDEWEB)
Rana, Anirudh Singh, E-mail: anirudh@uvic.ca [Department of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 52828 (Korea, Republic of); Struchtrup, Henning, E-mail: struchtr@uvic.ca [Department of Mechanical Engineering, University of Victoria, Victoria, British Columbia V8W 2Y2 (Canada)
2016-02-15
A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump, and thermal creep coefficients with linearized Boltzmann solutions for Maxwell’s accommodation model for different values of the accommodation coefficient. For this, the linearized R13 equations are solved for viscous slip, thermal creep, and temperature jump problems and the results are compared to the solutions of the linearized Boltzmann equation. The influence of different collision models (hard-sphere, Bhatnagar–Gross–Krook, and Maxwell molecules) and accommodation coefficients on the phenomenological coefficients is studied.
Geostrophic convective turbulence: The effect of boundary layers
Ostilla-Mónico, Rodolfo; Kunnen, Rudie P J; Verzicco, Roberto; Lohse, Detlef
2014-01-01
This Letter presents results of the first direct numerical simulations of rotating Rayleigh--B\\'enard convection in the so-called geostrophic regime, (hence very small Ekman numbers $\\mathcal{O}(10^{-7})$ and high Rayleigh numbers~$Ra=10^{10}$ and~$5\\cdot 10^{10}$), employing the \\emph{full} Navier--Stokes equations. In the geostrophic regime the criteria of very strong rotation and large supercriticality are met simultaneously, which is true for many geophysical and astrophysical flows. Until now, numerical approaches of this regime have been based on \\emph{reduced} versions of the Navier--Stokes equations (cf. Sprague \\emph{et al.} J. Fluid Mech., \\textbf{551}, 141 (2006)), omitting the effect of the viscous (Ekman) boundary layers. By using different velocity boundary conditions at the plates, we study the effect of these Ekman layers. We find that the formation of large-scale structures (Rubio \\emph{et al.} (Phys. Rev. Lett. \\textbf{112} (2014)), which indicates the presence of an inverse energy cascade, ...
Subgrid-scale turbulence in shock-boundary layer flows
Jammalamadaka, Avinash; Jaberi, Farhad
2015-04-01
Data generated by direct numerical simulation (DNS) for a Mach 2.75 zero-pressure gradient turbulent boundary layer interacting with shocks of different intensities are used for a priori analysis of subgrid-scale (SGS) turbulence and various terms in the compressible filtered Navier-Stokes equations. The numerical method used for DNS is based on a hybrid scheme that uses a non-dissipative central scheme in the shock-free turbulent regions and a robust monotonicity-preserving scheme in the shock regions. The behavior of SGS stresses and their components, namely Leonard, Cross and Reynolds components, is examined in various regions of the flow for different shock intensities and filter widths. The backscatter in various regions of the flow is found to be significant only instantaneously, while the ensemble-averaged statistics indicate no significant backscatter. The budgets for the SGS kinetic energy equation are examined for a better understanding of shock-tubulence interactions at the subgrid level and also with the aim of providing useful information for one-equation LES models. A term-by-term analysis of SGS terms in the filtered total energy equation indicate that while each term in this equation is significant by itself, the net contribution by all of them is relatively small. This observation is consistent with our a posteriori analysis.
On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers
Guedda, Mohamed
2008-01-01
The present work deals with the two-dimensional incompressible,laminar, steady-state boundary layer equations. First, we determinea family of velocity distributions outside the boundary layer suchthat these problems may have similarity solutions. Then, we examenin detail new exact solutions, called Pseudo--similarity, where the external velocity varies inversely-linear with the distance along the surface $ (U_e(x) = U_\\infty x^{-1}). The present work deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations. First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity solutions. Then, we examenin detail new exact solutions. The analysis shows that solutions exist only for a lateral suction. For specified conditions, we establish the existence of an infinite number of solutions, including monotonic solutions and solutions which oscillate an infinite number of times and tend to a certain limit. The properties o...
Large Eddy Simulation and Study of the Urban Boundary Layer
Institute of Scientific and Technical Information of China (English)
苗世光; 蒋维楣
2004-01-01
Based on a pseudo-spectral large eddy simulation (LES) model, an LES model with an anisotropy turbulent kinetic energy (TKE) closure model and an explicit multi-stage third-order Runge-Kutta scheme is established. The modeling and analysis show that the LES model can simulate the planetary boundary layer (PBL) with a uniform underlying surface under various stratifications very well. Then, similar to the description of a forest canopy, the drag term on momentum and the production term of TKE by subgrid city buildings are introduced into the LES equations to account for the area-averaged effect of the subgrid urban canopy elements and to simulate the meteorological fields of the urban boundary layer (UBL). Numerical experiments and comparison analysis show that: (1) the result from the LES of the UBL with a proposed formula for the drag coefficient is consistent and comparable with that from wind tunnel experiments and an urban subdomain scale model; (2) due to the effect of urban buildings, the wind velocity near the canopy is decreased, turbulence is intensified, TKE, variance, and momentum flux are increased, the momentum and heat flux at the top of the PBL are increased, and the development of the PBL is quickened; (3) the height of the roughness sublayer (RS) of the actual city buildings is the maximum building height (1.5-3 times the mean building height), and a constant flux layer (CFL) exists in the lower part of the UBL.
A Cautionary Note on the Thermal Boundary Layer Similarity Scaling for the Turbulent Boundary Layer
Weyburne, David
2016-01-01
Wang and Castillo have developed empirical parameters for scaling the temperature profile of the turbulent boundary layer flowing over a heated wall in the paper X. Wang and L. Castillo, J. Turbul., 4, 1(2003). They presented experimental data plots that showed similarity type behavior when scaled with their new scaling parameters. However, what was actually plotted, and what actually showed similarity type behavior, was not the temperature profile but the defect profile formed by subtracting the temperature in the boundary layer from the temperature in the bulk flow. We show that if the same data and same scaling is replotted as just the scaled temperature profile, similarity is no longer prevalent. This failure to show both defect profile similarity and temperature profile similarity is indicative of false similarity. The nature of this false similarity problem is discussed in detail.
Stabilization of the hypersonic boundary layer by finite-amplitude streaks
Ren, Jie; Fu, Song; Hanifi, Ardeshir
2016-02-01
Stabilization of two-dimensional disturbances in hypersonic boundary layer flows by finite-amplitude streaks is investigated using nonlinear parabolized stability equations. The boundary-layer flows at Mach numbers 4.5 and 6.0 are studied in which both first and second modes are supported. The streaks considered here are driven either by the so-called optimal perturbations (Klebanoff-type) or the centrifugal instability (Görtler-type). When the streak amplitude is in an appropriate range, i.e., large enough to modulate the laminar boundary layer but low enough to not trigger secondary instability, both first and second modes can effectively be suppressed.
On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers
Guedda, Mohamed; Hammouch, Zakia
2006-01-01
The present work deals with the two-dimensional incompressible,laminar, steady-state boundary layer equations. First, we determinea family of velocity distributions outside the boundary layer suchthat these problems may have similarity solutions. Then, we examenin detail new exact solutions, called Pseudo--similarity, where the external velocity varies inversely-linear with the distance along the surface $ (U_e(x) = U_\\infty x^{-1}). The present work deals with the two-dimensional incompressi...
Stationary plasma-field equilibrium states in astropause boundary layers
International Nuclear Information System (INIS)
The transition layer between a stellar wind plasma and the surrounding regime of magnetized interstellar plasma, i.e. the astropause boundary layer has been investigated theoretically. For the description of the 'microscopic' structures a planar representation of the transition zone geometry is used. Here the plasma is taken to be dominated by instability-induced collective relaxation processes as, for example, modified two-stream instabilities, keeping the effective electron and proton temperatures close to each other. These are caused by strong couplings between the plasma constituents and the equilibrium wave field. This permits a quasi-hydrodynamic description of the plasma flow in a two-fluid approximation. For this case a system of differential equations is developed describing consistently the dynamical variables of the plasma and the magnetic and electric fields in the transition region. Integrals of this system are discussed and it is shown that it can be reduced to one ordinary differential equation. This equation is solved in terms of elliptic integrals and gives an implicit representation of magnetic and electric fields and the density. (author)
Directory of Open Access Journals (Sweden)
Guotao Wang
2012-01-01
Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.
The Boundary Layer Interaction with Shock Wave and Expansion Fan
Institute of Scientific and Technical Information of China (English)
MaratA.Goldfeld; RomanV.Nestoulia; 等
2000-01-01
The results of experimental investigation of a turbulent boundary layer on compression and expansion surfaces are presented.They include the study of the shock wave and /or expansion fan action upon the boundary layer,boundary layer sepqartion and its relaxation.Complex events of paired interactions and the flow on compression convex-concave surfaces were studied.The posibility and conditions of the boundary layer relaminarization behind the expansion fan and its effect on the relaxation length are presented.Different model configurations for wide range conditions were investigated.Comparison of results for different interactions was carried out.
Solitons induced by boundary conditions from the Boussinesq equation
Chou, Ru Ling; Chu, C. K.
1990-01-01
The behavior of solitons induced by boundary excitation is investigated at various time-dependent conditions and different unperturbed water depths, using the Korteweg-de Vries (KdV) equation. Then, solitons induced from Boussinesq equations under similar conditions were studied, making it possible to remove the restriction in the KdV equation and to treat soliton head-on collisions (as well as overtaking collisions) and reflections. It is found that the results obtained from the KdV and the Boussinesq equations are in good agreement.
Institute of Scientific and Technical Information of China (English)
任景莉; 葛渭高
2003-01-01
A boundary value problems f or functional differenatial equations, with nonlinear boundary condition, is studied by the theorem of differential inequality. Using new method to construct the upper solution and lower solution, sufficient conditions for the existence of the problems' solution are established. A uniformly valid asymptotic expansions of the solution is also given.
Simulation of Wind turbines in the atmospheric boundary layer
DEFF Research Database (Denmark)
Chivaee, Hamid Sarlak; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming
Large eddy simulation of an arbitrary wind farm is studied in the neutral and thermally stratified atmospheric boundary Layer. Large eddy simulations of industrial flows usually requires full resolution of the flow near the wall and this is believed to be one of the main deficiencies of LES because...... in the boundary layer. In the current study, another approach has been implemented to simulate the flow in a fully developed wind farm boundary layer. The approach is based on Immersed Boundary Method and involves implementation of an arbitrary prescribed initial boundary layer. An initial boundary...... based on the turbine wakes and buoyancy contributions. The implemented method is capable of capturing the most important features of wakes of wind farms [2] while having the advantage of resolving the wall layer with a coarser grid than a typical required grid size for such problems. LES simulations are...
Abels, Helmut
2005-05-01
We study the generalized Stokes equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer Ω _0 = mathbb{R}^{n - 1} × ( - 1,1). Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. In this second part, we use pseudodifferential operator techniques to construct a parametrix to the reduced Stokes equations, which solves the system in Lq-Sobolev spaces, 1 calculus of the (reduced) Stokes operator.
Periodic solutions to nonlinear equations with oblique boundary conditions
Allergretto, Walter; Papini, Duccio
2012-01-01
We study the existence of positive periodic solutions to nonlinear elliptic and parabolic equations with oblique and dynamical boundary conditions and non-local terms. The results are obtained through fixed point theory, topological degree methods and properties of related linear elliptic problems with natural boundary conditions and possibly non-symmetric principal part. As immediate consequences, we also obtain estimates on the principal eigenvalue for non-symmetric elliptic ...
Characteristics of the boundary layer of magnetic clouds and a new definition of the cloud boundary
Institute of Scientific and Technical Information of China (English)
魏奉思; 刘睿; 范全林; 冯学尚
2003-01-01
Based on the analysis of the boundaries of 70 magnetic clouds from 1967 to 1998, and relatively complete spacecraft observations, it is indicated that the magnetic cloud boundaries are boundary layers formed through the interaction between the magnetic clouds and the ambient medium. Most of the outer boundaries of the layers, with relatively high proton temperature, density and plasma β, are magnetic reconnection boundaries, while the inner boundaries, with low proton temperature, proton density and plasma β, separate the main body of magnetic clouds, which has not been affected by the interaction, from the boundary layers. The average time scale of the front boundary layer is 1.7 h and that of the tail boundary layer 3.1 h. It is also found that the magnetic probability distribution function undergoes significant changes across the boundary layers. This new definition, supported by the preliminary numerical simulation in principle, could qualitatively explain the observations of interplanetary magnetic clouds, and could help resolve the controversy in identifying the boundaries of magnetic clouds. Our concept of the boundary layer may provide some understanding of what underlies the observations, and a fresh train of thought in the interplanetary dynamics research.
Traveling waves for a boundary reaction-diffusion equation
Caffarelli, L; Sire, Y
2011-01-01
We prove the existence of a traveling wave solution for a boundary reaction diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for traveling wave solutions of a free boundary problem obtained as singular limit for the reaction-diffusion equation (the so-called high energy activation energy limit). This explicit formula, which is interesting in itself, also allows us to get an estimate on the decay at infinity of the traveling wave (which turns out to be faster than the usual exponential decay).
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
[Objective] The aim was to study the characteristics of the changes of the urban boundary layer thermodynamic stability induced by heat island effect and their influences on precipitation.[Method] Proceeding from the thermodynamic equation,the changes of urban boundary layer thermodynamic stability caused by the urban heat disturbance and the mean state of heat island effect were discussed.The influence of the changes of urban boundary layer thermodynamic stability on the precipitation was expounded.Combini...
Linear boundary value problems for differential algebraic equations
Balla, Katalin; März, Roswitha
2003-01-01
By the use of the corresponding shift matrix, the paper gives a criterion for the unique solvability of linear boundary value problems posed for linear differential algebraic equations up to index 2 with well-matched leading coefficients. The solution is constructed by a proper Green function. Another characterization of the solutions is based upon the description of arbitrary affine linear subspaces of solutions to linear differential algebraic equations in terms of solutions to the adjoint ...
The Einstein Constraint Equations on Compact Manifolds with Boundary
Dilts, James
2013-01-01
We continue the study of the Einstein constraint equations on compact manifolds with boundary initiated by Holst and Tsogtgerel in their 2013 paper. In particular, we consider the full system and prove existence of solutions in both the near-CMC and far-from-CMC (for Yamabe positive metrics) cases. We also prove analogues many of the useful inequalities and results in previous "limit equation" papers by Dahl, Gicquaud, Humbert and others.
Institute of Scientific and Technical Information of China (English)
MO Jia-qi
2008-01-01
In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
Institute of Scientific and Technical Information of China (English)
Jingsun Yao; Jiaqi Mo
2005-01-01
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
Institute of Scientific and Technical Information of China (English)
MO Jia-qi; WANG Hui; LIN Wan-tao
2005-01-01
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, first, the outer solution of the original problem was obtained. Secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer was constructed. Finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied, and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.
Bhupesh Kumar Mahatha; Raj Nandkeolyar; Goutam Kumar Mahato; Precious Sibanda
2016-01-01
Two dimensional steady hydromagnetic boundary layer flow of a viscous, incompressible, and electrically conducting nanofluid past a stretching sheet with Newtonian heating, in the presence of viscous and Joule dissipations is studied. The transport equations include the combined effects of Brownian motion and thermophoresis. The governing nonlinear partial differential equations are transformed to a set of nonlinear ordinary differential equations which are then solved using Spect...
An analytical solution for the Marangoni mixed convection boundary layer flow
DEFF Research Database (Denmark)
Moghimi, M. A.; Kimiaeifar, Amin; Rahimpour, M.; Bagheri, G. H.
2010-01-01
In this article, an analytical solution for a Marangoni mixed convection boundary layer flow is presented. A similarity transform reduces the Navier-Stokes equations to a set of nonlinear ordinary differential equations, which are solved analytically by means of the homotopy analysis method (HAM...... control the convergence of the solution. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on the HAM....
Directory of Open Access Journals (Sweden)
JHANKAL ANUJ
2014-01-01
Full Text Available Using He’s Homotopy Perturbation Method (HPM, the system of non-linear partial differential equations governing the MHD boundary layer equations with low pressure gradient over a flat plate are solved. The main advantage of HPM is that it does not require the small parameters in the equations and hence the limitations of traditional perturbation can be eliminated. The influence of various relevant physical characteristics are presented and discussed.
Direct numerical simulation of turbulent thermal boundary layers
Kong, Hojin; Choi, Haecheon; Lee, Joon Sik
2000-10-01
In this paper, a method of generating realistic turbulent temperature fluctuations at a computational inlet is proposed and direct numerical simulations of turbulent thermal boundary layers developing on a flat plate with isothermal and isoflux wall boundary conditions are carried out. Governing equations are integrated using a fully implicit fractional-step method with 352×64×128 grids for the Reynolds number of 300, based on the free-stream velocity and the inlet momentum thickness, and the Prandtl number of 0.71. The computed Stanton numbers for the isothermal and isoflux walls are in good agreement with power-law relations without transient region from the inlet. The mean statistical quantities including root-mean-square temperature fluctuations, turbulent heat fluxes, turbulent Prandtl number, and skewness and flatness of temperature fluctuations agree well with existing experimental and numerical data. A quadrant analysis is performed to investigate the coherence between the velocity and temperature fluctuations. It is shown that the behavior of the wall-normal heat flux is similar to that of the Reynolds shear stress, indicating close correlation between the streamwise velocity and temperature. The effect of different thermal boundary conditions at the wall on the near-wall turbulence statistics is also discussed.
Transition Delay in Hypersonic Boundary Layers via Optimal Perturbations
Paredes, Pedro; Choudhari, Meelan M.; Li, Fei
2016-01-01
The effect of nonlinear optimal streaks on disturbance growth in a Mach 6 axisymmetric flow over a 7deg half-angle cone is investigated in an e ort to expand the range of available techniques for transition control. Plane-marching parabolized stability equations are used to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone, but subharmonic first mode instabilities, which are destabilized by the presence of the streaks, reach N = 6 near the end of the cone. These results suggest a passive flow control strategy of using micro vortex generators to induce streaks that would delay transition in hypersonic boundary layers.
Uddin Mohammed Jashim; Khan Waqar Ahamed; Ismail Ahmad Izani; Hamad M.A.A.
2015-01-01
A mathematical model is presented and analyzed for steady two-dimensional non-isothermal laminar free convective boundary layer flow along a convectively heated moving horizontal plate. New similarity transformations are developed using one parameter deductive group transformations and hence the governing transport equations are reduced to a system of coupled, nonlinear ordinary differential equations with associated boundary conditions. The reduced equatio...
High frequency ground temperature fluctuation in a Convective Boundary Layer
Garai, A.; Kleissl, J.; Lothon, M.; Lohou, F.; Pardyjak, E.; Saïd, F.; Cuxart, J.; Steeneveld, G.J.; Yaguë, C.; Derrien, S.; Alexander, D.; Villagrasa, D.M.
2012-01-01
To study influence of the turbulent structures in the convective boundary layer (CBL) on the ground temperature, during the Boundary Layer Late Afternoon and Sunset Turbulence (BLLAST) observational campaign, high frequency ground temperature was recorded through infra-red imagery from 13 June - 8 J
Numerical solutions of telegraph equations with the Dirichlet boundary condition
Ashyralyev, Allaberen; Turkcan, Kadriye Tuba; Koksal, Mehmet Emir
2016-08-01
In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.
Local boundary layer scales in turbulent Rayleigh-Benard convection
Scheel, Janet D
2014-01-01
We compute fully local boundary layer scales in three-dimensional turbulent Rayleigh-Benard convection. These scales are directly connected to the highly intermittent fluctuations of the fluxes of momentum and heat at the isothermal top and bottom walls and are statistically distributed around the corresponding mean thickness scales. The local boundary layer scales also reflect the strong spatial inhomogeneities of both boundary layers due to the large-scale, but complex and intermittent, circulation that builds up in closed convection cells. Similar to turbulent boundary layers, we define inner scales based on local shear stress which can be consistently extended to the classical viscous scales in bulk turbulence, e.g. the Kolmogorov scale, and outer scales based on slopes at the wall. We discuss the consequences of our generalization, in particular the scaling of our inner and outer boundary layer thicknesses and the resulting shear Reynolds number with respect to Rayleigh number. The mean outer thickness s...
Institute of Scientific and Technical Information of China (English)
MO Jiaqi; WANG Hui; LIN Wantao
2006-01-01
The perturbed boundary undercurrent is an exceptional event in the tropical atmosphere and ocean. It is a complicated nonlinear system. Its appearance badly affects not only natural conditions such as climate and environment,but also global economic development and human living, and brings about many calamities. Thus there is very attractive study on its rules in the international academic circles. Many scholars made more studies on its local and whole behaviors using different methods, such as self-anamnestic principle, Fokker-Plank Equation method, higher order singular pedigree and predictable study, rapid change on boundary, indeterminate adaptive control, multi-cogradient method and so on. Nonlinear perturbed theory and approximate method are very attractive studies in the international academic circles. Many scholars considered a class of nonlinear problems for the ordinary differential equation, the reaction diffusion equations, the boundary value of elliptic equation, the initial boundary value of hyperbolic equation, the shock layer solution of nonlinear equation and so on. In this paper, a class of perturbed mechanism for the western boundary undercurrents in the equator Pacific is considered. Under suitable conditions, using a homotopic mapping theory and method, we obtain a simple and rapid arbitrary order approximate solution for the corresponding nonlinear system. For example, a special case shows that using the homotopic mapping method, there is a high accuracy for the computed value.It is also provided from the results that the solution for homotopic mapping solving method can be used for analyzing operator for perturbed mechanism of western boundary undercurrents in the equator Pacific.
Navier-Stokes equation with slip-like boundary condition
Ken'ichi Hashizume; Tetsuya Koyama; Mitsuharu Otani
2009-01-01
The aim of this note is to investigate a time-discretized 2-dimensional Navier-Stokes equation with a slip-like boundary condition, which arises in the melting ice problem. We prove the existence and uniqueness of a weak solution.
Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition
Directory of Open Access Journals (Sweden)
Shengjun Li
2012-01-01
Full Text Available We study the existence of positive solutions for second-order nonlinear differential equations with nonseparated boundary conditions. Our nonlinearity may be singular in its dependent variable. The proof of the main result relies on a nonlinear alternative principle of Leray-Schauder. Recent results in the literature are generalized and significantly improved.
QUENCHING ON BOUNDARY TO THE NEWTON FILTRATION EQUATION (Ⅰ)
Institute of Scientific and Technical Information of China (English)
段志文; 谢春红; 卢伟明
2003-01-01
This paper discusses the global existence and quenching of the solution to the Newton filtration equation with the nonlinear boundary condition.The authors also discuss the profile of the quenching solution in the quenching time and obtain the quenching rate of the quenching solution.
Boundary Layer to a System of Viscous Hyperbolic Conservation Laws
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper, we investigate the large-time behavior of solutions to the initial-boundary value problem for nxn hyperbolic system of conservation laws with artificial viscosity in the half line (0, ∞). We first show that a boundary layer exists if the corresponding hyperbolic part contains at least one characteristic field with negative propagation speed. We further show that such boundary layer is nonlinearly stable under small initial perturbation. The proofs are given by an elementary energy method.
Institute of Scientific and Technical Information of China (English)
Mo Jiaqi
2007-01-01
A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.
Aerodynamic Heating in Hypersonic Boundary Layers:\\ Role of Dilatational Waves
Zhu, Yiding; Wu, Jiezhi; Chen, Shiyi; Lee, Cunbiao; Gad-el-Hak, Mohamed
2016-01-01
The evolution of multi-mode instabilities in a hypersonic boundary layer and their effects on aerodynamic heating are investigated. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors, fluorescent temperature-sensitive paint (TSP), and particle image velocimetry (PIV). Calculations are also performed based on both parabolized stability equations (PSE) and direct numerical simulations (DNS). It is found that second-mode dilatational waves, accompanied by high-frequency alternating fluid compression and expansion, produce intense aerodynamic heating in a small region that rapidly heats the fluid passing through it. As a result, the surface temperature rapidly increases and results in an overshoot over the nominal transitional value. When the dilatation waves decay downstream, the surface temperature decreases gradually until transition is completed. A theoretical analysis is provided to interpret the temperature distribution affected by ...
On the wave equation with semilinear porous acoustic boundary conditions
Graber, Philip Jameson
2012-05-01
The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.
Boundary layer flow on a moving surface in otherwise quiescent pseudo-plastic non-Newtonian fluids
Institute of Scientific and Technical Information of China (English)
Liancun Zheng; Liu Ting; Xinxin Zhang
2008-01-01
A theoretical analysis for the boundary layer flow over a continuous moving surface in an otherwise quiescent pseudo-plastic non-Newtonian fluid medium was presented. The types of potential flows necessary for similar solutions to the boundary layer equations were determined and the solutions were numerically presented for different values of power law exponent.
Gravity actions, boundary terms and second-order field equations
International Nuclear Information System (INIS)
The Lovelock action is a natural generalization of the Einstein-Hilbert gravity action in higher (more than four) dimensions. Certain boundary terms have to be added to this action because of various reasons which we briefly review. Dimensional reduction of the Lovelock action leads to a generalized Einstein-Yang-Mills (+ scalar field or σ-models) action in lower dimensions. Since the field equations derived from the Lovelock action are of second order only, the same holds for the dimensionally reduced action. The necessary boundary terms for the latter action are then obtained by dimensional reduction of the boundary terms in the Lovelock action. We consider reduction from n to n-1 dimensions in some detail and obtain generalizations of Horndeski's non-minimally coupled Einstein-Maxwell action with second-order field equations in more than four dimensions. (orig./HSI)
Numerical simulation of tsunami-scale wave boundary layers
DEFF Research Database (Denmark)
Williams, Isaac A.; Fuhrman, David R.
2016-01-01
, boundary layer thickness, turbulence, and bed shear stresses induced are systematically monitored and parameterised, under both hydraulically smooth and roughbed conditions. The results generally support a notion that the boundary layers induced by tsunami-scalewaves are both current-like, due...... layer properties beneath wind-waves maintain reasonable accuracy when extrapolated to full tsunami scales. Boundary layers driven by actual field-measured tsunami signals are likewise simulated, stemming from both the 2004 Indian Ocean as well as the 2011 Tohoku events. These results are reconciled...
Solving wave equation with spectral methods and nonreflecting boundary conditions
Novák, J; Novak, Jerome; Bonazzola, Silvano
2002-01-01
A multidomain spectral method for solving wave equations is presented. This method relies on the expansion of functions on basis of spherical harmonics $(Y_l^m(\\theta, \\phi))$ for the angular dependence and of Chebyshev polynomials $T_n(x)$ for the radial part. The spherical domains consist of shells surrounding a nucleus and cover the space up to a finite radius $R$ at which boundary conditions are imposed. Time derivatives are estimated using standard finite-differences second order schemes, which are chosen to be implicit to allow for (almost) any size of time-step. Emphasis is put on the implementation of absorbing boundary conditions that allow for the numerical boundary to be completely transparent to the physical wave. This is done using a multipolar expansion of an exact boundary condition for outgoing waves, which is truncated at some point. Using an auxiliary function, which is solution of a wave equation on the sphere defining the outer boundary of the numerical grid, the absorbing boundary conditi...
Study of effect of a smooth hump on hypersonic boundary layer instability
Park, Donghun; Park, Seung O.
2016-05-01
Effect of a two-dimensional smooth hump on linear instability of hypersonic boundary layer is studied by using parabolized stability equations. Linear evolution of mode S over a hump is analyzed for Mach 4.5 and 5.92 flat plate and Mach 7.1 sharp cone boundary layers. Mean flow for stability analysis is obtained by solving the parabolized Navier-Stokes equations. Hump with height smaller than local boundary layer thickness is considered. The case of flat plate and sharp cone without the hump are also studied to provide comparable data. For flat plate boundary layers, destabilization and stabilization effect is confirmed for hump located at upstream and downstream of synchronization point, respectively. Results of parametric studies to examine the effect of hump height, location, etc., are also given. For sharp cone boundary layer, stabilization influence of hump is also identified for a specific range of frequency. Stabilization influence of hump on convective instability of mode S is found to be a possible cause of previous experimental observations of delaying transition in hypersonic boundary layers.
Partial differential equations & boundary value problems with Maple
Articolo, George A
2009-01-01
Partial Differential Equations and Boundary Value Problems with Maple presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours- an investment that provides substantial returns. Maple''s animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations. Maple files can be found on the books website. Ancillary list: Maple files- http://www.elsevierdirect.com/companion.jsp?ISBN=9780123747327 Provides a quick overview of the software w/simple commands needed to get startedIncludes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equationsIncorporates an early introduction to Sturm-L...
Diffusive boundary layers over varying topography
Dell, R. W.
2015-03-25
Diffusive bottom boundary layers can produce upslope flows in a stratified fluid. Accumulating observations suggest that these boundary layers may drive upwelling and mixing in mid-ocean ridge flank canyons. However, most studies of diffusive bottom boundary layers to date have concentrated on constant bottom slopes. We present a study of how diffusive boundary layers interact with various idealized topography, such as changes in bottom slope, slopes with corrugations and isolated sills. We use linear theory and numerical simulations in the regional ocean modeling system (ROMS) model to show changes in bottom slope can cause convergences and divergences within the boundary layer, in turn causing fluid exchanges that reach far into the overlying fluid and alter stratification far from the bottom. We also identify several different regimes of boundary-layer behaviour for topography with oceanographically relevant size and shape, including reversing flows and overflows, and we develop a simple theory that predicts the regime boundaries, including what topographies will generate overflows. As observations also suggest there may be overflows in deep canyons where the flow passes over isolated bumps and sills, this parameter range may be particularly significant for understanding the role of boundary layers in the deep ocean.
Role of boundary layer processes on the mixed layer CO2-budget
D. Pino; Vilà-Guerau de Arellano, J.
2010-01-01
The diurnal and vertical variability of temperature, humidity and specially CO2 in the atmospheric boundary layer is studied by combining detailed observations taken at Cabauw (The Netherlands), Large-Eddy simulations (LES) and mixed layer theory. The research focus on the role played by the entrainment and other boundary layer driven processes on the distribution and diurnal evolution of CO2 in the boundary layer. The relative importance of this entrained air to ventilate CO2 will be analyze...
Role of residual layer and large-scale phenomena on the evolution of the boundary layer
Blay, E.; D. Pino; Vilà-Guerau de Arellano, J.; Boer; Coster, van, R.; I. Faloona; Garrouste, O.; Hartogensis, O. K.
2012-01-01
Mixed-layer theory and large-eddy simulations are used to analyze the dynamics of the boundary layer on two intensive operational periods during the Boundary Layer Late Afternoon and Sunset Turbulence (BLLAST) campaign: 1st and 2nd of July 2011, when convective boundary layers (CBLs) were observed. Continuous measurements made by several remote sensing and in situ instruments in combination with radiosoundings, and measurements done by unmanned aerial vehicles and an aircraft probed the verti...
Boundary-layer control by electric fields: A feasibility study
Mendes, R. Vilela; Dente, J. A.
1997-01-01
A problem of great concern in aviation and submarine propulsion is the control of the boundary layer and, in particular, the methods to extend the laminar region as a means to decrease noise and fuel consumption. In this paper we study the flow of air along an airfoil when a layer of ionized gas and a longitudinal electric field are created in the boundary layer region. By deriving scaling solutions and more accurate numerical solutions we discuss the possibility of achieving significant boun...
Strong, Stuart L.; Meade, Andrew J., Jr.
1992-01-01
Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.
Two-phase gas bubble-liquid boundary layer flow along vertical and inclined surfaces
International Nuclear Information System (INIS)
The behavior of a two-phase gas bubble-liquid boundary layer along vertical and inclined porous surfaces with uniform gas injection is investigated experimentally and analytically. Using argon gas and water as the working fluids, a photographical study of the two-phase boundary layer flow has been performed for various angles of inclination ranging from 450 to 1350 and gas injection rates ranging from 0.01 to 0.1 m/s. An integral method has been employed to solve the system of equations governing the two-phase motion. The effects of the gas injection rate and the angle of inclination on the growth of the boundary layer have been determined. The predicted boundary layer thickness is found to be in good agreement with the experimental results. The calculated axial liquid velocity and the void fraction in the two-phase region are also presented along with the observed flow behavior
Nefedov, N. N.; Ni, Minkang
2015-12-01
A singularly perturbed boundary value problem for a second-order ordinary differential equation known in applications as a stationary reaction-diffusion equation is studied. A new class of problems is considered, namely, problems with nonlinearity having discontinuities localized in some domains, which leads to the formation of sharp transition layers in these domains. The existence of solutions with an internal transition layer is proved, and their asymptotic expansion is constructed.
Characterization of the Martian Convective Boundary Layer
Martínez, Germán; Valero Rodríguez, Francisco; Vázquez Martínez, Luis
2009-01-01
The authors have carried out an extensive characterization of the Martian mixed layer formed under convective conditions. The values of the mixed layer height, convective velocity scale, convective temperature scale, mean temperature standard deviation, mean horizontal and vertical velocity standard deviations, and mean turbulent viscous dissipation rate have been obtained during the strongest convective hours for the mixed layer. In addition, the existing database of the surface layer has be...
Crosshatch roughness distortions on a hypersonic turbulent boundary layer
Peltier, S. J.; Humble, R. A.; Bowersox, R. D. W.
2016-04-01
The effects of periodic crosshatch roughness (k+ = 160) on a Mach 4.9 turbulent boundary layer (Reθ = 63 000) are examined using particle image velocimetry. The roughness elements generate a series of alternating shock and expansion waves, which span the entire boundary layer, causing significant (up to +50% and -30%) variations in the Reynolds shear stress field. Evidence of the hairpin vortex organization of incompressible flows is found in the comparative smooth-wall boundary layer case (Reθ = 47 000), and can be used to explain several observations regarding the rough-wall vortex organization. In general, the rough-wall boundary layer near-wall vortices no longer appear to be well-organized into streamwise-aligned packets that straddle relatively low-speed regions like their smooth-wall counterpart; instead, they lean farther away from the wall, become more spatially compact, and their populations become altered. In the lower half of the boundary layer, the net vortex swirling strength and outer-scaled Reynolds stresses increase relative to the smooth-wall case, and actually decrease in the outer half of the boundary layer, as ejection and entrainment processes are strengthened and weakened in these two regions, respectively. A spectral analysis of the data suggests a relative homogenizing of the most energetic scales near Λ = ˜ 0.5δ across the rough-wall boundary layer.
Maxwell boundary conditions impose non-Lindblad master equation
Bamba, Motoaki
2016-01-01
From the Hamiltonian connecting the inside and outside of an Fabry-Perot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to that Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultra-strong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical elec...
A spectral boundary integral equation method for the 2D Helmholtz equation
International Nuclear Information System (INIS)
In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the non-smoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the non-smoothness of the integral kernels in the spectral implementation. The present method is robust for a general smooth boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. Numerical examples of wave scattering are given in which the exponential accuracy of the present numerical method is demonstrated. 15 refs., 3 figs., 4 tabs
Bristled shark skin: a microgeometry for boundary layer control?
Energy Technology Data Exchange (ETDEWEB)
Lang, A W; Hidalgo, P; Westcott, M [Aerospace Engineering and Mechanics Department, University of Alabama, Box 870280, Tuscaloosa, AL 35487 (United States); Motta, P [Biology Department, University of South Florida, 4202 East Fowler Avenue, Tampa, FL 33620 (United States)], E-mail: alang@eng.ua.edu
2008-12-01
There exists evidence that some fast-swimming shark species may have the ability to bristle their scales during fast swimming. Experimental work using a water tunnel facility has been performed to investigate the flow field over and within a bristled shark skin model submerged within a boundary layer to deduce the possible boundary layer control mechanisms being used by these fast-swimming sharks. Fluorescent dye flow visualization provides evidence of the formation of embedded cavity vortices within the scales. Digital particle image velocimetry (DPIV) data, used to evaluate the cavity vortex formation and boundary layer characteristics close to the surface, indicate increased momentum in the slip layer forming above the scales. This increase in flow velocity close to the shark's skin is indicative of boundary layer control mechanisms leading to separation control and possibly transition delay for the bristled shark skin microgeometry.
ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION
MARKOWICH, P. A.
2009-10-01
We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results. © 2009 World Scientific Publishing Company.
Size distributions of boundary-layer clouds
Energy Technology Data Exchange (ETDEWEB)
Stull, R.; Berg, L.; Modzelewski, H. [Univ. of Wisconsin, Madison, WI (United States)
1996-04-01
Scattered fair-weather clouds are triggered by thermals rising from the surface layer. Not all surface layer air is buoyant enough to rise. Also, each thermal has different humidities and temperatures, resulting in interthermal variability of their lifting condensation levels (LCL). For each air parcel in the surface layer, it`s virtual potential temperature and it`s LCL height can be computed.
Stable Boundary Layer Education (STABLE) Final Campaign Summary
Energy Technology Data Exchange (ETDEWEB)
Turner, David D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2016-03-01
The properties of, and the processes that occur in, the nocturnal stable boundary layer are not well understood, making it difficult to represent adequately in numerical models. The nocturnal boundary layer often is characterized by a temperature inversion and, in the Southern Great Plains region, a low-level jet. To advance our understanding of the nocturnal stable boundary layer, high temporal and vertical resolution data on the temperature and wind properties are needed, along with both large-eddy simulation and cloud-resolving modeling.
Coupled wake boundary layer model of wind-farms
Stevens, Richard J. A. M.; Gayme, Dennice F.; Meneveau, Charles
2014-01-01
We present and test the coupled wake boundary layer (CWBL) model that describes the distribution of the power output in a wind-farm. The model couples the traditional, industry-standard wake model approach with a "top-down" model for the overall wind-farm boundary layer structure. This wake model captures the effect of turbine positioning, while the "top-down" portion of the model adds the interactions between the wind-turbine wakes and the atmospheric boundary layer. Each portion of the mode...
Krishnendu Bhattacharyya; Layek, G. C.
2014-01-01
A numerical investigation is made to study the thermal boundary layer for flow of incompressible Newtonian fluid over an exponentially stretching sheet with an exponentially moving free stream. The governing partial differential equations are transformed into self-similar ordinary differential equations using similarity transformations in exponential forms. Then those are solved numerically by shooting technique using Runge-Kutta method. The study reveals that the momentum boundary layer thic...
Assessment of a transitional boundary layer theory at low hypersonic Mach numbers
Shamroth, S. J.; Mcdonald, H.
1972-01-01
An investigation was carried out to assess the accuracy of a transitional boundary layer theory in the low hypersonic Mach number regime. The theory is based upon the simultaneous numerical solution of the boundary layer partial differential equations for the mean motion and an integral form of the turbulence kinetic energy equation which controls the magnitude and development of the Reynolds stress. Comparisions with experimental data show the theory is capable of accurately predicting heat transfer and velocity profiles through the transitional regime and correctly predicts the effects of Mach number and wall cooling on transition Reynolds number. The procedure shows promise of predicting the initiation of transition for given free stream disturbance levels. The effects on transition predictions of the pressure dilitation term and of direct absorption of acoustic energy by the boundary layer were evaluated.
Shock Wave-Boundary Layer Interaction in Forced Shock Oscillations
Institute of Scientific and Technical Information of China (English)
Piotr Doerffer; Oskar Szulc; Franco Magagnato
2003-01-01
The flow in transonic diffusers as well as in supersonic air intakes becomes often unsteady due to shock wave boundary layer interaction. The oscillations may be induced by natural separation unsteadiness or may be forced by boundary conditions. Significant improvement of CFD tools, increase of computer resources as well as development of experimental methods have again.drawn the attention of researchers to this topic.To investigate the problem forced oscillations of transonic turbulent flow in asymmetric two-dimensional Laval nozzle were considered. A viscous, perfect gas flow, was numerically simulated using the Reynolds-averaged compressible Navier-Stokes solver SPARC, employing a two-equation, eddy viscosity, turbulence closure in the URANS approach.For time-dependent and stationary flow simulations, Mach numbers upstream of the shock between 1.2 and 1.4 were considered. Comparison of computed and experimental data for steady states generally gave acceptable agreement. In the case of forced oscillations, a harmonic pressure variation was prescribed at the exit plane resulting in shock wave motion. Excitation frequencies between 0 Hz and 1024 Hz were investigated at the same pressure amplitude.The main result of the work carried out is the relation between the amplitude of the shock wave motion and the excitation frequency in the investigated range. Increasing excitation frequency resulted in decreasing amplitude of the shock movement. At high frequencies a natural mode of shock oscillation (of small amplitude) was observed which is not sensitive to forced excitement.
Reactive boundary layers in metallic rolling contacts
International Nuclear Information System (INIS)
thorough investigation into the effects of residual austenite on the properties of this material. The high-performance alternative steels, 36NiCrMoV1-5-7 (hot working steel) and 45SiCrMo6 (spring steel), were heat treated as recommended by their respective manufacturers, and were not case-hardened. The selection of materials with and materials without case-hardening allows for an investigation into whether or not case-hardening is even necessary to deliver acceptable friction behaviour and wear performance. Elemental analyses were conducted by multiple methods to ensure accurate results. Residual austenite contents of the steels and the depth profiles of residual stresses were determined by X-Ray diffraction (XRD), for 20MnCr5 ranging from approximately 6 - 14 vol.%, and under 2 vol.% for the alternative alloys. Hardness profiles were taken from the testing surfaces into the material core. The carburization of 20MnCr5 led to higher hardness and the greater concentration of carbon in the carburization zone more representative of a hardened SAE E52100, or 100Cr6/102Cr6, than of a non-case-hardened 20MnCr5. Residual stresses from machining and case-hardening were measured directly at the sample surface. The high-performance steels fulfilled manufacturer expectations in terms of elemental content, with hardness values between 50 - 55 HRC and strongly martensitic microstructure character. With characterization of the chosen materials complete, the materials could then be subjected to pre-conditioning. The first pre-conditioning method involved targeted generation of cold work hardening as induced boundary layers to protect the contact zone against wear. Work hardening was identified both by variations in residual stress profiles, i.e. the introduction of beneficial compressive residual stresses, and hardness increases in the contact zone, providing enhanced wear resistance. Parameters for work hardening were further optimized to reduce damage to the surface substrates of the
Reactive boundary layers in metallic rolling contacts
Energy Technology Data Exchange (ETDEWEB)
Burbank, John
2016-05-01
more thorough investigation into the effects of residual austenite on the properties of this material. The high-performance alternative steels, 36NiCrMoV1-5-7 (hot working steel) and 45SiCrMo6 (spring steel), were heat treated as recommended by their respective manufacturers, and were not case-hardened. The selection of materials with and materials without case-hardening allows for an investigation into whether or not case-hardening is even necessary to deliver acceptable friction behaviour and wear performance. Elemental analyses were conducted by multiple methods to ensure accurate results. Residual austenite contents of the steels and the depth profiles of residual stresses were determined by X-Ray diffraction (XRD), for 20MnCr5 ranging from approximately 6 - 14 vol.%, and under 2 vol.% for the alternative alloys. Hardness profiles were taken from the testing surfaces into the material core. The carburization of 20MnCr5 led to higher hardness and the greater concentration of carbon in the carburization zone more representative of a hardened SAE E52100, or 100Cr6/102Cr6, than of a non-case-hardened 20MnCr5. Residual stresses from machining and case-hardening were measured directly at the sample surface. The high-performance steels fulfilled manufacturer expectations in terms of elemental content, with hardness values between 50 - 55 HRC and strongly martensitic microstructure character. With characterization of the chosen materials complete, the materials could then be subjected to pre-conditioning. The first pre-conditioning method involved targeted generation of cold work hardening as induced boundary layers to protect the contact zone against wear. Work hardening was identified both by variations in residual stress profiles, i.e. the introduction of beneficial compressive residual stresses, and hardness increases in the contact zone, providing enhanced wear resistance. Parameters for work hardening were further optimized to reduce damage to the surface substrates
Galerkin Boundary Integral Analysis for the 3D Helmholtz Equation
Energy Technology Data Exchange (ETDEWEB)
Swager, Melissa [Emporia State University; Gray, Leonard J [ORNL; Nintcheu Fata, Sylvain [ORNL
2010-01-01
A linear element Galerkin boundary integral analysis for the three-dimensional Helmholtz equation is presented. The emphasis is on solving acoustic scattering by an open (crack) surface, and to this end both a dual equation formulation and a symmetric hypersingular formulation have been developed. All singular integrals are defined and evaluated via a boundary limit process, facilitating the evaluation of the (finite) hypersingular Galerkin integral. This limit process is also the basis for the algorithm for post-processing of the surface gradient. The analytic integrations required by the limit process are carried out by employing a Taylor series expansion for the exponential factor in the Helmholtz fundamental solutions. For the open surface, the implementations are validated by comparing the numerical results obtained by using the two different methods.
Singular-boundary reductions of type-Q ABS equations
Atkinson, James; Joshi, Nalini
2011-01-01
We study the fully discrete elliptic integrable model Q4 and its immediate trigonometric and rational counterparts (Q3, Q2 and Q1). Singular boundary problems for these equations are systematised in the framework of global singularity analysis. We introduce a technique to obtain solutions of such problems, in particular constructing the exact solution on a regular singularity-bounded strip. The solution technique is based on the multidimensional consistency and uses new insights into these eq...
Optimal Control of a Parabolic Equation with Dynamic Boundary Condition
International Nuclear Information System (INIS)
We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an Lp function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.
International Nuclear Information System (INIS)
An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible fluid over a linearly shrinking surface is presented. The flow is permeated by an externally applied magnetic field normal to the plane of the flow. The equations governing the flow and concentration field are reduced into a set of nonlinear ordinary differential equations using similarity variables. Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall mass flux (PMF) as boundary conditions. The study reveals that the concentration over a shrinking sheet is significantly different from that of a stretching surface. It is found that the solute boundary layer thickness is enhanced with the increasing values of the Schmidt number and the power-law index parameter, but decreases with enhanced values of magnetic and reaction rate parameters for the PSC case. For the PMF case, the solute boundary layer thickness decreases with the increase of the Schmidt number, magnetic and reaction rate parameter for power-law index parameter n = 0. Negative solute boundary layer thickness is observed for the PMF case when n = 1 and 2, and these facts may not be realized in real-world applications. (fundamental areas of phenomenology(including applications))
Boundary Layer Flow over a Continuously Moving Thin Needle in a Parallel Free Stream
Institute of Scientific and Technical Information of China (English)
Anuar Ishak; Roslinda Nazar; Ioan Pop
2007-01-01
We investigate the boundary-layer flow on a moving isothermal thin needle parallel to a moving stream. The governing equations are solved numerically by a finite-difference method. Dual solutions are found to exist when the needle and the free stream move in the opposite directions.
Calculation of the turbulent boundary layer in the initial section of pipe
Energy Technology Data Exchange (ETDEWEB)
Temirkhanov, A.M.; Spivak, V.M.
1987-11-01
This article constructs a flow model for the turbulent boundary layer in a pipe operating under conditions of pressure and gravitation encountered in a hydroelectric power plant. Pipe roughness and friction factors are taken into account as are hydraulic conductivity and pipe dimension considerations. Continuity equations are given and the accuracy of the model is compared against experimental data.
Coherent structures in wave boundary layers. Part 1. Oscillatory motion
DEFF Research Database (Denmark)
Carstensen, Stefan; Sumer, B. Mutlu; Fredsøe, Jørgen
2010-01-01
This work concerns oscillatory boundary layers over smooth beds. It comprises combined visual and quantitative techniques including bed shear stress measurements. The experiments were carried out in an oscillating water tunnel. The experiments reveal two significant coherent flow structures: (i) ...
Change of Surface Roughness and Planetary Boundary Layer
DEFF Research Database (Denmark)
Jensen, Niels Otto
1978-01-01
The ratio between upstream and far downstream surface friction velocities relative to a change in surface roughness is given on the basis of results from surface Rossby number similarity theory. By simple theories for the internal boundary layer, which are found to compare quite well with recent ...... numerical results from higher-order closure models, it is found that, even at a downwind distance such that the internal boundary layer has grown to the full height of the planetary boundary layers, the surface stress still considerably exceeds the equilibrium value......The ratio between upstream and far downstream surface friction velocities relative to a change in surface roughness is given on the basis of results from surface Rossby number similarity theory. By simple theories for the internal boundary layer, which are found to compare quite well with recent...
Spatially Developing Secondary Instabilities in Compressible Swept Airfoil Boundary Layers
Li, Fei; Choudhari, Meelan M.
2011-01-01
Two-dimensional eigenvalue analysis is used on a massive scale to study spatial instabilities of compressible shear flows with two inhomogeneous directions. The main focus of the study is crossflow dominated swept-wing boundary layers although the methodology can also be applied to study other type of flows, such as the attachment-line flow. Certain unique aspects of formulating a spatial, two-dimensional eigenvalue problem for the secondary instability of finite amplitude crossflow vortices are discussed, namely, fixing the spatial growth direction unambiguously through a non-orthogonal formulation of the linearized disturbance equations. A primary test case used for parameter study corresponds to the low-speed, NLF-0415(b) airfoil configuration as tested in the ASU Unsteady Wind Tunnel, wherein a spanwise periodic array of roughness elements was placed near the leading edge in order to excite stationary crossflow modes with a specified fundamental wavelength. The two classes of flow conditions selected for this analysis include those for which the roughness array spacing corresponds to either the naturally dominant crossflow wavelength, or a subcritical wavelength that serves to reduce the growth of the naturally excited dominant crossflow modes. Numerical predictions are compared with the measured database, both as indirect validation for the spatial instability analysis and to provide a basis for comparison with a higher Reynolds number, supersonic swept-wing configuration. Application of the eigenvalue analysis to the supersonic configuration reveals that a broad spectrum of stationary crossflow modes can sustain sufficiently strong secondary instabilities as to potentially cause transition over this configuration. Implications of this finding for transition control in swept wing boundary layers are examined.
Directory of Open Access Journals (Sweden)
A. Malvandi
2015-01-01
Full Text Available The objective of this paper is to consider both effects of slip and convective heat boundary conditions on steady two-dimensional boundary layer flow of a nanofluid over a stretching sheet in the presence of blowing/suction simultaneously. Flow meets the Navier's slip condition at the surface and Biot number is also used to consider the effects of convective heat transfer. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of nanoparticle migration owing to Brownian motion and thermophoresis. The basic partial boundary layer equations have been transformed into a two-point boundary value problem via similarity variables. Results for impermeable isothermal surface and also no-slip boundary condition were in best agreements with those existing in literatures. Effects of governing parameters such as Biot number (Bi, slip parameter (λ, thermophoresis (Nt, Prandtl number (Pr, Lewis number (Le, Brownian motion (Nb and blowing/suction (S on reduced Nusselt and Sherwood numbers are analyzed and discussed in details. The obtained results indicate that unlike heat transfer rate, concentration rate is very sensitive to all parameters among which Le, S and Pr are the most effective ones.
Theoretical investigation on shocklets in compressible boundary layers
Institute of Scientific and Technical Information of China (English)
袁湘江; 刘智勇; 沈洁; 李国良
2014-01-01
By the shock relationships, the wavy characteristics and the forming condi-tions of a shock wave are analyzed. The wavy characteristics of an Euler system are stud-ied theoretically. The present research focuses on the wavy characteristics of Tollmien-Schlichting (T-S) waves, the excitation conditions of shocklets in compressible boundary layers, and the viscous effect on shock. The possibility of existence of shocklets in the compressible boundary layer and the physical mechanism of formation are theoretically interpreted.
Tropical boundary layer equilibrium in the last ice age
Betts, Alan K.; Ridgway, W.
1992-01-01
A radiative-convective boundary layer model is used to assess the effect of changing sea surface temperature, pressure, wind speed, and the energy export from the tropics on the boundary layer equilibrium equivalent potential temperature. It remains difficult to reconcile the observations that during the last glacial maximum (18,000 yr BP) the snowline on the tropical mountains fell 950 m, while the tropical sea surface temperatures fell only 1-2 K.
Edwards, S.; Reuther, J.; Chattot, J. J.
The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjoint approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to a target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speeds.
Belyaev, Mikhail A; Stone, James M
2012-01-01
The nature of angular momentum transport in the boundary layers of accretion disks has been one of the central and long-standing issues of accretion disk theory. In this work we demonstrate that acoustic waves excited by supersonic shear in the boundary layer serve as an efficient mechanism of mass, momentum and energy transport at the interface between the disk and the accreting object. We develop the theory of angular momentum transport by acoustic modes in the boundary layer, and support our findings with 3D hydrodynamical simulations, using an isothermal equation of state. Our first major result is the identification of three types of global modes in the boundary layer. We derive dispersion relations for each of these modes that accurately capture the pattern speeds observed in simulations to within a few percent. Second, we show that angular momentum transport in the boundary layer is intrinsically nonlocal, and is driven by radiation of angular momentum away from the boundary layer into both the star an...
Hydrodynamic structure of the boundary layers in a rotating cylindrical cavity with radial inflow
Herrmann-Priesnitz, Benjamín; Calderón-Muñoz, Williams R.; Salas, Eduardo A.; Vargas-Uscategui, Alejandro; Duarte-Mermoud, Manuel A.; Torres, Diego A.
2016-03-01
A flow model is formulated to investigate the hydrodynamic structure of the boundary layers of incompressible fluid in a rotating cylindrical cavity with steady radial inflow. The model considers mass and momentum transfer coupled between boundary layers and an inviscid core region. Dimensionless equations of motion are solved using integral methods and a space-marching technique. As the fluid moves radially inward, entraining boundary layers develop which can either meet or become non-entraining. Pressure and wall shear stress distributions, as well as velocity profiles predicted by the model, are compared to numerical simulations using the software OpenFOAM. Hydrodynamic structure of the boundary layers is governed by a Reynolds number, Re, a Rossby number, Ro, and the dimensionless radial velocity component at the periphery of the cavity, Uo. Results show that boundary layers merge for Re > 0.1, and boundary layers become predominantly non-entraining for low Ro, low Re, and high Uo. Results may contribute to improve the design of technology, such as heat exchange devices, and turbomachinery.
Dynamic Boundary Layer Properties in Turbulent Thermal Convection
Xia, Ke-Qing; Har Cheung, Yin; Sun, Chao
2004-11-01
We report an experimental study on the properties of the velocity and temperature boundary layers in turbulent thermal convection in a rectangular-shaped box over a range of Rayleigh numbers and at a constant Prandtl number. Velocity components both parallel and perpendicular to the conducting plate are measured simultaneously using the PIV technique. Our results show that, for the given geometry of the cell, the velocity boundary layer at the conduction plate is of a Blasius type, i.e. the boundary layer thickness δv scales with the Reynolds number Re as δv ˜ Re-1/2. The measurement further reveals that, at the velocity boundary layer, the turbulent (Reynolds) shear tress becomes larger than the viscous shear stress when Ra reaches 1-2×10^10, indicating that the boundary layer becomes turbulent for Ra >10^10. The viscous dissipation rate calculated based on the measured velocity field shows that it is dominated by contribution from the bulk over that from the boundary layer.
Structure and Growth of the Marine Boundary Layer
Mccumber, M.
1984-01-01
LANDSAT visible imagery and a one-dimensional Lagrangian boundary layer model were used to hypothesize the nature and the development of the marine boundary layer during a winter episode of strong seaward cold air advection. Over-water heating and moistening of the cold, dry continental air is estimable from linear relations involving horizontal gradients of the near-surface air temperature and humidity. A line of enhanced convection paralleling the Atlantic U.S. coast from south of New York Bay to the vicinity of Virginia Beach, VA was attributed to stronger convergence at low levels. This feature was characterized as a mesoscale front. With the assistance of a three-dimensional mesoscale boundary layer model, initialized with data obtained from the MASEX, the marine boundary layer can be mapped over the entire Atlantic coastal domain and the evolution of the boundary layer can be studied as a function of different characteristics of important surface level forcings. The effects on boundary layer growth due to the magnitude and pattern of sea surface temperature, to the shape of the coastline, and to atmospheric conditions, such as the orientation of the prevailing wind are examined.
Dense gas boundary layer experiments: Visualization, pressure measurements, concentration evaluation
Energy Technology Data Exchange (ETDEWEB)
Reichenbach, H.; Neuwald, P. [Ernst-Mach-Institut, Freiburg (DE); Kuhl, A.L. [R and D Associates, Los Angeles, CA (United States)
1992-11-01
This technical report describes methods that were applied to investigate turbulent boundary layers generated by inviscid, baroclinic effects. The Cranz-Schardin 24-sparks camera was used to visualize the interactions of a planar shock wave with a Freon R12-layer. The shock propagates more slowly in the Freon layer than in air because of its smaller sound speed. This causes the shock front to be curved and to be reflected between the wall and the layer interface. As a consequence of the reflection process, a series of compression and expansion waves radiate from the layer. Large fluctuations in the streamwise velocity and in pressure develop for about 1 ms. These waves strongly perturb the interface shear layer, which rapidly transitions to a turbulent boundary flow. Pressure measurements showed that the fluctuations in the Freon layer reach a peak pressure 4 times higher than in the turbulent boundary flow. To characterize the preshock Freon boundary layer, concentration measurements were performed with a differential interferometry technique. The refraction index of Freon R12 is so high that Mach-Zehnder interferometry was not successful in these experiments. The evaluation of the concentration profile is described here in detail. Method and results of corresponding LDV measurements under the same conditions are presented in a different report, EMI Report T 9/92. The authors plan to continue the dense gas layer investigations with the gas combination helium/Freon.
Numerical simulations of coupled sea waves and boundary layer dynamics
Chalikov, D.
2009-04-01
potential equations, while an atmospheric model is based on Reynolds equations with 2nd order closing. Hundreds of long-term numerical experiments for different initial wave spectra were carried out to investigate statistical structure of the wave boundary layer (WBL) and particularly, for construction of effective beta-function, taking into account real shapes of waves, occasional separation of boundary layer and the effect of parameterized wave breaking. Naturally, beta-function determined in such a way, has a wide scatter, however extensive statistics allows to derive that function with high accuracy. Data on vertical distribution of spectral components of wave-produced momentum flux are used for construction of 1-D model of WBL. It is shown, that most of the momentum flux to waves is concentrated in a high wave number part of spectrum where dispersion relation is actually not valid. Wind waves form rough surface, so all of the momentum flux is absorbed by waves, while local tangent stress is negligibly small. The approach allows to investigate WBL structure for arbitrary wind conditions and wave spectra. It is shown that wide scatter for drag coefficient can be easily explained by different wave conditions. For example, decrease of effective surface roughness at storm winds can be explained by dumping of high-frequency waves by foam.
Plasma boundary layer and magnetopause layer of the earth's magnetosphere
Energy Technology Data Exchange (ETDEWEB)
Eastman, T.E.
1979-06-01
IMP 6 observations of the plasma boundary layer (PBL) and magnetopause layer (MPL) of the earth's magnetosphere indicate that plasma in the low-latitude portion of the PBL is supplied primarily by direct transport of magnetosheath plasma across the MPL and that this transport process is relatively widespread over the entire sunward magnetospheric boundary.
Beta limitation of matter-antimatter boundary layers
International Nuclear Information System (INIS)
A model has earlier been proposed for a boundary layer which separates a cloud of matter from one of antimatter in a magnetized ambiplasma. In this model steady pressure equilibrium ceases to exist when a certain beta limit is exceeded. The latter is defined as the ratio between the ambiplasma and magnetic field pressures which balance each other in the boundary layer. Thus, at an increasing density, the high-energy particles created by annihilation within the layer are 'pumped up' to a pressure which cannot be balanced by a given magnetic field. The boundary layer then 'disrupts'. The critical beta limit thus obtained falls within the observed parameter ranges of galaxies and other large cosmical objects. Provided that the considered matter-antimatter balance holds true, this limit is thus expected to impose certain existence conditions on matter-antimatter boundary layers. Such a limitation may apply to certain cosmical objects and cosmological models. The maximum time scale for the corresponding disruption development has been estimated to be in the range from about 10-4 to 102 seconds for boundary layers at ambiplasma particle densities in the range from 104 to 10-2 m-3, respectively. (author)
Three dimensional analysis of boundary layers in magnetohydrodynamic open channel flow
International Nuclear Information System (INIS)
The pumping of liquid metals through open channels by MHD effects can be applied to slag separation or continuous casting processes by the metallurgy industry. This study involves the analysis of the boundary layer structure of non-uniform open channel flow in a rectangular channel, with perfectly conducting sidewalls, an insulating bottom and a uniform magnetic field applied perpendicular to the bottom, the plane of which is sloped with respect to the horizontal. To supply the non-trivial three-dimensional sidewall boundary layer structure a boundary value problem is posed and reduced to two integral equations coupled in two unknowns. The twenty-four point Gauss-Legendre quadrature scheme used to represent the integrals, leads to a set of forty-eight simultaneous equations which is solved numerically for the unknowns. Once obtained, these unknowns are used in the numerical calculation of sample velocity profiles which illustrate and contrast MHD effects in open channel and closed duct flows
Energy Technology Data Exchange (ETDEWEB)
Ishak, Anuar [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia); Nazar, Roslinda [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia)], E-mail: rmn72my@yahoo.com; Pop, Ioan [Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253 (Romania)
2008-03-31
The mixed convection boundary layer flow through a stable stratified porous medium bounded by a vertical surface is investigated. The external velocity and the surface temperature are assumed to vary as x{sup m}, where x is measured from the leading edge of the vertical surface and m is a constant. Numerical solutions for the governing Darcy and energy equations are obtained. The results indicate that the thermal stratification significantly affects the surface shear stress as well as the surface heat transfer, besides delays the boundary layer separation.
Unsteady compressible boundary layer flow over a circular cone near aplane of symmetry
Chamkha, AJ; Takhar, HS; G. Nath
2005-01-01
An analysis has been performed to study the unsteady laminar compressible boundary layer governing the hypersonic flow over a circular cone at an angle of attack near a plane of symmetry with either in flow or out flow in the presence of suction. The flow is assumed to be steady at time t= 0 and at t > 0 it becomes unsteady due to the time-dependent free stream velocity which varies arbitrarily with time. The nonlinear coupled parabolic partial differential equations under boundary layer a...
A Nonlinear Singularly Perturbed Problem for Reaction Diffusion Equations with Boundary Perturbation
Institute of Scientific and Technical Information of China (English)
Jia-qi Mo; Wan-tao Lin
2005-01-01
A nonlinear singularly perturbed problems for reaction diffusion equation with boundary perturbation is considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems of reaction diffusion equations is studied using the theory of differential inequalities.
Boundary-layer control by electric fields A feasibility study
Mendes, R V
1998-01-01
A problem of great concern in aviation and submarine propulsion is the control of the boundary layer and, in particular, the methods to extend the laminar region as a means to decrease noise and fuel consumption. In this paper we study the flow of air along an airfoil when a layer of ionized gas and a longitudinal electric field are created in the boundary layer region. By deriving scaling solutions and more accurate numerical solutions we discuss the possibility of achieving significant boundary layer control for realistic physical parameters. Practical design formulas and criteria are obtained. We also discuss the perspectives for active control of the laminar-to-turbulent transition fluctuations by electromagnetic field modulation.
Response of neutral boundary-layers to changes of roughness
DEFF Research Database (Denmark)
Sempreviva, Anna Maria; Larsen, Søren Ejling; Mortensen, Niels Gylling;
1990-01-01
stratification, and the surface roughness is the main parameter. The analysis of wind data and two simple models, a surface layer and a planetary boundary layer (PBL) model, are described. Results from both models are discussed and compared with data analysis. Model parameters have been evaluated and the model......When air blows across a change in surface roughness, an internal boundary layer (IBL) develops within which the wind adapts to the new surface. This process is well described for short fetches, > 1 km. However, few data exist for large fetches on how the IBL grows to become a new equilibrium...... boundary layer where again the drag laws can be used to estimate the surface wind. To study this problem, data have been sampled for two years from four 30-m meteorological masts placed from 0 to 30 km inland from the North Sea coast of Jutland in Denmark. The present analysis is limited to neutral...
Vortex Generators to Control Boundary Layer Interactions
Babinsky, Holger (Inventor); Loth, Eric (Inventor); Lee, Sang (Inventor)
2014-01-01
Devices for generating streamwise vorticity in a boundary includes various forms of vortex generators. One form of a split-ramp vortex generator includes a first ramp element and a second ramp element with front ends and back ends, ramp surfaces extending between the front ends and the back ends, and vertical surfaces extending between the front ends and the back ends adjacent the ramp surfaces. A flow channel is between the first ramp element and the second ramp element. The back ends of the ramp elements have a height greater than a height of the front ends, and the front ends of the ramp elements have a width greater than a width of the back ends.
Directory of Open Access Journals (Sweden)
M. W. Dunlop
are analysed to confirm boundary orientation and motion. These further show evidence of an anti-sunward moving depression on the magnetopause (which is much smaller at Equator-S. The Tsyganenko model field is used routinely to assist in categorising the crossings and some comparison of models is carried out. We note that typically the T87 model fits the data better than the T89 model during conditions of low to intermediate K_{P} index near the magnetopause and also near the dawn-side tail current sheet in the dawnside region.
Key words. Magnetospheric physics (magnetopause · cusp · and boundary layers; magnetosheath; magneto- spheric configuration and dynamics.
Initial layer theory and model equations of Volterra type
International Nuclear Information System (INIS)
It is demonstrated here that there exist initial layers to singularly perturbed Volterra equations whose thicknesses are not of order of magnitude of 0(ε), ε → 0. It is also shown that the initial layer theory is extremely useful because it allows one to construct the approximate solution to an equation, which is almost identical to the exact solution. (author)
Chen, Gui-Qiang; Osborne, Dan; Qian, Zhongmin
2008-01-01
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure $p$ can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the so...
UNSTEADY BOUNDARY LAYER FLOW ALONG A STRETCHING CYLINDER AN ANALYTICAL SOLUTION
Directory of Open Access Journals (Sweden)
M. Y. Akl
2014-01-01
Full Text Available The axisymetric laminar boundary layer unsteady flow along a continuously stretching cylinder immersed in a viscous and incompressible fluid is studied. The governing partial boundary layer equations in cylindrical form are first transformed into ordinary differential equations these equations are solved analytically using the optimal modified Homotopy Asymptotic method in order to get a closed form solution for the dimensionless functions f and è. The main object of this study is to investigate the effect of an unsteady motion of a stretching cylinder on the flow and heat transfer characteristics such as surface skin friction and surface heat flux. These characteristics have a direct effect on the quality of the final product of the fiber manufacturing and extrusion processes. Considerable effects were found for the dynamic parameter (γ, the curvature parameter (ρ and the prandtl number (pr on the velocity and the heat transfer.
Direct simulation of turbulent supersonic boundary layers by an extended temporal approach
Maeder, Thierry; Adams, Nikolaus A.; Kleiser, Leonhard
2001-02-01
The present paper addresses the direct numerical simulation of turbulent zero-pressure-gradient boundary layers on a flat plate at Mach numbers 3, 4.5 and 6 with momentum-thickness Reynolds numbers of about 3000. Simulations are performed with an extended temporal direct numerical simulation (ETDNS) method. Assuming that the slow streamwise variation of the mean boundary layer is governed by parabolized Navier Stokes equations, the equations solved locally in time with a temporal DNS are modified by a distributed forcing term so that the parabolized Navier Stokes equations are recovered for the spatial average. The correct mean flow is obtained without a priori knowledge, the streamwise mean-flow evolution being approximated from its upstream history. ETDNS reduces the computational effort by up to two orders of magnitude compared to a fully spatial simulation.
Tokamak plasma shape identification based on the boundary integral equations
International Nuclear Information System (INIS)
A necessary condition for tokamak plasma shape identification is discussed and a new identification method is proposed in this article. This method is based on the boundary integral equations governing a vacuum region around a plasma with only the measurement of either magnetic fluxes or magnetic flux intensities. It can identify various plasmas with low to high ellipticities with the precision determined by the number of the magnetic sensors. This method is applicable to real-time control and visualization using a 'table-look-up' procedure. (author)
Periodic and Boundary Value Problems for Second Order Differential Equations
Indian Academy of Sciences (India)
Nikolaos S Papageorgiou; Francesca Papalini
2001-02-01
In this paper we study second order scalar differential equations with Sturm–Liouville and periodic boundary conditions. The vector field (, , ) is Caratheodory and in some instances the continuity condition on or is replaced by a monotonicity type hypothesis. Using the method of upper and lower solutions as well as truncation and penalization techniques, we show the existence of solutions and extremal solutions in the order interval determined by the upper and lower solutions. Also we establish some properties of the solutions and of the set they form.
Modelling Scalar Skewness in Cloudy Boundary Layers
Mironov, Dmitrii; Machulskaya, Ekaterina; Naumann, Ann Kristin; Seifert, Axel; Mellado, Juan Pedro
2015-04-01
Following the pioneering work of Sommeria and Deardorff (1977), statistical cloud schemes are widely used in numerical weather prediction (NWP) and climate models to parameterize the effect of shallow clouds on turbulent mixing and radiation fluxes. Statistical cloud schemes compute the cloud fraction, the amount of cloud condensate and the effect clouds on the buoyancy flux in a given atmospheric-model grid box. This is done with due regard for the sub-grid scale (SGS) fluctuations of temperature and humidity (and possibly the vertical velocity), thus providing an important coupling between cloudiness and the SGS mixing processes. The shape of the PDF of fluctuating fields is assumed, whereas the PDF moments should be provided to the cloud scheme as an input. For non-precipitation clouds, the mixing schemes are usually formulated in terms of quasi-conservative variable, e.g. the liquid (total) water potential temperature and the total water specific humidity. Then, the cloud schemes are conveniently cast in terms of the linearized saturation deficit, referred to as the "s" variable (Mellor 1977), that accounts for the combined effect of the two scalars. If a simple two-parameter single-Gaussian PDF is used, the only "turbulence" parameter to be provided to the cloud scheme is the variance of s. The single-Gaussian PDF ignores the skewed nature of SGS motions and fails to describe many important regimes, e.g. shallow cumuli. A number of more flexible skewed PDFs have been proposed to date. A three-parameter PDF, based on a double-Gaussian distribution and diagnostic relations between some PDF parameters derived from LES and observational data (Naumann et al. 2013), appears to be a good compromise between physical realism and computational economy. A crucial point is that the cloud schemes using non-Gaussian PDFs require the scalar skewness as an input. Using rather mild non-restrictive assumptions, we develop a transport equation for the s-variable triple
Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement. PMID:23166688
Directory of Open Access Journals (Sweden)
Mohammed J Uddin
Full Text Available Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.
Stabilization of boundary layer streaks by plasma actuators
International Nuclear Information System (INIS)
A flow's transition from laminar to turbulent leads to increased levels of skin friction. In recent years, dielectric barrier discharge actuators have been shown to be able to delay the onset of turbulence in boundary layers. While the laminar to turbulent transition process can be initiated by several different instability mechanisms, so far, only stabilization of the Tollmien–Schlichting path to transition has received significant attention, leaving the stabilization of other transition paths using these actuators less explored. To fill that void, a bi-global stability analysis is used here to examine the stabilization of boundary layer streaks in a laminar boundary layer. These streaks, which are important to both transient and by-pass instability mechanisms, are damped by the addition of a flow-wise oriented plasma body force to the boundary layer. Depending on the magnitude of the plasma actuation, this damping can be up to 25% of the perturbation's kinetic energy. The damping mechanism appears to be due to highly localized effects in the immediate vicinity of the body force, and when examined using a linearized Reynolds-averaged Navier–Stokes energy balance, indicate negative production of the perturbation's kinetic energy. Parametric studies of the stabilization have also been performed, varying the magnitude of the plasma actuator's body force and the spanwise wavenumber of the actuation. Based on these parametric studies, the damping of the boundary layer streaks appears to be linear with respect to the total amount of body force applied to the flow. (paper)
Highly buoyant bent-over plumes in a boundary layer
Tohidi, Ali; Kaye, Nigel B.
2016-04-01
Highly buoyant plumes, such as wildfire plumes, in low to moderate wind speeds have initial trajectories that are steeper than many industrial waste plumes. They will rise further into the atmosphere before bending significantly. In such cases the plume's trajectory will be influenced by the vertical variation in horizontal velocity of the atmospheric boundary layer. This paper examined the behavior of a plume in an unstratified environment with a power-law ambient velocity profile. Examination of previously published experimental measurements of plume trajectory show that inclusion of the boundary layer velocity profile in the plume model often provides better predictions of the plume trajectory compared to algebraic expressions developed for uniform flow plumes. However, there are many cases in which uniform velocity profile algebraic expressions are as good as boundary layer models. It is shown that it is only important to model the role of the atmospheric boundary layer velocity profile in cases where either the momentum length (square root of source momentum flux divided by the reference wind speed) or buoyancy length (buoyancy flux divided by the reference wind speed cubed) is significantly greater than the plume release height within the boundary layer. This criteria is rarely met with industrial waste plumes, but it is important in modeling wildfire plumes.
Turbulent boundary-layer structure of flows over freshwater biofilms
Walker, J. M.; Sargison, J. E.; Henderson, A. D.
2013-12-01
The structure of the turbulent boundary-layer for flows over freshwater biofilms dominated by the diatom Tabellaria flocculosa was investigated. Biofilms were grown on large test plates under flow conditions in an Australian hydropower canal for periods up to 12 months. Velocity-profile measurements were obtained using LDV in a recirculating water tunnel for biofouled, smooth and artificially sandgrain roughened surfaces over a momentum thickness Reynolds number range of 3,000-8,000. Significant increases in skin friction coefficient of up to 160 % were measured over smooth-wall values. The effective roughnesses of the biofilms, k s, were significantly higher than their physical roughness measured using novel photogrammetry techniques and consisted of the physical roughness and a component due to the vibration of the biofilm mat. The biofilms displayed a k-type roughness function, and a logarithmic relationship was found between the roughness function and roughness Reynolds number based on the maximum peak-to-valley height of the biofilm, R t. The structure of the boundary layer adhered to Townsend's wall-similarity hypothesis even though the scale separation between the effective roughness height and the boundary-layer thickness was small. The biofouled velocity-defect profiles collapsed with smooth and sandgrain profiles in the outer region of the boundary layer. The Reynolds stresses and quadrant analysis also collapsed in the outer region of the boundary layer.
The inner core thermodynamics of the tropical cyclone boundary layer
Williams, Gabriel J.
2016-02-01
Although considerable progress has been made in understanding the inner-core dynamics of the tropical cyclone boundary layer (TCBL), our knowledge of the inner-core thermodynamics of the TCBL remains limited. In this study, the inner-core budgets of potential temperature (θ ), specific humidity (q), and reversible equivalent potential temperature (θ _e ) are examined using a high-resolution multilevel boundary layer model. The potential temperature budgets show that the heat energy is dominated by latent heat release in the eyewall, evaporative cooling along the outer edge of the eyewall, and upward surface fluxes of sensible and latent heat from the underlying warm ocean. It is shown that the vertical θ advection overcompensates the sum of radial advective warming from the boundary layer outflow jet and latent heating for the development of cooling in the eyewall within the TCBL. The moisture budgets show the dominant upward transport of moisture in the eyewall updrafts, partly by the boundary-layer outflow jet from the bottom eye region, so that the eyewall remains nearly saturated. The θ _e budgets reveal that the TCBL is maintained thermodynamically by the upward surface flux of higher-θ _e air from the underlying warm ocean, the radial transport of low-θ _e air from the outer regions of the TCBL, and the dry adiabatic cooling associated by eyewall updrafts. These results underscore the significance of vertical motion and the location of the boundary layer outflow jet in maintaining the inner core thermal structure of the TCBL.
Effects of Nose Bluntness on Hypersonic Boundary-Layer Receptivity and Stability Over Cones
Kara, Kursat; Balakumar, Ponnampalam; Kandil, Osama A.
2011-01-01
The receptivity to freestream acoustic disturbances and the stability properties of hypersonic boundary layers are numerically investigated for boundary-layer flows over a 5 straight cone at a freestream Mach number of 6.0. To compute the shock and the interaction of the shock with the instability waves, the Navier-Stokes equations in axisymmetric coordinates were solved. In the governing equations, inviscid and viscous flux vectors are discretized using a fifth-order accurate weighted-essentially-non-oscillatory scheme. A third-order accurate total-variation-diminishing Runge-Kutta scheme is employed for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. The appearance of instability waves near the nose region and the receptivity of the boundary layer with respect to slow mode acoustic waves are investigated. Computations confirm the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundary-layer transition. The current solutions, compared with experimental observations and other computational results, exhibit good agreement.
Wave mediated angular momentum transport in astrophysical boundary layers
Hertfelder, Marius
2015-01-01
Context. Disk accretion onto weakly magnetized stars leads to the formation of a boundary layer (BL) where the gas loses its excess kinetic energy and settles onto the star. There are still many open questions concerning the BL, for instance the transport of angular momentum (AM) or the vertical structure. Aims. It is the aim of this work to investigate the AM transport in the BL where the magneto-rotational instability (MRI) is not operating owing to the increasing angular velocity $\\Omega(r)$ with radius. We will therefore search for an appropriate mechanism and examine its efficiency and implications. Methods. We perform 2D numerical hydrodynamical simulations in a cylindrical coordinate system $(r, \\varphi)$ for a thin, vertically inte- grated accretion disk around a young star. We employ a realistic equation of state and include both cooling from the disk surfaces and radiation transport in radial and azimuthal direction. The viscosity in the disk is treated by the {\\alpha}-model; in the BL there is no v...
Uranus evolution models with simple thermal boundary layers
Nettelmann, Nadine; Redmer, Ronald; Fortney, Jonathan J.; Hamel, Sebastien; Bethkenhagen, Mandy
2016-04-01
The strikingly low luminosity of Uranus imposes a long-standing challenge to our understanding of Ice Giant planets. Similar to the Earth, Uranus appears to evolve in equilibrium with the solar incident flux (Teq). Here we present the first Uranus structure and evolution models that are constructed to agree with both the observed low luminosity and the gravity field data. Our models make use of modern ab initio equations of state at high pressures for the icy components water, methane, and ammonia. We argue that the transition between the ice/rock-rich interior and the H/He-rich outer envelope should be stably stratified. Therefore, we introduce a simple thermal boundary layer (TBL) and adjust it to reproduce the luminosity. Due to this TBL, the deep interior of the Uranus models are up to a factor 3 warmer than adiabatic models, necessitating the presence of rocks there with a possible I:R of 1 x solar. Furthermore, we also allow for an equilibrium evolution (Teff ~ Teq) that begun prior to the present day, which would therefore no longer constitute a "special time" in Uranus' evolution. Once Teff ~ Teq happens, a shallow, subadiabatic zone in the atmosphere begins to develop. Its depth is adjusted to meet the luminosity constraint. This work provides a simple foundation for future Ice Giant structure and evolution models, that can be improved by properly treating the heat and particle fluxes in the diffusive zones.
Boundary layer parameterizations and long-range transport
International Nuclear Information System (INIS)
A joint work group between the American Meteorological Society (AMS) and the EPA is perusing the construction of an air quality model that incorporates boundary layer parameterizations of dispersion and transport. This model could replace the currently accepted model, the Industrial Source Complex (ISC) model. The ISC model is a Gaussian-plume multiple point-source model that provides for consideration of fugitive emissions, aerodynamic wake effects, gravitational settling and dry deposition. A work group of several Federal and State agencies is perusing the construction of an air quality modeling system for use in assessing and tracking visibility impairment resulting from long-range transport of pollutants. The modeling system is designed to use the hourly vertical profiles of wind, temperature and moisture resulting from a mesoscale meteorological processor that employs four dimensional data assimilation (FDDA). FDDA involves adding forcing functions to the governing model equations to gradually ''nudge'' the model state toward the observations (12-hourly upper air observations of wind, temperature and moisture, and 3-hourly surface observations of wind and moisture). In this way it is possible to generate data sets whose accuracy, in terms of transport, precipitation, and dynamic consistency is superior to both direct interpolation of synoptic-scale analyses of observations and purely predictive mode model result. (AB) ( 19 refs.)
Coupled vs. decoupled boundary layers in VOCALS-REx
Directory of Open Access Journals (Sweden)
C. R. Jones
2011-07-01
Full Text Available We analyze the extent of subtropical stratocumulus-capped boundary layer decoupling and its relation to other boundary-layer characteristics and forcings using aircraft observations from VOCALS-REx along a swath of the subtropical southeast Pacific Ocean running west 1600 km from the coast of Northern Chile. We develop two complementary and consistent measures of decoupling. The first is based on boundary layer moisture and temperature stratification in flight profiles from near the surface to above the capping inversion, and the second is based the difference between the lifted condensation level (LCL and a mean lidar-derived cloud base measured on flight legs at 150 m altitude. Most flights took place during early-mid morning, well before the peak in insolation-induced decoupling.
We find that the boundary layer is typically shallower, drier, and well mixed near the shore, and tends to deepen, decouple, and produce more drizzle further offshore to the west. Decoupling is strongly correlated to the "mixed layer cloud thickness", defined as the difference between the capping inversion height and the LCL; other factors such as wind speed, cloud droplet concentration, and inversion thermodynamic jumps have little additional explanatory power. The results are broadly consistent with the deepening-warming theory of decoupling.
In the deeper boundary layers observed well offshore, there was frequently nearly 100 % boundary-layer cloud cover despite pronounced decoupling. The cloud cover was more strongly correlated to a κ parameter related to the inversion jumps of humidity and temperature, though the exact functional relation is slightly different than found in prior large-eddy simulation studies.
Mixed convection boundary layer flow over a vertical cylinder with prescribed surface heat flux
Energy Technology Data Exchange (ETDEWEB)
Ishak, Anuar [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia)], E-mail: anuar_mi@ukm.my
2009-05-15
The steady mixed convection boundary layer flow along a vertical cylinder with prescribed surface heat flux is investigated in this study. The free stream velocity and the surface heat flux are assumed to vary linearly with the distance from the leading edge. Both the case of the buoyancy forces assisting and opposing the development of the boundary layer are considered. Similarity equations are derived, their solutions being dependent on the mixed convection parameter, the curvature parameter, as well as of the Prandtl number. Dual solutions are found to exist for both buoyancy assisting and opposing flows. It is also found that the boundary layer separation is delayed for a cylinder compared to a flat plate.
Shear Force Distribution and Heat Transfer in Laminar Boundary Layer Flows for Power Law Fluid
Institute of Scientific and Technical Information of China (English)
郑连存; 张欣欣
2002-01-01
Analytical and numerical solutions are presented for the momentum and energy laminar boundary layer equations in power law fluids utilizing a similarity transformation and the shooting technique. The results indicated that for power law exponents 0＜n≤1, the skin friction σ decreases with increasing n, and the dimensionless shear force decreases with increasing dimensionless velocity t. When Pr=1, the velocity distribution in the viscous boundary layer is the same as the temperature distribution in the thermal boundary layer and δ＝δT. For Pr＞1, the increase of the viscous diffusion exceeds that of thermal diffusion with increasing Pr, i.e., δT(t)＜δ(t). The thermal diffusion ratio increases with increasing n(0＜n≤1).
Behaviour of tracer diffusion in simple atmospheric boundary layer models
Directory of Open Access Journals (Sweden)
P. S. Anderson
2007-10-01
Full Text Available 1-D profiles and time series from an idealised atmospheric boundary layer model are presented, which show agreement with boundary layer measurements of polar NO_{x}. Diffusion models are increasingly being used as the framework for studying tropospheric air chemistry dynamics. Models based on standard boundary layer diffusivity profiles have an intrinsic behaviour that is not necessarily intuitive, due to the variation of turbulent diffusivity with height. The simple model presented captures the essence of the evolution of a trace gas released at the surface, and thereby provides both a programming and a conceptual tool in the analysis of observed trace gas evolution. A time scale inherent in the model can be tuned by fitting model time series to observations. This scale is then applicable to the more physically simple but chemically complex zeroth order or box models of chemical interactions.
Particle motion inside Ekman and Bödewadt boundary layers
Duran Matute, Matias; van der Linden, Steven; van Heijst, Gertjan
2014-11-01
We present results from both laboratory experiments and numerical simulations of the motion of heavy particles inside Ekman and Bödewadt boundary layers. The particles are initially at rest on the bottom of a rotating cylinder filled with water and with its axis parallel to the axis of rotation. The particles are set into motion by suddenly diminishing the rotation rate and the subsequent creation of a swirl flow with the boundary layer above the bottom plate. We consider both spherical and non-spherical particles with their size of the same order as the boundary layer thickness. It was found that the particle trajectories define a clear logarithmic spiral with its shape depending on the different parameters of the problem. Numerical simulations show good agreement with experiments and help explain the motion of the particles. This research is funded by NWO (the Netherlands) through the VENI Grant 863.13.022.
Large Eddy Simulation of the ventilated wave boundary layer
DEFF Research Database (Denmark)
Lohmann, Iris P.; Fredsøe, Jørgen; Sumer, B. Mutlu; Christensen, Erik Damgaard
2006-01-01
A Large Eddy Simulation (LES) of (1) a fully developed turbulent wave boundary layer and (2) case 1 subject to ventilation (i.e., suction and injection varying alternately in phase) has been performed, using the Smagorinsky subgrid-scale model to express the subgrid viscosity. The model was found...... overall (local) grid size. The results indicate that the large eddies develop in the resolved scale, corresponding to fluid with an effective viscosity decided by the sum of the kinematic and subgrid viscosity. Regarding case 2, the results are qualitatively in accordance with experimental findings....... Injection generally slows down the flow in the full vertical extent of the boundary layer, destabilizes the flow and decreases the mean bed shear stress significantly; whereas suction generally speeds up the flow in the full vertical extent of the boundary layer, stabilizes the flow and increases the mean...
Localized travelling waves in the asymptotic suction boundary layer
Kreilos, Tobias; Schneider, Tobias M
2016-01-01
We present two spanwise-localized travelling wave solutions in the asymptotic suction boundary layer, obtained by continuation of solutions of plane Couette flow. One of the solutions has the vortical structures located close to the wall, similar to spanwise-localized edge states previously found for this system. The vortical structures of the second solution are located in the free stream far above the laminar boundary layer and are supported by a secondary shear gradient that is created by a large-scale low-speed streak. The dynamically relevant eigenmodes of this solution are concentrated in the free stream, and the departure into turbulence from this solution evolves in the free stream towards the walls. For invariant solutions in free-stream turbulence, this solution thus shows that that the source of energy of the vortical structures can be a dynamical structure of the solution itself, instead of the laminar boundary layer.
Bypass transition and spot nucleation in boundary layers
Kreilos, Tobias; Schlatter, Philipp; Duguet, Yohann; Henningson, Dan S; Eckhardt, Bruno
2016-01-01
The spatio-temporal aspects of the transition to turbulence are considered in the case of a boundary layer flow developing above a flat plate exposed to free-stream turbulence. Combining results on the receptivity to free-stream turbulence with the nonlinear concept of a transition threshold, a physically motivated model suggests a spatial distribution of spot nucleation events. To describe the evolution of turbulent spots a probabilistic cellular automaton is introduced, with all parameters directly fitted from numerical simulations of the boundary layer. The nucleation rates are then combined with the cellular automaton model, yielding excellent quantitative agreement with the statistical characteristics for different free-stream turbulence levels. We thus show how the recent theoretical progress on transitional wall-bounded flows can be extended to the much wider class of spatially developing boundary-layer flows.
Wind Tunnel Simulation of the Atmospheric Boundary Layer
Hohman, Tristen; Smits, Alexander; Martinelli, Luigi
2013-11-01
To simulate the interaction of large Vertical Axis Wind Turbines (VAWT) with the Atmospheric Boundary Layer (ABL) in the laboratory, we implement a variant of Counihan's technique [Counihan 1969] in which a combination of a castellated barrier, elliptical vortex generators, and floor roughness elements is used to create an artificial ABL profile in a standard closed loop wind tunnel. To examine the development and formation of the artificial ABL hotwire and SPIV measurements were taken at various downstream locations with changes in wall roughness, wall type, and vortex generator arrangements. It was found possible to generate a boundary layer at Reθ ~106 , with a mean velocity that followed the 1/7 power law of a neutral ABL over rural terrain and longitudinal turbulence intensities and power spectra that compare well with the data obtained for high Reynolds number flat plate turbulent boundary layers [Hultmark et al. 2010]. Supported by Hopewell Wind Power Ltd., and the Princeton Grand Challenges Program.
International Nuclear Information System (INIS)
The boundary layer convective heat transfer equations with low pressure gradient over a flat plate are solved using Homotopy Perturbation Method, which is one of the semi-exact methods. The nonlinear equations of momentum and energy solved simultaneously via Homotopy Perturbation Method are in good agreement with results obtained from numerical methods. Using this method, a general equation in terms of Pr number and pressure gradient (λ) is derived which can be used to investigate velocity and temperature profiles in the boundary layer.
Coupled vs. decoupled boundary layers in VOCALS-REx
Directory of Open Access Journals (Sweden)
C. R. Jones
2011-03-01
Full Text Available We analyze the extent of subtropical stratocumulus-capped boundary layer decoupling and its relation to other boundary-layer characteristics and forcings using aircraft observations from VOCALS-REx along a swath of the subtropical southeast Pacific Ocean running west 1600 km from the coast of Northern Chile. We develop two complementary and consistent measures of decoupling. The first is based on boundary layer moisture stratification in flight profiles from near the surface to above the capping inversion, and the second is based the difference between the lifted condensation level (LCL and a mean lidar-derived cloud base measured on flight legs at 150m altitude. Most flights took place during early-mid morning, well before the peak in insolation-induced decoupling.
We find that the boundary layer is typically shallower, drier, and well mixed near the shore, and tends to deepen, decouple, and produce more drizzle further offshore to the west. Decoupling is strongly correlated to the “well-mixed cloud thickness”, defined as the difference between the capping inversion height and the LCL; other factors such as wind speed, cloud droplet concentration, and inversion thermodynamic jumps have little additional explanatory power. The results are broadly consistent with the deepening-warming theory of decoupling. In the deeper boundary layers observed well offshore, there was frequently nearly 100% boundary-layer cloud cover despite pronounced decoupling. The cloud cover was more strongly correlated to a κ parameter related to the inversion jumps of humidity and temperature, though the exact functional relation is slightly different than found in prior large-eddy simulation studies.
Numerical Modeling of the Evolving Stable Boundary Layer
Sorbjan, Z.
2013-12-01
A single-column model of the evolving stable boundary layer is tested for the consistency of turbulence parameterization, self-similar properties of the flow, and effects of ambient forcing. The turbulence closure of the model is based on the K-theory approach, with stability functions based on empirical data, and a semi-empirical form of the mixing length. The model has one internal, governing stability parameter, the Richardson number Ri, which dynamically adjusts to the boundary conditions and to external forcing. Model results, expressed in terms of local similarity scales, are universal functions of the Richardson number, i.e. they are satisfied in the entire stable boundary layer, for all instants of time, and all kinds of external forcing. Based on similarity expression, a realizability condition is derived for the minimum turbulent heat flux in the stable boundary layer. Numerical experiments show that the development of 'horse-shoe' shaped, 'fixed-elevation' wind hodographs in the interior of the stable boundary layer are solely caused by effects imposed by surface thermal forcing, and are not related to the inertial oscillation mechanism.
Numerical modeling of the transitional boundary layer over a flat plate
Ivanov, Dimitry; Chorny, Andrei
2015-11-01
Our example is connected with fundamental research on understanding how an initially laminar boundary layer becomes turbulent. We have chosen the flow over a flat plate as a prototype for boundary-layer flows around bodies. Special attention was paid to the near-wall region in order to capture all levels of the boundary layer. In this study, the numerical software package OpenFOAM has been used in order to solve the flow field. The results were used in a comparative study with data obtained from Large Eddy Simulation (LES). The composite SGS-wall model is presently incorporated into a computer code suitable for the LES of developing flat-plate boundary layers. Presently this model is extended to the LES of the zero-pressure gradient, flat-plate turbulent boundary layer. In current study the time discretization is based on a second order Crank-Nicolson/Adams-Bashforth method. LES solver using Smagorinsky and the one-equation LES turbulence models. The transition models significantly improve the prediction of the onset location compared to the fully turbulent models.LES methods appear to be the most promising new tool for the design and analysis of flow devices including transition regions of the turbulent flow.
Indian Academy of Sciences (India)
M Tajuddin; G Narayan Reddy
2005-08-01
A transcendental equation is derived relating wave number and phase velocity of propagation of waves in a partially saturated layered half-space under plane strain conditions. The period equation is derived and discussed for two types of boundaries, permeable and impermeable. In the limiting cases, the problem reduces to more simpliﬁed forms as discussed by earlier researchers.
Institute of Scientific and Technical Information of China (English)
Gui-Qiang Chen; Dan Osborne; Zhongmin Qian
2009-01-01
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in RN with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-fiat boundary. We observe that, under the nonhomogeneons boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition (without the incompressibility condition), which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in RN(n≥3) with nonhomogeneous vorticity boundary condition converge in L2 to the corresponding Euler equations satisfying the kinematic condition.
Conference on Boundary and Interior Layers : Computational and Asymptotic Methods
2015-01-01
This volume offers contributions reflecting a selection of the lectures presented at the international conference BAIL 2014, which was held from 15th to 19th September 2014 at the Charles University in Prague, Czech Republic. These are devoted to the theoretical and/or numerical analysis of problems involving boundary and interior layers and methods for solving these problems numerically. The authors are both mathematicians (pure and applied) and engineers, and bring together a large number of interesting ideas. The wide variety of topics treated in the contributions provides an excellent overview of current research into the theory and numerical solution of problems involving boundary and interior layers. .
The turning of the wind in the atmospheric boundary layer
DEFF Research Database (Denmark)
Pena Diaz, Alfredo; Gryning, Sven-Erik; Floors, Rogier Ralph
2014-01-01
periods of analysis, that under both barotropic and baroclinic conditions, the model predicts the gradient and geostrophic wind well, explaining for a particular case an 'unusual' backing of the wind. The observed conditions at the surface, on the other hand, explain the differences in wind veering. The......Here we use accurate observations of the wind speed vector to analyze the behavior with height of the wind direction. The observations are a combination of tall meteorological mast and long-range wind lidar measurements covering the entire atmospheric boundary layer. The observations were performed...... simulated winds underpredict the turning of the wind and the boundary-layer winds in general....
Lower Atmospheric Boundary Layer Experiment (LABLE) Final Campaign Report
Energy Technology Data Exchange (ETDEWEB)
Klein, P [University of Oklahoma - School of Meteorology; Bonin, TA; Newman, JF [National Renewable Energy Laboratory; Turner, DD [National Oceanic and Atmospheric Administration; Chilson, P [University of Oklahoma; Blumberg, WG [University of Oklahoma; Mishra, S; Wainwright, CE; Carney, M [University of Oklahoma - School of Meteorology; Jacobsen, EP [University of Oklahoma; Wharton, S [Lawrence Livermore National Laboratory
2015-11-01
The Lower Atmospheric Boundary Layer Experiment (LABLE) included two measurement campaigns conducted at the Atmospheric Radiation Measurement (ARM) Southern Great Plains site in Oklahoma during 2012 and 2013. LABLE was designed as a multi-phase, low-cost collaboration among the University of Oklahoma, the National Severe Storms Laboratory, Lawrence Livermore National Laboratory, and the ARM program. A unique aspect was the role of graduate students in LABLE. They served as principal investigators and took the lead in designing and conducting experiments using different sampling strategies to best resolve boundary-layer phenomena.
Oscillations of the Boundary Layer and High-frequency QPOs
Directory of Open Access Journals (Sweden)
Blinova A. A.
2014-01-01
Full Text Available We observed persistent high-frequency oscillations of the boundary layer near an accreting, weakly-magnetized star in global 3D MHD simulations. The tilted dipole magnetic field is not strong enough to open a gap between the star and the disk. Instead, it forms a highly-wrapped azimuthal field near the surface of the star which slows down rotation of the disk matter, while a small tilt of the field excites oscillations of the boundary layer with a frequency below the Keplerian frequency. This mechanism may be responsible for the high-frequency oscillations in accreting neutron stars, white dwarfs and classical T Tauri stars.
Multilevel Model of Planetary Boundary-layer Suitable for use with Mesoscale Dynamic Models
DEFF Research Database (Denmark)
Busch, N. E.; Chang, S. W.; Anthes, R. A.
1976-01-01
In this paper a simple model of the planetary boundary layer (PBL) is proposed. The surface layer is modeled according to established similarity theory. Above the surface layer a prognostic equation for the mixing length is introduced. The time-dependent mixing length is a function of the PBL cha...... characteristics, including the height of the capping inversion, the local friction velocity and the surface heat flux. In a preliminary experiment, the behavior of the PBL is compared with observations from the Great Plains Experiment....
Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet
Directory of Open Access Journals (Sweden)
Masood Khan
2015-10-01
Full Text Available This article studies the Carreau viscosity model (which is a generalized Newtonian model and then use it to obtain a formulation for the boundary layer equations of the Carreau fluid. The boundary layer flow and heat transfer to a Carreau model over a nonlinear stretching surface is discussed. The Carreau model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the fluids having shear thinning properties and fluids with shear thickening properties for numerical values of the power law exponent n. The modeled boundary layer conservation equations are converted to non-linear coupled ordinary differential equations by a suitable transformation. Numerical solution of the resulting equations are obtained by using the Runge-Kutta Fehlberg method along with shooting technique. This analysis reveals many important physical aspects of flow and heat transfer. Computations are performed for different values of the stretching parameter (m, the Weissenberg number (We and the Prandtl number (Pr. The obtained results show that for shear thinning fluid the fluid velocity is depressed by the Weissenberg number while opposite behavior for the shear thickening fluid is observed. A comparison with previously published data in limiting cases is performed and they are in excellent agreement.
Boundary value problemfor multidimensional fractional advection-dispersion equation
Directory of Open Access Journals (Sweden)
Khasambiev Mokhammad Vakhaevich
2015-05-01
Full Text Available In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and are non-local. Many processes in complex systems have nonlocality and long-time memory. Fractional integral operators and fractional differential operators allow describing some of these properties. The use of the fractional calculus will be helpful for obtaining the dynamical models, in which integro-differential operators describe power long-time memory by time and coordinates, and three-dimensional nonlocality for complex medium and processes.Differential equations of fractional order appear when we use fractal conception in physics of the condensed medium. The transfer, described by the operator with fractional derivatives at a long distance from the sources, leads to other behavior of relatively small concentrations as compared with classic diffusion. This fact redefines the existing ideas about safety, based on the ideas on exponential velocity of damping. Fractional calculus in the fractal theory and the systems with memory have the same importance as the classic analysis in mechanics of continuous medium.In recent years, the application of fractional derivatives for describing and studying the physical processes of stochastic transfer is very popular too. Many problems of filtration of liquids in fractal (high porous medium lead to the need to study boundary value problems for partial differential equations in fractional order.In this paper the
Solution of the Stokes system by boundary integral equations and fixed point iterative schemes
International Nuclear Information System (INIS)
The solution to the exterior three dimensional Stokes problem is sought in the form of a single layer potential of unknown density. This reduces the problem to a boundary integral equation of the first kind whose operator is the velocity component of the single layer potential. It is shown that this component is an isomorphism between two appropriate Sobolev spaces containing the unknown densities and the data respectively. The isomorphism corresponds to a variational problem with coercive bilinear form. The latter property allows us to consider various fixed point iterative schemes that converge to the unique solution of the integral equation. Explicit error estimates are also obtained. The successive approximations are also considered in a more computable form by using the product integration method of Atkinson. (author). 47 refs
Directory of Open Access Journals (Sweden)
M. RAHIMI EOSBOEE,
2010-12-01
Full Text Available In this study magnetohydrodynamics (MHD boundary layer flow of an upper-convected Maxwell fluid has been investigated. Similarity transformation has been used to reduce the governing differential equations into an ordinary non-linear differential equation. homotopy perturbation Method (HPM has applied to solve this developed nonlinear equation. In this article firstly, the basic idea of the HPM for solving nonlinear differential equations is briefly ntroduced and then it is employed to derive solution of nonlinear governing equation of MHD boundary layer flow with highly nonlinear term. The obtained results from HPM have been compared with numerical Boundary Value problem Method (BVP to verify the accuracy of the proposed method. The effects of the Hartman number (M and Deborah number (β for various conditions have been shown through graphs.
Diffusive Boltzmann equation, its fluid dynamics, Couette flow and Knudsen layers
Abramov, Rafail V
2016-01-01
In the current work we propose a diffusive modification of the Boltzmann equation. This naturally leads to the corresponding diffusive fluid dynamics equations, which we numerically investigate in a simple Couette flow setting. This diffusive modification is based on the assumption of the "imperfect" model collision term, which is unable to track all collisions in the corresponding real gas particle system. The effect of missed collisions is then modeled by an appropriately scaled long-term homogenization process of the particle dynamics. The corresponding diffusive fluid dynamics equations are produced in a standard way by closing the hierarchy of the moment equations using either the Euler or the Grad closure. In the numerical experiments with the Couette flow, we discover that the diffusive Euler equations behave similarly to the conventional Navier-Stokes equations, while the diffusive Grad equations additionally exhibit Knudsen-like velocity boundary layers. We compare the simulations with the correspond...
DNS Study on Physics of Late Boundary Layer Transition
Liu, Chaoqun
2014-01-01
This paper serves as a review of our recent new DNS study on physics of late boundary layer transition. This includes mechanism of the large coherent vortex structure formation, small length scale generation and flow randomization. The widely spread concept vortex breakdown to turbulence,which was considered as the last stage of flow transition, is not observed and is found theoretically incorrect. The classical theory on boundary layer transition is challenged and we proposed a new theory with five steps, i.e. receptivity, linear instability, large vortex formation, small length scale generation, loss of symmetry and randomization to turbulence. We have also proposed a new theory about turbulence generation. The new theory shows that all small length scales (turbulence) are generated by shear layer instability which is produced by large vortex structure with multiple level vortex rings, multiple level sweeps and ejections, and multiple level negative and positive spikes near the laminar sub-layers.Therefore,...
MHD Boundary Layer Flow of Dilatant Fluid in a Divergent Channel with Suction or Blowing
Institute of Scientific and Technical Information of China (English)
Krishnendu Bhattacharyya; G.C.Layek
2011-01-01
@@ An analysis is carried out to study a steady magnetohydrodynamic(MHD) boundary layer How of an electrically conducting incompressible power-law non-Newtonian fluid through a divergent channel.The channel walls are porous and subjected to either suction or blowing of equal magnitude of the same kind of fluid on both walls.The fluid is permeated by a magnetic field produced by electric current along the line of intersection of the channel walls.The governing partial differential equation is transformed into a self-similar nonlinear ordinary differential equation using similarity transformations.The possibility of boundary layer flow in a divergent channel is analyzed with the power-law fluid model.The analysis reveals that the boundary layer flow (without separation) is possible for the case of the dilatant fluid model subjected to suitable suction velocity applied through its porous walls,even in the absence of a magnetic field.Further, it is found that the boundary layer flow is possible even in the presence of blowing for a suitable value of the magnetic parameter.It is found that the velocity increases with increasing values of the power-law index for the case of dilatant fluid.The effects of suction/blowing and magnetic field on the velocity are shown graphically and discussed physical尔
Receptivity and Forced Response to Acoustic Disturbances in High-Speed Boundary Layers
Balakumar, P.; King, Rudolph A.; Chou, Amanda; Owens, Lewis R.; Kegerise, Michael A.
2016-01-01
Supersonic boundary-layer receptivity to freestream acoustic disturbances is investigated by solving the Navier-Stokes equations for Mach 3.5 flow over a sharp flat plate and a 7-deg half-angle cone. The freestream disturbances are generated from a wavy wall placed at the nozzle wall. The freestream acoustic disturbances radiated by the wavy wall are obtained by solving the linearized Euler equations. The results for the flat plate show that instability modes are generated at all the incident angles ranging from zero to highly oblique. However, the receptivity coefficient decreases by about 20 times when the incident angle increases from zero to a highly oblique angle of 68 degrees. The results for the cone show that no instability modes are generated when the acoustic disturbances impinge the cone obliquely. The results show that the perturbations generated inside the boundary layer by the acoustic disturbances are the response of the boundary layer to the external forcing. The amplitude of the forced disturbances inside the boundary layer are about 2.5 times larger than the incoming field for zero azimuthal wavenumber and they are about 1.5 times for large azimuthal wavenumbers.
Effects of Nose Bluntness on Stability of Hypersonic Boundary Layers over Blunt Cone
Kara, K.; Balakumar, P.; Kandil, O. A.
2007-01-01
Receptivity and stability of hypersonic boundary layers are numerically investigated for boundary layer flows over a 5-degree straight cone at a free-stream Mach number of 6.0. To compute the shock and the interaction of shock with the instability waves, we solve the Navier-Stokes equations in axisymmetric coordinates. The governing equations are solved using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. Generation of instability waves from leading edge region and receptivity of boundary layer to slow acoustic waves are investigated. Computations are performed for a cone with nose radii of 0.001, 0.05 and 0.10 inches that give Reynolds numbers based on the nose radii ranging from 650 to 130,000. The linear stability results showed that the bluntness has a strong stabilizing effect on the stability of axisymmetric boundary layers. The transition Reynolds number for a cone with the nose Reynolds number of 65,000 is increased by a factor of 1.82 compared to that for a sharp cone. The receptivity coefficient for a sharp cone is about 4.23 and it is very small, approx.10(exp -3), for large bluntness.
Interaction between surface and atmosphere in a convective boundary layer /
Garai, Anirban
2013-01-01
Solar heating of the surface causes the near surface air to warm up and with sufficient buoyancy it ascends through the atmosphere as surface-layer plumes and thermals. The cold fluid from the upper part of the boundary layer descends as downdrafts. The downdrafts and thermals form streamwise roll vortices. All these turbulent coherent structures are important because they contribute most of the momentum and heat transport. While these structures have been studied in depth, their imprint on t...
Chitta, Subhashini; Steinhoff, John
2015-11-01
This paper describes the use of Vorticity Confinement (VC) to efficiently treat complex blunt bodies with thin shed vortex sheets and attached boundary layers. Because these flows involve turbulence in the vortical regions, there is currently no ab initio method to treat them on current or foreseeable computers. In fact, in spite of years of turbulence modeling efforts (such as LES or RANS), serious flaws in aerodynamic design involving vortex shedding may still be left undetected until the expensive prototype or production stage. Our basic premise is that, for a class of real-world problems requiring simulating ensembles of flow conditions for overall accuracy, conventional turbulence models suffer cost constraints. For these reasons, VC is used to rapidly simulate many operating conditions, as is often done in expensive testing programs for flying prototypes, and in realistic simulations. To achieve dramatically lower computational cost, VC treats the entire flow in a uniform, coarse grid with solid surfaces ``immersed'' in the grid so that they can be quickly generated for many configurations with no requirement for adaptive or conforming fine grids. Also, the VC method has the efficiency of panel methods, but the generality and ease of use of Euler equation methods. We would like to thank Dr. Frank Caradonna for his suggestions and support.
International Nuclear Information System (INIS)
The reflection equation algebra of Sklyanin is extended to the supersymmetric case. A graded reflection equation algebra is proposed and the corresponding graded (supersymmetric) boundary quantum inverse scattering method (QISM) is formulated. As an application, integrable open-boundary conditions for the doped spin-1 chain of the supersymmetric t-J model are studied in the framework of the boundary QISM. Diagonal boundary K-matrices are found and four classes of integrable boundary terms are determined. (author)
Hussain Ahmad; Tariq Javed; Abuzar Ghaffari
2016-01-01
In the present article, radiation effect on mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder with constant heat flux has been numerically analyzed. The governing boundary layer equations are transformed to dimensionless nonlinear partial differential equations. The equations are solved numerically by using Keller-box method. The computed results are in excellent agreement with the previous studies. Skin friction coefficient and Nusselt number ar...
Clear-air radar observations of the atmospheric boundary layer
Ince, Turker
2001-10-01
This dissertation presents the design and operation of a high-resolution frequency-modulated continuous-wave (FM- CW) radar system to study the structure and dynamics of clear-air turbulence in the atmospheric boundary layer (ABL). This sensitive radar can image the vertical structure of the ABL with both high spatial and temporal resolutions, and provide both qualitative information about the morphology of clear-air structures and quantitative information on the intensity of fluctuations in refractive-index of air. The principles of operation and the hardware and data acquisition characteristics of the radar are described in the dissertation. In October 1999, the radar participated in the Cooperative Atmosphere-Surface Exchange Study (CASES'99) Experiment to characterize the temporal structure and evolution of the boundary-layer features in both convective and stable conditions. The observed structures include clear-air convection, boundary layer evolution, gravity waves, Kelvin-Helmholtz instabilities, stably stratified layers, and clear-air turbulence. Many of the S-band radar images also show high- reflectivity returns from Rayleigh scatterers such as insects. An adaptive median filtering technique based on local statistics has, therefore, been developed to discriminate between Bragg and Rayleigh scattering in clear-air radar observations. The filter is tested on radar observations of clear air convection with comparison to two commonly used image processing techniques. The dissertation also examines the statistical mean of the radar-measured C2n for clear-air convection, and compares it with the theoretical predictions. The study also shows that the inversion height, local thickness of the inversion layer, and the height of the elevated atmospheric layers can be estimated from the radar reflectivity measurements. In addition, comparisons to the radiosonde-based height estimates are made. To examine the temporal and spatial structure of C2n , the dissertation
Directory of Open Access Journals (Sweden)
Ivanović Dečan
2005-01-01
Full Text Available Through the porous contour in perpendicular direction, the fluid of the same properties as incompressible fluid in basic flow, has been injected or ejected with velocity who is a function of the contour longitudinal coordinate and time. The corresponding equations of unsteady boundary layer, by introducing the appropriate variable transformations, momentum and energy equations and two similarity parameters sets, are transformed into generalized form. These parameters are expressing the influence of the outer flow velocity, the injection or ejection velocity and the flow history in boundary layer, on the boundary layer characteristics. Obtained generalized solutions are used to calculate the distributions of velocity, and shear stress in laminar-turbulent transition of unsteady incompressible boundary layer on different porous contours: circular cylinder, thin elliptical cylinder and aerofoil, whose centers velocities changes in time as a degree functions. The ejection of fluid postpones the boundary layer separation, i.e. laminar-turbulent transition, and vice versa the injection of fluid favors the separation. Boundary layer characteristics are found directly, no further numerical integration of momentum equation.
RESTRICTED NONLINEAR APPROXIMATION AND SINGULAR SOLUTIONS OF BOUNDARY INTEGRAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Reinhard Hochmuth
2002-01-01
This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1 ] are chosen as a starting point for characterizations of functions in Besov spaces B , (0,1) with 0＜σ＜∞ and (1+σ)-1＜τ＜∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
Numerical analysis has become the basic tool for both design and research problems in solid mechanics. The need for accuracy and detail, plus the availablity of the high speed computer has led to the development of many new modeling methods ranging from general purpose structural analysis finite element programs to special purpose research programs. The boundary-integral equation (BIE) method is based on classical mathematical techniques but is finding new life as a basic stress analysis tool for engineering applications. The paper summarizes some advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referencing some of the much broader developmental effort. Future emphasis is needed to exploit the BIE method in conjunction with other techniques such as the finite element method through the creation of hybrid stress analysis methods. (Auth.)
Boundary-Layer Wind Structure in a Landfalling Tropical Cyclone
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this study, a slab boundary layer model with a constant depth is used to analyze the boundary-layer wind structure in a landfalling tropical cyclone. Asymmetry is found in both the tangential and radial components of horizontal wind in the tropical cyclone boundary layer at landfall. For a steady tropical cyclone on a straight coastline at landfall, the magnitude of the radial component is greater in the offshoreflow side and the tangential component is greater over the sea, slightly offshore, therefore the greater total wind speed occurs in the offshore-flow side over the sea. The budget analysis suggests that: (1) a greater surface friction over land produces a greater inflow and the nonlinear effect advects the maximum inflow downstream, and (2) a smaller surface friction over the sea makes the decrease of the tangential wind component less than that over land. Moreover, the boundary layer wind structures in a tropical cyclone are related to the locations of the tropical cyclone relative to the coastline due to the different surface frictions. During tropical cyclone landfall, the impact of rough terrain on the cyclone increases, so the magnitude of the radial component of wind speed increases in the offshore-flow side and the tangential component outside the radius of maximum wind speed decreases gradually.
Two Phases of Coherent Structure Motions in Turbulent Boundary Layer
Institute of Scientific and Technical Information of China (English)
LIU Jian-Hua; JIANG Nan
2007-01-01
Two phases of coherent structure motion are acquired after obtaining conditional phase-averaged waveforms for longitudinal velocity of coherent structures in turbulent boundary layer based on Harr wavelet transfer. The correspondences of the two phases to the two processes (i.e. ejection and sweep) during a burst are determined.
A parametric study of adverse pressure gradient turbulent boundary layers
International Nuclear Information System (INIS)
There are many open questions regarding the behaviour of turbulent boundary layers subjected to pressure gradients and this is confounded by the large parameter space that may affect these flows. While there have been many valuable investigations conducted within this parameter space, there are still insufficient data to attempt to reduce this parameter space. Here, we consider a parametric study of adverse pressure gradient turbulent boundary layers where we restrict our attention to the pressure gradient parameter, β, the Reynolds number and the acceleration parameter, K. The statistics analyzed are limited to the streamwise fluctuating velocity. The data show that the mean velocity profile in strong pressure gradient boundary layers does not conform to the classical logarithmic law. Moreover, there appears to be no measurable logarithmic region in these cases. It is also found that the large-scale motions scaling with outer variables are energised by the pressure gradient. These increasingly strong large-scale motions are found to be the dominant contributor to the increase in turbulence intensity (scaled with friction velocity) with increasing pressure gradient across the boundary layer.
Full-Scale Spectrum of Boundary-Layer Winds
DEFF Research Database (Denmark)
Larsén, Xiaoli Guo; Larsen, Søren Ejling; Lundtang Petersen, Erik
2016-01-01
Extensive mean meteorological data and high frequency sonic anemometer data from two sites in Denmark, one coastal onshore and one offshore, have been used to study the full-scale spectrum of boundary-layer winds, over frequencies f from about 1 yr−1 to10 Hz. 10-min cup anemometer data are used t...
On the growth of turbulent regions in laminar boundary layers
Gad-El-hak, M.; Riley, J. J.; Blackwelder, R. F.
1981-01-01
Turbulent spots evolving in a laminar boundary layer on a nominally zero pressure gradient flat plate are investigated. The plate is towed through an 18 m water channel, using a carriage that rides on a continuously replenished oil film giving a vibrationless tow. Turbulent spots are initiated using a solenoid valve that ejects a small amount of fluid through a minute hole on the working surface. A novel visualization technique that utilizes fluorescent dye excited by a sheet of laser light is employed. Some new aspects of the growth and entrainment of turbulent spots, especially with regard to lateral growth, are inferred from the present experiments. To supplement the information on lateral spreading, a turbulent wedge created by placing a roughness element in the laminar boundary layer is also studied both visually and with probe measurements. The present results show that, in addition to entrainment, another mechanism is needed to explain the lateral growth characteristics of a turbulent region in a laminar boundary layer. This mechanism, termed growth by destabilization, appears to be a result of the turbulence destabilizing the unstable laminar boundary layer in its vicinity. To further understand the growth mechanisms, the turbulence in the spot is modulated using drag-reducing additives and salinity stratification.
On the Effects of Surface Roughness on Boundary Layer Transition
Choudhari, Meelan M.; Li, Fei; Chang, Chau-Lyan; Edwards, Jack
2009-01-01
Surface roughness can influence laminar-turbulent transition in many different ways. This paper outlines selected analyses performed at the NASA Langley Research Center, ranging in speed from subsonic to hypersonic Mach numbers and highlighting the beneficial as well as adverse roles of the surface roughness in technological applications. The first theme pertains to boundary-layer tripping on the forebody of a hypersonic airbreathing configuration via a spanwise periodic array of trip elements, with the goal of understanding the physical mechanisms underlying roughness-induced transition in a high-speed boundary layer. The effect of an isolated, finite amplitude roughness element on a supersonic boundary layer is considered next. The other set of flow configurations examined herein corresponds to roughness based laminar flow control in subsonic and supersonic swept wing boundary layers. A common theme to all of the above configurations is the need to apply higher fidelity, physics based techniques to develop reliable predictions of roughness effects on laminar-turbulent transition.
CISM Course on Recent Advances in Boundary Layer Theory
1998-01-01
Recent advances in boundary-layer theory have shown how modern analytical and computational techniques can and should be combined to deepen the understanding of high Reynolds number flows and to design effective calculation strategies. This is the unifying theme of the present volume which addresses laminar as well as turbulent flows.
The collapse of turbulence in the atmospheric boundary layer
Energy Technology Data Exchange (ETDEWEB)
Van de Wiel, B J H; Clercx, H J H [Department of Physics, Eindhoven University of Technology (Netherlands); Moene, A F [Department of Meteorology and Air Quality, Wageningen University and Research Centre (Netherlands); Jonker, H J J, E-mail: b.j.h.v.d.wiel@tue.nl [Department of Multi-scale Pysics, Delft University of Technology (Netherlands)
2011-12-22
A well-known phenomenon in the atmospheric boundary layer is the fact that winds may become very weak in the evening after a clear sunny day. In these quiet conditions usually hardly any turbulence is present. Consequently this type of boundary layer is referred to as the quasi-laminar boundary layer. In spite of its relevance, the appearance of laminar boundary layers is poorly understood and forms a long standing problem in meteorological research. Here we investigate an analogue problem in the form of a stably stratified channel flow. The flow is studied with a simplified atmospheric model as well as with Direct Numerical Simulations. Both models show remarkably similar behaviour with respect to the mean variables such as temperature and wind speed. The similarity between both models opens new way for understanding and predicting the laminarization process. Mathematical analysis on the simplified model shows that relaminarization can be understood from the existence of a definite limit in the maximum sustainable heat flux under stably stratified conditions. This fascinating aspect will be elaborated in future work.
Passive Control of Supersonic Rectangular Jets through Boundary Layer Swirl
Han, Sang Yeop; Taghavi, Ray R.; Farokhi, Saeed
2013-06-01
Mixing characteristics of under-expanded supersonic jets emerging from plane and notched rectangular nozzles are computationally studied using nozzle exit boundary layer swirl as a mean of passive flow control. The coupling of the rectangular jet instability modes, such as flapping, and the swirl is investigated. A three-dimensional unsteady Reynolds-Averaged Navier-Stokes (RANS) code with shock adaptive grids is utilized. For plane rectangular nozzle with boundary layer swirl, the flapping and spanwise oscillations are captured in the jet's small and large dimensions at twice the frequencies of the nozzles without swirl. A symmetrical oscillatory mode is also observed in the jet with double the frequency of spanwise oscillation mode. For the notched rectangular nozzle with boundary layer swirl, the flapping oscillation in the small jet dimension and the spanwise oscillation in the large jet dimension are observed at the same frequency as those without boundary layer swirl. The mass flow rates in jets at 11 and 8 nozzle heights downstream of the nozzles increased by nearly 25% and 41% for the plane and notched rectangular nozzles respectively, due to swirl. The axial gross thrust penalty due to induced swirl was 5.1% for the plane and 4.9% for the notched rectangular nozzle.
Boundary Layer Flows in Porous Media with Lateral Mass Flux
DEFF Research Database (Denmark)
Nemati, H; H, Bararnia; Noori, F;
2015-01-01
Solutions for free convection boundary layers on a heated vertical plate with lateral mass flux embedded in a saturated porous medium are presented using the Homotopy Analysis Method and Shooting Numerical Method. Homotopy Analysis Method yields an analytic solution in the form of a rapidly...
Analysis of diabatic flow modification in the internal boundary layer
DEFF Research Database (Denmark)
Floors, Rogier; Gryning, Sven-Erik; Pena Diaz, Alfredo;
2011-01-01
Measurements at two meteorological masts in Denmark, Horns Rev in the sea and Høvsøre near the coastline on land, are used to analyze the behaviour of the flow after a smooth-to-rough change in surface conditions. The study shows that the wind profile within the internal boundary layer is...
Vortex Generator Induced Flow in a High Re Boundary Layer
DEFF Research Database (Denmark)
Velte, Clara Marika; Braud, C.; Coudert, S.;
2012-01-01
Stereoscopic Particle Image Velocimetry measurements have been conducted in cross-planes behind three different geometries of Vortex Generators (VGs) in a high Reynolds number boundary layer. The VGs have been mounted in a cascade producing counter-rotating vortices and the downstream flow...
Vortex Generator Induced Flow in a High Re Boundary Layer
DEFF Research Database (Denmark)
Velte, Clara Marika; Braud, C.; Coudert, S.;
2014-01-01
Stereoscopic Particle Image Velocimetry measurements have been conducted in cross-planes behind three different geometries of Vortex Generators (VGs) in a high Reynolds number boundary layer. The VGs have been mounted in a cascade producing counter-rotating vortices and the downstream flow...
Turbulent spots detection during boundary layer by-pass transition
Czech Academy of Sciences Publication Activity Database
Jonáš, Pavel; Elsner, W.; Mazur, Oton; Uruba, Václav; Wysocki, M.
-, č. 80 (2009), s. 16-19. ISSN N R&D Projects: GA AV ČR(CZ) IAA200760614; GA MŠk MEB050810 Institutional research plan: CEZ:AV0Z20760514 Keywords : turbulent spot * boundary layer * by-pass transition * turbulent spot detection Subject RIV: BK - Fluid Dynamics
Spatially developing turbulent boundary layer on a flat plate
Lee, J H; Hutchins, N; Monty, J P
2012-01-01
This fluid dynamics video submitted to the Gallery of Fluid motion shows a turbulent boundary layer developing under a 5 metre-long flat plate towed through water. A stationary imaging system provides a unique view of the developing boundary layer as it would form over the hull of a ship or fuselage of an aircraft. The towed plate permits visualisation of the zero-pressure-gradient turbulent boundary layer as it develops from the trip to a high Reynolds number state ($Re_\\tau \\approx 3000$). An evolving large-scale coherent structure will appear almost stationary in this frame of reference. The visualisations provide an unique view of the evolution of fundamental processes in the boundary layer (such as interfacial bulging, entrainment, vortical motions, etc.). In the more traditional laboratory frame of reference, in which fluid passes over a stationary body, it is difficult to observe the full evolution and lifetime of turbulent coherent structures. An equivalent experiment in a wind/water-tunnel would requ...
Institute of Scientific and Technical Information of China (English)
Chandaneswar Midya
2012-01-01
An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible Buid over a linearly shrinking surface is presented. The Row is permeated by an externally applied magnetic Geld normal to the plane of the flow. The equations governing the Row and concentration Reid are reduced into a set of nonlinear ordinary differential equations using similarity variables. Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall mass flux (PMF) as boundary conditions. The study reveals that the concentration over a shrinking sheet is signiRcantly different from that of a stretching surface. It s found that te solute boundary layer thickness is enhanced with the increasing values of the Schmidt number and the power-law index parameter, but decreases with enhanced vaJues of magnetic and reaction rate parameters for the PSC case. For the PMF case, the solute boundary layer thickness decreases with the increase of the Schmidt number, magnetic and reaction rate parameter for power-law index parameter n = 0. Negative solute boundary layer thickness is observed for the PMF case when n = 1 and 2, and these facts may not be realized in real-world applications.%An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible fluid over a linearly shrinking surface is presented.The flow is permeated by an externally applied magnetic field normal to the plane of the flow.The equations governing the flow and concentration field are reduced into a set of nonlinear ordinary differential equations using similarity variables.Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall
Analytic Study of Magnetohydrodynamic Flow and Boundary Layer Control Over a Wedge
Institute of Scientific and Technical Information of China (English)
M. Chandrasekar; S. Baskaran
2008-01-01
A genuine variational principle developed by Gyarmati, in the field of thermodynamics of irreversible processes unifying the theoretical requirements of technical, environmental and biological sciences is employed to study the effects of uniform suction and injection on MHD flow adjacent to an isothermal wedge with pressure gradient in the presence of a transverse magnetic field. The velocity distribution inside the boundary layer has been considered as a simple polynomial function and the variational principle is formulated. The Euler-Lagrange equation is reduced to a simple polynomial equation in terms of momentum boundary layer thickness. The velocity profiles, displacement thickness and the coefficient of skin friction are calculated for various values of wedge angle parameter m, magnetic parameter ε and suction/injection parameter H. The present results are compared with known available results and the comparison is found to be satisfactory. The present study establishes high accuracy of results obtained by this variational technique.
Unsteady Boundary-Layer Flow over Jerked Plate Moving in a Free Stream of Viscoelastic Fluid
Directory of Open Access Journals (Sweden)
Sufian Munawar
2014-01-01
Full Text Available This study aims to investigate the unsteady boundary-layer flow of a viscoelastic non-Newtonian fluid over a flat surface. The plate is suddenly jerked to move with uniform velocity in a uniform stream of non-Newtonian fluid. Purely analytic solution to governing nonlinear equation is obtained. The solution is highly accurate and valid for all values of the dimensionless time 0≤τ<∞. Flow properties of the viscoelastic fluid are discussed through graphs.
Series Solution for Unsteady Boundary-Layer Flows Due to Impulsively Stretching Plate
Institute of Scientific and Technical Information of China (English)
Seripah Awang Kechil; Ishak Hashim
2007-01-01
@@ The third-order nonlinear partial differential equation modelling the unsteady boundary-layer flows caused by an impulsively stretching flat plate is solved by using the Adomian decomposition method (ADM). The ADM yields analytic solution in the form of a rapidly convergent infinite series with easily computable terms. The series solution using the ADM for the unsteady flows is presented for the first time.
A turbulence model for steady and unsteady boundary layers in strong pressure gradients
Hytopoulos, Evangelos
1994-01-01
A new turbulence model designed for two-dimensional, steady and unsteady boundary layers in strong adverse pressure gradients is described. The model is developed in a rational way based on an understanding of the flow physics obtained from recent experimental observations. The turbulent shear stress is given by a mixing length model, but the variation of the mixing length in the outer region is not constant; it varies according to an integral form of the turbulence kinetic-energy equation. T...
Weyburne, David
2015-01-01
The use of the defect profile instead of the experimentally observed velocity profile for the search for similarity parameters has become firmly imbedded in the turbulent boundary layer literature. However, a search of the literature reveals that there are no theoretical reasons for this defect profile preference over the more traditional velocity profile. In the report herein, we use the flow governing equation approach to develop similarity criteria for the two profiles. Results show that t...
Wave mediated angular momentum transport in astrophysical boundary layers
Hertfelder, Marius; Kley, Wilhelm
2015-07-01
Context. Disk accretion onto weakly magnetized stars leads to the formation of a boundary layer (BL) where the gas loses its excess kinetic energy and settles onto the star. There are still many open questions concerning the BL, for instance the transport of angular momentum (AM) or the vertical structure. Aims: It is the aim of this work to investigate the AM transport in the BL where the magneto-rotational instability (MRI) is not operating owing to the increasing angular velocity Ω(r) with radius. We will therefore search for an appropriate mechanism and examine its efficiency and implications. Methods: We perform 2D numerical hydrodynamical simulations in a cylindrical coordinate system (r,ϕ) for a thin, vertically integrated accretion disk around a young star. We employ a realistic equation of state and include both cooling from the disk surfaces and radiation transport in radial and azimuthal direction. The viscosity in the disk is treated by the α-model; in the BL there is no viscosity term included. Results: We find that our setup is unstable to the sonic instability which sets in shortly after the simulations have been started. Acoustic waves are generated and traverse the domain, developing weak shocks in the vicinity of the BL. Furthermore, the system undergoes recurrent outbursts where the activity in the disk increases strongly. The instability and the waves do not die out for over 2000 orbits. Conclusions: There is indeed a purely hydrodynamical mechanism that enables AM transport in the BL. It is efficient and wave mediated; however, this renders it a non-local transport method, which means that models of a effective local viscosity like the α-viscosity are probably not applicable in the BL. A variety of further implications of the non-local AM transport are discussed.
A Fast Spectral Galerkin Method for Hypersingular Boundary Integral Equations in Potential Theory
Energy Technology Data Exchange (ETDEWEB)
Nintcheu Fata, Sylvain [ORNL; Gray, Leonard J [ORNL
2009-01-01
This research is focused on the development of a fast spectral method to accelerate the solution of three-dimensional hypersingular boundary integral equations of potential theory. Based on a Galerkin approximation, the Fast Fourier Transform and local interpolation operators, the proposed method is a generalization of the Precorrected-FFT technique to deal with double-layer potential kernels, hypersingular kernels and higher-order basis functions. Numerical examples utilizing piecewise linear shape functions are included to illustrate the performance of the method.
Minimum Wind Dynamic Soaring Trajectories under Boundary Layer Thickness Limits
Bousquet, Gabriel; Triantafyllou, Michael; Slotine, Jean-Jacques
2015-11-01
Dynamic soaring is the flight technique where a glider, either avian or manmade, extracts its propulsive energy from the non-uniformity of horizontal winds. Albatrosses have been recorded to fly an impressive 5000 km/week at no energy cost of their own. In the sharp boundary layer limit, we show that the popular image, where the glider travels in a succession of half turns, is suboptimal for travel speed, airspeed, and soaring ability. Instead, we show that the strategy that maximizes the three criteria simultaneously is a succession of infinitely small arc-circles connecting transitions between the calm and windy layers. The model is consistent with the recordings of albatross flight patterns. This lowers the required wind speed for dynamic soaring by over 50% compared to previous beliefs. In the thick boundary layer limit, energetic considerations allow us to predict a minimum wind gradient necessary for sustained soaring consistent with numerical models.
Energy Technology Data Exchange (ETDEWEB)
Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1996-08-01
The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)
International Nuclear Information System (INIS)
The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)
The height of the atmospheric boundary layer during unstable conditions
Energy Technology Data Exchange (ETDEWEB)
Gryning, S.E.
2005-11-01
The height of the convective atmospheric boundary layer, also called the mixed-layer, is one of the fundamental parameters that characterise the structure of the atmosphere near the ground. It has many theoretical and practical applications such as the prediction of air pollution concentrations, surface temperature and the scaling of turbulence. However, as pointed out by Builtjes (2001) in a review paper on Major Twentieth Century Milestones in Air Pollution Modelling and Its Application, the weakest point in meteorology data is still the determination of the height of the mixed-layer, the so-called mixing height. A simple applied model for the height of the mixed-layer over homogeneous terrain is suggested in chapter 2. It is based on a parameterised budget for the turbulent kinetic energy. In the model basically three terms - the spin-up term and the production of mechanical and convective turbulent kinetic energy - control the growth of the mixed layer. The interplay between the three terms is related to the meteorological conditions and the height of the mixed layer. A stable layer, the so-called entrainment zone, which is confined between the mixed layer and the free air above, caps the mixed layer. A parameterisation of the depth of the entrainment zone is also suggested, and used to devise a combined model for the height of the mixed layer and the entrainment zone. Another important aspect of the mixed layer development exists in coastal areas where an internal boundary layer forms downwind from the coastline. A model for the growth of the internal boundary layer is developed in analogy with the model for mixed layer development over homogeneous terrain. The strength of this model is that it can operate on a very fine spatial resolution with minor computer resources. Chapter 3 deals with the validation of the models. It is based in parts on data from the literature, and on own measurements. For the validation of the formation of the internal boundary layer
Random Boundary Simulation of Pumping Groundwater on Two-layer Soft Soil Structure with Porous Media
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Based on random theory,fluid dynamics,porous media and soil mechanics,the porosity and random characteristic of the two-layer soft soil in Wuhan region were studied in this paper.The random seepage coefficient on the two-layer soft soil was analyzed,and the seepage model and its random distribution function were given.The groundwater flow differential equations related to the two layer soft soil structure were also established.The evaluation procedure of effect boundary on the pumping water in deep foundation pit was put forward.Moreover,with an engineering example,the probability distribution on random boundary prediction for pumping water of foundation pit was computed.
Edge Plasma Boundary Layer Generated By Kink Modes in Tokamaks
International Nuclear Information System (INIS)
This paper describes the structure of the electric current generated by external kink modes at the plasma edge using the ideally conducting plasma model. It is found that the edge current layer is created by both wall touching and free boundary kink modes. Near marginal stability, the total edge current has a universal expression as a result of partial compensation of the (delta)-functional surface current by the bulk current at the edge. The resolution of an apparent paradox with the pressure balance across the plasma boundary in the presence of the surface currents is provided.
Two-phase boundary layer prediction in upward boiling flow
International Nuclear Information System (INIS)
In the present work, the numerical modelling of the two-phase turbulent boundary layer in upward boiling flow was investigated. First, non-dimensional liquid velocity and temperature profiles in the two-phase boundary layer were validated on the one-dimensional section of a pipe with prescribed radial void fraction profiles. Simulations were performed on a fine grid with a commercial code CFX-5 using the k-ω turbulence model. A significant deviation of results from the analytical single-phase and two-phase wall functions from the literature was observed. Second, a wall boiling model in a vertical heated pipe was simulated (CFX-5) on the coarse grid. Here the prediction of the two-phase thermal boudary layer was compared to the experimental data, k-ω calculation on the fine grid and against the singlephase analytical wall function. Again a major deviation against single-phase temperature wall function was obtained. Presented analyses suggest that the existing analytical velocity and temperature wall functions cannot be valid for the boiling boundary layer with the high void fraction on the wall. (author)
RANS-based simulation of turbulent wave boundary layer and sheet-flow sediment transport processes
DEFF Research Database (Denmark)
Fuhrman, David R.; Schløer, Signe; Sterner, Johanna
2013-01-01
with bed and suspended load descriptions, the latter based on an unsteady turbulent-diffusion equation, for simulation of sheet-flow sediment transport processes. In addition to standard features common within such RANS-based approaches, the present model includes: (1) hindered settling velocities at high......A numerical model coupling the horizontal component of the incompressible Reynolds-averaged Navier–Stokes (RANS) equationswith two-equation k−ω turbulence closure is presented and used to simulate a variety of turbulent wave boundary layer processes. The hydrodynamic model is additionally coupled...
Acoustic Radiation From a Mach 14 Turbulent Boundary Layer
Zhang, Chao; Duan, Lian; Choudhari, Meelan M.
2016-01-01
Direct numerical simulations (DNS) are used to examine the turbulence statistics and the radiation field generated by a high-speed turbulent boundary layer with a nominal freestream Mach number of 14 and wall temperature of 0:18 times the recovery temperature. The flow conditions fall within the range of nozzle exit conditions of the Arnold Engineering Development Center (AEDC) Hypervelocity Tunnel No. 9 facility. The streamwise domain size is approximately 200 times the boundary-layer thickness at the inlet, with a useful range of Reynolds number corresponding to Re 450 ?? 650. Consistent with previous studies of turbulent boundary layer at high Mach numbers, the weak compressibility hypothesis for turbulent boundary layers remains applicable under this flow condition and the computational results confirm the validity of both the van Driest transformation and Morkovin's scaling. The Reynolds analogy is valid at the surface; the RMS of fluctuations in the surface pressure, wall shear stress, and heat flux is 24%, 53%, and 67% of the surface mean, respectively. The magnitude and dominant frequency of pressure fluctuations are found to vary dramatically within the inner layer (z/delta 0.< or approx. 0.08 or z+ < or approx. 50). The peak of the pre-multiplied frequency spectrum of the pressure fluctuation is f(delta)/U(sub infinity) approx. 2.1 at the surface and shifts to a lower frequency of f(delta)/U(sub infinity) approx. 0.7 in the free stream where the pressure signal is predominantly acoustic. The dominant frequency of the pressure spectrum shows a significant dependence on the freestream Mach number both at the wall and in the free stream.
Institute of Scientific and Technical Information of China (English)
Jia-qi Mo; Wan-tao Lin
2006-01-01
A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems is studied using the theory of differential inequalities.
Institute of Scientific and Technical Information of China (English)
OuyangCheng; MoJiaqi
2005-01-01
The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied.
A Priori Estimates for Solutions of Boundary Value Problems for Fractional-Order Equations
Alikhanov, A A
2011-01-01
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.
An initial-boundary value problem for three-dimensional Zakharov-Kuznetsov equation
Faminskii, Andrei V.
2016-02-01
An initial-boundary value problem with homogeneous Dirichlet boundary conditions for three-dimensional Zakharov-Kuznetsov equation is considered. Results on global existence, uniqueness and large-time decay of weak solutions in certain weighted spaces are established.
LIMIT BEHAVIOUR OF SOLUTIONS TO EQUIVALUED SURFACE BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
LI Fengquan
2002-01-01
In this paper, we discuss the limit behaviour of solutions to equivalued surface boundary value problem for parabolic equations when the equivalued surface boundary shrinks to a point and the space dimension of the domain is two or more.
SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR ELLIPTIC EQUATION WITH A CURVE OF TURNING POINT
Institute of Scientific and Technical Information of China (English)
MoJiaqi
2002-01-01
The singularly perturbed elliptic equation boundary value problem with a curve of turning point is considered. Using the method of multiple scales and the comparison theorem,the asymptotic behavior of solution for the boundary value problem is studied.
Self-similar analysis of fluid flow and heat-mass transfer of nanofluids in boundary layer
Avramenko, A. A.; Blinov, D. G.; Shevchuk, I. V.
2011-08-01
Processes of heat, momentum, and concentration transport in a boundary layer of a nanofluid near a flat wall were studied. The study was performed by means of numerical analysis of boundary layer equations in a self-similar form. Self-similar forms of these equations were obtained based on symmetry properties (Lie groups). In doing so, dependence of physical properties (viscosity, thermal conductivity, and diffusion coefficient) on concentration of nanofluids and temperature were taken into account. Effects of concentration of the nano-particles on velocity and temperature profiles, as well as on the relative Nusselt numbers and skin-friction coefficients, were elucidated.
Monotone iterative technique for fractional differential equations with periodic boundary conditions
Directory of Open Access Journals (Sweden)
J. D. Ramírez
2009-01-01
Full Text Available In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.
Monotone iterative technique for fractional differential equations with periodic boundary conditions
J. D. Ramírez; A. S. Vatsala
2009-01-01
In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary con...
A Thermal Plume Model for the Martian Convective Boundary Layer
Colaïtis, Arnaud; Hourdin, Frédéric; Rio, Catherine; Forget, François; Millour, Ehouarn
2013-01-01
The Martian Planetary Boundary Layer [PBL] is a crucial component of the Martian climate system. Global Climate Models [GCMs] and Mesoscale Models [MMs] lack the resolution to predict PBL mixing which is therefore parameterized. Here we propose to adapt the "thermal plume" model, recently developed for Earth climate modeling, to Martian GCMs, MMs, and single-column models. The aim of this physically-based parameterization is to represent the effect of organized turbulent structures (updrafts and downdrafts) on the daytime PBL transport, as it is resolved in Large-Eddy Simulations [LESs]. We find that the terrestrial thermal plume model needs to be modified to satisfyingly account for deep turbulent plumes found in the Martian convective PBL. Our Martian thermal plume model qualitatively and quantitatively reproduces the thermal structure of the daytime PBL on Mars: superadiabatic near-surface layer, mixing layer, and overshoot region at PBL top. This model is coupled to surface layer parameterizations taking ...
Quano, Y H
2001-01-01
The $A^{(1)}_{n-1}$-face model with boundary reflection is considered on the basis of the boundary CTM bootstrap. We construct the fused boundary Boltzmann weights to determine the normalization factor. We derive difference equations of the quantum Knizhnik-Zamolodchikov type for correlation functions of the present model. The simplest difference equations are solved the in the case of the free boundary condition.
The stabilizing role of anisotropy in the free stream on boundary layer development
Frohnapfel, Bettina
2005-11-01
An experimental study on the transition of a flat plate boundary layer was conducted in the large wind tunnel of the chair of fluid dynamics (LSTM) in Erlangen, Germany. Although this is not an especially designed transition tunnel it was possible to maintain a stable laminar regime up to Rex=4x10^6, one of the highest transition Reynolds numbers achieved in a flat plate boundary layer. It is argued that this was possible due to a stabilizing effect originating from the high anisotropy level in the free stream disturbances that exists in the tunnel. Based on a statistical analysis of the dynamical equations for small axisymmetric disturbances, the influence of anisotropy on the dynamics of those disturbances in a laminar boundary layer was studied. The derived transition criterion is formulated in terms of a transition Reynolds number - based on intensity and Taylor length scale of the disturbances - that shows a dependency on the anisotropy level of the free stream disturbances. In this respect all available existing measurements on natural boundary layer transition at high Reynolds numbers were analyzed.
The effect of a shear boundary layer on the stability of a capillary jet
Ganan-Calvo, Alfonso; Montanero, Jose M.; Herrada, Miguel A.
2014-11-01
The generic stabilization effect of a shear boundary layer over the free surface of a capillary jet is here studied from analytical (asymptotic), numerical and experimental approaches. In first place, we show the consistency of the proposed asymptotic analysis by a linear stability (numerical) analysis of the Navier-Stokes equations for a finite boundary layer thickness. We show how the convective-to-absolute instability transition departs drastically from the flat velocity profile case as the axial coordinate becomes closer to the origin of the boundary layer development. For large enough axial distances from that origin, Rayleigh's dispersion relation is recovered. A collection of experimental observations is analyzed from the perspective provided by these results. We propose a systematic framework to the dynamics of capillary jets issued from a nozzle, either by direct injection into a quiescent atmosphere or in a co-flow (e.g. gas flow-focused jets), which exhibit peculiarities now definitely attributable in first order to the formation of shear boundary layers. Partial support from the Ministry of Economy and Competitiveness, Junta de Extremadura, and Junta de Andalucia (Spain) through Grant Nos. DPI2010-21103, GR10047, P08-TEP-04128, and TEP-7465, respectively, is gratefully acknowledged.
Shear flow beneath oceanic plates: Local nonsimilarity boundary layers for olivine rheology
International Nuclear Information System (INIS)
The principle of local similarity, which has been used to model the two-dimensional boundary layers in the oceanic upper mantle, permits calculation of the temperature, velocity, and stress fields with essentially analytic techniques. Finite difference numerical methods are hard pressed to resolve the detail required by the large variation of viscosity between the lithosphere and the asthenosphere. In this paper the local similarity approximation has been justified by quantitatively evaluating the effect of nonsimilarity due to viscous heating, nonlinear temperature- and pressure-dependent rheology, buoyancy, adiabatic cooling, etc. Nonsimilar effects produce only small modifications of the locally similar boundary layers; important geophysical observables such as surface heat flux and ocean floor topography are given to better than 10% by the locally similar solution. A posteriori evaluations of the term neglected in the boundary layer simplification of the complete equations have been conducted on the locally similar temperature and velocity profiles close to the spreading ridge. The boundary layer models are valid to depths of 100 km at 3 m.y. and 10 km at 0.3 m.y
Infrared propagation in the air-sea boundary layer
Larsen, R.; Preedy, K. A.; Drake, G.
1990-03-01
Over the oceans and other large bodies of water the structure of the lowest layers of the atmosphere is often strongly modified by evaporation of water vapor from the water surface. At radio wavelengths this layer will usually be strongly refracting or ducting, and the layer is commonly known as the evaporation duct. However, the refractive index of air at infrared wavelengths differs from that at radio wavelengths, and the effects of the marine boundary layer on the propagation of infrared radiation are examined. Meteorological models of the air-sea boundary layer are used to compute vertical profiles of temperature and water-vapor pressure. From these are derived profiles of atmospheric refractive index at radio wavelengths and at infrared wavelengths in the window regions of low absorption. For duct propagation to occur it is necessary that the refractivity of air decreases rapidly with increasing height above the surface. At radio wavelengths this usually occurs when there is a strong lapse of water vapor pressure with increasing height. By contrast, at infrared wavelengths the refractive index is almost independent of water vapor pressure, and it is found that an infrared duct is formed only when there is a temperature inversion.
Bandgap tunability at single-layer molybdenum disulphide grain boundaries
Huang, Yu Li
2015-02-17
Two-dimensional transition metal dichalcogenides have emerged as a new class of semiconductor materials with novel electronic and optical properties of interest to future nanoelectronics technology. Single-layer molybdenum disulphide, which represents a prototype two-dimensional transition metal dichalcogenide, has an electronic bandgap that increases with decreasing layer thickness. Using high-resolution scanning tunnelling microscopy and spectroscopy, we measure the apparent quasiparticle energy gap to be 2.40±0.05 eV for single-layer, 2.10±0.05 eV for bilayer and 1.75±0.05 eV for trilayer molybdenum disulphide, which were directly grown on a graphite substrate by chemical vapour deposition method. More interestingly, we report an unexpected bandgap tunability (as large as 0.85±0.05 eV) with distance from the grain boundary in single-layer molybdenum disulphide, which also depends on the grain misorientation angle. This work opens up new possibilities for flexible electronic and optoelectronic devices with tunable bandgaps that utilize both the control of two-dimensional layer thickness and the grain boundary engineering.
CFD Modeling of Non-Neutral Atmospheric Boundary Layer Conditions
DEFF Research Database (Denmark)
Koblitz, Tilman
For wind resource assessment, the wind industry is increasingly relying on Computational Fluid Dynamics models that focus on modeling the airflow in a neutrally stratified surface-layer. Physical processes like the Coriolis force, buoyancy forces and heat transport, that are important to the...... atmospheric boundary-layer, are mostly ignored so far. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include atmospheric stability and the Coriolis effect. Within the present work a RANS model framework is developed and implemented into...
An algorithm for detecting layer boundaries in sediments
Directory of Open Access Journals (Sweden)
K. Bube
2006-01-01
Full Text Available In this paper we present an algorithm based on wavelet multiscale decomposition, designed to detect lines of maximal gradients in horizontal direction within two-dimensional data sets. The algorithm is capable of identifying layer boundaries within sediment profiles, as demonstrated for artificial as well as two field data sets. Layers are detected with a good resolution within (i digital images of a deep sea sediment core (IODP-expedition 301, core 15H and (ii chemical concentration patterns of recent tidal sediments (North Sea.
Boundary Layer Turbulence Index: Progress and Recent Developments
Pryor, Kenneth L
2008-01-01
A boundary layer turbulence index (TIBL) product has been developed to assess the potential for turbulence in the lower troposphere, generated using RUC-2 numerical model data. The index algorithm approximates boundary layer turbulent kinetic energy by parameterizing vertical wind shear, responsible for mechanical production of TKE, and kinematic heat flux, parameterized by the vertical temperature lapse rate and responsible for buoyant production of TKE. Validation for the TIBL product has been conducted for selected nonconvective wind events during the 2008 winter season over the Idaho National Laboratory mesonet domain. This paper presents studies of four significant wind events between December 2007 and February 2008 over southeastern Idaho. Based on the favorable results highlighted from validation statistics and in the case studies, the RUC TIBL product has demonstrated operational utility in assessing turbulence hazards to low-flying aircraft and ground transportation, and in the assessment of wildfire...
Behaviour of tracer diffusion in simple atmospheric boundary layer models
Directory of Open Access Journals (Sweden)
P. S. Anderson
2006-12-01
Full Text Available 1-D profiles and time series from an idealised atmospheric boundary layer model are presented, which show agreement with measurements of polar photogenic NO and NO_{2}. Diffusion models are increasingly being used as the framework for studying tropospheric air chemistry dynamics. Models based on standard boundary layer diffusivity profiles have an intrinsic behaviour that is not necessarily intuitive, due to the variation of turbulent diffusivity with height. The relatively simple model provides both a programming and a conceptual tool in the analysis of observed trace gas evolution. A time scale inherent in the model can be tuned by fitting model time series to observations. This scale is then applicable to the more physically simple but chemically complex zeroth order or box models of chemical interactions.
Stereoscopic PIV measurement of boundary layer affected by DBD actuator
Directory of Open Access Journals (Sweden)
Procházka Pavel
2016-01-01
Full Text Available The effect of ionic wind generated by plasma actuator on developed boundary layer inside a narrow channel was investigated recently. Since the main investigated plane was parallel to the channel axis, the description of flow field was not evaluated credibly. This paper is dealing with cross-section planes downstream the actuator measured via 3D time-resolved PIV. The actuator position is in spanwise or in streamwise orientation so that ionic wind is blown in the same direction as the main flow or in opposite direction or perpendicularly. The interaction between boundary layer and ionic wind is evaluated for three different velocities of main flow and several parameters of plasma actuation (steady and unsteady regime, frequency etc.. Statistical properties of the flow are shown as well as dynamical behaviour of arising longitudinal vortices are discussed via phase-locked measurement and decomposition method.
Construction of a Non-Equilibrium Thermal Boundary Layer Facility
Biles, Drummond; Ebadi, Alireza; Ma, Allen; White, Christopher
2015-11-01
A thermally conductive, electrically heated wall-plate forming the bottom wall of a wind tunnel has been constructed and validation tests have been performed. The wall-plate is a sectioned wall design, where each section is independently heated and controlled. Each section consists of an aluminum 6061 plate, an array of resistive heaters affixed to the bottom of the aluminum plate, and a calcium silicate holder used for thermal isolation. Embedded thermocouples in the aluminum plates are used to monitor the wall temperature and for feedback control of wall heating. The wall-plate is used to investigate thermal transport in both equilibrium and non-equilibrium boundary layers. The non-equilibrium boundary layer flow investigated is oscillatory flow produced by a rotor-stator mechanism placed downstream of the test section of the wind tunnel.
Flight Experiment Verification of Shuttle Boundary Layer Transition Prediction Tool
Berry, Scott A.; Berger, Karen T.; Horvath, Thomas J.; Wood, William A.
2016-01-01
Boundary layer transition at hypersonic conditions is critical to the design of future high-speed aircraft and spacecraft. Accurate methods to predict transition would directly impact the aerothermodynamic environments used to size a hypersonic vehicle's thermal protection system. A transition prediction tool, based on wind tunnel derived discrete roughness correlations, was developed and implemented for the Space Shuttle return-to-flight program. This tool was also used to design a boundary layer transition flight experiment in order to assess correlation uncertainties, particularly with regard to high Mach-number transition and tunnel-to-flight scaling. A review is provided of the results obtained from the flight experiment in order to evaluate the transition prediction tool implemented for the Shuttle program.
Works on theory of flapping wing. [considering boundary layer
Golubev, V. V.
1980-01-01
It is shown mathematically that taking account of the boundary layer is the only way to develop a theory of flapping wings without violating the basic observations and mathematics of hydromechanics. A theory of thrust generation by flapping wings can be developed if the conventional downstream velocity discontinuity surface is replaced with the observed Karman type vortex streets behind a flapping wing. Experiments show that the direction of such vortices is the reverse of that of conventional Karman streets. The streets form by breakdown of the boundary layer. Detailed analysis of the movements of certain birds and insects during flight 'in place' is fully consistent with this theory of the lift, thrust and drag of flapping wings. Further directions for research into flight with flapping wings are indicated.
Electrical properties of boundary layers of fatty acids
Deryagin, B. V.; Snitkovskii, M. M.
1992-05-01
Nonlinear current-voltage and coulomb-voltage characteristics with a hysteresis loop, which is peculiar to ferroelectrics, were observed in the boundary layers of individual saturated organic acids and oleic acid which have a domain structure and also an anomalously high conductivity which corresponds, in its order of magnitude, to the lower conductivity limit for metals. These effects are related with the formation of a volume space charge and by the cording of the current (formation of conductivity channels). The electrical properties of the boundary layers change in relation to the thickness: for subcritical thicknesses Ohm's Law is obeyed but for larger thicknesses strong field effects are observed. The thickness at which the system changes into the nonconducting stage has meaning as a physical characteristic of the system.
Leading-edge effects on boundary-layer receptivity
Gatski, Thomas B.; Kerschen, Edward J.
1990-01-01
Numerical calculations are presented for the incompressible flow over a parabolic cylinder. The computational domain extends from a region upstream of the body downstream to the region where the Blasius boundary-layer solution holds. A steady mean flow solution is computed and the results for the scaled surface vorticity, surface pressure and displacement thickness are compared to previous studies. The unsteady problem is then formulated as a perturbation solution starting with and evolving from the mean flow. The response to irrotational time harmonic pulsation of the free-stream is examined. Results for the initial development of the velocity profile and displacement thickness are presented. These calculations will be extended to later times to investigate the initiation of instability waves within the boundary-layer.
Turbulence Scales Simulations in Atmospheric Boundary Layer Wind Tunnels
Elena-Carmen Teleman; Radu Silion; Elena Axinte; Radu Pescaru
2008-01-01
The simulation of the air flow over models in atmospheric boundary layer tunnels is a research domain based on advanced scientific technologies imposed by the necessity of studying the turbulent fluid movements in the proximity of the Earth’s surface. The experiment presented herein is developed in the wind tunnel from the Laboratory of Structural Aerodynamics of the Faculty of Civil Engineering and Building Services in Iassy. Measurements necessary for the determination of the turbulence sca...
Simulation of aerosol substance transfer in the atmospheric boundary layer
Lezhenin, A. A.; Raputa, V. F.; Shlychkov, V. Ð. ń.
2014-11-01
A model for the reconstruction of the surface concentration of a heavy non-homogeneous substance transfered in the atmosphere is proposed. The model is used to simulate the snow surface contamination by benzo(a)pyren in the vicinity of Power Station-3 in the city of Barnaul. The effects of wind rotation in the atmospheric boundary layer on the field of long-term aerosol substance are assessed.
Pressure gradient effect in natural convection boundary layers
Higuera Antón, Francisco; Liñán Martínez, Amable
1993-01-01
The high Grashof number laminar natural convection flow around the lower stagnation point of a symmetric bowl- shaped heated body is analyzed. A region is identified where the direct effect on the flow of the component of the buoyancy force tangential to the body surface is comparable to the indirect effect of the component normal to the surface, which acts through the gradient of the nonuniform pressure that it induces in the boundary layer. Analysis of this region provides a description ...
Iodine monoxide in the Western Pacific marine boundary layer
Directory of Open Access Journals (Sweden)
K. Großmann
2012-10-01
Full Text Available A latitudinal cross-section and vertical profiles of iodine monoxide (IO are reported from the marine boundary layer of the Western Pacific. The measurements were taken using Multi-Axis Differential Optical Absorption Spectroscopy (MAX-DOAS during the TransBrom cruise of the German research vessel Sonne, which led from Tomakomai, Japan (42° N, 141° E through the Western Pacific to Townsville, Australia (19° S, 146° E in October 2009. In the marine boundary layer within the tropics (between 20° N and 5° S, IO mixing ratios ranged between 1 and 2.2 ppt, whereas in the subtropics and at mid-latitudes typical IO mixing ratios were around 1 ppt in the daytime. The profile retrieval reveals that the bulk of the IO was located in the lower part of the marine boundary layer. Photochemical simulations indicate that the organic iodine precursors observed during the cruise (CH_{3}I, CH_{2}I_{2}, CH_{2}ClI, CH_{2}BrI are not sufficient to explain the measured IO mixing ratios. Reasonable agreement between measured and modelled IO can only be achieved, if an additional sea-air flux of inorganic iodine (e.g. I_{2} is assumed in the model. Our observations add further evidence to previous studies that reactive iodine is an important oxidant in the marine boundary layer.
Numerical solution of 2D flows in atmospheric boundary layer
Czech Academy of Sciences Publication Activity Database
Šimonek, J.; Tauer, J.; Kozel, K.; Jaňour, Zbyněk; Příhoda, Jaromír
Praha : Ústav termomechaniky AV ČR, v. v. i., 2008 - (Jonáš, P.; Uruba, V.), s. 51-52 ISBN 978-80-87012-14-7. [Colloquium FLUID DYNAMICS 2008. Praha (CZ), 22.10.2008-24.10.2008] R&D Projects: GA AV ČR 1ET400760405 Institutional research plan: CEZ:AV0Z20760514 Keywords : numerical simulation * atmospheric boundary layer * stratified flow Subject RIV: BK - Fluid Dynamics
Flat Plate Boundary Layer Under Negative Pressure Gradient
Czech Academy of Sciences Publication Activity Database
Antoš, Pavel; Jonáš, Pavel; Procházka, Pavel P.; Skála, Vladislav
Pretoria, South Africa: HEFAT, 2015 - (Meyer, J.), s. 251-253 ISBN 978-1-77592-108-0. [International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics : HEFAT 2015 /11./. SKUKUZA (ZA), 20.07.2015-23.07.2015] R&D Projects: GA ČR GAP101/12/1271 Institutional support: RVO:61388998 Keywords : boundary layer in decelerating flow * adverse pressure gradient * hot-wire anemometry Subject RIV: BK - Fluid Dynamics
Ozone in the Atlantic Ocean marine boundary layer
Patrick Boylan; Detlev Helmig; Samuel Oltmans
2015-01-01
Abstract In situ atmospheric ozone measurements aboard the R/V Ronald H. Brown during the 2008 Gas-Ex and AMMA research cruises were compared with data from four island and coastal Global Atmospheric Watch stations in the Atlantic Ocean to examine ozone transport in the marine boundary layer (MBL). Ozone measurements made at Tudor Hill, Bermuda, were subjected to continental outflow from the east coast of the United States, which resulted in elevated ozone levels above 50 ppbv. Ozone measurem...
Grey zone simulations of the morning convective boundary layer development
Efstathiou, G. A.; Beare, R. J.; Osborne, S.; Lock, A. P.
2016-05-01
Numerical simulations of two cases of morning boundary layer development are conducted to investigate the impact of grid resolution on mean profiles and turbulent kinetic energy (TKE) partitioning from the large eddy simulation (LES) to the mesoscale limit. Idealized LES, using the 3-D Smagorinsky scheme, is shown to be capable of reproducing the boundary layer evolution when compared against measurements. However, increasing grid spacing results in the damping of resolved TKE and the production of superadiabatic temperature profiles in the boundary layer. Turbulence initiation is significantly delayed, exhibiting an abrupt onset at intermediate resolutions. Two approaches, the bounding of vertical diffusion coefficient and the blending of the 3-D Smagorinsky with a nonlocal 1D scheme, are used to model subgrid diffusion at grey zone resolutions. Simulations are compared against the coarse-grained fields from the validated LES results for each case. Both methods exhibit particular strengths and weaknesses, indicating the compromise that needs to be made currently in high-resolution numerical weather prediction. The blending scheme is able to reproduce the adiabatic profiles although turbulence is underestimated in favor of the parametrized heat flux, and the spin-up of TKE remains delayed. In contrast, the bounding approach gives an evolution of TKE that follows the coarse-grained LES very well, relying on the resolved motions for the nonlocal heat flux. However, bounding gives unrealistic static instability in the early morning temperature profiles (similar to the 3-D Smagorinsky scheme) because model dynamics are unable to resolve TKE when the boundary layer is too shallow compared to the grid spacing.
Aerodynamic Optimization and Boundary Layer Control On Sailplane Wing Sections
Czech Academy of Sciences Publication Activity Database
Popelka, Lukáš; Matějka, Milan; Součková, Natálie
Berlin: CEAS Council of European Aerospace Societies, 2007, s. 1763-1767. ISSN 0070-4083. [CEAS European Air and Space Conference /1./. Berlin (DE), 10.09.2007-13.09.2007] R&D Projects: GA MŠk(CZ) 1M06031; GA AV ČR IAA2076403; GA AV ČR(CZ) IAA200760614 Institutional research plan: CEZ:AV0Z20760514 Keywords : boundary layer control * sailplane wing section Subject RIV: BK - Fluid Dynamics
Defects and boundary layers in non-Euclidean plates
Gemmer, John
2012-01-01
We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the F\\"oppl-von K\\'arm\\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. We also investigate the scaling with thickness of boundary layers where the stretching energy is concentrated with decreasing thickness.
Glyoxal observations in the global marine boundary layer
Mahajan, Anoop S.; Prados-Roman, Cristina; Hay, Timothy D.; Lampel, Johannes; Pöhler, Denis; Groβmann, Katja; Tschritter, Jens; Frieß, Udo; Platt, Ulrich; Johnston, Paul; Kreher, Karin; Wittrock, Folkard; Burrows, John P; Plane, John M. C.; Saiz-Lopez, Alfonso
2014-01-01
Glyoxal is an important intermediate species formed by the oxidation of common biogenic and anthropogenic volatile organic compounds such as isoprene, toluene and acetylene. Although glyoxal has been shown to play an important role in urban and forested environments, its role in the open ocean environment is still not well understood, with only a few observations showing evidence for its presence in the open ocean marine boundary layer (MBL). In this study, we report observations of glyoxal f...
Vortical Structures in a Boundary Layer Separation Region
Czech Academy of Sciences Publication Activity Database
Uruba, Václav; Sedlák, K.
Plzeň : ZČU Plzeň, 2009 - (Žitek, P.; Milčák, P.; Krivánka, D.), s. 209-214 ISBN 978-80-7043-804-9. [Conference on Power System Engineering /8./. Plzeň (CZ), 18.06.2009] R&D Projects: GA ČR GA101/08/1112 Institutional research plan: CEZ:AV0Z20760514 Keywords : vortex * boundary layer * separation Subject RIV: BK - Fluid Dynamics
Sensitivity of African easterly waves to boundary layer conditions
A. Lenouo; Mkankam Kamga, F.
2008-01-01
A linearized version of the quasi-geostrophic model (QGM) with an explicit Ekman layer and observed static stability parameter and profile of the African easterly jet (AEJ), is used to study the instability properties of the environment of the West African wave disturbances. It is found that the growth rate, the propagation velocity and the structure of the African easterly waves (AEW) can be well simulated. Two different lower boundary conditions are applied. One assumes a lack of vertical g...
On the modulational instability of large amplitude waves in supersonic boundary layers
Hall, Philip; Papageorgiou, Demetrios T.
1995-01-01
The evolution of large amplitude Tollmien-Schlichting waves in a supersonic boundary layer is investigated. Disturbances which have their wavenumber and frequency slowly varying in time and space are described using a phase equation type of approach. Unlike the incompressible case we find that the initial bifurcation to a finite amplitude Tollmien-Schlichting wave is subcritical for most Mach numbers. In fact the bifurcation is only supercritical for a small range of Mach numbers and even then for only a finite range of wave propagation angles. The modulational instability of large amplitude wavetrains is considered and is shown to be governed by an equation similar to Burgers equation but with the viscous term replaced by a fractional derivative. A numerical investigation of the solution of this equation is described. It is shown that uniform wavetrains are unstable.
Using UAV's to Measure the Urban Boundary Layer
Jacob, R. L.; Sankaran, R.; Beckman, P. H.
2015-12-01
The urban boundary layer is one of the most poorly studied regions of the atmospheric boundary layer. Since a majority of the world's population now lives in urban areas, it is becoming a more important region to measure and model. The combination of relatively low-cost unmanned aerial vehicles and low-cost sensors can together provide a new instrument for measuring urban and other boundary layers. We have mounted a new sensor and compute platform called Waggle on an off-the-shelf XR8 octo-copter from 3DRobotics. Waggle consists of multiple sensors for measuring pressure, temperature and humidity as well as trace gases such as carbon monoxide, nitrogen dioxide, sulfur dioxide and ozone. A single board computer running Linux included in Waggle on the UAV allows in-situ processing and data storage. Communication of the data is through WiFi or 3G and the Waggle software can save the data in case communication is lost during flight. The flight pattern is a deliberately simple vertical ascent and descent over a fixed location to provide vertical profiles and so flights can be confined to urban parks, industrial areas or the footprint of a single rooftop. We will present results from test flights in urban and rural areas in and around Chicago.
Turbulent Boundary Layers in the Vicinity of Separation
Indinger, Thomas; Buschmann, Matthias H.; Gad-El-Hak, Mohamed
2004-11-01
There has been some controversy regarding the behavior of the mean velocity profile of turbulent boundary layers approaching separation. While a number of experiments show that the logarithmic law is sustained even under strong adverse-pressure-gradient and non-equilibrium conditions, other experiments and DNS results reveal that the mean velocity profile breaks down in the vicinity of separation. Measurements at TU Dresden of a decelerated, fully developed turbulent boundary layer over a smooth flat plate in a closed water channel show that the classical log law no longer describes the mean velocity in the overlap region after a certain fraction of the flow travels in the upstream direction. This finding is consistent with the physical explanation advanced by Dengel & Fernholz (J. Fluid Mech. 212, 1990) that the log law failure is caused by the first occurrence of reverse flow. Analyzing adverse-pressure-gradient turbulent boundary layer data from three independent groups, we demonstrate that the log law can be restored by replacing y^+ with a new variable depending both on the wall-normal coordinate and the reverse-flow parameter \\chi_w. This finding is of importance in cases where other complexities such as surface roughness or structured walls (riblets, dimples, etc.) are involved and a universal profile in inner variables is desired.
Coupled wake boundary layer model of wind-farms
Stevens, Richard J A M; Meneveau, Charles
2014-01-01
We present and test a coupled wake boundary layer (CWBL) model that describes the distribution of the power output in a wind-farm. The model couples the traditional, industry-standard wake expansion/superposition approach with a top-down model for the overall wind-farm boundary layer structure. The wake expansion/superposition model captures the effect of turbine positioning, while the top-down portion adds the interaction between the wind-turbine wakes and the atmospheric boundary layer. Each portion of the model requires specification of a parameter that is not known a-priori. For the wake model the wake expansion coefficient is required, while the top-down model requires an effective span-wise turbine spacing within which the model's momentum balance is relevant. The wake expansion coefficient is obtained by matching the predicted mean velocity at the turbine from both approaches, while the effective span-wise turbine spacing depends on turbine positioning and thus can be determined from the wake expansion...
New insights into adverse pressure gradient boundary layers
George, William K.; Stanislas, Michel; Laval, Jean-Philippe
2010-11-01
In a recent paper Shah et al. 2010 (Proc. of the WALLTURB Meeting, 2009), Lille, FR, Springer, in press) documented a number of adverse pressure gradient flows (APG's), with and without wall curvature, where the turbulence intensity peak moved quite sharply away from the wall with increasing distance. They further suggested that this peak was triggered by the adverse pressure gradient and had its origin in an instability hidden in the turbulent boundary layer, developing soon after the change of sign of the pressure gradient. They then offered that this may explain the difficulties encountered up to now in finding a universal scaling for turbulent boundary layers. We build on these observations, and show that in fact there is clear evidence in the literature (in most experiments, both old and new) for such a development downstream of the imposition of an adverse pressure gradient. The exact nature of the evolution and the distance over which it occurs depends on the upstream boundary layer and the manner in which the APG is imposed. But far enough downstream the mean velocity profile in all cases becomes an inflectional point profile with the location of the inflection point corresponding quite closely to the observed peak in the streamwise turbulence intensity. This does not seem to have been previously noticed.
Manipulation of Turbulent Boundary Layers Using Synthetic Jets
Berger, Zachary; Gomit, Guillaume; Lavoie, Philippe; Ganapathisubramani, Bharath
2015-11-01
This work focuses on the application of active flow control, in the form of synthetic jet actuators, of turbulent boundary layers. An array of 2 synthetic jets are oriented in the spanwise direction and located approximately 2.7 meters downstream from the leading edge of a flat plate. Actuation is applied perpendicular to the surface of the flat plate with varying blowing ratios and reduced frequencies (open-loop). Two-component large window particle image velocimetry (PIV) was performed at the University of Southampton, in the streamwise-wall-normal plane. Complementary stereo PIV measurements were performed at the University of Toronto Institute for Aerospace Studies (UTIAS), in the spanwise-wall-normal plane. The freestream Reynolds number is 3x104, based on the boundary layer thickness. The skin friction Reynolds number is 1,200 based on the skin friction velocity. The experiments at Southampton allow for the observation of the control effects as the flow propagates downstream. The experiments at UTIAS allow for the observation of the streamwise vorticity induced from the actuation. Overall the two experiments provide a 3D representation of the flow field with respect to actuation effects. The current work focuses on the comparison of the two experiments, as well as the effects of varying blowing ratios and reduced frequencies on the turbulent boundary layer. Funded Supported by Airbus.
Turbulent thermal boundary layers subjected to severe acceleration
Araya, Guillermo; Castillo, Luciano
2013-11-01
Favorable turbulent boundary layers are flows of great importance in industry. Particularly, understanding the mechanisms of quasi-laminarization by means of a very strong favorable streamwise pressure gradient is indeed crucial in drag reduction and energy management applications. Furthermore, due to the low Reynolds numbers involved in the quasi-laminarization process, abundant experimental investigation can be found in the literature for the past few decades. However, several grey zones still remain unsolved, principally associated with the difficulties that experiments encounter as the boundary layer becomes smaller. In addition, little attention has been paid to the heat transfer in a quasi-laminarization process. In this investigation, DNS of spatially-developing turbulent thermal boundary layers with prescribed very strong favorable pressure gradients (K = 4 × 10-6) are performed. Realistic inflow conditions are prescribed based on the Dynamic Multi-scale Approach (DMA) [Araya et al. JFM, Vol. 670, pp. 581-605, 2011]. In this sense the flow carries the footprint of turbulence, particularly in the streamwise component of the Reynolds stresses.
Improving Subtropical Boundary Layer Cloudiness in the 2011 NCEP GFS
Energy Technology Data Exchange (ETDEWEB)
Fletcher, J. K.; Bretherton, Christopher S.; Xiao, Heng; Sun, Ruiyu N.; Han, J.
2014-09-23
The current operational version of National Centers for Environmental Prediction (NCEP) Global Forecasting System (GFS) shows significant low cloud bias. These biases also appear in the Coupled Forecast System (CFS), which is developed from the GFS. These low cloud biases degrade seasonal and longer climate forecasts, particularly of short-wave cloud radiative forcing, and affect predicted sea surface temperature. Reducing this bias in the GFS will aid the development of future CFS versions and contributes to NCEP's goal of unified weather and climate modelling. Changes are made to the shallow convection and planetary boundary layer parameterisations to make them more consistent with current knowledge of these processes and to reduce the low cloud bias. These changes are tested in a single-column version of GFS and in global simulations with GFS coupled to a dynamical ocean model. In the single-column model, we focus on changing parameters that set the following: the strength of shallow cumulus lateral entrainment, the conversion of updraught liquid water to precipitation and grid-scale condensate, shallow cumulus cloud top, and the effect of shallow convection in stratocumulus environments. Results show that these changes improve the single-column simulations when compared to large eddy simulations, in particular through decreasing the precipitation efficiency of boundary layer clouds. These changes, combined with a few other model improvements, also reduce boundary layer cloud and albedo biases in global coupled simulations.
Boundary integral equation methods and numerical solutions thin plates on an elastic foundation
Constanda, Christian; Hamill, William
2016-01-01
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...
Directory of Open Access Journals (Sweden)
Bhupesh Kumar Mahatha
2016-01-01
Full Text Available Two dimensional steady hydromagnetic boundary layer flow of a viscous, incompressible, and electrically conducting nanofluid past a stretching sheet with Newtonian heating, in the presence of viscous and Joule dissipations is studied. The transport equations include the combined effects of Brownian motion and thermophoresis. The governing nonlinear partial differential equations are transformed to a set of nonlinear ordinary differential equations which are then solved using Spectral Relaxation Method (SRM and the results are validated by comparison with numerical approximations obtained using the Matlab in-built boundary value problem solver bvp4c, and with existing results available in literature. Numerical values of fluid velocity, fluid temperature and species concentration are displayed graphically versus boundary layer coordinate for various values of pertinent flow parameters whereas those of skin friction, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. Such nanofluid flows are useful in many applications in heat transfer, including microelectronics, fuel cells, pharmaceutical processes, and hybrid-powered engines, engine cooling/vehicle thermal management, domestic refrigerator, chiller, heat exchanger, in grinding, machining and in boiler flue gas temperature reduction.
Institute of Scientific and Technical Information of China (English)
S PANIGRAHI; M REZA; A K MISHRA
2014-01-01
Suﬃcient conditions are found for the existence of similar solutions of the mixed convection flow of a Powell-Eyring fluid over a nonlinear stretching permeable sur-face in the presence of magnetic field. To achieve this, one parameter linear group trans-formation is applied. The governing momentum and energy equations are transformed to nonlinear ordinary differential equations by use of a similarity transformation. These equations are solved by the homotopy analysis method (HAM) to obtain the approximate solutions. The effects of magnetic field, suction, and buoyancy on the Powell-Eyring fluid flow with heat transfer inside the boundary layer are analyzed. The effects of the non-Newtonian fluid (Powell-Eyring model) parametersεandδ on the skin friction and local heat transfer coeﬃcients for the cases of aiding and opposite flows are investigated and discussed. It is observed that the momentum boundary layer thickness increases and the thermal boundary layer thickness decreases with the increase inεwhereas the momentum boundary layer thickness decreases and thermal boundary layer thickness increases with the increase in δ for both the aiding and opposing mixed convection flows.
Directory of Open Access Journals (Sweden)
Pierluigi Colli
2015-07-01
Full Text Available In this paper we establish second-order sufficient optimality conditions for a boundary control problem that has been introduced and studied by three of the authors in the preprint arXiv:1407.3916. This control problem regards the viscous Cahn–Hilliard equation with possibly singular potentials and dynamic boundary conditions.
Institute of Scientific and Technical Information of China (English)
A.S. BERDYSHEV; A. CABADA; B.Kh. TURMETOV
2014-01-01
This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.
Institute of Scientific and Technical Information of China (English)
WANG Liang; FU Song
2009-01-01
Based on Reynolds-averaged Navier-Stokes approach, a laminar-turbulence transition model is proposed in this study that takes into account the effects of different instability modes associated with the variations in Mach numbers of compressible boundary layer flows. The model is based on k-ω-γ three-equation eddy-viscosity concept with k representing the fluctuating kinetic energy, ωthe specific dissipation rate and the intermittency factor γ.The particular features of the model are that: 1) k includes the non-turbulent, as well as turbulent fluctuations; 2) a transport equation for the intermittency factor γis proposed here with a source term set to trigger the transition onset; 3) through the introduction of a new length scale normal to wall, the present model employs the local variables only avoiding the use of the integral parameters, like the boundary layer thickness δ,which are often cost-ineffective with the modern CFD (Computational Fluid Dynamics) methods; 4) in the fully turbulent region, the model retreats to the well-known k-ωSST (Shear Stress Transport) model. This model is validated with a number of available experiments on boundary layer transitions including the incompressible, supersonic and hypersonic flows past flat plates, straight/flared cones at zero incidences, etc. It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Based on Reynolds-averaged Navier-Stokes approach,a laminar-turbulence transition model is proposed in this study that takes into account the effects of different instability modes associated with the variations in Mach numbers of compressible boundary layer flows.The model is based on k-ω-γ three-equation eddy-viscosity concept with k representing the fluctuating kinetic energy,ωthe specific dissipation rate and the intermittency factorγ.The particular features of the model are that:1)k includes the non-turbulent,as well as turbulent fluctuations;2)a transport equation for the intermittency factorγis proposed here with a source term set to trigger the transition onset;3)through the introduction of a new length scale normal to wall,the present model employs the local variables only avoiding the use of the integral parameters,like the boundary layer thicknessδ,which are often cost-ineffective with the modern CFD(Computational Fluid Dynamics)methods;4)in the fully turbulent region,the model retreats to the well-known k-ωSST(Shear Stress Transport)model.This model is validated with a number of available experiments on boundary layer transitions including the incompressible,supersonic and hypersonic flows past flat plates,straight/flared cones at zero incidences,etc.It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition.
Influence of rigid boundary on the propagation of torsional surface wave in an inhomogeneous layer
Indian Academy of Sciences (India)
Shishir Gupta; Rehena Sultana; Santimoy Kundu
2015-02-01
The present work illustrates a theoretical study on the effect of rigid boundary for the propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. It is believed that the inhomogeneity in the half space arises due to hyperbolic variation in shear modulus and density whereas the layer has linear variation in shear modulus and density. The dispersion equation has been obtained in a closed form by using Whittaker’s function, which shows the variation of phase velocity with corresponding wave number. Numerical results show the dispersion equations, which are discussed and presented by means of graphs. Results in some special cases are also compared with existing solutions available from analytical methods, which show a close resemblance. It is also observed that, for a layer over a homogeneous half space, the velocity of torsional waves does not coincide with that of Love waves in the presence of the rigid boundary, whereas it does at the free boundary. Graphical user interface (GUI) software has been developed using MATLAB 7.5 to generalize the effect of various parameter discussed.
Wind-US Code Contributions to the First AIAA Shock Boundary Layer Interaction Prediction Workshop
Georgiadis, Nicholas J.; Vyas, Manan A.; Yoder, Dennis A.
2013-01-01
This report discusses the computations of a set of shock wave/turbulent boundary layer interaction (SWTBLI) test cases using the Wind-US code, as part of the 2010 American Institute of Aeronautics and Astronautics (AIAA) shock/boundary layer interaction workshop. The experiments involve supersonic flows in wind tunnels with a shock generator that directs an oblique shock wave toward the boundary layer along one of the walls of the wind tunnel. The Wind-US calculations utilized structured grid computations performed in Reynolds-averaged Navier-Stokes mode. Four turbulence models were investigated: the Spalart-Allmaras one-equation model, the Menter Baseline and Shear Stress Transport k-omega two-equation models, and an explicit algebraic stress k-omega formulation. Effects of grid resolution and upwinding scheme were also considered. The results from the CFD calculations are compared to particle image velocimetry (PIV) data from the experiments. As expected, turbulence model effects dominated the accuracy of the solutions with upwinding scheme selection indicating minimal effects.
Study of Transitions in the Atmospheric Boundary Layer Using Explicit Algebraic Turbulence Models
Lazeroms, W. M. J.; Svensson, G.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.
2016-08-01
We test a recently developed engineering turbulence model, a so-called explicit algebraic Reynolds-stress (EARS) model, in the context of the atmospheric boundary layer. First of all, we consider a stable boundary layer used as the well-known first test case from the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS1). The model is shown to agree well with data from large-eddy simulations (LES), and this agreement is significantly better than for a standard operational scheme with a prognostic equation for turbulent kinetic energy. Furthermore, we apply the model to a case with a (idealized) diurnal cycle and make a qualitative comparison with a simpler first-order model. Some interesting features of the model are highlighted, pertaining to its stronger foundation on physical principles. In particular, the use of more prognostic equations in the model is shown to give a more realistic dynamical behaviour. This qualitative study is the first step towards a more detailed comparison, for which additional LES data are needed.
A Study of the Navier-Stokes Equations with the Kinematic and Navier Boundary Conditions
Chen, Gui-Qiang; Qian, Zhongmin
2008-01-01
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the Navier boundary condition in terms of the vorticity, which is motivated by the Hodge theory on manifolds with boundary from the viewpoint of differential geometry, and establish basic elliptic estimates for vector fields subject to the kinematic and Navier b...
International Nuclear Information System (INIS)
In this paper, the combined effects of radiation, temperature dependent viscosity, suction and injection on thermal boundary layer over a permeable flat plate with a convective heat exchange at the surface are investigated. By taking suitable similarity variables, the governing boundary layer equations are transformed into a boundary value problem of coupled nonlinear ordinary differential equations and solved numerically using the shooting technique with sixth-order Runge-Kutta integration scheme. The solutions for the velocity and temperature distributions together with the skin friction coefficient and Nusselt number depend on six parameters: Prandtl number Pr, Brinkmann number Br, the radiation parameter Ra, the viscosity variation parameter a, suction/injection parameter fw and convection Biot number Bi. Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters on thermal boundary layer. The thermal boundary layer thickens with a rise in the local temperature as the viscous dissipation, wall injection, and convective heating each intensifies, but decreases with increasing suction and thermal radiation. For fixed Pr, Ra, Br and Bi, both the skin friction coefficient and the Nusselt number increase with a decrease in fluid viscosity and an increase in suction. A comparison with previously published results on special case of the problem shows excellent agreement
Conjugate conduction-convection heat transfer with a high-speed boundary layer
Shope, Frederick L.
1994-04-01
A space-marching boundary-layer program has been extensively modified to model conjugate conduction-convection heat transfer for the case of co-flowing high-speed gas and liquid coolant. Solid body conduction is modeled as one-dimensional, constant property heat transfer. The coolant is modeled empirically as a bulk fluid with combined forced convection and subcooled nucleate boiling. The flow solver was modified to solve the group of conjugate boundary equations simultaneously and implicitly with the existing momentum and energy equations for the gas. The resulting conjugate conduction-convection program has been applied to analysis of failure of a backside water-cooled nozzle for a high enthalpy, supersonic wind tunnel. The computational results have been used to establish that the primary failure mode is nucleate-boiling burnout and to propose a numerical burnout limit applicable to the specific nozzle configuration.
Numerical study of the anode boundary layer in atmospheric pressure arc discharges
Semenov, I. L.; Krivtsun, I. V.; Reisgen, U.
2016-03-01
The anode boundary layer in atmospheric pressure arc discharges is studied numerically on the basis of the hydrodynamic (diffusion) equations for plasma components. The governing equations are formulated in a unified manner without the assumptions of thermal equilibrium, ionization equilibrium or quasi-neutrality. For comparison, a quasi-neutral model of the anode layer is also considered. The numerical computations are performed for an argon arc at typical values of the current density in anode layers (500-2000 A cm-2). The results of numerical modelling show that the common collisionless model of the sheath fails to describe the sheath region for the problem under consideration. For this reason, a detailed analysis of the anode sheath is performed using the results of unified modelling. In addition, the distributions of plasma parameters in the anode layer are analysed and the basic characteristics of the layer (anode voltage drop, sheath voltage drop, anode layer thickness, sheath thickness, heat flux to the anode) are calculated. Our results are found to be in good agreement with the existing theoretical predictions and experimental data. The dependence of the anode layer characteristics on the current density is also discussed.
Wave boundary layer over a stone-covered bed
DEFF Research Database (Denmark)
Dixen, Martin; Hatipoglu, Figen; Sumer, B. Mutlu;
2008-01-01
This paper summarizes the results of an experimental investigation on wave boundary layers over a bed with large roughness, simulating stone/rock/armour block cover on the sea bottom. The roughness elements used in the experiments were stones the size of 1.4cm and 3.85cm in one group of experiments...... ping-pong ball experiments to study the influence of packing pattern, packing density, number of layers and surface roughness of the roughness elements. The results show that the friction factor seems to be not extremely sensitive to these factors. The results also show that the friction factor for...... extremely sensitive to the packing pattern, the packing density, the number of layers and the surface roughness of the roughness elements. There exists a steady streaming near the bed in the direction of wave propagation, in agreement with the existing work. The present data indicate that the steady...
Grain-boundary layering transitions and phonon engineering
Rickman, J. M.; Harmer, M. P.; Chan, H. M.
2016-09-01
We employ semi-grand canonical Monte Carlo simulation to investigate layering transitions at grain boundaries in a prototypical binary alloy. We demonstrate the existence of such transitions among various interfacial states and examine the role of elastic fields in dictating state equilibria. The results of these studies are summarized in the form of diagrams that highlight interfacial state coexistence in this system. Finally, we examine the impact of layering transitions on the phononic properties of the system, as given by the specific heat and, by extension, the thermal conductivity. Thus, it is suggested that by inducing interfacial layering transitions via changes in temperature or pressure, one can thereby engineer thermodynamic and transport properties in materials.
THE INTERIOR LAYER FOR A NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATION
Institute of Scientific and Technical Information of China (English)
Wang Aifeng; Ni Mingkang
2012-01-01
In this article,the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered.Using the methods of boundary function and fractional steps,we construct the formula of asymptotic expansion and point out that the boundary layer at t =0 has a great influence upon the interior layer at t =σ.At the same time,on the basis of differential inequality techniques,the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved.Finally,an example is given to demonstrate the effectiveness of our result.The result of this article is new and it complements the previously known ones.
Tumin, Anatoli
2015-11-01
Zavol'skii and Reutov (1983), Luchini (2008, 2010), Fedorov (2010, 2012, 2014) explored potential role of kinetic fluctuations (KF) in incompressible and calorically perfect gas boundary layer flows. The results indicate that role of KF is comparable with other disturbance sources in flight experiments and in quiet wind tunnels. The analysis is based on the Landau and Lifshitz (1957) concept of fluctuating hydrodynamics representing the dissipative fluxes as an average and fluctuating parts. We are extending analysis of the receptivity problem to the fluctuating dissipative fluxes in chemically reacting nonequilibrium boundary layer flows of binary mixtures. There are new terms in the energy, and the species equations. The species conservation equation includes the dissipative diffusion flux and the species generation due to dissociation. The momentum equation includes fluctuating stress tensor. The energy equation includes fluctuating heat flux, energy flux due to diffusion of the species, and fluctuating dissipative flux due to viscosity. The effects are compared for the cases stemming from constraints of the HTV project (Klentzman and Tumin, AIAA Paper 2013-2882). Supported by AFOSR.
Viscous boundary layers of radiation-dominated, relativistic jets. I. The two-stream model
Coughlin, Eric R
2015-01-01
Using the relativistic equations of radiation hydrodynamics in the viscous limit, we analyze the boundary layers that develop between radiation-dominated jets and their environments. In this paper we present the solution for the self-similar, 2-D, plane-parallel two-stream problem, wherein the jet and the ambient medium are considered to be separate, interacting fluids, and we compare our results to those of previous authors. (In a companion paper we investigate an alternative scenario, known as the free-streaming jet model.) Consistent with past findings, we show that the boundary layer that develops between the jet and its surroundings creates a region of low-density material. These models may be applicable to sources such as super-Eddington tidal disruption events and long gamma-ray bursts.
Boundary-layer theory, strong-coupling series, and large-order behavior
International Nuclear Information System (INIS)
The introduction of a lattice converts a singular boundary-layer problem in the continuum into a regular perturbation problem. However, the continuum limit of the discrete problem is extremely nontrivial and is not completely understood. This article examines two singular boundary-layer problems taken from mathematical physics, the instanton problem and the Blasius equation, and in each case examines two strategies, Pade resummation and variational perturbation theory, to recover the solution to the continuum problem from the solution to the associated discrete problem. Both resummation procedures produce good and interesting results for the two cases, but the results still deviate from the exact solutions. To understand the discrepancy a comprehensive large-order behavior analysis of the strong-coupling lattice expansions for each of the two problems is done
Jin, C; Reeks, M W
2014-01-01
We present a simple stochastic quadrant model for calculating the transport and deposition of heavy particles in a fully developed turbulent boundary layer based on the statistics of wall-normal fluid velocity fluctuations obtained from a fully developed channel flow. Individual particles are tracked through the boundary layer via their interactions with a succession of random eddies found in each of the quadrants of the fluid Reynolds shear stress domain in a homogeneous Markov chain process. Deposition rates for a range of heavy particles predicted by the model compare well with benchmark experimental measurements. In addition deposition rates are compared with those obtained from continuous random walk (CRW) models including those based on a Langevin equation for the turbulent fluctuations. Various statistics related to the particle near wall behavior are also presented.
Reeks, Michael; Jin, Chunyu; Potts, Ian
2015-11-01
We present a simple stochastic quadrant model for calculating the transport and deposition of heavy particles in a fully developed turbulent boundary layer based on the statistics of wall-normal fluid velocity fluctuations obtained from a fully developed channel flow. Individual particles are tracked through the boundary layer via their interactions with a succession of random eddies found in each of the quadrants of the fluid Reynolds shear stress domain in a homogeneous Markov chain process. Deposition rates for a range of heavy particles predicted by the model compare well with benchmark experimental measurements. In addition deposition rates are compared with those obtained continuous random walk (CRW) models including those based on the Langevin equation for the turbulent fluctuations. In addition, various statistics related to the particle near wall behavior are also presented.
Application of a transitional boundary-layer theory in the low hypersonic Mach number regime
Shamroth, S. J.; Mcdonald, H.
1975-01-01
An investigation is made to assess the capability of a finite-difference boundary-layer procedure to predict the mean profile development across a transition from laminar to turbulent flow in the low hypersonic Mach-number regime. The boundary-layer procedure uses an integral form of the turbulence kinetic-energy equation to govern the development of the Reynolds apparent shear stress. The present investigation shows the ability of this procedure to predict Stanton number, velocity profiles, and density profiles through the transition region and, in addition, to predict the effect of wall cooling and Mach number on transition Reynolds number. The contribution of the pressure-dilatation term to the energy balance is examined and it is suggested that transition can be initiated by the direct absorption of acoustic energy even if only a small amount (1 per cent) of the incident acoustic energy is absorbed.
DEFF Research Database (Denmark)
Kirca, V. S. Ozgur; Sumer, B. Mutlu; Steffensen, Michael;
2016-01-01
The present research aims at getting an understanding of the process of dispersion of surface sediment in an oscillatory boundary layer, which may represent an idealised case of, for example, a stockpile area where excavated sediment is stockpiled temporarily (or permanently). The process is...... studied numerically, using a random-walk particle model with the input data for the mean and turbulence characteristics of the wave boundary layer picked up from a transitional two-equation k–ω Reynolds averaged Navier–Stokes model and plugged in the random-walk model. First, the flowmodel is validated...... against experimental data in the literature. Then, the random-walk dispersion model is run for different oscillatory flow cases and for a number of steady flow cases for comparison. The primary sediment grains of concern are fine sediments (with low fall velocity), which would stay in suspension for most...
Analytical solutions for thermal forcing vortices in boundary layer and its applications
Institute of Scientific and Technical Information of China (English)
LIU Xiao-ran; LI Guo-ping
2007-01-01
Using the Boussinesq approximation, the vortex in the boundary layer is assumed to be axisymmetrical and thermal-wind balanced system forced by diabatic heating and friction, and is solved as an initial-value problem of linearized vortex equation set in cylindrical coordinates. The impacts of thermal forcing on the flow field structure of vortex are analyzed. It is found that thermal forcing has significant impacts on the flow field structure, and the material representative forms of these impacts are closely related to the radial distribution of heating. The discussion for the analytical solutions for the vortex in the boundary layer can explain some main structures of the vortex over the Tibetan Plateau.
Viscous boundary layers of radiation-dominated, relativistic jets. II. The free-streaming jet model
Coughlin, Eric R
2015-01-01
We analyze the interaction of a radiation-dominated jet and its surroundings using the equations of radiation hydrodynamics in the viscous limit. In a previous paper we considered the two-stream scenario, which treats the jet and its surroundings as distinct media interacting through radiation viscous forces. Here we present an alternative boundary layer model, known as the free-streaming jet model -- where a narrow stream of fluid is injected into a static medium -- and present solutions where the flow is ultrarelativistic and the boundary layer is dominated by radiation. It is shown that these jets entrain material from their surroundings and that their cores have a lower density of scatterers and a harder spectrum of photons, leading to observational consequences for lines of sight that look "down the barrel of the jet." These jetted outflow models may be applicable to the jets produced during long gamma-ray bursts and super-Eddington phases of tidal disruption events.
Edge states for the turbulence transition in the asymptotic suction boundary layer
Kreilos, Tobias; Schneider, Tobias M; Eckhardt, Bruno
2013-01-01
We demonstrate the existence of an exact invariant solution to the Navier-Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interpolates between plane Couette flow and the boundary layer we demonstrate that the periodic orbit emerges in a saddle-node infinite-period (SNIPER) bifurcation of two symmetry-related travelling wave solutions of plane Couette flow. Physically, the long period is due to a slow streak instability which leads to a violent breakup of a streak associated with the bursting and the reformation of the streak at a different spanwi...
DNS of a spatially developing turbulent boundary layer with passive scalar transport
International Nuclear Information System (INIS)
A direct numerical simulation (DNS) of a spatially developing turbulent boundary layer over a flat plate under zero pressure gradient (ZPG) has been carried out. The evolution of several passive scalars with both isoscalar and isoflux wall boundary condition are computed during the simulation. The Navier-Stokes equations as well as the scalar transport equation are solved using a fully spectral method. The highest Reynolds number based on the free-stream velocity U∞ and momentum thickness θ is Reθ=830, and the molecular Prandtl numbers are 0.2, 0.71 and 2. To the authors' knowledge, this Reynolds number is to date the highest with such a variety of scalars. A large number of turbulence statistics for both flow and scalar fields are obtained and compared when possible to existing experimental and numerical simulations at comparable Reynolds number. The main focus of the present paper is on the statistical behaviour of the scalars in the outer region of the boundary layer, distinctly different from the channel-flow simulations. Agreements as well as discrepancies are discussed while the influence of the molecular Prandtl number and wall boundary conditions is also highlighted. A Pr scaling for various quantities is proposed in outer scalings. In addition, spanwise two-point correlation and instantaneous fields are employed to investigate the near-wall streak spacing and the coherence between the velocity and the scalar fields. Probability density functions (PDF) and joint probability density functions (JPDF) are shown to identify the intermittency both near the wall and in the outer region of the boundary layer. The present simulation data will be available online for the research community.
DNS of a spatially developing turbulent boundary layer with passive scalar transport
Energy Technology Data Exchange (ETDEWEB)
Li Qiang [Linne Flow Centre, KTH Mechanics, Osquars Backe 18, SE-100 44 Stockholm (Sweden)], E-mail: qiang@mech.kth.se; Schlatter, Philipp; Brandt, Luca; Henningson, Dan S. [Linne Flow Centre, KTH Mechanics, Osquars Backe 18, SE-100 44 Stockholm (Sweden)
2009-10-15
A direct numerical simulation (DNS) of a spatially developing turbulent boundary layer over a flat plate under zero pressure gradient (ZPG) has been carried out. The evolution of several passive scalars with both isoscalar and isoflux wall boundary condition are computed during the simulation. The Navier-Stokes equations as well as the scalar transport equation are solved using a fully spectral method. The highest Reynolds number based on the free-stream velocity U{sub {infinity}} and momentum thickness {theta} is Re{sub {theta}}=830, and the molecular Prandtl numbers are 0.2, 0.71 and 2. To the authors' knowledge, this Reynolds number is to date the highest with such a variety of scalars. A large number of turbulence statistics for both flow and scalar fields are obtained and compared when possible to existing experimental and numerical simulations at comparable Reynolds number. The main focus of the present paper is on the statistical behaviour of the scalars in the outer region of the boundary layer, distinctly different from the channel-flow simulations. Agreements as well as discrepancies are discussed while the influence of the molecular Prandtl number and wall boundary conditions is also highlighted. A Pr scaling for various quantities is proposed in outer scalings. In addition, spanwise two-point correlation and instantaneous fields are employed to investigate the near-wall streak spacing and the coherence between the velocity and the scalar fields. Probability density functions (PDF) and joint probability density functions (JPDF) are shown to identify the intermittency both near the wall and in the outer region of the boundary layer. The present simulation data will be available online for the research community.
Defining the Entrainment Zone in Stratocumulus-topped Boundary Layers
Wang, Q.; Zhou, M.; Kalogiros, J. A.; Lenschow, D. H.; Dai, C.; Wang, S.
2010-12-01
The presence of an entrainment zone near the top of the stratocumulus-topped boundary layers has been identified by many early studies. However, the definition of the entrainment zone was rather vague. We have examined the fine vertical variations of cloud liquid water content, wind, temperature and humidity near the stratocumulus top and developed a new method to identify the entrainment zone objectively. Aircraft measurements from various field projects in stratocumulus-topped boundary layers are used, taking advantage of the fast sampling capability of many of the aircraft sensors. Because of the inhomogeneous mixing of two air masses with distinctively different thermodynamic properties, the magnitude of temperature perturbations within the entrainment zone is significantly larger than those above or below. This characteristics is used to define the upper and lower boundaries of the entrainment zone using a wavelet spectra analyses. The definition of the entrainment zone is further evaluated by the presence of a linear mixing line through mixing line analyses. Various other interfaces at the cloud top are also examined, including the cloud interface, temperature interface (inversion), and moisture interface. The heights of these interfaces are examined relative to the height of the entrainment zone. This study also systematically revealed the presence of turbulence above the local cloud top and/or above the entrainment zone. Wind shear near the cloud top is one possible source that generated local turbulence. Other potential sources of turbulence will also be discussed.
Well-posed initial-boundary value problems for the Zakharov-Kuznetsov equation
Directory of Open Access Journals (Sweden)
Andrei V. Faminskii
2008-09-01
Full Text Available This paper deals with non-homogeneous initial-boundary value problems for the Zakharov-Kuznetsov equation, which is one of the variants of multidimensional generalizations of the Korteweg-de Vries equation. Results on local and global well-posedness are established in a scale of Sobolev-type spaces under natural assumptions on initial and boundary data.
REGULARITY THEORY FOR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.
Two-phase wall function for modeling of turbulent boundary layer in subcooled boiling flow
International Nuclear Information System (INIS)
Full text of publication follows: The heat transfer and phase-change mechanisms in the subcooled flow boiling are governed mainly by local multidimensional mechanisms near the heated wall, where bubbles are generated. The structure of such 'wall boiling flow' is inherently non-homogeneous and is further influenced by the two-phase flow turbulence, phase-change effects in the bulk, interfacial forces and bubble interactions (collisions, coalescence, break-up). In this work the effect of two-phase flow turbulence on the development of subcooled boiling flow is considered. Recently, the modeling of two-phase flow turbulence has been extensively investigated. A notable progress has been made towards deriving reliable models for description of turbulent behaviour of continuous (liquid) and dispersed phase (bubbles) in the bulk flow. However, there is a lack of investigation considering the modeling of two-phase flow boundary layer. In most Eulerian two-fluid models standard single-phase wall functions are used for description of turbulent boundary layer of continuous phase. That might be a good approximation at adiabatic flows, but their use for boundary layers with high concentration of dispersed phase is questionable. In this work, the turbulent boundary layer near the heated wall will be modeled with the so-called 'two-phase' wall function, which is based on the assumption of additional turbulence due to bubble-induced stirring in the boundary layer. In the two-phase turbulent boundary layer the wall function coefficients strongly depend on the void fraction. Moreover, in the turbulent boundary layer with nucleating bubbles, the bubble size variation also has a significant impact on the liquid phase. As a basis, the wall function of Troshko and Hassan (2001), developed for adiabatic bubbly flows will be used. The simulations will be performed by a general-purpose CFD code CFX-4.4 using additional models provided by authors. The results will be compared to the boiling
On the partially reacted boundary layer in rate sticks
Partom, Y.
2014-05-01
Using our temperature dependent reactive flow model (TDRR) to simulate detonation in a rate stick, we observe that a partially reacted layer (PRL) is formed near the boundary. We are not aware that such a PRL has been observed in tests, and this is why we regarded it in the past as a numerical artifact. Assuming that such an artefact may be caused by the finite rise time of the detonation shock, we showed in [1] how it can be eliminated by delaying the outward boundary motion for a length of time comparable with the shock rise time. Here we revisit the PRL problem. We first show that it is not a numerical artifact but a real phenomenon. We do this by repeating the reactive flow run with a finer mesh. By looking at the PRL structure, we see that doubling the resolution affects the PRL only slightly. We then conjecture that the PRL formation has to do with the finite duration of the reaction process (or the finite extent of the reaction zone). By the time the boundary rarefaction reaches a cell near the boundary, it may be only partially reacted, and its reaction may therefore be cut off. To establish our conjecture we show how the PRL structure changes with the reaction duration.
Analytical approach for solving the radiative transfer equation in two-dimensional layered media
International Nuclear Information System (INIS)
This study presents an analytical approach for obtaining Green's function of the two-dimensional radiative transfer equation to the boundary-value problem of a layered medium. A conventional Fourier transform and a modified Fourier series which is defined in a rotated reference frame are applied to derive an analytical solution of the radiance in the transformed space. The Monte Carlo method was used for a successful validation of the derived solutions. - Highlights: ► Analytical solution of the radiative transfer equation for two-dimensional layered media. ► The required numerical part for evaluation of the derived solution is reduced to a minimum. ► The presented method is transferable to the three-dimensional layered medium.
The Jovian boundary layer as formed by magnetic-anomaly effects
Dessler, A. J.
1979-01-01
A model is presented in which a plasma boundary layer of Jupiter is formed from plasma of internal origin. It is proposed that, unlike the Earth's boundary layer, which is thought to consist principally of solar wind plasma, Jupiter's boundary layer consists principally of sulphur and oxygen from the Io plasma torus, plus a small component of hydrogen from Jupiter's ionosphere. Fresh plasma is supplied to the boundary layer once each planetary rotation period by a convection pattern that rotates with Jupiter.
Radiative instabilities of atmospheric jets and boundary layers
International Nuclear Information System (INIS)
Complex flows occur in the atmosphere and they can be source of internal gravity waves. We focus here on the sources associated with radiative and shear (or Kelvin-Helmholtz) instabilities. Stability studies of shear layers in a stably stratified fluid concern mainly cases where shear and stratification are aligned along the same direction. In these cases, Miles (1961) and Howard (1961) found a necessary condition for stability based on the Richardson number: Ri ≥ 1/4. In this thesis, we show that this condition is not necessary when shear and stratification are not aligned: we demonstrate that a two-dimensional planar Bickley jet can be unstable for all Richardson numbers. Although the most unstable mode remains 2D, we show there exists an infinite family of 3D unstable modes exhibiting a radiative structure. A WKBJ theory is found to provide the main characteristics of these modes. We also study an inviscid and stratified boundary layer over an inclined wall with non-Boussinesq and compressible effects. We show that this flow is unstable as soon as the wall is not horizontal for all Froude numbers and that strongly stratified 3D perturbations behave exactly like compressible 2D perturbations. Applications of the results to the jet stream and the atmospheric boundary layer are proposed. (author)
Compatibility between shape equation and boundary conditions of lipid membranes with free edges.
Tu, Z C
2010-02-28
Only some special open surfaces satisfying the shape equation of lipid membranes can be compatible with the boundary conditions. As a result of this compatibility, the first integral of the shape equation should vanish for axisymmetric lipid membranes, from which two theorems of nonexistence are verified: (i) there is no axisymmetric open membrane being a part of torus satisfying the shape equation; (ii) there is no axisymmetric open membrane being a part of a biconcave discodal surface satisfying the shape equation. Additionally, the shape equation is reduced to a second-order differential equation while the boundary conditions are reduced to two equations due to this compatibility. Numerical solutions to the reduced shape equation and boundary conditions agree well with the experimental data [A. Saitoh et al., Proc. Natl. Acad. Sci. U.S.A. 95, 1026 (1998)]. PMID:20192294
Partial differential equations IX elliptic boundary value problems
Egorov, Yu; Shubin, M
1997-01-01
This EMS volume gives an overview of the modern theory of elliptic boundary value problems. The contribution by M.S. Agranovich is devoted to differential elliptic boundary problems, mainly in smooth bounded domains, and their spectral properties. This article continues his contribution to EMS 63. The contribution by A. Brenner and E. Shargorodsky concerns the theory of boundary value problems for elliptic pseudodifferential operators. Problems both with and without the transmission property, as well as parameter-dependent problems are considered. The article by B. Plamenevskij deals with general differential elliptic boundary value problems in domains with singularities.
Local existence of solution to free boundary value problem for compressible Navier-Stokes equations
Liu, Jian
2015-01-01
This paper is concerned with the free boundary value problem for multi-dimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. A local (in time) existence of weak solution is established, in particular, the density is positive and the solution is regular away from the free boundary.
A thermal plume model for the Martian convective boundary layer
Colaïtis, A.; Spiga, A.; Hourdin, F.; Rio, C.; Forget, F.; Millour, E.
2013-07-01
The Martian planetary boundary layer (PBL) is a crucial component of the Martian climate system. Global climate models (GCMs) and mesoscale models (MMs) lack the resolution to predict PBL mixing which is therefore parameterized. Here we propose to adapt the "thermal plume" model, recently developed for Earth climate modeling, to Martian GCMs, MMs, and single-column models. The aim of this physically based parameterization is to represent the effect of organized turbulent structures (updrafts and downdrafts) on the daytime PBL transport, as it is resolved in large-eddy simulations (LESs). We find that the terrestrial thermal plume model needs to be modified to satisfyingly account for deep turbulent plumes found in the Martian convective PBL. Our Martian thermal plume model qualitatively and quantitatively reproduces the thermal structure of the daytime PBL on Mars: superadiabatic near-surface layer, mixing layer, and overshoot region at PBL top. This model is coupled to surface layer parameterizations taking into account stability and turbulent gustiness to calculate surface-atmosphere fluxes. Those new parameterizations for the surface and mixed layers are validated against near-surface lander measurements. Using a thermal plume model moreover enables a first-order estimation of key turbulent quantities (e.g., PBL height and convective plume velocity) in Martian GCMs and MMs without having to run costly LESs.
Allaerts, Dries; Meyers, Johan
2015-06-01
Under conventionally neutral conditions, the boundary layer is frequently capped by an inversion layer, which counteracts vertical entrainment of kinetic energy. Very large wind farms are known to depend on vertical entrainment to transport energy from above the farm towards the turbines. In this study, large eddy simulations of an infinite wind-turbine array in a conventionally neutral atmospheric boundary layer are performed. By carefully selecting the initial potential-temperature profile, the influence of the height and the strength of a capping inversion on the power output of a wind farm is investigated. Results indicate that both the height and the strength have a significant effect on the boundary layer flow, and that the height of the neutral boundary layer is effectively controlled by the capping inversion. In addition, it is shown that the vertical entrainment rate decreases for increasing inversion strength or height. In our infinite wind-farm simulations, varying the inversion characteristics leads to differences in power extraction on the order of 13% ± 0.2% (for increasing the strength from 2.5 to 10 K), and 31% ± 0.4% (for increasing the height from 500 to 1500 m). A detailed analysis of the mean kinetic-energy equation is included, showing that the variation in power extraction originates from the work done by the driving pressure gradient related to the boundary layer height and the geostrophic angle, while entrainment of kinetic energy from the free atmosphere does not play a significant role. Also, the effect of inversion strength on power extraction is energetically not related to different amounts of energy entrained, but explained by a difference in boundary layer growth, leading to higher boundary layers for lower inversion strengths. We further present a simple analytical model that allows to obtain wind-farm power output and driving power for the fully developed regime as function of Rossby number and boundary layer height.
Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
Arnold, Douglas N.; Nicolae Tarfulea
2007-01-01
Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this problem for the Einstein--Christoffel (EC) symmetric hyperbolic formulation of Einstein's equations linearized around flat spacetime. First, we prescribe simple boundary conditions that make the problem well posed and preserve the constraints. Next, we indi...
Turbulent thermal boundary layers with temperature-dependent viscosity
International Nuclear Information System (INIS)
Highlights: • Turbulent thermal boundary layers with temperature-dependent viscosity are simulated. • Effect of temperature-dependent viscosity on the statistics of the scalar field. • An identity for the Stanton number is derived and analyzed. • Effect of temperature-dependent viscosity on the statistics of scalar transfer rate. • Modification of turbulent flow field leads to an enhanced scalar transfer rate. - Abstract: Direct numerical simulations (DNS) of turbulent boundary layers (TBLs) over isothermally heated walls were performed, and the influence of the wall-heating on the thermal boundary layers was investigated. The DNS adopt an empirical relation for the temperature-dependent viscosity of water. The Prandtl number therefore changes with temperature, while the Péclet number is constant. Two wall temperatures (Tw = 70 °C and 99 °C) were considered relative to T∞ = 30 °C, and a reference simulation of TBL with constant viscosity was also performed for comparison. In the variable viscosity flow, the mean and variance of the scalar, when normalized by the friction temperature deficit, decrease relative to the constant viscosity flow. A relation for the mean scalar which takes into account the variable viscosity is proposed. Appropriate scalings for the scalar fluctuations and the scalar flux are also introduced, and are shown to be applicable for both variable and constant viscosity flows. Due to the modification of the near-wall turbulence, the Stanton number and the Reynolds analogy factor are augmented by 10% and 44%, respectively, in the variable viscosity flow. An identity for the Stanton number is derived and shows that the mean wall-normal velocity and wall-normal scalar flux cause the increase in the heat transfer coefficient. Finally, the augmented near-wall velocity fluctuations lead to an increase of the wall-normal scalar flux, which contributes favorably to the enhanced heat transfer at the wall
Planetary Boundary Layer Dynamics over Reno, Nevada in Summer
Liming, A.; Sumlin, B.; Loria Salazar, S. M.; Holmes, H.; Arnott, W. P.
2014-12-01
Quantifying the height of the planetary boundary layer (PBL) is important to understand the transport behavior, mixing, and surface concentrations of air pollutants. In Reno, NV, located in complex, mountainous terrain with high desert climate, the daytime boundary layer can rise to an estimated 3km or more on a summer day due to surface heating and convection. The nocturnal boundary layer, conversely, tends to be much lower and highly stable due to radiative cooling from the surface at night and downslope flow of cool air from nearby mountains. With limited availability of radiosonde data, current estimates of the PBL height at any given time or location are potentially over or underestimated. To better quantify the height and characterize the PBL physics, we developed portable, lightweight sensors that measure CO2 concentrations, temperature, pressure, and humidity every 5 seconds. Four of these sensors are used on a tethered balloon system to monitor CO2 concentrations from the surface up to 300m. We will combine this data with Radio Acoustic Sounding System (RASS) data that measures vertical profiles of wind speed, temperature, and humidity from 40m to 400m. This experiment will characterize the diurnal evolution of CO2 concentrations at multiple heights in the PBL, provide insight into PBL physics during stability transition periods at sunrise and sunset, and estimate the nighttime PBL depth during August in Reno. Further, we expect to gain a better understanding of the impact of mixing volume changes (i.e., PBL height) on air quality and pollution concentrations in Reno. The custom portable sensor design will also be presented. It is expected that these instruments can be used for indoor or outdoor air quality studies, where lightness, small size, and battery operation can be of benefit.
A Kind of Discrete Non-Reflecting Boundary Conditions for Varieties of Wave Equations
Institute of Scientific and Technical Information of China (English)
Xiu-min Shao; Zhi-ling Lan
2002-01-01
In this paper, a new kind of discrete non-reflecting boundary conditions is developed. It can be used for a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic wave equations and the equations for wave propagation in multi-phase media and so on. In this kind of boundary conditions, the composition of all artificial reflected waves, but not the individual reflected ones, is considered and eliminated. Thus, it has a uniform formula for different wave equations. The velocity CA of the composed reflected wave is determined in the way to make the reflection coefficients minimal, the value of which depends on equations. In this paper, the construction of the boundary conditions is illustrated and CA is found, numerical results are presented to illustrate the effectiveness of the boundary conditions.
Surface Temperature and Surface-Layer Turbulence in a Convective Boundary Layer
Garai, A.; Pardyjak, E.; Steeneveld, G.J.; Kleissl, J.
2013-01-01
Previous laboratory and atmospheric experiments have shown that turbulence influences the surface temperature in a convective boundary layer. The main objective of this study is to examine land-atmosphere coupled heat transport mechanism for different stability conditions. High frequency infrared im
Dinarvand Saeed; Abbassi Abbas; Hosseini Reza; Pop Ioan
2015-01-01
This article deals with the study of the steady axisymmetric mixed convective boundary layer flow of a nanofluid over a vertical circular cylinder with prescribed external flow and surface temperature. By means of similarity transformation, the governing partial differential equations are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique namely homotopy a...
Numerical modelling of pollution dispersion in 3D atmospheric boundary layer
Energy Technology Data Exchange (ETDEWEB)
Benes, L.; Bodnar, T.; Kozel, K. [Czech Technical Univ. of Prague (Czech Republic). Dept. of Technical Mathematics; Fraunie, Ph. [Univ. de Toulon et du Var, La Garde (France). Lab. de Sondages Electromagnetiques et Environnemental Terrestre
2002-07-01
The main goal of this work is to present the applicable models and numerical methods for solution of flow and pollution dispersion in 3D atmospheric boundary layer (ABL). Mathematical models are based on the system of Reynolds averaged Navier-Stokes equations and its simplifications. The sets of governing equations are completed by the transport equations for passive impurities and potential temperature. A simple algebraic turbulent closure model is used. The thermal stability phenomenon is taken into account. For each mathematical model a numerical scheme based on finite-difference or finite-volume discretization is proposed and discussed. Some results of numerical tests are presented for pollution dispersion from point sources and flows over simple geometries. (orig.)
Boundary layer flow and heat transfer of Cross fluid over a stretching sheet
Khan, Masood; Rahman, Masood ur
2016-01-01
The current study is a pioneering work in presenting the boundary layer equations for the two-dimensional flow and heat transfer of the Cross fluid over a linearly stretching sheet. The system of partial differential equations is turned down into highly non-linear ordinary differential equations by applying suitable similarity transformations. The stretching sheet solutions are presented via. a numerical technique namely the shooting method and graphs are constructed for the shear-thinning as well as shear-thickening regime. The impact of the emerging parameters namely the power-law index , the local Weissenberg number and the Prandtl number on the velocity and temperature fields are investigated through graphs. Numerical values of the local skin friction coefficient and the local Nusselt number are also presented in tabular form. For some limiting cases, comparisons with previously available results in the literature are made and an excellent agreement is achieved.
Large Eddy Simulation of Pollen Transport in the Atmospheric Boundary Layer
Chamecki, Marcelo; Meneveau, Charles; Parlange, Marc B.
2007-11-01
The development of genetically modified crops and questions about cross-pollination and contamination of natural plant populations enhanced the importance of understanding wind dispersion of airborne pollen. The main objective of this work is to simulate the dispersal of pollen grains in the atmospheric surface layer using large eddy simulation. Pollen concentrations are simulated by an advection-diffusion equation including gravitational settling. Of great importance is the specification of the bottom boundary conditions characterizing the pollen source over the canopy and the deposition process everywhere else. The velocity field is discretized using a pseudospectral approach. However the application of the same discretization scheme to the pollen equation generates unphysical solutions (i.e. negative concentrations). The finite-volume bounded scheme SMART is used for the pollen equation. A conservative interpolation scheme to determine the velocity field on the finite volume surfaces was developed. The implementation is validated against field experiments of point source and area field releases of pollen.
Effects of Joule Heating and Viscous Dissipation on MHD Marangoni Convection Boundary Layer Flow
Directory of Open Access Journals (Sweden)
Rohana Abdul Hamid
2011-09-01
Full Text Available An analysis is performed to study the effects of the Joule heating and viscous dissipation on the magnetohydrodynamics (MHD Marangoni convection boundary layer flow. The governing partial differential equations are reduced to a system of ordinary differential equations via the similarity transformations. Numerical results of the similarity equations are obtained using the Runge-Kutta-Fehlberg method. Effects of the magnetic field parameter, and the combined effects of the Joule heating and the viscous dissipation are investigated and the numerical results are tabulated in tables and figures. It is found that the magnetic field reduces the fluid velocity but increases the fluid temperature. On the other hand, the combined effects of the Joule heating and viscous dissipation have significantly influenced the surface temperature gradient.
Investigation of turbulent spot production rate in boundary layer
Czech Academy of Sciences Publication Activity Database
Jonáš, Pavel; Elsner, W.; Mazur, Oton; Uruba, Václav; Wysocki, M.
Žilina : Žilinská univerzita, 2010, s. 1-6. ISBN 978-80-554-0189-8. [Aplikácia experimentálnych a numerických metód v mechanike tekutín a energetike. Bojnice (SK), 28.04.2010-30.04.2010] R&D Projects: GA AV ČR(CZ) IAA200760614 Institutional research plan: CEZ:AV0Z20760514 Keywords : turbulent spot * by- pas boundary layer transition * transitional intermittency * wavelet analysis Subject RIV: BK - Fluid Dynamics
Laboratory simulation of rotating atmospheric boundary layer flows over obstacles
International Nuclear Information System (INIS)
The present study fits in the frame of a research program concerning in general the dynamics of airflow in the atmospheric boundary layer and in particular the influence of terrestrial rotation on the movements of air masses interacting with natural extended obstacles (mountains). The experiment has been performed by the method of hydraulic simulation, using schematic models at reduced scale in a channel placed on a rotating platform. Only the case of a neutral atmosphere was considered; the wake of an obstacle with semi-circular section and the reciprocal interaction of two obstacles of this kind placed perpendicular to the flow were studied
Experiments on the active control of transitional boundary layers
Nelson, P. A.; Rioual, J.-L.; Fisher, M. J.
Experimental results are presented which demonstrate that the streamwise position of the transition region of a flat plate boundary layer can be actively controlled. The means of control is through the application of suction through the surface of the plate, a progressive increase in suction rate being capable of producing transition at progressively larger distances downstream from the plate leading edge. A simple digital feedback regulator based on an integral control law is shown to be most effective in regulating the position of transition, an error signal being derived from measurements of pressure fluctuations on the surface of the plate.
On Hairpin Vortices in a Transitional Boundary Layer
Czech Academy of Sciences Publication Activity Database
Hladík, Ondřej; Jonáš, Pavel; Uruba, Václav
Liberec : Technical University of Liberec, 2011 - (Vít, T.; Dančová, P.; Novotný, P.), s. 163-170 ISBN 978-80-7372-784-0. - (Vol. 2). [Experimental Fluid Mechanics 2011. Jičín (CZ), 22.11.2011-25.11.2011] R&D Projects: GA ČR GA101/08/1112; GA ČR GAP101/10/1230 Institutional research plan: CEZ:AV0Z20760514 Keywords : turbulence transition * boundary layer * hairpin vortex Subject RIV: BK - Fluid Dynamics http:// orion .kez.tul.cz/efm/
Dynamics of Controlled Boundary Layer Separation on a Circular Cylinder
Czech Academy of Sciences Publication Activity Database
Uruba, Václav; Matějka, Milan; Procházka, Pavel
Praha : Ústav termomechaniky AV ČR, v. v. i., 2008 - (Jonáš, P.; Uruba, V.), s. 61-62 ISBN 978-80-87012-14-7. [Colloquium FLUID DYNAMICS 2008. Praha (CZ), 22.10.2008-24.10.2008] R&D Projects: GA AV ČR IAA2076403; GA ČR GA101/08/1112 Institutional research plan: CEZ:AV0Z20760514 Keywords : boundary layer * separation * control * synthetic jet Subject RIV: BK - Fluid Dynamics www.it.cas.cz/dt
Dynamics of controlled boundary layer separation on a circular cylinder
Czech Academy of Sciences Publication Activity Database
Uruba, Václav; Matějka, Milan
Ostritz - St.Marienthal : DLR Berlin, 2008 - (Hage, W.; Wassen, E.; Choi, K.), s. 1-2 [European Drag Reduction and Flow Control Meeting 2008. Ostritz - St.Marienthal (DE), 08.09.2008-11.09.2008] R&D Projects: GA AV ČR IAA2076403; GA ČR GA101/08/1112 Institutional research plan: CEZ:AV0Z20760514 Keywords : boundary layer * separation * dynamics Subject RIV: BK - Fluid Dynamics http://edrfcm2008.cfd.tu-berlin.de/
A wavenumber-frequency spectral model for atmospheric boundary layers
International Nuclear Information System (INIS)
Motivated by the need to characterize power fluctuations in wind farms, we study spatio-temporal correlations of a neutral atmospheric boundary layer in terms of the joint wavenumber-frequency spectrum of the streamwise velocity fluctuations. To this end, we perform a theoretical analysis of a simple advection model featuring the advection of small- scale velocity fluctuations by the mean flow and large-scale velocity fluctuations. The model is compared to data from large-eddy simulations (LES). We find that the model captures the trends observed in LES, specifically a Doppler shift of frequencies due to the mean flow as well as a Doppler broadening due to random sweeping effects
Role of the vertical pressure gradient in wave boundary layers
DEFF Research Database (Denmark)
Jensen, Karsten Lindegård; Sumer, B. Mutlu; Vittori, Giovanna;
2014-01-01
By direct numerical simulation (DNS) of the flow in an oscillatory boundary layer, it is possible to obtain the pressure field. From the latter, the vertical pressure gradient is determined. Turbulent spots are detected by a criterion involving the vertical pressure gradient. The vertical pressure...... gradient is also treated as any other turbulence quantity like velocity fluctuations and statistical properties of the vertical pressure gradient are calculated from the DNS data. The presence of a vertical pressure gradient in the near bed region has significant implications for sediment transport....
Transition in Hypersonic Boundary Layers: Role of Dilatational Waves
Zhu, Yiding; Yuan, Huijing; Wu, Jiezhi; Chen, Shiyi; Lee, Cunbiao; Gad-el-Hak, Mohamed
2015-01-01
Transition and turbulence production in a hypersonic boundary layer is investigated in a Mach 6 quiet wind tunnel using Rayleigh-scattering visualization, fast-response pressure measurements, and particle image velocimetry. It is found that the second instability acoustic mode is the key modulator of the transition process. The second mode experiences a rapid growth and a very fast annihilation due to the effect of bulk viscosity. The second mode interacts strongly with the first vorticity mode to directly promote a fast growth of the latter and leads to immediate transition to turbulence.
Fluid Mechanics and Heat Transfer in Transitional Boundary Layers
Wang, Ting
2007-01-01
Experiments have been performed to investigate the effects of elevated free-stream turbulence and streamwise acceleration on flow and thermal structures in transitional boundary layers. The free-stream turbulence ranges from 0.5 to 6.4% and the streamwise acceleration ranges from K = 0 to 0.8 x 10(exp -6). The onset of transition, transition length and the turbulent spot formation rate are determined. The statistical results and conditionally sampled results of th streamwise and cross-stream velocity fluctuations, temperature fluctuations, Reynolds stress and Reynolds heat fluxes are presented.
Injection-induced turbulence in stagnation-point boundary layers
Park, C.
1984-02-01
A theory is developed for the stagnation point boundary layer with injection under the hypothesis that turbulence is produced at the wall by injection. From the existing experimental heat transfer rate data obtained in wind tunnels, the wall mixing length is deduced to be a product of a time constant and an injection velocity. The theory reproduces the observed increase in heat transfer rates at high injection rates. For graphite and carbon-carbon composite, the time constant is determined to be 0.0002 sec from the existing ablation data taken in an arc-jet tunnel and a balistic range.
Boundary singularities and characteristics of Hamilton–Jacobi equation
Melikyan, A.; Olsder, G.J.
2010-01-01
Boundary-value problems for first order PDEs are locally considered, when the classical sufficient condition for the solution existence does not hold, but a solution still exists, possibly defined on one or both sides of the boundary surface. We note three situations when such a surface (locally) ar
Solution of Moving Boundary Space-Time Fractional Burger’s Equation
Directory of Open Access Journals (Sweden)
E. A.-B. Abdel-Salam
2014-01-01
Full Text Available The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger’s equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time. The linear and periodic moving boundaries for the kink solution of the Burger’s equation are presented graphically and discussed.
Porosity of Free Boundaries in the Obstacle Problem for Quasilinear Elliptic Equations
Indian Academy of Sciences (India)
Jun Zheng; Zhihua Zhang; Peihao Zhao
2013-08-01
In this paper, we establish growth rate of solutions near free boundaries in the identical zero obstacle problem for quasilinear elliptic equations. As a result, we obtain porosity of free boundaries, which is naturally an extension of the previous works by Karp et al. (J. Diff. Equ. 164 (2000) 110–117) for -Laplacian equations, and by Zheng and Zhang (J. Shaanxi Normal Univ. 40(2) (2012) 11–13, 18) for -Laplacian type equations.
Atmospheric Boundary Layer Characteristics during BOBMEX-Pilot Experiment
Indian Academy of Sciences (India)
G S Bhat; S Ameenulla; M Venkataramana; K Sengupta
2000-06-01
The atmospheric boundary layer characteristics observed during the BOBMEX-Pilot experiment are reported. Surface meteorological data were acquired continuously through an automatic weather monitoring system and manually every three hours. High resolution radiosondes were launched to obtain the vertical thermal structure of the atmosphere. The study area was convectively active, the SSTs were high, surface air was warm and moist, and the surface air moist static energy was among the highest observed over the tropical oceans. The mean sea air temperature difference was about 1.25°C and the sea skin temperature was cooler than bucket SST by 0.5°C. The atmospheric mixed layer was shallow, fluctuated in response to synoptic conditions from 100 m to 900 m with a mean around 500 m.
Interactions between the thermal internal boundary layer and sea breezes
Energy Technology Data Exchange (ETDEWEB)
Steyn, D.G. [The Univ. of British Columbia, Dept. of Geography, Atmospheric Science Programme, Vancouver (Canada)
1997-10-01
In the absence of complex terrain, strongly curved coastline or strongly varying mean wind direction, the Thermal Internal Boundary Layer (TIBL) has well known square root behaviour with inland fetch. Existing slab modeling approaches to this phenomenon indicate no inland fetch limit at which this behaviour must cease. It is obvious however that the TIBL cannot continue to grow in depth with increasing fetch, since the typical continental Mixed Layer Depths (MLD) of 1500 to 2000 m must be reached between 100 and 200 km from the shoreline. The anticyclonic conditions with attendant strong convection and light winds which drive the TIBL, also drive daytime Sea Breeze Circulations (SBC) in the coastal zone. The onshore winds driving mesoscale advection of cool air are at the core of TIBL mechanisms, and are invariably part of a SBC. It is to be expected that TIBL and SBC be intimately linked through common mechanisms, as well as external conditions. (au)
Bhattacharya, Ritthik; Stevens, Bjorn
2016-03-01
A two Turbulence Kinetic Energy (2TKE) model is developed to address the boundary layer "grey zone" problem. The model combines ideas from local and nonlocal models into a single energetically consistent framework. By applying the Reynolds averaging to the large eddy simulation (LES) equations that employ Deardorff's subgrid TKE, we arrive at a system of equations for the boundary layer quantities and two turbulence kinetic energies: one which encapsulates the TKE of large boundary-layer-scale eddies and another which represents the energy of eddies subgrid to the vertical grid size of a typical large-scale model. These two energies are linked via the turbulent cascade of energy from larger to smaller scales and are used to model the mixing in the boundary layer. The model is evaluated for three dry test cases and found to compare favorably to large eddy simulations. The usage of two TKEs for mixing helps reduce the dependency of the model on the vertical grid scale as well as on the free tropospheric stability and facilitates a smoother transition from convective to stable regimes. The usage of two TKEs representing two ranges of scales satisfies the prerequisite for modeling the boundary layer in the "grey zone": an idea that is explored further in a companion paper.
International Nuclear Information System (INIS)
In this work, we solve analytically, without losing generality, the neutron diffusion equation for monoenergetic neutrons in a multilayered slab. To this end, we initially determine the solution of the neutron diffusion equation for a generic slab using standard results of second order linear ordinary differential equation with constant coefficients. The global solution for the multilayered slab is then determined applying the boundary condition and continuity of the flux and current at interface. Once the neutron flux is known, the albedo boundary condition is straightly obtained for an arbitrary number of layers in the baffle-reflecting regions, by just using the definition of albedo. We also present numerical simulation for the results neutron flux and comparison with the in literature. (author)
A scaling analysis of the turbulent boundary-layer in a shallow urban lake
Mezemate, Yacine; Fitton, George; Tchiguirinskaia, Ioulia; Schertzer, Daniel; Bonhomme, Céline; Soulignac, Frédéric; Lemaire, Bruno; Vinçon Leite, Brigitte
2014-05-01
The turbulent boundary-layer (TBL) has been the focus of countless experimental and numerical studies. Due to its complex nature the dynamics of the TBL are still far from being understood. Thus, to study, in particular the scaling properties of a TBL, we use a three-dimensional velocity time-series measured from an Acoustic Doppler Current Profiler(ADCP). The ADCP is particularly useful for analysing the TBL as it is able to measure the 3D velocity in the vertical, 127 cells over 3 meters. The ADCP is positioned next to a storm water discharge point at the bottom of a shallow urban lake in Créteil, a region in Paris. The positioning of the ADCP, in a stable, stratified lake, with a strong turbulent flow occurring close to the surface has given us a unique situation in which a turbulent bounded-layer can be analysed. Vertical profiles measured in the atmospheric boundary-layer are typically intrusive due to the requirement of masts and other complex measuring structures. Moreover atmospheric profilers are normally coarsely spaced in the vertical. In order to analyse the scaling properties of the velocity we compute its energy spectrum. In a log- log plot, if the velocity is scaling, the spectral exponent is its slope. It frequently that in the presence of a boundary-layer, a -1 spectral exponent is observed. Dimensional arguments suggest a -1 spectral exponent when the energy flux becomes dependent on the friction velocity instead of the length-scale. Due to the fine vertical spacing of the measurements we are not only able to observe a -1 spectral exponent, but observe a smooth transition from a free-stream turbulent regime (spectral exponent close to -5/3) to a boundary-layer -1 exponent. Because the transition shows such a strong a depth dependence we are able to propose a general model based on dynamical equations for the scaling exponent as a function of height. This generalised scaling boundary-layer model allows one to easily reproduce the turbulent
The Dirichlet problem for the two-dimensional Helmholtz equation for an open boundary
Hayashi, Y.
1973-01-01
Development of a complete theory of the two-dimensional Dirichlet problem for an open boundary. It is shown that the solution of the Dirichlet problem for an open boundary requires the solution of a Fredholm integral equation of the first kind. Although a Fredholm integral equation of the first kind usually has no solution if the kernel is continuous, owing to the logarithmic singularity of the kernel, the equation in this case is converted to a singular integral equation with a Cauchy kernel. It is proven that the homogeneous adjoint equation of the singular integral equation has no nonzero solution. By virtue of this result, and with the aid of an existence theorem known in the theory of singular integral equations, the existence of solutions of the singular integral equation, and then of the unique solution of the Fredholm integral equation of the first kind is proved.
Hyers-Ulam stability for second-order linear differential equations with boundary conditions
Directory of Open Access Journals (Sweden)
Pasc Gavruta
2011-06-01
Full Text Available We prove the Hyers-Ulam stability of linear differential equations of second-order with boundary conditions or with initial conditions. That is, if y is an approximate solution of the differential equation $y''+ eta (x y = 0$ with $y(a = y(b =0$, then there exists an exact solution of the differential equation, near y.
KdV equation under periodic boundary conditions and its perturbations
Huang, Guan; Kuksin, Sergei
2013-01-01
In this paper we discuss properties of the KdV equation under periodic boundary conditions, especially those which are important to study perturbations of the equation. Next we review what is known now about long-time behaviour of solutions for perturbed KdV equations.
The KdV equation under periodic boundary conditions and its perturbations
Guan, Huang; Kuksin, Sergei
2014-09-01
In this paper we discuss properties of the Korteweg-de Vries (KdV) equation under periodic boundary conditions, especially those which are important for studying perturbations of the equation. We then review what is known about the long-time behaviour of solutions for perturbed KdV equations.
Dimension reduction for periodic boundary value problems of functional differential equations
Sieber, Jan
2010-01-01
Periodic boundary-value problems for functional differential equations can be reduced to finite-dimensional algebraic systems of equations. The smoothness assumptions on the right-hand side follow those of the review by Hartung et al. (2006) and are set up such that the result can be applied to differential equations with state-dependent delays.
Application of Arnoldi method to boundary layer instability
Zhang, Yong-Ming; Luo, Ji-Sheng
2015-12-01
The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory (LST) for two-dimensional (2D) disturbance on one-dimensional (1D) basic flow, comparison with LST for three-dimensional (3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence (FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien-Schlichting (TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous’ in secondary instability. Project supported by the National Natural Science Foundation of China (Grant Nos. 11202147, 11332007, 11172203, and 91216111) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120032120007).
Characteristics of turbulent boundary layer flow over algal biofilm
Murphy, Elizabeth; Barros, Julio; Schultz, Michael; Steppe, Cecily; Flack, Karen; Reidenbach, Matthew
2015-11-01
Algal biofilms are an important fouling community on ship hulls, with severe economic consequences due to drag-induced increases in fuel use and cleaning costs. Here, we characterize the boundary layer flow structure in turbulent flow over diatomaceous slime, a type of biofilm. Diatomaceous slime composed of three species of diatoms commonly found on ship hulls was grown on acrylic test plates under shear stress. The slime averages 1.6 mm in thickness and has a high density of streamers, which are flexible elongated growths with a length on the order of 1- 2 mm located at the top of the biofilm that interact with the flow. Fouled acrylic plates were placed in a water tunnel facility specialized for detailed turbulent boundary layer measurements. High resolution Particle Image Velocimetry (PIV) data are analyzed for mean velocity profile as well as local turbulent stresses and turbulent kinetic energy (TKE) production, dissipation and transport. Quadrant analysis is used to characterize the impact of the instantaneous events of Reynolds shear stress (RSS) in the flow. To investigate the coherence of the large-scale motion in the flow two-point correlation analysis is employed. Funding provided by the Office of Naval Research and the National Science Foundation.
Using GPS Radio Occultation to study polar boundary layer properties
Ganeshan, M.; Wu, D. L.
2015-12-01
The sensitivity of GPS RO refractivity to moisture and temperature variations in polar regions is explored using radiosonde observations from the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment. A retrieval algorithm for the boundary layer inversion height and surface-based inversion (SBI) frequency is developed for dry atmospheric conditions (total precipitable water < 3.6 mm) that typically exist during polar winter, as well as in high-latitude, elevated regions such as eastern Antarctica and central Greenland. The algorithm is applied to the high-resolution refractivity profiles obtained over the polar Arctic region using the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) dataset for the period 2006-2013. The method is found useful for capturing the spatiotemporal variability in Arctic inversion properties. For the Arctic Ocean, the spatial patterns show a minimum inversion height (maximum SBI frequency) over the ice-covered Pacific sector similar to that observed in past studies. Monthly evolution of the inversion characteristics suggests a surface temperature control in the multi-year sea ice region, with the peak in SBI frequency occurring during the transition period from winter to spring. For central Greenland, the seasonal peak in SBI frequency occurs during winter. The diurnal variability in SBI frequency is forced mainly by solar heating, consistent with past observations. Despite some limitations, the RO refractivity profile is found quite useful for monitoring the Arctic boundary layer, and is able to capture the interannual variability of inversion characteristics.
Delaying natural transition of a boundary layer using smooth steps
Xu, Hui; Sherwin, Spencer J
2015-01-01
The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on the delay of the transition to turbulence. The interaction between the Tollmien-Schlichting (T-S) waves and the base flow over a single/two forward facing smooth steps is conducted by linear analysis indicating the amplitude of the T-S waves are attenuated in the boundary layer over a single smooth plate. Furthermore, we show that two smooth forward facing steps give rise to a further reduction of the amplitude of the T-S waves. A direct numerical simulation (DNS) is performed for the two smooth forward steps correlating favourably with the linear analysis and showing that for the investigated parameters, the K-type transition is inhibited whereas the turbulence onset of the H-type transition is postponed albeit not suppressed. Transition is indeed delayed and drag reduced for both these transition scenarios suggesting smooth forward facing steps could be leveraged as a passive flow control strategy to de...
Competing disturbance amplification mechanisms in two-fluid boundary layers
Saha, Sandeep; Page, Jacob; Zaki, Tamer
2015-11-01
The linear stability of boundary layers above a thin wall film of lower viscosity is analyzed. Appropriate choice of the film thickness and viscosity excludes the possibility of interfacial instabilities. Transient amplification of disturbances is therefore the relevant destabilizing influence, and can take place via three different mechanisms in the two-fluid configuration. Each is examined in detail by solving an initial value problem whose initial condition comprises a pair of appropriately chosen eigenmodes from the discrete, continuous and interface modes. Two regimes are driven by the lift-up mechanism: (i) The response to a streamwise vortex and (ii) the normal vorticity generated by a stable Tollmien-Schlichting wave. Both are damped due to the film. The third regime is associated with the wall-normal vorticity that is generated by the interface displacement. It can lead to appreciable streamwise velocity disturbances in the near-wall region at relatively low viscosity ratios. The results demonstrate that a wall film can stabilize the early linear stages of boundary-layer transition, and explain the observations from the recent nonlinear direct numerical simulations of this configuration by Jung & Zaki (J. Fluid Mech., vol 772, 2015, 330-360).
Optimizing EDMF parameterization for stratocumulus-topped boundary layer
Jones, C. R.; Bretherton, C. S.; Witek, M. L.; Suselj, K.
2014-12-01
We present progress in the development of an Eddy Diffusion / Mass Flux (EDMF) turbulence parameterization, with the goal of improving the representation of the cloudy boundary layer in NCEP's Global Forecast System (GFS), as part of a multi-institution Climate Process Team (CPT). Current GFS versions substantially under-predict cloud amount and cloud radiative impact over much of the globe, leading to large biases in the surface and top of atmosphere energy budgets. As part of the effort to correct these biases, the CPT is developing a new EDMF turbulence scheme for GFS, in which local turbulent mixing is represented by an eddy diffusion term while nonlocal shallow convection is represented by a mass flux term. The sum of both contributions provides the total turbulent flux. Our goal is for this scheme to more skillfully simulate cloud radiative properties without negatively impacting other measures of weather forecast skill. One particular challenge faced by an EDMF parameterization is to be able to handle stratocumulus regimes as well as shallow cumulus regimes. In order to isolate the behavior of the proposed EDMF parameterization and aid in its further development, we have implemented the scheme in a portable MATLAB single column model (SCM). We use this SCM framework to optimize the simulation of stratocumulus cloud top entrainment and boundary layer decoupling.
On boundary layer modelling using the ASTEC code
International Nuclear Information System (INIS)
The modelling of fluid boundary layers adjacent to non-slip, heated surface using the ASTEC code is described. The pricipal boundary layer characteristics are derived using simple dimensional arguments and these are developed into criteria for optimum placement of the computational mesh to achieve realistic simulation. In particular, the need for externally-imposed drag and heat transfer correlations as a function of the local mesh concentration is discussed in the context of both laminar and turbulent flow conditions. Special emphasis is placed in the latter case on the (k-ε) turbulence model, which is standard in the code. As far as possible, the analyses are pursued from first principles, so that no comprehensive knowledge of the history of the subject is required for the general ASTEC user to derive practical advice from the document. Some attention is paid to the use of heat transfer correlations for internal solid/fluid surfaces, whose treatment is not straightforward in ASTEC. It is shown that three formulations are possible to effect the heat transfer, called Explicit, Jacobian and Implicit. The particular advantages and disadvantages of each are discussed with regard to numerical stability and computational efficiency. (author) 18 figs., 1 tab., 39 refs
Second Law Analysis of the Turbulent Flat Plate Boundary Layer
Directory of Open Access Journals (Sweden)
Dragos Isvoranu
2000-09-01
Full Text Available
Until now the second law analysis of turbulent flow relied only on the irreversibilities performed by the mean velocity and mean temperature gradients. Using the Reynolds decomposition of the volumetric entropy generation rate expression we found that the dissipation rates of both, turbulent kinetic energy and fluctuating temperature variance, also represent the irreversibilities of the flow. Applying the above results, the second law analysis of the turbulent boundary layer shows that the maximum values of the "mean motion irreversibilities" (generated by the mean velocity and mean temperature gradient are located at the wall, while the maximum values of the "turbulent irreversibilities" (performed by the dissipation rate of turbulent kinetic energy and fluctuating temperature variance are located in the buffer sublayer. As a consequence, for a given location on the plate, the integral values of the "mean motion irreversibilities" are approximately constant and the "turbulent irreversibilities" grow up with the boundary layer thickness.
BOUNDARY VALUE PROBLEM TO DYNAMIC EQUATION ON TIME SCALE
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper we consider a nonlinear first-order boundary value problem on a time scale. The existence results of three positive solutions are obtained using fixed point theorems. Finally,examples are presented to illustrate the main results.
Direct spatial resonance in the laminar boundary layer due to a rotating-disk
Indian Academy of Sciences (India)
M Turkyilmazoglu; J S B Gajjar
2000-12-01
Numerical treatment of the linear stability equations is undertaken to investigate the occurrence of direct spatial resonance events in the boundary layer flow due to a rotating-disk. A spectral solution of the eigenvalue problem indicates that algebraic growth of the perturbations shows up, prior to the amplification of exponentially growing instability waves. This phenomenon takes place while the flow is still in the laminar state and it also tends to persist further even if the non-parallelism is taken into account. As a result, there exists the high possibility of this instability mechanism giving rise to nonlinearity and transition, long before the unboundedly growing time-amplified waves.
A law of the wall for turbulent boundary layers with suction: Stevenson's formula revisited
Vigdorovich, Igor
2016-08-01
The turbulent velocity field in the viscous sublayer of the boundary layer with suction to a first approximation is homogeneous in any direction parallel to the wall and is determined by only three constant quantities — the wall shear stress, the suction velocity, and the fluid viscosity. This means that there exists a finite algebraic relation between the turbulent shear stress and the longitudinal mean-velocity gradient, using which as a closure condition for the equations of motion, we establish an exact asymptotic behavior of the velocity profile at the outer edge of the viscous sublayer. The obtained relationship provides a generalization of the logarithmic law to the case of wall suction.
Boundary integral equation method calculations of surface regression effects in flame spreading
Altenkirch, R. A.; Rezayat, M.; Eichhorn, R.; Rizzo, F. J.
1982-01-01
A solid-phase conduction problem that is a modified version of one that has been treated previously in the literature and is applicable to flame spreading over a pyrolyzing fuel is solved using a boundary integral equation (BIE) method. Results are compared to surface temperature measurements that can be found in the literature. In addition, the heat conducted through the solid forward of the flame, the heat transfer responsible for sustaining the flame, is also computed in terms of the Peclet number based on a heated layer depth using the BIE method and approximate methods based on asymptotic expansions. Agreement between computed and experimental results is quite good as is agreement between the BIE and the approximate results.
A formal derivation for the Blasius similarity solution for flat-plate boundary layer
Lin, Hao
2015-11-01
The Blasius solution is a classical solution for a laminar boundary layer attached to a semi-infinite flat plate. The key of the solution strategy is to reduce the boundary layer equations, which are PDEs, to a set of ODEs, using a similarity variable transform. Conceptually, the similarity suggests that the velocity profile in each transverse cross-section appears ``self-similar''. In many classical text books and typical classroom lectures on fluid mechanics, the existence of the similarity solution is argued heuristically. The similarity variable is defined a priori so as to collapse the PDEs. It appears somewhat mystical that the PDEs can be perfectly reduced via such an approach. Here we present a rigorous derivation for the existence of a similarity solution, which naturally arises from the fact that there is no apparent streamwise length scale for a semi-infinite plate. Conversely, a similarity solution cannot exist if the plate size is finite. This derivation can be useful in fluids education, in topics including similarity, scaling arguments, and boundary layer theory.
A numerical study of shock wave/boundary layer interaction in a supersonic compressor cascade
International Nuclear Information System (INIS)
A numerical analysis of shock wave boundary layer interaction in transonic/supersonic axial flow compressor cascade has been performed by using a characteristic upwind Navier-Stokes method with various turbulence models. Two equation turbulence models were applied to transonic/supersonic flows over a NACA 0012 airfoil. The results are superion to those from an algebraic turbulence model. High order TVD schemes predicted shock wave/boundary layer interactions reasonably well. However, the prediction of SWBLI depends more on turbulence models than high order schemes. In a supersonic axial flow cascade at M=1.59 and exit/inlet static pressure ratio of 2.21, k-ω and Shear Stress Transport (SST) models were numerically stables. However, the k-ω model predicted thicker shock waves in the flow passage. Losses due to shock/shock and shock/boundary layer interactions in transonic/supersonic compressor flowfields can be higher losses than viscous losses due to flow separation and viscous dissipation
On the Impact of Wind Farms on a Convective Atmospheric Boundary Layer
Lu, Hao; Porté-Agel, Fernando
2015-10-01
With the rapid growth in the number of wind turbines installed worldwide, a demand exists for a clear understanding of how wind farms modify land-atmosphere exchanges. Here, we conduct three-dimensional large-eddy simulations to investigate the impact of wind farms on a convective atmospheric boundary layer. Surface temperature and heat flux are determined using a surface thermal energy balance approach, coupled with the solution of a three-dimensional heat equation in the soil. We study several cases of aligned and staggered wind farms with different streamwise and spanwise spacings. The farms consist of Siemens SWT-2.3-93 wind turbines. Results reveal that, in the presence of wind turbines, the stability of the atmospheric boundary layer is modified, the boundary-layer height is increased, and the magnitude of the surface heat flux is slightly reduced. Results also show an increase in land-surface temperature, a slight reduction in the vertically-integrated temperature, and a heterogeneous spatial distribution of the surface heat flux.
Representation of the grey zone of turbulence in the atmospheric boundary layer
Honnert, Rachel
2016-04-01
Numerical weather prediction model forecasts at horizontal grid lengths in the range of 100 to 1 km are now possible. This range of scales is the "grey zone of turbulence". Previous studies, based on large-eddy simulation (LES) analysis from the MésoNH model, showed that some assumptions of some turbulence schemes on boundary-layer structures are not valid. Indeed, boundary-layer thermals are now partly resolved, and the subgrid remaining part of the thermals is possibly largely or completely absent from the model columns. First, some modifications of the equations of the shallow convection scheme have been tested in the MésoNH model and in an idealized version of the operational AROME model at resolutions coarser than 500 m. Secondly, although the turbulence is mainly vertical at mesoscale (> 2 km resolution), it is isotropic in LES (production of turbulence cannot be neglected at resolutions finer than half of the boundary-layer height. Thus, in the grey zone, fully unidirectional turbulence scheme should become tridirectional around 500 m resolution. At Météo-France, the dynamical turbulence is modelled by a K-gradient in LES as well as at mesoscale in both MésoNH and AROME, which needs mixing lengths in the formulation. Vertical and horizontal mixing lengths have been calculated from LES of neutral and convective cases at resolutions in the grey zone.
The effect of non-Newtonian viscosity on the stability of the Blasius boundary layer
Griffiths, P. T.; Gallagher, M. T.; Stephen, S. O.
2016-07-01
We consider, for the first time, the stability of the non-Newtonian boundary layer flow over a flat plate. Shear-thinning and shear-thickening flows are modelled using a Carreau constitutive viscosity relationship. The boundary layer equations are solved in a self-similar fashion. A linear asymptotic stability analysis, that concerns the lower-branch structure of the neutral curve, is presented in the limit of large Reynolds number. It is shown that the lower-branch mode is destabilised and stabilised for shear-thinning and shear-thickening fluids, respectively. Favourable agreement is obtained between these asymptotic predictions and numerical results obtained from an equivalent Orr-Sommerfeld type analysis. Our results indicate that an increase in shear-thinning has the effect of significantly reducing the value of the critical Reynolds number, this suggests that the onset of instability will be significantly advanced in this case. This postulation, that shear-thinning destabilises the boundary layer flow, is further supported by our calculations regarding the development of the streamwise eigenfunctions and the relative magnitude of the temporal growth rates.
Kawai, Soshi
2014-11-01
In this talk, we first propose a numerical strategy that is robust and high-order accurate for enabling to simulate transcritical flows at supercritical pressures under abrupt variations in thermodynamic properties due to the real fluid effects. The method is based on introducing artificial density diffusion in a physically-consistent manner in order to capture the steep variation of thermodynamic properties in transcritical conditions robustly, while solving a pressure evolution equation to achieve pressure equilibrium at the transcritical interfaces. We then discuss the direct numerical simulation (DNS) of transcritical heated turbulent boundary layers on a zero-pressure-gradient flat plate at supercritical pressures. To the best of my knowledge, the present DNS is the first DNS of zero-pressure-gradient flat-plate transcritical turbulent boundary layer. The turbulent kinetic budget indicates that the compressibility effects (especially, pressure-dilatation correlation) are not negligible at the transcritical conditions even if the flow is subsonic. The unique and interesting interactions between the real fluid effects and wall turbulence, and their turbulence statistics, which have never been seen in the ideal-fluid turbulent boundary layers, are also discussed. This work was supported in part by Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Young Scientists (A) KAKENHI 26709066 and the JAXA International Top Young Fellowship Program.
Effect of leading-edge geometry on boundary-layer receptivity to freestream sound
Lin, Nay; Reed, Helen L.; Saric, W. S.
1991-01-01
The receptivity to freestream sound of the laminar boundary layer over a semi-infinite flat plate with an elliptic leading edge is simulated numerically. The incompressible flow past the flat plate is computed by solving the full Navier-Stokes equations in general curvilinear coordinates. A finite-difference method which is second-order accurate in space and time is used. Spatial and temporal developments of the Tollmien-Schlichting wave in the boundary layer, due to small-amplitude time-harmonic oscillations of the freestream velocity that closely simulate a sound wave travelling parallel to the plate, are observed. The effect of leading-edge curvature is studied by varying the aspect ratio of the ellipse. The boundary layer over the flat plate with a sharper leading edge is found to be less receptive. The relative contribution of the discontinuity in curvature at the ellipse-flat-plate juncture to receptivity is investigated by smoothing the juncture with a polynomial. Continuous curvature leads to less receptivity. A new geometry of the leading edge, a modified super ellipse, which provides continuous curvature at the juncture with the flat plate, is used to study the effect of continuous curvature and inherent pressure gradient on receptivity.
A novel unsplit perfectly matched layer for the second-order acoustic wave equation.
Ma, Youneng; Yu, Jinhua; Wang, Yuanyuan
2014-08-01
When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach. PMID:24794509
Climatic impacts of the boundary layer circulation over Antarctica
International Nuclear Information System (INIS)
Prolonged periods of strong radiational cooling over the sloping ice fields of Antarctica produce cold, negatively buoyant air in the lowest layers of the atmosphere. This cooling generates a continental-scale, near-surface wind-field which is highly irregular. Cold air in the interior is channeled into narrow zones that enable the downstream coastal katabatic winds to become anomalously strong and persistent. This probably means that the boundary layer transport of air across the Antarctic coastline is concentrated in a small number of narrow regions, and that previous quantitative evaluations of the importance of this boundary layer circulation are likely to be substantially in error. From continuity considerations, the time-averaged outflow of cold surface air must be compensated by inflow aloft and sinking over the continent. This time-averaged meridional mass circulation plays a dominant role in the heat budget of the Antarctic atmosphere by adiabatic compression in the statically stable atmosphere. The tropospheric convergence and sinking motion also generate cyclonic vorticity which is comparable in magnitude to that arising from the temperature contrast between the ice sheet and the surrounding ocean. That is, the circumpolar vortex is centered over the East Antarctic ice sheet in pan because of the tropospheric mass convergence. The concentration of cold surface air transport from the ice sheet into narrow coastal zones has important consequences for sea ice formation and cyclonic development. Katabatic jets can force coastal polynyas where very active sea ice formation and associated brine rejection produce saline shelf water. This water mass is a component of Antarctic Bottom Water. Such water mass formation provides a way to couple climatic variations over the ice sheet to the deep ocean on relatively short time scales
International Nuclear Information System (INIS)
This paper presents an investigation for magnetohydrodynamic (MHD) viscoelastic fluid boundary layer flow and radiation heat transfer over an unsteady stretching sheet in presence of heat source. Time dependent fractional derivative is first introduced in formulating the boundary layer equations. Numerical solutions are obtained by using the finite difference scheme and L1-algorithm approximation. Results indicate that the proposed model describes a basic delaying times framework for viscoelastic flow and radiation heat transfer. The effects of involved parameters on velocity and temperature fields are shown graphically and analyzed in detail
Yao, Chengwei; Pal Arya, S.; Davis, Jerry; Main, Charles E.
Numerical solutions of the diffusion equation of Peronospora tabacina spores from a finite-area source over flat terrain in the evolving convective boundary layer are presented. Temporal variations in the release of spores, atmospheric stability, wind speed, and eddy diffusivity are considered. The model also includes the vertical variations of wind and eddy diffusivity. The model results indicate that ground level concentrations decrease with time as wind speed and eddy diffusivity increase in the evolving convective boundary layer. The loss of P. tabacina spores due to deposition at the surface also decrease with increasing instability and wind speed. Deposition is found to be particularly important close to the source area.
Energy Technology Data Exchange (ETDEWEB)
Shen, Bingyu; Zheng, Liancun, E-mail: liancunzheng@ustb.edu.cn; Chen, Shengting [School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083 (China)
2015-10-15
This paper presents an investigation for magnetohydrodynamic (MHD) viscoelastic fluid boundary layer flow and radiation heat transfer over an unsteady stretching sheet in presence of heat source. Time dependent fractional derivative is first introduced in formulating the boundary layer equations. Numerical solutions are obtained by using the finite difference scheme and L1-algorithm approximation. Results indicate that the proposed model describes a basic delaying times framework for viscoelastic flow and radiation heat transfer. The effects of involved parameters on velocity and temperature fields are shown graphically and analyzed in detail.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper deals with boundary value problems for linear uniformly elliptic systems. First the general linear uniformly elliptic system of the first order equations is reduced to complex form, and then the compound boundary value problem for the complex equations of the first order is discussed. The approximate solutions of the boundary value problem are found by the variation-difference method, and the error estimates for the approximate solutions are derived.Finally the approximate method of the oblique derivative problem for linear uniformly elliptic equations of the second or der is introduced.
FOREWORD: International Conference on Planetary Boundary Layer and Climate Change
Djolov, G.; Esau, I.
2010-05-01
One of the greatest achievements of climate science has been the establisment of the concept of climate change on a multitude of time scales. The Earth's complex climate system does not allow a straightforward interpretation of dependences between the external parameter perturbation, internal stochastic system dynamics and the long-term system response. The latter is usually referred to as climate change in a narrow sense (IPCC, 2007). The focused international conference "Planetary Boundary Layers and Climate Change" has addressed only time scales and dynamical aspects of climate change with possible links to the turbulent processes in the Planetary Boundary Layer (PBL). Although limited, the conference topic is by no means singular. One should clearly understand that the PBL is the layer where 99% of biosphere and human activity are concentrated. The PBL is the layer where the energy fluxes, which are followed by changes in cryosphere and other known feedbacks, are maximized. At the same time, the PBL processes are of a naturally small scale. What is the averaged long-term effect of the small-scale processes on the long-term climate dynamics? Can this effect be recognized in existing long-term paleo-climate data records? Can it be modeled? What is the current status of our theoretical understanding of this effect? What is the sensitivity of the climate model projections to the representation of small-scale processes? Are there significant indirect effects, e.g. through transport of chemical components, of the PBL processes on climate? These and other linked questions have been addressed during the conference. The Earth's climate has changed many times during the planet's history, with events ranging from ice ages to long periods of warmth. Historically, natural factors such as the amount of energy released from the Sun, volcanic eruptions and changes in the Earth's orbit have affected the Earth's climate. Beginning late in the 18th century, human activities
Intermittent phenomena in the boiling two-phase boundary layer
International Nuclear Information System (INIS)
In order to investigate statistical properties of temperature fluctuation in a boiling two-phase boundary layer the corresponding intermittency functions, which describe liquid, vapour and interface region at an individual fixed point, have been defined. In water boiling on a horizontal surface the temperature fluctuation was measured with a microthermocouple and the signal was processed through the digital computer with the detector function specified for liquid, vapor and interface region. The results obtained confirm that the temperature fluctuation in the boiling two-phase layer can be divided into three parts corresponding to individual regions and that its statistical distribution depends on the properties of respective systems. It has also been shown that the temperature fluctuation in the interface region is determinative and corresponds to the temperature changes in the liquid layer surrounding vapor bubble growth. Amplitude distribution in the liquid region changes its form with the distance from the wall as a result of the change in intensity of turbulence at different distances. The probability density distribution in the vapor region shows very small amplitude fluctuation and is almost constant for all distances. (author)
Fichtl, G. H.
1973-01-01
The realistic simulation of flow in the atmospheric boundary layers at heights greater than two kilometers is discussed. Information concerning horizontally homogeneous and statistically stationary atmospheric boundary layer flows is presented. The problems related to the incorporation of the information into atmospheric wind simulation programs are analyzed. The information which the meteorologist must acquire in order to provide a basis for improving the simulation of atmospheric boundary flows is explained.
A Lagrangian Study of Southeast Pacific Boundary Layer Clouds
Painter, Gallia
concentration which extend far offshore into regions of normally very clean cloud. We use Lagrangian trajectories to investigate the source of the high droplet concentrations of the mesoscale "hooks", and evaluate whether boundary layer transport of coastal pollutants alone can account for their extent. We find that boundary layer trajectories past 85 W do not pass sufficiently close to the coastline to explain high aerosol concentrations offshore.
Ferdows, M.
2012-01-01
Magnetohydrodynamic (MHD) boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed. 2012 M. Ferdows et al.
Talpos, Simona; Apostol, Marian
2015-12-01
It is shown that the Reynolds equations for a turbulent flow over an unbounded flat surface in the presence of a constant pressure-gradient lead to a displaced logarithmic profile of the velocity distribution; the displaced logarithmic profile is obtained by assuming a constant production rate of turbulence energy. The displacement height measured on the (vertical) axis perpendicular to the surface is either positive or negative. For a positive displacement height the boundary layer exhibits an inversion, while for a negative displacement height the boundary layer is a direct one. In an inversion boundary layer the logarithmic velocity profile is disrupted into two distinct branches separated by a logarithmic singularity. The viscosity transforms this logarithmic singularity into a sharp edge, governed by a generalized Reynolds number. The associated temperature distribution is calculated, and the results are discussed in relation to meteorological boundary-layer jets and stratified layers. The effects of gravitation and atmospheric thermal or fluid-mixture concentration gradients ("external forcings") are also considered; it is shown that such circumstances may lead to various modifications of the boundary layers. A brief presentation of a similar situation is described for a circular pipe.
Afzal, Bushra; Noor Afzal Team; Bushra Afzal Team
2014-11-01
The momentum and thermal turbulent boundary layers over a continuous moving sheet subjected to a free stream have been analyzed in two layers (inner wall and outer wake) theory at large Reynolds number. The present work is based on open Reynolds equations of momentum and heat transfer without any closure model say, like eddy viscosity or mixing length etc. The matching of inner and outer layers has been carried out by Izakson-Millikan-Kolmogorov hypothesis. The matching for velocity and temperature profiles yields the logarithmic laws and power laws in overlap region of inner and outer layers, along with friction factor and heat transfer laws. The uniformly valid solution for velocity, Reynolds shear stress, temperature and thermal Reynolds heat flux have been proposed by introducing the outer wake functions due to momentum and thermal boundary layers. The comparison with experimental data for velocity profile, temperature profile, skin friction and heat transfer are presented. In outer non-linear layers, the lowest order momentum and thermal boundary layer equations have also been analyses by using eddy viscosity closure model, and results are compared with experimental data. Retired Professor, Embassy Hotel, Rasal Ganj, Aligarh 202001 India.
Boundary value problemfor multidimensional fractional advection-dispersion equation
Khasambiev Mokhammad Vakhaevich
2015-01-01
In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. T...
The viscous boundary layer at the free surface of a rotating baroclinic fluid
Hide, R.
2011-01-01
The properties of the viscous boundary layer at the free surface of a rotating baroclinic fluid are analyzed and compared with those of the well-known Ekman boundary layer at a rigid surface. Although the ageostrophic components of the flow in the free surface boundary layer are weaker than in the Ekman layer, there are problems of practical interest in which their effects are not negligible.DOI: 10.1111/j.2153-3490.1964.tb00188.x
Uranus evolution models with simple thermal boundary layers
Nettelmann, N; Fortney, J J; Hamel, S; Yellamilli, S; Bethkenhagen, M; Redmer, R
2016-01-01
The strikingly low luminosity of Uranus (Teff ~ Teq) constitutes a long-standing challenge to our understanding of Ice Giant planets. Here we present the first Uranus structure and evolution models that are constructed to agree with both the observed low luminosity and the gravity field data. Our models make use of modern ab initio equations of state at high pressures for the icy components water, methane, and ammonia. Proceeding step by step, we confirm that adiabatic models yield cooling times that are too long, even when uncertainties in the ice:rock ratio (I:R) are taken into account. We then argue that the transition between the ice/rock-rich interior and the H/He-rich outer envelope should be stably stratified. Therefore, we introduce a simple thermal boundary and adjust it to reproduce the low luminosity. Due to this thermal boundary, the deep interior of the Uranus models are up to 2--3 warmer than adiabatic models, necessitating the presence of rocks in the deep interior with a possible I:R of $1\\tim...
Randall, David A.; Abeles, James A.; Corsetti, Thomas G.
1985-04-01
The UCLA general circulation model (GCM) has been used to simulate the seasonally varying planetary boundary layer (PBL), as well as boundary-layer stratus and stratocumulus clouds. The PBL depth is a prognostic variable of the GCM, incorporated through the use of a vertical coordinate system in which the PBL is identified with the lowest model layer.Stratocumulus clouds are assumed to occur whenever the upper portion of the PBL becomes saturated, provided that the cloud-top entrainment instability does not occur. As indicated by Arakawa and Schubert, cumulus clouds are assumed to originate at the PBL top, and tend to make the PBL shallow by drawing on its mass.Results are presented from a three-year simulation, starting from a 31 December initial condition obtained from an earlier run with a different version of the model. The simulated seasonally varying climates of the boundary layer and free troposphere are realistic. The observed geographical and seasonal variations of stratocumulus cloudiness are fairly well simulated. The simulation of the stratocumulus clouds associated with wintertime cold-air outbreaks is particularly realistic. Examples are given of individual events. The positions of the subtropical marine stratocumulus regimes are realistically simulated, although their observed frequency of occurrence is seriously underpredicted. The observed summertime abundance of Arctic stratus clouds is also underpredicted.In the GCM results, the layer cloud instability appears to limit the extent of the marine subtropical stratocumulus regimes. The instability also frequently occurs in association with cumulus convection over land.Cumulus convection acts as a very significant sink of PBL mass throughout the tropics, and over the midlatitude continents in summer.Three experiments have been performed to investigate the sensitivity of the GCM results to aspects of the PBL and stratocumulus parameterizations. For all three experiments, the model was started from 1
Turbulence Scales Simulations in Atmospheric Boundary Layer Wind Tunnels
Directory of Open Access Journals (Sweden)
Elena-Carmen Teleman
2008-01-01
Full Text Available The simulation of the air flow over models in atmospheric boundary layer tunnels is a research domain based on advanced scientific technologies imposed by the necessity of studying the turbulent fluid movements in the proximity of the Earth’s surface. The experiment presented herein is developed in the wind tunnel from the Laboratory of Structural Aerodynamics of the Faculty of Civil Engineering and Building Services in Iassy. Measurements necessary for the determination of the turbulence scales of the wind action in urban environment were conducted. The data obtained were processed and analyzed and interpreted with specific software. The results are used for a synthesis regarding the scales of turbulence of the model of flow and the actual accuracy of measurements. The paper presents some of the important elements of this synthesis.
Aeroelectric structures and turbulence in the atmospheric boundary layer
Directory of Open Access Journals (Sweden)
S. V. Anisimov
2013-10-01
Full Text Available Complex electrical measurements with the use of sodar data show that electric field pulsation analysis is useful for electrodynamics/turbulence monitoring under different conditions. In particular, the number of aeroelectric structures (AES generated per hour is a convenient measure of the turbulence intensity. During convectively unstable periods, as many as 5–10 AES form per hour. Under stable conditions, AES occasionally form as well, indicating the appearance of occasional mixing events reflected in the electric field perturbations. AES magnitudes under stable conditions are relatively small, except in special cases such as high humidity and fog. The analysis of electric field (EF spectra gives additional useful information on the parameters of the atmospheric boundary layer and its turbulence. A rather sharp change in the spectrum slope takes place in the vicinity of 0.02 Hz under stable conditions. The characteristic slope of the spectrum and its change are reproduced in a simple model of EF formation.
Compressible Turbulent Boundary Layers on a Strongly Heated Wall
Institute of Scientific and Technical Information of China (English)
无
1993-01-01
This paper concerns the theoretical and experimental modelling of the flat wall,highly heated,compressible turbulent boundary layer.Its final objective is to develop a numerical Navier-Stokes solver and to conclude on its capability to correctly represent complex aerothermic viscous flows near the wall.The paper presents a constructed numerical method with particular attention given to the turbulence modelling at low Reynolds number and comparisons with supersonic and transonic experimental data.For the transonic experiment,very high wall temperature(Tw=1100K)is realized.The method of this difficult experimental set up is discussed.The comparison between experimental and computational data conducts to the first conclusion and gives some indications for the future work.
A Qualitative Description of Boundary Layer Wind Speed Records
Kavasseri, R G; Nagarajan, Radhakrishnan
2006-01-01
The complexity of the atmosphere endows it with the property of turbulence by virtue of which, wind speed variations in the atmospheric boundary layer (ABL) exhibit highly irregular fluctuations that persist over a wide range of temporal and spatial scales. Despite the large and significant body of work on microscale turbulence, understanding the statistics of atmospheric wind speed variations has proved to be elusive and challenging. Knowledge about the nature of wind speed at ABL has far reaching impact on several fields of research such as meteorology, hydrology, agriculture, pollutant dispersion, and more importantly wind energy generation. In the present study, temporal wind speed records from twenty eight stations distributed through out the state of North Dakota (ND, USA), ($\\sim$ 70,000 square-miles) and spanning a period of nearly eight years are analyzed. We show that these records exhibit a characteristic broad multifractal spectrum irrespective of the geographical location and topography. The rapi...
Coherent vorticity extraction in turbulent boundary layers using orthogonal wavelets
Energy Technology Data Exchange (ETDEWEB)
Khujadze, George; Oberlack, Martin [Chair of Fluid Dynamics, Technische Universitaet Darmstadt (Germany); Yen, Romain Nguyen van [Institut fuer Mathematik, Freie Universitaet Berlin (Germany); Schneider, Kai [M2P2-CNRS and CMI, Universite de Provence, Marseille (France); Farge, Marie, E-mail: khujadze@fdy.tu-darmstadt.de [LMD-IPSL-CNRS, Ecole Normale Superieure, Paris (France)
2011-12-22
Turbulent boundary layer data computed by direct numerical simulation are analyzed using orthogonal anisotropic wavelets. The flow fields, originally given on a Chebychev grid, are first interpolated on a locally refined dyadic grid. Then, they are decomposed using a wavelet basis, which accounts for the anisotropy of the flow by using different scales in the wall-normal direction and in the planes parallel to the wall. Thus the vorticity field is decomposed into coherent and incoherent contributions using thresholding of the wavelet coefficients. It is shown that less than 1% of the coefficients retain the coherent structures of the flow, while the majority of the coefficients corresponds to a structureless, i.e., noise-like background flow. Scale-and direction-dependent statistics in wavelet space quantify the flow properties at different wall distances.
Combined core/boundary layer transport simulations in tokamaks
International Nuclear Information System (INIS)
Significant new numerical results are presented from self-consistent core and boundary or scrape-off layer plasma simulations with 3-D neutral transport calculations. For a symmetric belt limiter it is shown that, for plasma conditions considered here, the pump limiter collection efficiency increases from 11% to 18% of the core efflux as a result of local reionization of blade deflected neutrals. This hitherto unobserved effect causes a significant amplification of upstream ion flux entering the pump limiter. Results from coupling of an earlier developed two-zone edge plasma model ODESSA to the PROCTR core plasma simulation code indicates that intense recycling divertor operation may not be possible because of stagnation of upstream flow velocity. This results in a self-consistent reduction of density gradient in an intermediate region between the central plasma and separatrix, and a concomitant reduction of core-efflux. There is also evidence of increased recycling at the first wall
Centralised versus Decentralised Active Control of Boundary Layer Instabilities
Dadfar, R; Bagheri, S; Henningson, D S
2014-01-01
We use linear control theory to construct an output feedback controller for the attenuation of small-amplitude Tollmien-Schlichting (TS) wavepackets in a flat-plate boundary layer.We distribute evenly in the spanwise direction up to 72 localized objects near the wall (18 disturbances sources, 18 actuators, 18 estimation sensors and 18 objective sensors). In a fully three-dimensional configuration,the interconnection between inputs and outputs becomes quickly unfeasible when the number of actuators and sensors increases in the spanswise direction. The objective of this work is to understand how an efficient controller may be designed by connecting only a subset of the actuators to sensors, thereby reducing the complexity of the controller, without comprising the efficiency. We find that using a semi-decentralized approach - where small control units consisting of 3 estimation sensors connected to 3 actuators are replicated 6 times along the spanwise direction - results only in a 11% reduction of control perfor...
Unsteady Phenomena in Shock Wave/Boundary Layer Interaction
Dolling, D. S.
1993-01-01
A brief review is given of the unsteadiness of shock wave/turbulent boundary layer interaction. The focus is on interactions generated by swept and unswept compression ramps, by flares, steps and incident shock waves, by cylinders and blunt fins, and by glancing shock waves. The effects of Mach number, Reynolds number, and separated flow scale are discussed as are the physical causes of the unsteadiness. The implications that the unsteadiness has for interpreting time-average surface and flowfield data, and for comparisons of such experimental data with computation, is also briefly discussed. Finally, some suggestions for future work are given. It is clear that there are large gaps in the data base and that many aspects of such phenomena are poorly understood. Much work remains to be done.
Segregation in the Atmospheric Boundary Layer - A Discussion
Dlugi, Ralph; Berger, Martina; Zelger, Michael; Hofzumahaus, Andreas; Rohrer, Franz; Holland, Frank; Lu, Keding; Tsokankunku, Anywhere; Sörgel, Matthias; Kramm, Gerhard; Mölders, Nicole
2016-04-01
Segregation is a well known topic in technical chemistry and means an incomplete mixing of the reactants. Incomplete mixing reduces the rate of reaction which is of utmost importance in technical chemistry but has been payed less attention in atmospheric chemistry. Different observational and modelling studies on chemical reactions in the turbulent and convective atmospheric boundary layer are analysed for the influences of segregation in the systems NO ‑ NO2 ‑ O3 and OH + V OCs (with main focus on isoprene). Also some estimates on reactions like HO2 + NO (an important recycling mechanism for OH) will be given. Especially, different terms of the intensity of segregation IS (correlation coefficients, standard deviations of mixing ratios) are compared and are related to characteristics of the flow regimes, such as mixing conditions and Damköhler numbers. Also influences of fluctuations of actinic fluxes are discussed which influence the mostly photo chemically driven reactions that were investigated.
Numerical analysis of the turbulent natural convection boundary layer
International Nuclear Information System (INIS)
It is considered to be one of options of nuclear fuel cycle policies in Japan to store spent fuel before reprocessing. Then we have to evaluate of the thermal integrity for dry type cask storage system. But the turbulent natural convection boundary layer is a flow with relatively large fluctuations of velocity and temperature at low velocity, and measurements of turbulent quantities near the wall are especially difficult. So, the turbulent structure has not been elucidated. On the other hand, numerical analyses of natural convection using turbulence models have been developed. However, there are not the models which are suitable for prediction of natural convection exactly, so it's effective to analyze of direct numerical simulation (DNS). The propose of this study is to simulate (DNS) for buoyant flow as economical as possible. We calculate two different grid size to investigate to numerical accuracy. (author)