Analysis of Laminar Boundary Layer Equations
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
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
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
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.
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
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
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.
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
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
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...
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
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.
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 ...
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
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.
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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.
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
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
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
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
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
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
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
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
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
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
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.
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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.
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
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
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).
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.
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.
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.
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
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....
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...
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
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)
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
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.
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
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
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
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
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
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?
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
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
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
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
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
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
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
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.
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
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
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
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
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.
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
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
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
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
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
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
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
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
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.
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
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
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
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)