Download or read book Nonlinear Wave Propagation in Stratified Shear Flows written by David John Brown and published by . This book was released on 1995 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Propagation of Waves in Shear Flows written by Anatoli? L?vovich Fabrikant and published by World Scientific. This book was released on 1998 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of well-known theorems of the hydrodynamic theory of stability are interpreted in terms of the interaction of the waves having different energy signs. Attention is drawn to the plasma-hydrodynamic analogy, which is a powerful tool for physical analyses of general mechanisms of wave amplification and absorption in flows. Various wave-flow interaction problems are considered, for instance, sound generation in whistlers, wave scattering and amplification by vortices, methods of wave remote sounding, and some nonlinear dynamical and chaotic phenomena.
Download or read book PROPAGATION OF NONLINEAR WAVES written by Wing-Chiu Derek Lai and published by Open Dissertation Press. This book was released on 2017-01-27 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "The Propagation of Nonlinear Waves in Layered and Stratified Fluids" by Wing-chiu, Derek, Lai, 黎永釗, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the thesis entitled THE PROPAGATION OF NONLINEAR WAVES IN LAYERED AND STRATIFIED FLUIDS submitted by Derek Wing-Chiu Lai for the degree of Doctor of Philosophy at the University of Hong Kong in April 2001 In this thesis the propagation of nonlinear waves in layered and stratified fluids is investigated. In the first part of this research, "unconventional" solitary waves are obtained and their interactions are investigated by the Hirota bilinear transformation. Such solitary waves are "unconventional" because they can be expressed analytically as some mixed exponential - algebraic expressions. Furthermore, the separation of the crests goes like a logarithm, rather than a linear function, in the time scale. In a proper frame of reference these unconventional solitary waves are usually counterpropagating waves. These counterpropagating waves and their interactions are investigated for several nonlinear evolution equations which are of fluid dynamical interests. Firstly, 2- and 3-soliton expansions are obtained for the Manakov system, a coupled set of nonlinear Schrodinger equations arising from the propagation of multiphase modes when the group velocity projections overlap. A pair of counterpropagating waves is observed if the technique of "merger" of the wavenumbers is performed for a 2-soliton expansion, and the separation of the crests goes like a i logarithm in time. Furthermore, temporal modulation of the amplitude is observed if the same technique is applied to a 3-soliton expansion. A similar procedure is then applied to the (2+1)-dimensional (2 spatial and 1 temporal dimensions) long wave-short wave resonance interaction equations in a two-layer fluid. Such long-short resonance interactions can be considered as a degenerate case of triad resonance. The required condition is that the phase velocity of the long wave matches the group velocity of the short wave. The "merger" technique can also be extended to the dromion solutions. Dromions are exact, localized solutions of (2 + 1) (2 spatial and 1 temporal) dimensions that decay exponentially in all directions. In a two-layer fluid the modified Korteweg-de Vries (mKdV) systems will be the governing equation if the quadratic nonlinearity vanishes. The required condition for the case of irrotational flow is that the density ratio is approximately equal to the square of the depth ratio. Under the irrotational flow assumption only the mKdV systems with the cubic nonlinear and the dispersive terms of opposite signs (mKdV-) exist. Our contribution here is to investigate the wave propagation in a two- layer fluid with shear flows in order to demonstrate the existence of mKdV systems with the cubic nonlinear and the dispersive terms of the same sign (mKdV+). A class of counterpropagating waves and their interactions are studied for the mKdV+. From the perspective of fluid dynamics the propagation of nonlinear waves in the first part of this research is considered in the ii weakly nonlinear regime. In the second part of this research fully nonlinear internal solitary waves in stratified fluids are calculated. Such internal waves for the exponential and linear density profiles are obtained by computing the higher order terms in an asymptotic expansion where the Boussinesq and long wave parameters are comparably small. With increasing amplitude the wavelength of the solitary waves generally decreases and
Download or read book Stability and Nonlinear Waves in Stratified Shear Flows written by David J. Benney and published by . This book was released on 1974* with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Propagation of Waves in Shear Flows written by Anatolii Lʹvovich Fabrikant and published by . This book was released on 1998 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Environmental Stratified Flows written by Roger Grimshaw and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of flows in density-stratified fluids has been and remains now an important topic for scientific enquiry. Such flows arise in many contexts, ranging from industrial settings to the oceanic and atmospheric environments. It is the latter topic which is the focus of this book. Both the ocean and atmosphere are characterised by the basic vertical density stratification, and this feature can affect the dynamics on all scales ranging from the micro-scale to the planetary scale. The aim of this book is to provide a “state-of-the-art” account of stratified flows as they are relevant to the ocean and atmosphere with a primary focus on meso-scale phenomena; that is, on phenomena whose time and space scales are such that the density stratification is a dominant effect, so that frictional and diffusive effects on the one hand and the effects of the earth’s rotation on the other hand can be regarded as of less importance. This in turn leads to an emphasis on internal waves.
Download or read book Nonlinear Waves written by Mark J. Ablowitz and published by . This book was released on 1988 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has important applications in fluid dynamics (e.g. long waves in stratified fluids, solitons generated by ships), nonlinear optics (e.g. self-induced transparence, and self-focussing of light), digital communications via solitons, inverse scattering in one and higher dimensions. Areas of Study Include: Solutions of nonlinear multidimensional systems; arising in Physics; inverse problems, especially in multidimensions; and DBAR methodololgy; Riemann-Hilbert boundary value problems; and inverse problems; Solitons in multidimensional systems, solitons, generated by ships in narrow channels; Nonlinear systems with external focussing; Semi infinite boundary value problems; IST for nonlinear singular integro-differential equations; the Benjamin-Ono equation, the intermediate Long Wave Equation, the Sine-Hilbert equation, multidimensional generalizations; Discrete IST and numerical simulations; Painleve equations; Focussing singularities in nonlinear wave propagation; Applications to surface waves, internal waves, shear flows; nonlinear optics, S.I.T., relativity etc; Direct linearizing methods for nonlinear evolution equations; Multidimensional generalizations of the Sine-Gordon and wave equations arising in differential geometry; Algebraic methods and symmetries of multidimensional nonlinear evolution equations; and Solutions to semiperiodic multidimensional equations.
Download or read book Nonlinear Phenomena In Physics Of Fluids And Plasmas Proceedings Of The Enea Workshop On Nonlinear Dynamics Volume 2 written by M Pettini and published by World Scientific. This book was released on 1991-03-22 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Workshop in nonlinear dynamics and mathematical physics, organized by the Italian Nuclear Energy Agency (ENEA) in Bologna, is intended to give an updated overview of modern trends in the field of nonlinear dynamics with emphasis on applications to physics, quantum theory, plasma physics and fluid dynamics, optics and electrodynamics, computer simulation, and neural networks.
Download or read book Nonlinear Waves in Waveguides written by Sergei B. Leble and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Download or read book Wave Propagation and Diffraction written by Igor T. Selezov and published by Springer. This book was released on 2017-09-05 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents two distinct aspects of wave dynamics – wave propagation and diffraction – with a focus on wave diffraction. The authors apply different mathematical methods to the solution of typical problems in the theory of wave propagation and diffraction and analyze the obtained results. The rigorous diffraction theory distinguishes three approaches: the method of surface currents, where the diffracted field is represented as a superposition of secondary spherical waves emitted by each element (the Huygens–Fresnel principle); the Fourier method; and the separation of variables and Wiener–Hopf transformation method. Chapter 1 presents mathematical methods related to studying the problems of wave diffraction theory, while Chapter 2 deals with spectral methods in the theory of wave propagation, focusing mainly on the Fourier methods to study the Stokes (gravity) waves on the surface of inviscid fluid. Chapter 3 then presents some results of modeling the refraction of surf ace gravity waves on the basis of the ray method, which originates from geometrical optics. Chapter 4 is devoted to the diffraction of surface gravity waves and the final two chapters discuss the diffraction of waves by semi-infinite domains on the basis of method of images and present some results on the problem of propagation of tsunami waves. Lastly, it provides insights into directions for further developing the wave diffraction theory.
Download or read book Selected Topics in Nonlinear Wave Mechanics written by C.I. Christov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an overview ofthe current state of nonlinear wave mechanics with emphasis on strong discontinuities (shock waves) and localized self preserving shapes (solitons) in both elastic and fluid media. The exposition is intentionallyat a detailed mathematical and physical level, our expectation being that the reader will enjoy coming to grips in a concrete manner with advances in this fascinating subject. Historically, modern research in nonlinear wave mechanics began with the famous 1858 piston problem paper of Riemann on shock waves and con tinued into the early part of the last century with the work of Hadamard, Rankine, and Hugoniot. After WWII, research into nonlinear propagation of dispersive waves rapidly accelerated with the advent of computers. Works of particular importance in the immediate post-war years include those of von Neumann, Fermi, and Lax. Later, additional contributions were made by Lighthill, Glimm, Strauss, Wendroff, and Bishop. Dispersion alone leads to shock fronts of the propagating waves. That the nonlinearity can com pensate for the dispersion, leading to propagation with a stable wave having constant velocity and shape (solitons) came as a surprise. A solitary wave was first discussed by J. Scott Russell in 1845 in "Report of British Asso ciations for the Advancement of Science. " He had, while horseback riding, observed a solitary wave travelling along a water channel and followed its unbroken progress for over a mile.
Download or read book Introduction to Wave Propagation in Nonlinear Fluids and Solids written by D. S. Drumheller and published by Cambridge University Press. This book was released on 1998-02-13 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Waves occur widely in nature and have innumerable commercial uses. Pressure waves are responsible for the transmission of speech, bow waves created by meteors can virtually ignite the earth's atmosphere, ultrasonic waves are used for medical imaging, and shock waves are used for the synthesis of new materials. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models. It covers gases, liquids, and solids as integral parts of the subject. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Graduate students, as well as professional engineers and applied physicists, will value this clear, comprehensive introduction to the study of wave phenomena.
Download or read book Nonlinear Waves written by Lokenath Debnath and published by CUP Archive. This book was released on 1983-12-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Download or read book Linear and Nonlinear Dynamics in Stratified Shear Flows written by Jeremy Parker and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1974 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pulses and Other Wave Processes in Fluids written by M. Kelbert and published by Springer. This book was released on 1996-02-29 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents a comprehensive treatment of both classical and modern problems of pulse propagation. The authors provide a physical insight in the intriguing problem of pulse propagation in non-equilibrium media (unstable or admitting attenuation). A refined analysis of the acoustic-gravity waves generation in a compressible stratified fluid is also presented. The solution describes sophisticated wave pictures near the front of the perturbation where previously known methods fail. Finally a detailed account of a relatively new field of investigation related to continuous spectrum waves in shear flows is given. Audience: This volume will be of use to researchers and scientists with a background in wave motion, fluid mechanics and calculus including elementary aspects of asymptotic methods. A major source of information for academians specialized in acoustics, hydrodynamics and geophysics.
Download or read book SOLITONS WAVE PROPAGATION IN written by Chun-Chung Mak and published by Open Dissertation Press. This book was released on 2017-01-27 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Solitons and Wave Propagation in Hydrodynamical and Optical Media" by Chun-chung, Mak, 麥振忠, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstractofthesisentitled SolitonsandWavePropagation inHydrodynamicalandOpticalMedia submittedby Chun-ChungMAK forthedegreeofMasterofPhilosophy attheUniversityofHongKong inAugust2004 Solitons, which have been extensively studied over the past five decades, rep- resent one of the most important concepts in nonlinear science. These particle-like nonlinearwaveshavebeendemonstratedboththeoreticallyandexperimentally, and arebelievedtohavehighengineeringpotentialinsomeapplications. Theaimofthis studywastostudythesolitonswhichexistinsomeconfigurationsofhydrodynam- ical and optical media. In particular, soliton solutions of a number of completely integrablenonlinearevolutionequationsarenewlyobtainedorre-derived. The Hirota's bilinear method is adopted to obtain the exact soliton solutions in this study. This differentiation-based method, which requires no sophisticated mathematics, isabletoderiveexact, analyticsolutionsefficiently. An optical fiber system with decaying/amplifying and broadening/compressing effects is modelled by a variable coefficient nonlinear Schro]dinger (NLS) equa- tion. This equation is also able to describe the propagation of optical pulses in a dispersion-managed fiber system, averaged over one dispersion map. Bright anddark, one- and two-soliton solutions are obtained. These solitons are shown to havevaryingwavenumberandfrequencyintheirsolitonexpansions. Inadditionto the decaying and broadening effects, the bright solitons also demonstrate a special property, namely that the trajectory of their center of mass can have three possible modesinthex-t domain. A coupled NLS system with a group velocity mismatch is considered to be the relevant equation for a three-layer stratified shear flow. While the coupled NLS systemhasbeenstudiedindetail, theeffectofaddingagroupvelocitymismatchis still unknown. Dark one- and two-soliton solutions are obtained for an integrable system. TheSasa-Satsumaequationisoneintegrablesettingofthemoregeneralhigher- orderNLSequation, whichtakesintoaccounthigher-ordernonlineareffects. Adark one-solitonsolutionisobtained, butitisfoundtohaveonelessarbitraryparameter than its NLS counterpart. Because of this additional constraint, a dark two-soliton solutionisnotfound. Somespecialexpansionseriesmaybeneededforthebilinear formtoobtainmulti-solitonsolutions, andtheseareleftforfuturestudies. Inmicrochannelflows, interfacialeffectssuchastheelectricdoublelayercannot be neglected. This layer will interact with the ions and hence the liquid flow in the microchannel. The associated electric potential is shown to be modelled by the sinh-Poisson equation, a different version of which also has applications in vortex dynamics. Techniques from nonlinear waves are applied to solve for one- to three- solitonsolutions, buttheyarefoundtobethesameasthoseobtainedforthecontexts of vortex dynamics. A comparison is also made between an exact doubly periodic solutionandanapproximatesolutionfromtheDebye-Hu]ckelapproximation, anda considerableamountofdifferenceisfoundinsomeregions. DOI: 10.5353/th_b3051366 Subjects: Solitons Fiber optics Hydrodynamics
