Nonlinear Waves In Fluids Recent Advances And Modern Applications

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Nonlinear Waves in Fluids: Recent Advances and Modern Applications

Author : Roger Grimshaw
Publisher : Springer Science & Business Media
ISBN 13 : 3211380256
Total Pages : 202 pages
Book Rating : 4.2/5 (113 download)

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Book Synopsis Nonlinear Waves in Fluids: Recent Advances and Modern Applications by : Roger Grimshaw

Download or read book Nonlinear Waves in Fluids: Recent Advances and Modern Applications written by Roger Grimshaw and published by Springer Science & Business Media. This book was released on 2007-03-23 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although nonlinear waves occur in nearly all branches of physics and engi neering, there is an amazing degree of agreement about the fundamental con cepts and the basic paradigms. The underlying unity of the theory for linearized waves is already well-established, with the importance of such universal concepts as group velocity and wave superposition. For nonlinear waves the last few decades have seen the emergence of analogous unifying comcepts. The pervasiveness of the soliton concept is amply demonstrated by the ubiquity of such models as the Korteweg-de Vries equation and the nonlinear Schrodinger equation. Similarly, there is a universality in the study of wave-wave interactions, whether determin istic or statistical, and in the recent developments in the theory of wave-mean flow interactions. The aim of this text is to present the basic paradigms of weakly nonlinear waves in fluids. This book is the outcome of a CISM Summer School held at Udine from September 20-24, 2004. . Like the lectures given there the text covers asymptotic methods for the derivation of canonical evolution equations, such as the Kortew- de Vries and nonlinear Schrodinger equations, descriptions of the basic solution sets of these evolution equations, and the most relevant and compelling applica tions. These themes are interlocked, and this will be demonstrated throughout the text . The topics address any fluid flow application, but there is a bias towards geophysical fluid dynamics, reflecting for the most part the areas where many applications have been found.

Nonlinear Waves

Author : Lokenath Debnath
Publisher : CUP Archive
ISBN 13 : 9780521254687
Total Pages : 376 pages
Book Rating : 4.2/5 (546 download)

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Book Synopsis Nonlinear Waves by : Lokenath Debnath

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.

Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances

Author :
Publisher : Elsevier
ISBN 13 : 008048946X
Total Pages : 401 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances by :

Download or read book Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances written by and published by Elsevier. This book was released on 2007-04-03 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wave emission, the role of essentially nonlinear wave phenomena. The specificity of the book is that analytical, numerical, and experimental approaches are presented together and complement each other. Special attention is paid on explaining the methodology, e.g. multiple time-scale asymptotic expansions, averaging and removal of resonances, in what concerns theory, high-resolution finite-volume schemes, in what concerns numerical simulations, and turntable experiments with stratified fluids, in what concerns laboratory simulations. A general introduction into GFD is given at the beginning to introduce the problematics for non-specialists. At the same time, recent new results on nonlinear geostrophic adjustment, nonlinear waves, and equatorial dynamics, including some exact results on the existence of the slow manifold, wave breaking, and nonlinear wave solutions are presented for the first time in a systematic manner. · Incorporates analytical, numerical and experimental approaches in the geophysical fluid dynamics context· Combination of essentials in GFD, of the description of analytical, numerical and experimental methods (tutorial part), and new results obtained by these methods (original part)· Provides the link between GFD and mechanics (averaging method, the method of normal forms); GFD and nonlinear physics (shocks, solitons, modons, anomalous transport, periodic nonlinear waves)

Ray Methods for Nonlinear Waves in Fluids and Plasmas

Author : Marcelo Anile
Publisher : CRC Press
ISBN 13 : 1000447588
Total Pages : 268 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Ray Methods for Nonlinear Waves in Fluids and Plasmas by : Marcelo Anile

Download or read book Ray Methods for Nonlinear Waves in Fluids and Plasmas written by Marcelo Anile and published by CRC Press. This book was released on 2021-06-24 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.

Symmetry, Phase Modulation and Nonlinear Waves

Author : Thomas J. Bridges
Publisher : Cambridge University Press
ISBN 13 : 1107188849
Total Pages : 239 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Symmetry, Phase Modulation and Nonlinear Waves by : Thomas J. Bridges

Download or read book Symmetry, Phase Modulation and Nonlinear Waves written by Thomas J. Bridges and published by Cambridge University Press. This book was released on 2017-07-03 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridges studies the origin of Korteweg-de Vries equation using phase modulation and its implications in dynamical systems and nonlinear waves.

Nonlinear Waves and Weak Turbulence

Author : Vladimir Evgenʹevich Zakharov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821841136
Total Pages : 212 pages
Book Rating : 4.8/5 (411 download)

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Book Synopsis Nonlinear Waves and Weak Turbulence by : Vladimir Evgenʹevich Zakharov

Download or read book Nonlinear Waves and Weak Turbulence written by Vladimir Evgenʹevich Zakharov and published by American Mathematical Soc.. This book was released on 1998 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincare normal forms and the inverse scattering method.

Nonlinear Ocean Waves and the Inverse Scattering Transform

Author : Alfred Osborne
Publisher : Academic Press
ISBN 13 : 9780080925103
Total Pages : 944 pages
Book Rating : 4.9/5 (251 download)

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Book Synopsis Nonlinear Ocean Waves and the Inverse Scattering Transform by : Alfred Osborne

Download or read book Nonlinear Ocean Waves and the Inverse Scattering Transform written by Alfred Osborne and published by Academic Press. This book was released on 2010-04-07 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 200 years, the Fourier Transform has been one of the most important mathematical tools for understanding the dynamics of linear wave trains. Nonlinear Ocean Waves and the Inverse Scattering Transform presents the development of the nonlinear Fourier analysis of measured space and time series, which can be found in a wide variety of physical settings including surface water waves, internal waves, and equatorial Rossby waves. This revolutionary development will allow hyperfast numerical modelling of nonlinear waves, greatly advancing our understanding of oceanic surface and internal waves. Nonlinear Fourier analysis is based upon a generalization of linear Fourier analysis referred to as the inverse scattering transform, the fundamental building block of which is a generalized Fourier series called the Riemann theta function. Elucidating the art and science of implementing these functions in the context of physical and time series analysis is the goal of this book. Presents techniques and methods of the inverse scattering transform for data analysis Geared toward both the introductory and advanced reader venturing further into mathematical and numerical analysis Suitable for classroom teaching as well as research

Introduction to Wave Propagation in Nonlinear Fluids and Solids

Author : Douglas S. Drumheller
Publisher : Cambridge University Press
ISBN 13 : 9780521583138
Total Pages : 536 pages
Book Rating : 4.5/5 (831 download)

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Book Synopsis Introduction to Wave Propagation in Nonlinear Fluids and Solids by : Douglas S. Drumheller

Download or read book Introduction to Wave Propagation in Nonlinear Fluids and Solids written by Douglas S. Drumheller and published by Cambridge University Press. This book was released on 1998-02-13 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Waves occur widely in nature and have innumerable commercial uses. Waves are responsible for the sound of speech, meteors igniting the atmosphere, radio and television broadcasting, medical diagnosis using ultrasound. 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 for a variety of gases, liquids, and solids. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Students at an advanced undergraduate/graduate level will find this text a clear and comprehensive introduction to the study of nonlinear wave phenomena, and it will also be valuable as a professional reference in engineering and applied physics.

Solitary Waves in Fluids

Author : R. Grimshaw
Publisher : WIT Press
ISBN 13 : 1845641574
Total Pages : 209 pages
Book Rating : 4.8/5 (456 download)

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Book Synopsis Solitary Waves in Fluids by : R. Grimshaw

Download or read book Solitary Waves in Fluids written by R. Grimshaw and published by WIT Press. This book was released on 2007 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited by R.H.J. Grimshaw, this book covers the topic of solitary waves in fluids.

Nonlinear Waves and Pattern Dynamics

Author : Nizar Abcha
Publisher : Springer
ISBN 13 : 3319781936
Total Pages : 229 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Nonlinear Waves and Pattern Dynamics by : Nizar Abcha

Download or read book Nonlinear Waves and Pattern Dynamics written by Nizar Abcha and published by Springer. This book was released on 2018-04-20 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physics of the Russian Academy of Sciences in Nizhny Novgorod (Russia). The chapters have been written by leading scientists in Nonlinear Physics, and the topics chosen so as to cover all the fields to which Prof. Ezersky himself contributed, by means of experimental, theoretical and numerical approaches. The volume will appeal to advanced students and researchers studying nonlinear waves and pattern dynamics, as well as other scientists interested in their applications in various natural media.

Analytical Properties of Nonlinear Partial Differential Equations

Author : Alexei Cheviakov
Publisher : Springer Nature
ISBN 13 : 3031530748
Total Pages : 322 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Analytical Properties of Nonlinear Partial Differential Equations by : Alexei Cheviakov

Download or read book Analytical Properties of Nonlinear Partial Differential Equations written by Alexei Cheviakov and published by Springer Nature. This book was released on with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Waves in Real Fluids

Author : A. Kluwick
Publisher : Springer
ISBN 13 : 3709126088
Total Pages : 336 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Nonlinear Waves in Real Fluids by : A. Kluwick

Download or read book Nonlinear Waves in Real Fluids written by A. Kluwick and published by Springer. This book was released on 2014-05-04 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of materials which exhibit new and unconventional properties is of central importance for the devel- opment of advanced and refined technologies in many fields of engineering science. In this connection there has been a rapidly growing interest in real fluid effects on wave phenomena in the past few years. A prominent example is provided by Bethe-Zel'dovich-Thompson (BZT) fluids which have the distinguishing feature that they exhibit negative nonlinearity over a finite range of temperature and pressures in the pure vapour phase. However, two phase flows with and without phase change are an even richer source of new unexpected and previously thought impossible phenomena. Topics covered by this volume include waves in gases near the critical point, waves in retrograde fluids, temperature waves in superfluid helium and density waves in suspensions of particles in liquids. Clearly, the aim of the various contributions is twofold. First, they are intended to provide scientists and engineers working in these and related areas with an overview of various new physical phenomena as for example expansion shocks, sonic shocks, shock splitting, evaporation and liquafaction shocks and the experimental techniques needed to study these phenomena. Second, an attempt is made to discuss aspects of their mathematical modeling with special emphasis on properties which these phenomena have in common.

Selected Topics in Nonlinear Wave Mechanics

Author : C.I. Christov
Publisher : Springer Science & Business Media
ISBN 13 : 1461200954
Total Pages : 274 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Selected Topics in Nonlinear Wave Mechanics by : C.I. Christov

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.

Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics

Author : Ramon G. Rubio
Publisher : Springer
ISBN 13 : 3642340709
Total Pages : 799 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics by : Ramon G. Rubio

Download or read book Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics written by Ramon G. Rubio and published by Springer. This book was released on 2013-05-30 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the research areas covered by the famous Instituto Pluridisciplinar at the Universidad Complutense of Madrid, which he co-founded over two decades ago, and include: fluid physics and related nonlinear phenomena at interfaces and in other geometries, wetting and spreading dynamics, geophysical and astrophysical flows, and novel aspects of electronic transport in anharmonic lattices, as well as topics in neurodynamics and robotics.

New Approaches to Nonlinear Waves

Author : Elena Tobisch
Publisher : Springer
ISBN 13 : 3319206907
Total Pages : 298 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis New Approaches to Nonlinear Waves by : Elena Tobisch

Download or read book New Approaches to Nonlinear Waves written by Elena Tobisch and published by Springer. This book was released on 2015-08-19 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the applicability of these novel methods and approaches to a wide class of evolutionary dispersive PDEs, e.g. equations from Benjamin-Oro, Boussinesq, Hasegawa-Mima, KdV-type, Klein-Gordon, NLS-type, Serre, Shamel , Whitham and Zakharov. This makes the book interesting for professionals in the fields of nonlinear physics, applied mathematics and fluid mechanics as well as students who are studying these subjects. The book can also be used as a basis for a one-semester lecture course in applied mathematics or mathematical physics.

IUTAM Symposium on Turbulence in the Atmosphere and Oceans

Author : David Dritschel
Publisher : Springer Science & Business Media
ISBN 13 : 9400703600
Total Pages : 298 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis IUTAM Symposium on Turbulence in the Atmosphere and Oceans by : David Dritschel

Download or read book IUTAM Symposium on Turbulence in the Atmosphere and Oceans written by David Dritschel and published by Springer Science & Business Media. This book was released on 2010-12-09 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text of the Persian poet Rum ̄ ̄ ?, written some eight centuries ago, and reproduced at the beginning of this book is still relevant to many of our pursuits of knowledge, not least of turbulence. The text illustrates the inability people have in seeing the whole thing, the ‘big picture’. Everybody looks into the problem from his/her vi- point, and that leads to disagreement and controversy. If we could see the whole thing, our understanding would become complete and there would be no cont- versy. The turbulent motion of the atmosphere and oceans, at the heart of the observed general circulation, is undoubtedly very complex and dif?cult to understand in its entirety. Even ‘bare’ turbulence, without rotation and strati?cation whose effects are paramount in the atmosphere and oceans, still poses great fundamental ch- lenges for understanding after a century of research. Rotating strati?ed turbulence is a relatively new research topic. It is also far richer, exhibiting a host of distinct wave types interacting in a complicated and often subtle way with long-lived - herent structures such as jets or currents and vortices. All of this is tied together by basic ?uid-dynamical nonlinearity, and this gives rise to a multitude of phen- ena: spontaneous wave emission, wave-induced transport, both direct and inverse energy scale cascades, lateral and vertical anisotropy, fronts and transport barriers, anomalous transport in coherent vortices, and a very wide range of dynamical and thermodynamical instabilities.

Waves and Compressible Flow

Author : Hilary Ockendon
Publisher : Springer
ISBN 13 : 1493933817
Total Pages : 243 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Waves and Compressible Flow by : Hilary Ockendon

Download or read book Waves and Compressible Flow written by Hilary Ockendon and published by Springer. This book was released on 2016-01-21 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its second edition, this book continues to give readers a broad mathematical basis for modelling and understanding the wide range of wave phenomena encountered in modern applications. New and expanded material includes topics such as elastoplastic waves and waves in plasmas, as well as new exercises. Comprehensive collections of models are used to illustrate the underpinning mathematical methodologies, which include the basic ideas of the relevant partial differential equations, characteristics, ray theory, asymptotic analysis, dispersion, shock waves, and weak solutions. Although the main focus is on compressible fluid flow, the authors show how intimately gasdynamic waves are related to wave phenomena in many other areas of physical science. Special emphasis is placed on the development of physical intuition to supplement and reinforce analytical thinking. Each chapter includes a complete set of carefully prepared exercises, making this a suitable textbook for students in applied mathematics, engineering, and other physical sciences. Reviews of the first edition: "This book ... is an introduction to the theory of linear and nonlinear waves in fluids, including the theory of shock waves. ... is extraordinarily accurate and free of misprints ... . I enjoyed reading this book. ... most attractive and enticing appearance, and I’m certain that many readers who browse through it will wish to buy a copy. The exercises ... are excellent. ... A beginner who worked through these exercises would not only enjoy himself or herself, but would rapidly acquire mastery of techniques used...in JFM and many other journals..." (C. J. Chapman, Journal of Fluid Mechanics, Vol. 521, 2004) "The book targets a readership of final year undergraduates and first year graduates in applied mathematics. In the reviewer’s opinion, it is very well designed to catch the student’s interest ... while every chapter displays essential features in some important area of fluid dynamics. Additionally, students may practice by solving 91 exercises. This volume is mainly devoted to inviscid flows. ... The book is very well written." (Denis Serre, Mathematical Reviews, 2004)