Nonlinear Waves and Weak Turbulence

Nonlinear Waves and Weak Turbulence

This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media.

Author: Vladimir Evgenʹevich Zakharov

Publisher: American Mathematical Soc.

ISBN: 0821841130

Category: Mathematics

Page: 197

View: 924

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.
Categories: Mathematics

Nonlinear Waves and Weak Turbulence

Nonlinear Waves and Weak Turbulence

This book is an outgrowth of the NSF-CBMS conference Nonlinear Waves £3 Weak Turbulence held at Case Western Reserve University in May 1992.

Author: FITZMAURICE

Publisher: Springer Science & Business Media

ISBN: 9781461203315

Category: Technology & Engineering

Page: 345

View: 754

This book is an outgrowth of the NSF-CBMS conference Nonlinear Waves £3 Weak Turbulence held at Case Western Reserve University in May 1992. The principal speaker at the conference was Professor V. E. Zakharov who delivered a series of ten lectures outlining the historical and ongoing developments in the field. Some twenty other researchers also made presentations and it is their work which makes up the bulk of this text. Professor Zakharov's opening chapter serves as a general introduction to the other papers, which for the most part are concerned with the application of the theory in various fields. While the word "turbulence" is most often associated with f:l. uid dynamics it is in fact a dominant feature of most systems having a large or infinite number of degrees of freedom. For our purposes we might define turbulence as the chaotic behavior of systems having a large number of degrees of freedom and which are far from thermodynamic equilibrium. Work in field can be broadly divided into two areas: • The theory of the transition from smooth laminar motions to the disordered motions characteristic of turbulence. • Statistical studies of fully developed turbulent systems. In hydrodynamics, work on the transition question dates back to the end of the last century with pioneering contributions by Osborne Reynolds and Lord Rayleigh.
Categories: Technology & Engineering

Nonlinear Waves and Weak Turbulence

Nonlinear Waves and Weak Turbulence

This book is an outgrowth of the NSF-CBMS conference Nonlinear Waves £3 Weak Turbulence held at Case Western Reserve University in May 1992.

Author: FITZMAURICE

Publisher: Birkhäuser

ISBN: 1461267110

Category: Science

Page: 345

View: 205

This book is an outgrowth of the NSF-CBMS conference Nonlinear Waves £3 Weak Turbulence held at Case Western Reserve University in May 1992. The principal speaker at the conference was Professor V. E. Zakharov who delivered a series of ten lectures outlining the historical and ongoing developments in the field. Some twenty other researchers also made presentations and it is their work which makes up the bulk of this text. Professor Zakharov's opening chapter serves as a general introduction to the other papers, which for the most part are concerned with the application of the theory in various fields. While the word "turbulence" is most often associated with f:l. uid dynamics it is in fact a dominant feature of most systems having a large or infinite number of degrees of freedom. For our purposes we might define turbulence as the chaotic behavior of systems having a large number of degrees of freedom and which are far from thermodynamic equilibrium. Work in field can be broadly divided into two areas: • The theory of the transition from smooth laminar motions to the disordered motions characteristic of turbulence. • Statistical studies of fully developed turbulent systems. In hydrodynamics, work on the transition question dates back to the end of the last century with pioneering contributions by Osborne Reynolds and Lord Rayleigh.
Categories: Science

Wave Turbulence

Wave Turbulence

This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way.

Author: Sergey Nazarenko

Publisher: Springer Science & Business Media

ISBN: 9783642159411

Category: Science

Page: 279

View: 450

Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as “frozen” turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field.
Categories: Science

Advances In Wave Turbulence

Advances In Wave Turbulence

A special emphasis is made upon the links between the theory and experiment. Each of the reviews is devoted to a particular field of application (there is no overlap), or a novel approach or idea.

Author: Victor Shrira

Publisher: World Scientific

ISBN: 9789814520805

Category: Mathematics

Page: 296

View: 319

Wave or weak turbulence is a branch of science concerned with the evolution of random wave fields of all kinds and on all scales, from waves in galaxies to capillary waves on water surface, from waves in nonlinear optics to quantum fluids. In spite of the enormous diversity of wave fields in nature, there is a common conceptual and mathematical core which allows to describe the processes of random wave interactions within the same conceptual paradigm, and in the same language. The development of this core and its links with the applications is the essence of wave turbulence science (WT) which is an established integral part of nonlinear science.The book comprising seven reviews aims at discussing new challenges in WT and perspectives of its development. A special emphasis is made upon the links between the theory and experiment. Each of the reviews is devoted to a particular field of application (there is no overlap), or a novel approach or idea. The reviews cover a variety of applications of WT, including water waves, optical fibers, WT experiments on a metal plate and observations of astrophysical WT.
Categories: Mathematics

On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation

On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation

MR1079519 (91k:76087) [4] A. M. Balk and V. E. Zakharov, Stability of weak-turbulence Kolmogorov spectra, Nonlinear waves and weak turbulence, Amer. Math. Soc. Transl. Ser. 2, vol. 182, Amer. Math. Soc., Providence, RI, 1998, pp. 31–81.

Author: M. Escobedo

Publisher: American Mathematical Soc.

ISBN: 9781470414344

Category: SCIENCE

Page: 107

View: 573

The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.
Categories: SCIENCE

Nonlinear Waves in Fluids Recent Advances and Modern Applications

Nonlinear Waves in Fluids  Recent Advances and Modern Applications

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.

Author: Roger Grimshaw

Publisher: Springer Science & Business Media

ISBN: 9783211380253

Category: Technology & Engineering

Page: 196

View: 292

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.
Categories: Technology & Engineering

Wave Turbulence Under Parametric Excitation

Wave Turbulence Under Parametric Excitation

The present book deals with parametric wave turbulence.

Author: Victor S. L'vov

Publisher: Springer Science & Business Media

ISBN: 9783642752957

Category: Science

Page: 330

View: 239

WAVE TURBULENCE is a state of a system of many simultaneously excited and interacting waves characterized by an energy distribution which is not in any sense close to thermodynamic equilibrium. Such situations in a choppy sea, in a hot plasma, in dielectrics under arise, for example, a powerful laser beam, in magnets placed in a strong microwave field, etc. Among the great variety of physical situations in which wave turbulence arises, it is possible to select two large limiting groups which allow a detailed analysis. The first is fully developed wave turbulence arising when energy pumping and dissipation have essentially different space scales. In this case there is a wide power spectrum of turbulence. This type of turbulence is described in detail e. g. in Zakharov et al. 1 In the second limiting case the scales in which energy pumping and dissipation occur are the same. As a rule, in this case a narrow, almost singular spectrum of turbulence appears which is concentrated near surfaces, curves or even points in k-space. One of the most important, widely investigated and instructive examples of this kind of turbulence is parametric wave turbulence appearing as a result of the evolution of a parametric instability of waves in media under strong external periodic modulation (laser beam, microwave electromagnetic field, etc. ). The present book deals with parametric wave turbulence.
Categories: Science

Nonlinear PDEs in Condensed Matter and Reactive Flows

Nonlinear PDEs in Condensed Matter and Reactive Flows

L'vov, Y. V., R. Binder and A. C. Newell: 1998, Quantum Weak Turbulence with applications to Semiconductor Lasers, Physica D 121, 317-343. 41. Dispersive Nonlinear Waves and Weak Turbulence, AMS Translations Series 2, Vol.

Author: Henri Berestycki

Publisher: Springer Science & Business Media

ISBN: 1402009739

Category: Mathematics

Page: 526

View: 904

Proceedings of the NATO Advanced Study Institute on PDEs in Models of Superfluidity, Superconductivity and Reactive Flows, held in Cargèse, France, from 21 June to 3 July 1999
Categories: Mathematics

Methods in Nonlinear Plasma Theory

Methods in Nonlinear Plasma Theory

WEAK TURBULENCE THEORY OF NONLINEAR WAVE-WAVE INTERACTIONS 13.1 Introduction In situations where the waves are weakly coupled to the particles, i.e., when linear wave—particle and nonlinear wave—particle interactions are sufliciently ...

Author: Ronald Davidson

Publisher: Elsevier

ISBN: 9780323153386

Category: Science

Page: 376

View: 722

Methods in Nonlinear Plasma Theory is from lectures given in graduate classes in both University of Maryland and University of California at Berkeley. To be able to understand fully the contents in this book, the reader is assumed to be a graduate student with background of classical physics and linear plasma waves and instabilities. This text is divided into two major parts. Part I deals with the coherent nonlinear phenomena, while Part II discusses the turbulent nonlinear phenomena. Six chapters comprise Part I, where basic equations and methods are described and discussed. Some of these methods are Vlasov-Maxwell equations and Korteweg-de Vries equation. Part II meanwhile has eight chapters that discuss frameworks and theories for weak plasma turbulence. Specifically, the weak turbulence theory is presented as it is applied to electromagnetic wave-particle interactions, nonlinear wave-wave interactions, and nonlinear wave-particle interactions. This book is a useful reference for students and researchers in the study of classical physics and plasma theory.
Categories: Science

Nonlinear Resonance Analysis

Nonlinear Resonance Analysis

Wave resonances in systems with discrete spectra. In Nonlinear Waves and Weak Turbulence, ed. V. E. Zakharov (AMS Trans. 2, 1998), 95–129. [111] E. Kartashova. Fast computation algorithm for discrete resonances among gravity waves.

Author: Elena Kartashova

Publisher: Cambridge University Press

ISBN: 9781139493086

Category: Science

Page:

View: 759

Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780521763608.
Categories: Science

Proceedings of the 5th International Conference on Applications in Nonlinear Dynamics

Proceedings of the 5th International Conference on Applications in Nonlinear Dynamics

We have reported results of laboratory experiments on nonlinear waves on the surface of a fluid covered by an elastic sheet (where both tension and ... When wave amplitudes are high enough, weak turbulence theory predicts a nonlinear ...

Author: Visarath In

Publisher: Springer

ISBN: 9783030108922

Category: Technology & Engineering

Page: 330

View: 509

This book presents collaborative research presented by experts in the field of nonlinear science provides the reader with contemporary, cutting-edge, research works that bridge the gap between theory and device realizations of nonlinear phenomena. The conference provides a unique forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: chaos gates, social networks, communication, sensors, lasers, molecular motors, biomedical anomalies, and stochastic resonance. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2018) held in Maui, Hawaii, 2018. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.
Categories: Technology & Engineering

Advances in Wave Interaction and Turbulence

Advances in Wave Interaction and Turbulence

The turbulence of weakly nonlinear dispersive waves is studied by numerically integrating a three-parameter one-dimensional model equation. In particular the validity of weak turbulence theory is assessed. The predicted power-law ...

Author: AMS-IMS-SIAM Joint Summer Research Conference on Dispersive Wave Turbulence

Publisher: American Mathematical Soc.

ISBN: 9780821827147

Category: Mathematics

Page: 116

View: 693

We often think of our natural environment as being composed of very many interacting particles, undergoing individual chaotic motions, of which only very coarse averages are perceptible at scales natural to us. However, we could as well think of the world as being made out of individual waves. This is so not just because the distinction between waves and particles becomes rather blurred at the atomic level, but also because even phenomena at much larger scales are better described in terms of waves rather than of particles. It is rare in both fluids and solids to observe energy being carried from one region of space to another by a given set of material particles; much more often, this transfer occurs through chains of particles, neither of them moving much, but each communicating with the next, and hence creating these immaterial objects we call waves.Waves occur at many spatial and temporal scales. Many of these waves have small enough amplitude that they can be approximately described by linear theory. However, the joint effect of large sets of waves is governed by nonlinear interactions which are responsible for huge cascades of energy among very disparate scales. Understanding these energy transfers is crucial in order to determine the response of large systems, such as the atmosphere and the ocean, to external forcings and dissipation mechanisms which act on scales decades apart. The field of wave turbulence attempts to understand the average behavior of large ensembles of waves, subjected to forcing and dissipation at opposite ends of their spectrum. It does so by studying individual mechanisms for energy transfer, such as resonant triads and quartets, and attempting to draw from them effects that should not survive averaging.This book presents the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Dispersive Wave Turbulence held at Mt. Holyoke College (MA). It drew together a group of researchers from many corners of the world, in the context of a perceived renaissance of the field, driven by heated debate about the fundamental mechanism of energy transfer among large sets of waves, as well as by novel applications-and old ones revisited-to the understanding of the natural world. These proceedings reflect the spirit that permeated the conference, that of friendly scientific disagreement and genuine wonder at the rich phenomenology of waves.
Categories: Mathematics

Kolmogorov Spectra of Turbulence I

Kolmogorov Spectra of Turbulence I

This volume is dedicated to developed wave turbulence in different media.

Author: Vladimir E. Zakharov

Publisher: Springer Science & Business Media

ISBN: 9783642500527

Category: Science

Page: 264

View: 322

Since the human organism is itself an open system, we are naturally curious about the behavior of other open systems with fluxes of matter, energy or information. Of the possible open systems, it is those endowed with many degrees of freedom and strongly deviating from equilibrium that are most challenging. A simple but very significant example of such a system is given by developed turbulence in a continuous medium, where we can discern astonishing features of universality. This two-volume monograph deals with the theory of turbulence viewed as a general physical phenomenon. In addition to vortex hydrodynamic turbulence, it considers various cases of wave turbulence in plasmas, magnets, atmosphere, ocean and space. A sound basis for discussion is provided by the concept of cascade turbulence with relay energy transfer over different scales and modes. We shall show how the initial cascade hypothesis turns into an elegant theory yielding the Kolmogorov spectra of turbulence as exact solutions. We shall describe the further development of the theory discussing stability prob lems and modes of Kolmogorov spectra formation, as well as their matching with sources and sinks. This volume is dedicated to developed wave turbulence in different media.
Categories: Science

Nonlinear Stochastic PDEs

Nonlinear Stochastic PDEs

[26] D. SURGAILIS, W.A. WoyczYNSKI, Long range prediction and scaling limits for statistical solutions of the Burgers' equation, in Nonlinear Waves and Weak Turbulence, edited by N. Fitzmaurice et al. (Birkhaüser, Boston, 1993), pp.

Author: Tadahisa Funaki

Publisher: Springer Science & Business Media

ISBN: 9781461384687

Category: Mathematics

Page: 312

View: 908

This IMA Volume in Mathematics and its Applications NONLINEAR STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS' TURBULENCE is based on the proceedings of the period of concentration on Stochas tic Methods for Nonlinear PDEs which was an integral part of the 1993- 94 IMA program on "Emerging Applications of Probability." We thank Tadahisa Funaki and Wojbor A. Woyczynski for organizing this meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foundation and the Army Research Office, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. xiii PREFACE A workshop on Nonlinear Stochastic Partial Differential Equations was held during the week of March 21 at the Institute for Mathematics and Its Applications at the University of Minnesota. It was part of the Special Year on Emerging Applications of Probability program put together by an organizing committee chaired by J. Michael Steele. The selection of topics reflected personal interests of the organizers with two areas of emphasis: the hydrodynamic limit problems and Burgers' turbulence and related models. The talks and the papers appearing in this volume reflect a number of research directions that are currently pursued in these areas.
Categories: Mathematics

Optical Remote Sensing of Ocean Hydrodynamics

Optical Remote Sensing of Ocean Hydrodynamics

... weak wave turbulence theory (WT) dealing with stochastic nonlinear wave fields in incompressible turbulent fluid. ... of energy among turbulent, weakly nonlinear, dispersive waves in plasma and fluid (Kadomtsev 1965; Zakharov et al.

Author: Victor Raizer

Publisher: CRC Press

ISBN: 9781351119160

Category: Technology & Engineering

Page: 280

View: 721

Optical Remote Sensing is one of the main technologies used in sea surface monitoring. Optical Remote Sensing of Ocean Hydrodynamics investigates and demonstrates capabilities of optical remote sensing technology for enhanced observations and detection of ocean environments. It provides extensive knowledge of physical principles and capabilities of optical observations of the oceans at high spatial resolution, 1-4m, and on the observations of surface wave hydrodynamic processes. It also describes the implementation of spectral-statistical and fusion algorithms for analyses of multispectral optical databases and establishes physics-based criteria for detection of complex wave phenomena and hydrodynamic disturbances including assessment and management of optical databases. This book explains the physical principles of high-resolution optical imagery of the ocean surface, discusses for the first time the capabilities of observing hydrodynamic processes and events, and emphasizes the integration of optical measurements and enhanced data analysis. It also covers both the assessment and the interpretation of dynamic multispectral optical databases and includes applications for advanced studies and nonacoustic detection. This book is an invaluable resource for researches, industry professionals, engineers, and students working on cross-disciplinary problems in ocean hydrodynamics, optical remote sensing of the ocean and sea surface remote sensing. Readers in the fields of geosciences and remote sensing, applied physics, oceanography, satellite observation technology, and optical engineering will learn the theory and practice of optical interactions with the ocean.
Categories: Technology & Engineering

Nonlinear MHD Waves and Turbulence

Nonlinear MHD Waves and Turbulence

This volume, which includes expanded versions of oral contributions pre sented at this meeting, should be of interest for a large community of resear chers in space plasmas and nonlinear sciences.

Author: Thierry Passot

Publisher: Springer

ISBN: 9783540470380

Category: Science

Page: 385

View: 125

The workshop "Nonhnear MHD Waves and Turbulence" was held at the - servatoire de Nice, December 1-4, 1998 and brought together an international group of experts in plasma physics, fluid dynamics and applied mathematics. The aim of the meeting was to survey the current knowledge on two main topics: (i) propagation of plasma waves (like Alfven, whistler or ion-acoustic waves), their instabilities and the development of a nonlinear dynamics lea ding to solitonic structures, wave collapse or weak turbulence; (ii) turbulence in magnetohydrodynamic flows and its reduced description in the presence of a strong ambient magnetic fleld. As is well known, both aspects play an important role in various geophysical or astrophysical media such as the - gnetospheres of planets, the heliosphere, the solar wind, the solar corona, the interplanetary and interstellar media, etc. This volume, which includes expanded versions of oral contributions pre sented at this meeting, should be of interest for a large community of resear chers in space plasmas and nonlinear sciences. Special effort was made to put the new results into perspective and to provide a detailed literature review. A main motivation was the attempt to relate more closely the theoretical un derstanding of MHD waves and turbulence (both weak and strong) with the most recent observations in space plasmas. Some papers also bring interesting new insights into the evolution of hydrodynamic or magnetohydrodynamic structures, based on systematic asymptotic methods.
Categories: Science

Nonlinear Instability of Nonparallel Flows

Nonlinear Instability of Nonparallel Flows

D. Wundrow, L. S. Hultgren, and M. E. Goldstein, ”Interaction of oblique instability waves with a nonlinear plane wave. ... Oblique instability waves in nearly parallel shear flows,” in Nonlinear Waves and Weak Turbulence with ...

Author: S.P. Lin

Publisher: Springer Science & Business Media

ISBN: 9783642850844

Category: Science

Page: 473

View: 304

The IUTAM Symposium on Nonlinear Instability of Nonparallel Flows was held at Clarkson University, Potsdam, NY 13699-5725, USA from 26 to 31 July 1993. It consisted of 9 general speeches, 35 lectures and 15 poster-seminar presentations. The papers were grouped in fairly focused sessions on boundary layers, shear flows, vortices, wakes, nonlinear waves and jets. The symposium was fol lowed by a workshop in which the subject matter discussed was sum marized and some further work for future investigation was recom mended. The highlights of the workshop will be reported elsewhere. In this book many of the papers that describe the ideas presented at the symposium are collected to provide a reference for researchers in charting the future course of their studies in the area of nonlinear instability of nonparallel flows. The papers in this book are grouped under the following headings: • Boundary layers and shear flows • Compressibility and thermal effects • Vortices and wakes • Nonlinear waves and jets In the lead paper ofthis book M. E. Goldstein describes an asymp totic theory of nonlinear interaction between two spatially growing oblique waves on nonparallel boundary and free-shear layers. The wave interaction originates from the nonlinear critical layer and is responsive to weakly nonparallel effects. The theory results in a sys tem of integral differential equations which appear to be relevant near the upper branch of the neutral curve.
Categories: Science