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Birkhäuser

Nonlinear Waves and Weak Turbulence

with Applications in Oceanography and Condensed Matter Physics

  • Book
  • © 1993

Overview

Editors:
  1. N. Fitzmaurice

    1. Center for Stochastic and Chaotic Processes, Case Western Reserve University, Cleveland, USA

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  2. D. Gurarie

    1. Center for Stochastic and Chaotic Processes, Case Western Reserve University, Cleveland, USA

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  3. F. McCaughan

    1. Center for Stochastic and Chaotic Processes, Case Western Reserve University, Cleveland, USA

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  4. W. A. Woyczyński

    1. Center for Stochastic and Chaotic Processes, Case Western Reserve University, Cleveland, USA

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 11)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xvi
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  3. Flow Stability

    1. Front Matter

      Pages 145-145
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    2. Chaotic Motion in Unsteady Vortical Flows

      • J. J. Li
      Pages 147-158

    3. Oblique Instability Waves in Nearly Parallel Shear Flows

      • M. E. Goldstein, S. S. Lee
      Pages 159-177

    4. Modeling Turbulence by Systems of Coupled Gyrostats

      • A. Gluhovsky
      Pages 179-197

  4. Nonlinear Waves in Condensed Matter

    1. Front Matter

      Pages 198-198
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    2. Soliton Turbulence in Nonlinear Optical Phenomena

      • A. B. Aceves
      Pages 199-210

    3. Soliton Propagation in Optical Fibers with Random Parameters

      • D. Gurarie, P. Mishnayevskiy
      Pages 211-225

    4. Collision Dynamics of Solitary Waves in Nematic Liquid Crystals

      • X. Y. Wang, S. M. Sun, S. Q. Wang
      Pages 227-236

  5. Statistical Problems

    1. Front Matter

      Pages 237-237
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    2. Statistical Mechanics, Euler’s Equation, and Jupiter’s Red Spot

      • P. B. Weichman
      Pages 239-277

    3. Stochastic Burgers’ Flows

      • W. A. Woyczyński
      Pages 279-311
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Keywords

About this book

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.

Editors and Affiliations

  • Center for Stochastic and Chaotic Processes, Case Western Reserve University, Cleveland, USA

    N. Fitzmaurice, D. Gurarie, F. McCaughan, W. A. Woyczyński

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