Nonlinear Waves and Weak Turbulence

1. Front Matter

   Pages i-xvi

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2. Hamiltonian Systems

   1. Front Matter

      Pages 1-1

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   2. Turbulence in Hamiltonian Systems

      • V. V. Zakharov

      Pages 3-18

   3. Revised Universality Concept in the Theory of Turbulence

      • G. E. Falkovich

      Pages 19-44

   4. Wave Spectra of Developed Seas

      • R. E. Glazman

      Pages 45-68

   5. Gravity Waves in the Large Scales of the Atmosphere

      • J. Herring

      Pages 69-82

   6. Physical Applications of Wave Turbulence: Wind Waves and Classical Collective Modes

      • A. Larraza

      Pages 83-95

   7. Strong and Weak Turbulence for Gravity Waves and The Cubic Schrödinger Equation

      • H. H. Shen

      Pages 97-120

   8. Hidden Symmetries of Hamiltonian Systems Over Holomorphic Curves

      • S. J. Alber

      Pages 121-144

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

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.

• Chaos
• Schrödinger equation
• Soliton
• calculus
• digital elevation model
• maximum principle
• mechanics
• model
• modeling
• statistics
• thermodynamics

• 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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