I Hamiltonian Systems.- 1 Turbulence in Hamiltonian Systems.- 1.1 Introduction.- 1.2 Some examples.- 1.3 Classical hydrodynamic turbulence.- 1.4 Order from chaos.- 1.5 Bibliography.- 2 Revised Universality Concept in the Turbulence Theory.- 2.1 Steady spectra and their instabilities.- 2.2 Multi-flux spectra.- 2.3 Four-wave case.- 2.4 Turbulence of incompressible fluid.- 2.5 Summary.- 2.6 Bibliography.- 3 Wave Spectra of Developed Seas.- 3.1 Introduction.- 3.2 Buoy observations of developed seas.- 3.3 Shape of the wave spectrum.- 3.4 Spatially inhomogeneous wave field.- 3.5 Effect of energy and action advection.- 3.6 Gravity wave turbulence.- 3.7 Conclusions.- 3.8 Bibliography.- 4 Gravity Waves in the Large Scales of the Atmosphere.- 4.1 Introduction.- 4.2 Stratified vs. 2-D turbulence.- 4.3 Physics of 2-D turbulence.- 4.4 Numerical experiments.- 4.5 Concluding comments.- 4.6 Bibliography.- 5 Physical Applications of Wave Turbulence: Wind Waves and Classical Collective Modes.- 5.1 Introduction.- 5.2 Scaling for wave turbulence.- 5.3 Collective modes.- 5.4 Experimental Perspectives.- 5.5 Bibliography.- 6 Strong and Weak Turbulence for Gravity Waves and the Cubic Schrödinger Equation.- 6.1 Introduction.- 6.2 Gravity waves: Hopf formulation.- 6.3 Statistical steady states.- 6.4 Cubic Schrödinger equation.- 6.5 Rossby waves: statistical steady states Ill.- 6.6 Readability.- 6.7 Conclusion.- 6.8 Bibliography.- 7 Hidden Symmetries of Hamiltonian Systems over Holomorphic Curves.- 7.1 Introduction.- 7.2 Hidden Hamiltonians.- 7.3 Linear Hamiltonian flows.- 7.4 Linear collections of curves.- 7.5 Triangular collections of curves.- 7.6 Multiparameter and discrete systems.- 7.7 Vector bundles of Hamiltonian algebras.- 7.8 Bibliography.- II Flow Stability.- 8 Chaotic Motion in Unsteady Vortical Flows.- 8.1 Introduction.- 8.2 Vortex triplet.- 8.3 Resulting chaotic motion.- 8.4 Concluding remarks.- 8.5 Bibliography.- 9 Oblique Instability Waves in Nearly Parallel Shear Flows.- 9.1 Introduction.- 9.2 Analysis of outer linear flow.- 9.3 Critical layer analysis.- 9.4 Mean flow change.- 9.5 Pure oblique mode interaction.- 9.6 Pure parametric resonance interaction.- 9.7 Parametric resonance.- 9.8 Fully interactive case.- 9.9 Bibliography.- 10 Modeling Turbulence by Systems of Coupled Gyrostats.- 10.1 Introduction.- 10.2 Volterra gyrostat.- 10.3 Coupled gyrostats in GFD problems.- 10.4 Cascade of gyrostats.- 10.5 Conclusion.- 10.6 Bibliography.- III Nonlinear Waves in Condensed Matter.- 11 Soliton Turbulence in Nonlinear Optical Phenomena.- 11.1 Introduction.- 11.2 Governing equations and dynamics.- 11.3 Soliton-like solutions.- 11.4 Bibliography.- 12 Solitons Propagation in Optical Fibers with Random Parameters.- 12.1 Introduction.- 12.2 Hamiltonian structure.- 12.3 Soliton-like solutions.- 12.4 Fokker-Plank equation.- 12.5 Appendix.- 12.6 Bibliography.- 13 Collision Dynamics of Solitary Waves in Nematic Liquid Crystals.- 13.1 Introduction.- 13.2 Collision of walls.- 13.3 Nonlinear diffusion equation.- 13.4 Discussion.- 13.5 Bibliography.- IV Statistical Problems.- 14 Statistical Mechanics, Euler’s Equation, and Jupiter’s Red Spot.- 14.1 Introduction.- 14.2 Vorticity field and Hamiltonian.- 14.3 Thermodynamic formalism.- 14.4 Thermodynamics of the vorticity field.- 14.5 Examples and generalizations.- 14.6 Dressed vorticity corollary.- 14.7 Toy model for Euler equation.- 14.8 Bibliography.- 15 Stochastic Burgers’ Flows.- 15.1 Nondispersive waves.- 15.2 Exact solutions.- 15.3 Propagation of chaos.- 15.4 Scaling limits.- 15.5 Maximum principle.- 15.6 Statistics of shocks.- 15.7 Gravitational instability.- 15.8 Bibliography.- 16 Long Range Prediction and Scaling Limit for Statistical Solutions of the Burgers’ Equation.- 16.1 Introduction.- 16.2 Preliminaries.- 16.3 A general scaling limit result.- 16.4 Shot noise initial data.- 16.5 Non-Gaussian scaling limits.- 16.6 Bibliography.- 17 A Remark on Shocks in Inviscid Burgers’ Turbulence.- 17.1 Introduction.- 17.2 Hausdorff dimension of shock points.- 17.3 Bibliography.
