Kolmogorov Spectra of Turbulence I: Wave Turbulence - Softcover

Inhaltsangabe

0. Introduction.- 1. Equations of Motion and the Hamiltonian Formalism.- 1.1 The Hamiltonian Formalism for Waves in Continuous Media.- 1.1.1 The Hamiltonian in Normal Variables.- 1.1.2 Interaction Hamiltonian for Weak Nonlinearity.- 1.1.3 Dynamic Perturbation Theory. Elimination of Nonresonant Terms.- 1.1.4 Dimensional Analysis of the Hamiltonian Coefficients.- 1.2 The Hamiltonian Formalism in Hydrodynamics.- 1.2.1 Clebsh Variables for Ideal Hydrodynamics.- 1.2.2 Vortex Motion in Incompressible Fluids.- 1.2.3 Sound in Continuous Media.- 1.2.4 Interaction of Vortex and Potential Motions in Compressible Fluids.- 1.2.5 Waves on Fluid Surfaces.- 1.3 Hydrodynamic-Type Systems.- 1.3.1 Langmuir and Ion-Sound Waves in Plasma.- 1.3.2 Atmospheric Rossby Waves and Drift Waves in Inhomogeneous Magnetized Plasmas.- 1.4 Spin Waves.- 1.4.1 Magnetic Order, Energy and Equations of Motion.- 1.4.2 Canonical Variables.- 1.4.3 The Hamiltonian of a Heisenberg Ferromagnet.- 1.4.4 The Hamiltonian of Antiferromagnets.- 1.5 Universal Models.- 1.5.1 Nonlinear Schrödinger Equation for Envelopes.- 1.5.2 Kadomtsev-Petviashvili Equation for Weakly Dispersive Waves.- 1.5.3 Interaction of Three Wave Packets.- 2. Statistical Description of Weak Wave Turbulence.- 2.1 Kinetic Wave Equation.- 2.1.1 Equations of Motion.- 2.1.2 Transition to the Statistical Description.- 2.1.3 The Three-Wave Kinetic Equation.- 2.1.4 Applicability Criterion of the Three-Wave Kinetic Equation (KE).- 2.1.5 The Four-Wave Kinetic Equation.- 2.1.6 The Quantum Kinetic Equation.- 2.2 General Properties of Kinetic Wave Equations.- 2.2.1 Conservation Laws.- 2.2.2 Boltzmann's H-Theorem and Thermodynamic Equilibrium.- 2.2.3 Stationary Nonequilibrium Distributions.- 3. Stationary Spectra of Weak Wave Turbulence.- 3.1 Kolmogorov Spectra of Weak Turbulence in Scale-Invariant Isotropic Media.- 3.1.1 Dimensional Estimations and Self-Similarity Analysis.- 3.1.2 Exact Stationary Solutions of the Three-Wave Kinetic Equation.- 3.1.3 Exact Stationary Solutions for the Four-Wave Kinetic Equations.- 3.1.4 Exact Power Solutions of the Boltzmann Equation..- 3.2 Kolmogorov Spectra of Weak Turbulence in Nearly Scale-Invariant Media.- 3.2.1 Weak Acoustic Turbulence.- 3.2.2 Media with Two Types of Interacting Waves.- 3.3 Kolmogorov Spectra of Weak Turbulence in Anisotropic Media.- 3.3.1 Stationary Power Solutions.- 3.3.2 Fluxes of Integrals of Motion and Families of Anisotropic Power Solutions.- 3.4 Matching Kolmogorov Distributions with Pumping and Damping Regions.- 3.4.1 Matching with the Wave Source.- 3.4.2 Influence of Dissipation.- 4. The Stability Problem and Kolmogorov Spectra.- 4.1 The Linearized Kinetic Equation and Neutrally Stable Modes.- 4.1.1 The Linearized Collision Term.- 4.1.2 General Stationary Solutions and Neutrally Stable Modes.- 4.2 Stability Problem for Kolmogorov Spectra of Weak Turbulence.- 4.2.1 Perturbation of the Kolmogorov Spectrum.- 4.2.2 Behavior of Kolmogorov-Like Turbulent Distributions. Stability Criterion.- 4.2.3 Physical Examples.- 4.3 Nonstationary Processes and the Formation of Kolmogorov Spectra.- 4.3.1 Analysis of Self-Similar Substitutions.- 4.3.2 Method of Moments.- 4.3.3 Numerical Simulations.- 5. Physical Applications.- 5.1 Weak Acoustic Turbulence.- 5.1.1 Three-Dimensional Acoustics with Positive Dispersion: Magnetic Sound and Phonons in Helium.- 5.1.2 Two-Dimensional Acoustics with Positive Dispersion: Gravity-Capillary Waves on Shallow Water and Waves in Flaky Media.- 5.1.3 Nondecay Acoustic Turbulence: Ion Sound, Gravity Waves on Shallow Water and Inertio-Gravity Waves.- 5.2 Wave Turbulence on Water Surfaces.- 5.2.1 Capillary Waves on Deep Water.- 5.2.2 Gravity Waves on Deep Water.- 5.2.3 Capillary Waves on Shallow Fluids.- 5.3 Turbulence Spectra in Plasmas, Solids, and the Atmosphere.- 5.3.1 Langmuir Turbulence in Isotropic Plasmas.- 5.3.2 Optical Turbulence in Nonlinear Dielectrics and Turbulence of Envelopes.- 5.3.3 Spin Wave Turbulence in Magnetic Dielectrics

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