Joel C.A. Vorticity and Turbulence

Springer-Verlag New York, Inc., 1994. 173 р.The Equations of Motion
The Euler and Navier-Stokes Equations
Vorticity Form of the Equations
Discrete Vortex Representations
Magnetization Variables
Fourier Representation for Periodic FlowRandom Flow and Its Spectra
Introduction to Probability Theory
Random Fields
Random Solutions of the Navier-Stokes Equations
Random Fourier Transform of a Homogeneous Flow Field
Brownian Motion and Brownian WalksThe Kolmogorov Theory
The Goals of Turbulence Theory: Universal Equilibrium
Kolmogorov Theory: Dimensional Considerations
The Kolmogorov Spectrum and an Energy Cascade
Fractal Dimension
A First Discussion of IntermittencyEquilibrium Flow in Spectral Variables and in Two Space Dimensions
Statistical Equilibrium
The "Absolute" Statistical Equilibrium in Wave Number Space
The Combinatorial Method: The Approach to Equilibrium and Negative Temperatures
The Onsager Theory and the Joyce-Montgomery Equation
The Continuum Limit and the Role of Invariants
The Approach to Equilibrium, Viscosity, and Inertial Power LawsVortex Stretching
Vortex Lines Stretch
Vortex Filaments
Self-Energy and the Folding of Vortex Filaments
Fractalization and Capacity
Intermittency
Vortex Cross-Sections
Enstrophy and EquilibriumPolymers, Percolation, Renormalization
Spins, Critical Points and Metropolis Flow
Polymers and the Flory Exponent
The Vector-Vector Correlation Exponent for Polymers
Percolation
Polymers and Percolation
Renormalization
The Kosterlitz-Thouless Transition
Vortex Percolation/Л Transition in Three Space DimensionsVortex Equilibria in Three-Dimensional Space
A Vortex Filament Model
Self-Avoiding Filaments of Finite Length
The Limit N — ∞ and the Kolmogorov Exponent
Dynamics of a Vortex Filament: Viscosity and Reconnection
Relation to the A Transition in Superfluids: Denser Suspen- Suspensions of Vortices
Renormalization of Vortex Dynamics in a Turbulent Regime