Klyatskin V.I. Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 2: Coherent Phenomena in Stochastic Dynamic Systems

Springer, 2015. - 491 pp.
In some cases, certain coherent structures can exist in stochastic dynamic systems almost in every particular realization of random parameters describing these systems. Dynamic localization in one-dimensional dynamic systems, vortex genesis (vortex production) in hydrodynamic flows, and phenomenon of clustering of various fields in random media (i.e., appearance of small regions with enhanced content of the field against the nearly vanishing background of this field in the remaining portion of space) are examples of such structure formation. The general methodology presented in Volume 1 is used in Volume 2 to expound the theory of these phenomena in some specific fields of stochastic science, among which are hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics. The material of this volume includes particle and field clustering in the cases of scalar (density field) and vector (magnetic field) passive tracers in a random velocity field, dynamic localization of plane waves in layered random media, as well as monochromatic wave propagation and caustic structure formation in random media in terms of the scalar parabolic equation.Equilibrium Distributions for Hydrodynamic Flows.
Rogue Waves as an Object of Statistical Topography.
Main Features of the Problem and Determining Equations.
Statistical Description of Inertialess Tracer Diffusion and Clustering.
Integral One-Point Statistical Characteristics of Density Field.
Tracer Diffusion and Clustering in Random Nondivergent Flows.
Diffusion and Clustering of Settling Tracer in Random Flows.
Probabilistic Description of Magnetic Field in Random Velocity Field.
Probabilistic Description of Magnetic Energy in Random Velocity Field.
Integral One-Point Statistical Characteristics of Magnetic Field.
General Remarks.
Statistics of Scattered Field at Layer Boundaries.
Statistical Description of a Wavefield in Random Medium.
Eigenvalue and Eigenfunction Statistics.
Multidimensional Wave Problems in Layered Random Media.
Two-Layer Model of the Medium.
Method of Stochastic Equation.
Geometrical Optics Approximation in Randomly Inhomogeneous Media.
Method of Path Integral.
Caustic Structure of Wavefield in Random Media.