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, vortexgenesis (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 Coherent Phenomena in Stochastic Dynamic Systems 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.
Author(s): Valery I. Klyatskin (auth.)
Series: Understanding Complex Systems
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: 491
Tags: Complexity; Nonlinear Dynamics; Dynamical Systems and Ergodic Theory; Engineering Fluid Dynamics
Front Matter....Pages 1-16
Front Matter....Pages 1-1
Equilibrium Distributions for Hydrodynamic Flows....Pages 3-14
Rogue Waves as an Object of Statistical Topography....Pages 15-23
Front Matter....Pages 25-25
Main Features of the Problem and Determining Equations....Pages 27-37
Statistical Description of Inertialess Tracer Diffusion and Clustering....Pages 39-78
Integral One-Point Statistical Characteristics of Density Field....Pages 79-88
Tracer Diffusion and Clustering in Random Nondivergent Flows....Pages 89-113
Diffusion and Clustering of Settling Tracer in Random Flows....Pages 115-136
Front Matter....Pages 137-137
Probabilistic Description of Magnetic Field in Random Velocity Field....Pages 139-143
Probabilistic Description of Magnetic Energy in Random Velocity Field....Pages 145-171
Integral One-Point Statistical Characteristics of Magnetic Field....Pages 173-182
Front Matter....Pages 183-183
General Remarks....Pages 185-190
Statistics of Scattered Field at Layer Boundaries....Pages 191-211
Statistical Description of a Wavefield in Random Medium....Pages 213-251
Eigenvalue and Eigenfunction Statistics....Pages 253-260
Multidimensional Wave Problems in Layered Random Media....Pages 261-275
Two-Layer Model of the Medium....Pages 277-286
Front Matter....Pages 287-287
Method of Stochastic Equation....Pages 289-323
Geometrical Optics Approximation in Randomly Inhomogeneous Media....Pages 325-341
Method of Path Integral....Pages 343-361
Caustic Structure of Wavefield in Random Media....Pages 363-371
Back Matter....Pages 373-489
