Main Features of the Problem and Determining Equations
One of concerns of statistical hydrodynamics is the problem on spreading a passive tracer in random velocity field, which is of significant importance in ecological problems of tracer diffusion in Earth’s atmosphere and oceans [50, 239, 258, 263, 268], in the diffusion in porous media , and in the problem on the large-scale mass distribution at the last stage of the formation of universe . This problem is extensively investigated beginning from pioneer works [23, 24, 311, 312]. Further, many researchers obtained different equations for describing passive tracer statistical characteristics in both Eulerian and Lagrangian descriptions. Derivation of such type equations (for both moment functions of the tracer concentration field and tracer concentration probability density) for different models of fluctuating parameters in different approximations and their analysis was actively continued even in the last decade.
KeywordsIndicator Function Moment Function Liouville Equation Particle Number Density Lagrangian Description
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