Probability Distributions of Passive Tracers in Randomly Moving Media

Abstract

The main goal of the present chapter is to investigate probabilistic and spatiotemporal characteristics of the passive tracer in a randomly moving medium with random velocity field ${\varvec{v}}({\varvec{x}}, t)$. Both, the case of compressible, and of incompressible $({{\varvec{\nabla }}}\cdot {\varvec{v}}\equiv 0)$ media will be considered. The material is based on the authors’ paper [1]. In the previous chapter, we have investigated the passive tracer transport in randomly moving media governed by a simplified hydrodynamic model of Burgers turbulence. The full program of such investigation should include prior recovery of the statistical properties of the velocity field ${\varvec{v}}({\varvec{x}}, t)$ satisfying fully nonlinear equations of the hydrodynamic type such as the Navier–Stokes equation for an incompressible fluid, which however, is beyond the scope of this book.