Some topics in turbulent diffusion

Abstract

Consider a stochastic variable: X(t), which for example denotes the position of a randomly moving fluid particle, with an associated probability density function P(x), with the following properties

$$ P\left( x \right) \geqslant 0,{\text{ }}\int {P\left( x \right)dx = 1} {\text{ }}\overline {X^n } = \int {P\left( x \right)x^n dx.} $$

(5.1)

A stochastic process can in general then be defined as the function: Y(X,t). Note that the function may depend on more than one stochastic variable.