Description of Turbulence in Terms of Lagrangian Variables

Publisher Summary This chapter reviews that the method of describing turbulence in terms of Lagrangian variables is in giving statistical characteristics of the state of an “indicator” system. The state of each indicator is determined by its coordinate x and the velocity v. The consideration of the statistical characteristics of the track of a single indicator may present valuable information on the properties of the flow in the form of a distribution function φ(x, v). The chapter discusses that it makes it possible to obtain all one-point characteristics of turbulence and some characteristics of turbulent diffusion also. The description of the flow with two indicators is similar and leads to the consideration of a double-distribution function and of two-point characteristics of turbulence related with it. The conditional distribution function φT(x, v) is the principal characteristic of the motion in Lagrangian variables, such as the probability of the selected particle, which at the initial moment has the coordinate xo and the velocity vo, having after a certain period of time T the coordinate x and the velocity v.