Diffusion in a Field of Homogeneous Turbulence. I. Eulerian Analysis

Abstract

This paper considers the mechanism of diffusion in the simple case of a homogeneous field of turbulence. It is shown to be useful to distinguish between diffusion from fixed and moving centres, and only the former is considered here. The diffusion of a cloud of marked fluid particles about the average position of their centre is known when the statistical behaviour of a single fluid particle is known. Theory shows that the dispersion of a fluid particle about its initial position increases first as the square of the time of flight, t, then more slowly, and eventually increases linearly in t. Several different experiments have shown that the probability distribution of the displacement of a fluid particle is normal for all values of the time of flight. As a consequence of these two facts, it is possible to represent the diffusion by a differential equation of the heat-conduction type, with a diffusion coefficient which initially increases with t and eventually becomes constant. Some consequences of the analysis are presented. Part II of this paper will discuss the more important case of diffusion about a moving centre.