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

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.