The Statistical Theory of Diffusion by Turbulent Eddies

Abstract

In the statistical theory of turbulence consideration is given to the frequency distributions, correlation coefficients, and other statistical properties of the irregular random motions and fluctuations that occur in a turbulent fluid. The diffusion of particles is known to depend upon the Lagrangian correlation coefficient R_ξ defined as the correlation between the velocity of a fluid particle at any instant and that of the same particle after a time interval ξ. However, most modern turbulence theory and practical experiments are based upon the Eulerian coordinate system in which the scale and intensity of turbulence are expressed in terms of the fluctuations at fixed points. Application of probability theory suggests that the rate of diffusion of particles can be related to the Eulerian correlations. Some of the most important unsolved problems of statistical turbulence theory are discussed as well as the difficulties in applying the theory to diffusion in the atmosphere.