THE STATISTICAL THEORY OF TURBULENCE AND THE PROBLEM OF DIFFUSION IN THE ATMOSPHERE

Abstract

Developments in the statistical theory of turbulence during the past thirty years have been used by a number of investigators studying the problem of eddy diffusion. Taylor has derived a formula for the diffusion of particles from a point source. This formula and its extension by Sutton make use of a Lagrangian correlation coefficient R? defined as the correlation between the velocity of a fluid particle at any instant and that of the same particle after a time interval ?. A more general formula that takes account of the initial distance between the particles is presented here and it is shown that the Taylor formula can be derived as a special case of this formula. An experiment is described where modern radar equipment was used to measure the scatter of a cluster of balloons released simultaneously in the free atmosphere. Questions are raised as to the usefulness of balloon data in obtaining estimates of the rate of diffusion, due to such factors as variable ascension rates of balloons, the change of wind speed and direction with height, and the failure of large balloons to respond to smaller-scale eddies that might contribute considerably to the diffusion of small particles such as smoke.