Statistical Approach to Diffusion of a Passive Scalar in Homogeneous Turbulence

Abstract

Fluctuation of a passive scalar in homogeneous turbulence with known statistics is analysed by means of a statistical method (A. Yoshizawa: J. Phys. Soc. Jpn. 45 (1978) 1734) developed in the study of the small-scale structure of the velocity field. A Galilean transformation based on the velocity of big eddies is applied to the diffusion equation for a passive scalar in order to remove their convection effect. The equation thus found is combined with the direct-interaction formalism, and the −5⁄3 power law for the spectrum of the mean-squared scalar fluctuation is derived in good agreement with experimental measurements.