The diffusion behind a line source in homogeneous turbulence

Abstract

The theory of turbulent diffusion by continuous movements relates the mean particle diffusion from a fixed source to the Lagrangian velocity correlation function, and measurements of the diffusion of heat behind a thin heated wire in a uniform turbulent flow have been used to compute this correlation, assuming that the processes of diffusion by continuous movements and molecular conduction are statistically independent. A series of measurements both of the mean temperatures and the temperature fluctuations in the wake of a thin heated wire has been made in the uniform turbulent flow behind bi-plane grids, for grid Reynolds numbers between 2700 and 21 000 and within the initial period of decay of the turbulence. In these measurements, the rate of spread of the heat wake was determined in two ways, directly from measurements of the turbulent transport of heat and by numerical differentiation of widths computed from observations of mean temperature. The extent of the accelerated diffusion of heat, which is caused by intensification of the temperature gradients by the turbulent motion, can be computed from the measurements of lateral temperature correlations in the flow, and was found to be comparable with the total diffusion. Both the total diffusion process and the process of accelerated molecular diffusion are very nearly self-preserving during decay in the initial period, with a time scale that varies as the decay time and a velocity scale varying inversely as the square root of the decay time, which is consistent with the observed self-preservation of Eulerian correlations. The rate of spread of the heat wake is simply related to the particle diffusion only for short diffusion times at ordinary Reynolds numbers, and the mean-square particle acceleration can be computed. The results are significantly larger than those found by other workers who have neglected the additional spread of the wake by accelerated molecular diffusion.