On the Probability-Density Function of Concentration in Turbulent Diffusion

Abstract

The probability dΓ, that at location and time t contaminant fluid with concentration between Γ and Γ + dΓwill be encountered, is investigated. When a finite quantity of contaminant material is released in a large-Reynolds-number flow, and while the contaminant cloud so formed remains of smaller dimension than the energy containing scales of turbulent motion, it is argued that will be of self-similar form over the range of Γ that is indicative of values in the strands of contaminant fluid of which the cloud is comprised. A nondimensional stringiness factor S(t) is defined, using , as a measure of the extent to which contaminant material has been pulled out by the convective turbulent motion into long threads. S(t) is shown to relate the average of the median value of concentration throughout each realization of the cloud to the ensemble-average concentration . It is suggested that many of the results of the paper apply in a more general category of diffusion problems, and some experimental results are reviewed.