The structure of the probability density function of concentration in turbulent diffusion
Abstract
Recognizing that ensemble mean quantities are never observed in a single experiment, the authors have recently studied the variation with position and time of certain statistical properties associated with diffusing contaminant by first examining the separate realizations forming the ensemble. This approach is currently being used in an investigation of the probability density function of concentration, and this paper presents some of the results so far obtained. The ways in which random advection, molecular diffusion and finite cloud size influence the probability density function are discussed qualitatively, and this discussion is illustrated by some exact solutions obtained when the velocity field is a uniform strain with randomly oriented principal axes. For this velocity field, initially small spherical blobs of contaminant are deformed into threads or sheets, and the paper concludes with a discussion of how the probability density function in more realistic velocity fields might be obtained by regarding the cloud (or plume) of contaminant as constituted of a random collection of connected sheets or threads. In this final part of the paper, reference is made to the problem of predicting the likelihood of having flammable mixtures in a jet of methane surrounded by air.
 Publication:

American Institute of Aeronautics and Astronautics
 Pub Date:
 July 1980
 Bibcode:
 1980fpdy.confQ....C
 Keywords:

 Advection;
 Diffusion Theory;
 Molecular Diffusion;
 Probability Density Functions;
 Statistical Analysis;
 Turbulent Diffusion;
 Density Distribution;
 Flow Theory;
 Gas Mixtures;
 Maximum Likelihood Estimates;
 Methane;
 Random Processes;
 Statistical Mechanics;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer