A TIME CONTINUOUS STOCHASTIC MIXING MODEL - DIFFERENTIAL APPROXIMATION OF THE CONCENTRATION PROBABILITY DENSITY-FUNCTION EQUATION AND ITS SOLUTION FOR THE CASE OF HOMOGENEOUS TURBULENCE

This Note presents the results obtained from the theoretical analysis of the continuous stochastic mixing model (CSM model) and its discreti sed counterpart. The CSM model contains an unspecified coefficient xi. When xi is a random variable uniformly distributed in the range [0, 1 ], the CSM model is reduced to the Hsu and Chen (1991) model. Differen tial approximation of the concentration pdf equation corresponding to the discretised CSM model for homogeneous turbulence is derived The an alysis shows that the pdf shape tends to a Gaussian shape only in the case when xi is a deterministic variable. The model is then in agreeme nt with experimental data (Jayesh and Warhaft, 1992).