A pdf modeling study of self-similar turbulent free shear flows.

A modelled transport equation for the joint probability density function (pdf) of the velocities and a scalar was solved numerically for four self-similar turbulent free shear flows: the plane mixing layer, the plane wake, the plane jet and the axisymmetric jet. In the pdf equation, convection is treated exactly but the effects of viscosity, molecular diffusion and the fluctuating pressure gradient have to be modelled. Five different models were evaluated; four of these are based on the Langevin equation for fluid particle velocities and the fifth is a particle pair interaction model. In each case, a stochastic mixing model represents the effects of molecular diffusion and conditional modelling is included to account for intermittency. The resulting modelled probability density function equation was solved by a Monte Carlo method. Calculated spreading rates and profiles of the mean velocity and Reynolds stresses show generally good agreement with experimental data for three of the five velocity models. However, discrepancies between the calculated and measured intermittency factor profiles, in particular for the plane mixing layer, reveal weaknesses in the conditional modelling. (A)