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A modeled transport equation for the joint probability density function (pdf) of the velocities and a scalar has been 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 modeled. Five different models are evaluated; four of these are based on the Langevin equation for the 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 modeling is included to account for intermittency. The resulting modeled pdf equation is 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 modeling.
Haworth et al. (Wed,) studied this question.