Advances in PDF modeling for inhomogeneous turbulent flows

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Abstract
Probability density function (PDF) models which are based on an exact representation of rapidly distorting homogeneous turbulence are applied to a free shear flow, the temporal mixing layer. These velocity wave-vector models were constructed in a previous paper by Van Slooten and Pope [Phys. Fluids 9, 1085 (1997)], but were only tested in cases of homogeneous turbulence. At the edges of free shear flows both turbulent–nonturbulent intermittency and pressure transport are demonstrated to play a significant role in the behavior of the flow. A natural treatment of intermittency is obtained by extending the PDF formulation to include a model for the turbulent frequency following a fluid particle. A model for the pressure transport is also constructed via a scaling analysis. The resulting velocity wave-vector turbulent-frequency PDF model with the pressure transport model yields a good comparison with the available direct numerical simulation data for the temporal shear layer.