The transport equation for the probability density function of a scalar in turbulent shear flow is analyzed and the closure based on the gradient flux model for the turbulent flux and an integral model for the scalar dissipation term is put forward. The probability density function equation is complemented by a two-equation turbulence model. Application to several shear flows proves the capability of the closure model to determine the probability density function of passive scalars.
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Kollmann et al. (1982) studied this question.
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