The velocity-dissipation probability density function model for turbulent flows

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Abstract
In probability density function (pdf) methods, statistics of inhomogeneous turbulent flow fields are calculated by solving a modeled transport equation for a one‐point joint probability density function. The method based on the joint pdf of velocity and fluid compositions is particularly successful since the most important processes—convection and reaction—do not have to be modeled. However, this joint pdf contains no length‐scale or time‐scale information that can be used in the modeling of other processes. This deficiency can be remedied by considering the joint pdf of velocity, dissipation, and composition. In this paper, by reference to the known properties of homogeneous turbulence, a modeled equation for the joint pdf of velocity and dissipation is developed. This is achieved by constructing stochastic models for the velocity and dissipation following a fluid particle.