Application of the velocity-dissipation probability density function model to inhomogeneous turbulent flows

Recently Pope and Chen [Phys. Fluids A 2, 1437 (1990)] developed a turbulence model based on the one-point Eulerian joint probability density function (pdf) of velocity and dissipation. The modeling is performed by constructing stochastic processes for the velocity and dissipation following fluid particles. In the original work, these models were constructed by reference to the known statistics of homogenous turbulence, and the applicability of the model was restricted to this narrow class of flows. In this paper the model is extended to inhomogeneous flows, and calculations are presented to demonstrate aspects of the model’s performance. The model equation admits a similarity solution corresponding to the log-law region of the turbulent boundary layer, and the principal statistics obtained from this solution are in good agreement with experimental data. Application of the model to the momentumless wake and to the plane mixing layer demonstrate its ability to represent turbulent/nonturbulent intermittency in these free flows: in the intermittent regions, the pdf of dissipation is bimodal, with a spike at zero corresponding to nonturbulent fluid. Fluid-particle paths in the turbulent mixing layer obtained from the model correspond to large-scale coherent motions, rather than to the small-scale incoherent motion characteristic of diffusive transport.