Dilatation dissipation: The concept and application in modeling compressible mixing layers

In this paper a concept of dilatation dissipation εd for high Reynolds number compressible turbulence is introduced. The concept is predicated on the existence of shocklike structures embedded within energetic turbulent eddies. A parametric expression for εd is found that contains calculable parameters of a turbulent field: turbulence energy and length scale, rms (turbulent) Mach number, and the kurtosis of the fluctuating velocity. The dilatation dissipation is incorporated in a second-order closure model for compressible mixing layers and model predictions of mean and turbulence quantities are presented and, where possible, compared with experiments. It is shown that the model is capable of predicting the reduction of layer growth rates as a function of the convective Mach number Mc in accordance with Papamoschou--Roshko experiments; the computations are also shown to compare well with available measurements of Reynolds stresses at Mc=0.5--0.86. Finally, the physical implications of the new model and results obtained are discussed and compared with other existing explanations of the Mach number effect on mixing layer dynamics