Modeling the pressure-dilatation correlation

It is generally accepted that pressure dilatation, which is an additional compressibility term in turbulence transport equations, may be important for high speed flows. Recent direct simulations of homogeneous shear turbulence have given concrete evidence that the pressure dilatation is important insofar that it contributes to the reduced growth of turbulent kinetic energy due to compressibility effects. The problem of modeling pressure dilatation is addressed. A component of the pressure dilatation is isolated which exhibits temporal oscillations and, using direct numerical simulations of homogeneous shear turbulence and isotropic turbulence, show that it has a negligible contribution to the evolution of turbulent kinetic energy. Then, an analysis for the case of homogeneous turbulence is performed to obtain a model for the nonoscillatory pressure dilatation. This model algebraically relates the pressure dilatation to quantities traditionally obtained in incompressible turbulence closures. The model is validated by direct comparison with the pressure dilatation data obtained from the simulations.