Compressibility effects due to turbulent fluctuations

Abstract

This paper deals with intrinsic effects of compressibility, i.e. with dilatation fluctuations in response to pressure fluctuations. Three different types of turbulent flows are considered in more detail: homogeneous turbulent shear flow, wall-bounded turbulent shear flow and shock/turbulence interaction. A survey of the present knowledge in this field, mainly based on DNS data, is given. Using the linear inviscid perturbation equations a direct link between fluctuations of dilatation and of velocity in the direction of mean shear is presented for homogeneous shear flow. This relation might form the basis for a more universal pressure-dilatation model. It is conjectured that the insignificance of intrinsic compressibility effects in wall-bounded supersonic shear flow is mainly due to the impermeability constraint of the wall. To this end, a linear stability analysis of supersonic channel flow along cooled, but permeable walls has been performed based on Coleman et al.'s [5] mean flow data. It shows an increase in the moduli of eigenfunctions related to compressibility, like pressure, and in moduli of quantities derived from eigenfunctions such as ‘pressure dilatation’ and squared dilatation. Although these results do not prove our hypothesis they provide hints in this direction. Shock/turbulence interaction is viewed as a source of compressibility. Former DNS data of Hannappel and Friedrich [10] for shock/isotropic turbulence interaction showing the effect of compressibility on the amplification of fluctuations are interpreted based on linear perturbation equations.