Compressible Turbulent Shear Layers

It is generally accepted that the direct effects of density fluctuations on turbulence are small if the root-mean-square density fluctuation is small compared with the absolute density: this is Morkovin's hypothesis (Favre 1964, p. 367). This means that the turbulence structure of boundary layers and wakes at free-stream Mach numbers Me less than about 5, and of jets at Mach numbers less than about 1.5, is closely the same as in the corrcsponding constant-density flow. By "turbulence structure" we mean dimensionless properties like correlation coefficients and spectrum shapes: the skin-friction coefficient cf == Tw/tPeU; and other ratios of turbulence quantities to mean flow quantities are greatly affected by the influence of mean density changes on the mean motion. The effect of mean density variations in x or y on the turbulence structure is not covered by Morkovin's hypothesis, but is often negligible at the lower Mach numbers if stream wise pressure gradients are small. Therefore assumptions about turbulence structure that give good results in calculation methods for constant-density /low will, if properly scaled, give good results in compressible boundary layers or wakes for Me 5, say. Basic equations for compressible shear layers are given by Howarth (1953) and Lin (1959). More recent treatments (FavJe 1971, Cebeci & Smith 1974, Rubesin & Rose 1973, Bilger 1975) use "mass-weighted" variables, which remove density iluctuations from the time-averaged equations of motion but not from the turbulence or from the response of measuring instruments (although Laufer, in Birch et aI1972, p. 462, suggests that pitot tubes probably yield mass-averaged velocities). It seems probable that the difference between conventional and mass-weighted averages rises more slowly with Mach number than current errors in measuring either. Of problems 1 The author is grateful for a number of helpful comments or contributions, especialIy