Morkovin hypothesis and the modeling of wall-bounded compressible turbulent flows

Modeling of compressible wall-bounded turbulent flows relies on the hypothesis of Morkovin, who suggested that compressibility effects on turbulence could be accounted for by the mean density variations alone. This hypothesis has been shown to yield good results for the mean velocity and mean temperature fields when the incompressible turbulence models are extended directly to calculate compressible turbulent boundary layers. However, its applicability for the turbulence field has been less closely scrutinized. The reason is the lack of sufficiently detailed compressible turbulence data for comparison. Such data are now becoming available. Therefore, the purpose here is to assess the applicability of the Morkovin hypothesis to the turbulence field using direct numerical simulation data of a supersonic, flat plate boundary layer A near-wall Reynolds-stress closure based on a quasi-linear pressure-strain model is used to calculate this supersonic, boundary-layer flow. Comparisons between calculations and direct numerical simulation data show that the Morkovin hypothesis is just as applicable for the turbulence field and there is a dynamic similarity between the near-wall turbulence field of an incompressible and a compressible wall-bounded turbulent flow, In addition, the validation of this model is reported for compressible flow calculations covering a wide range of Mach numbers with adiabatic and constant-temperature wall boundary conditions, These results show that the model yields good predictions of Bat-plate turbulent boundary layers up to a Mach number of 10.31.