Morkovin Hypothesis and the Modeling of Wall-Bounded Compressible Turbulent Flows

Modelingofcompressiblewall-boundedturbulente owsreliesonthehypothesisofMorkovin,who suggestedthat 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 e elds when the incompressible turbulence models are extended directly to calculate compressible turbulent boundary layers. However, its applicability for the turbulence e eld has been less closely scrutinized. The reason is the lack of sufe ciently 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 e eld using direct numerical simulation data of a supersonic, e at plate boundary layer. A near-wall Reynolds-stress closure based on a quasi-linear pressure-strain model is used to calculatethis supersonic, boundary-layer e ow. Comparisons between calculations and direct numerical simulation data show that the Morkovin hypothesis is just as applicable for the turbulence e eld and there is a dynamic similarity between the near-wall turbulence e eld of an incompressible and a compressible wall-bounded turbulent e ow. In addition, the validation of this model is reported for compressible e ow 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 e at-plate turbulent boundary layers up to a Mach number of 10.31.