Appendix: Final Form of the Algebraic Mass Ux Model

The turbulent mass ux, or equivalently the uctuating Favre velocity mean, appears in the rst and second moment equations of compressible k " and Reynolds stress closures. Mathematically it is the di erence between the unweighted and density-weighted averages of the velocity eld and is therefore a measure of the e ects of compressibility through variations in density. It appears to be fundamental to an inhomogeneous compressible turbulence, in which it characterizes the e ects of the mean density gradients, in the same way the anisotropy tensor characterizes the e ects of the mean velocity gradients. An evolution equation for the turbulent mass ux is derived. A truncation of this equation produces an algebraic expression for the mass ux. The mass ux is found to be proportional to the mean density gradients with a tensor eddy-viscosity that depends on both the mean deformation and the Reynolds stresses. The model is tested in a wall bounded DNS at Mach 4.5 with notable results. This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681.