Numerical Study of Spatially-Developing Supersonic Turbulent Shear Layers

Direct Numerical Simulations of a spatially-developing supersonic planar shear layer are conducted for a range of convective Mach numbers (M_c) and velocity parameters (λ) to investigate the combined effects of compressibility and advection on the growth rate and self-similarity of the layer. For all cases considered, self-similarity is reached at far downstream locations. Although the profiles of lower and higher order statistics are very different for different M_c and λ, they all collapse in the self-similar region using our suggested self-similar scaling. The observed numerical trends and profiles are shown to be consistent with the available experimental and numerical results in the literature and are explained through compressible self-similar equations and models. The self-similar normalized density distribution inside the layer is used to explain the effects of compressibility on various flow statistics including the far-field cross-stream velocity on the low-speed side. As the center of the shear layer shifts toward the low-speed side, the asymmetry of the layer, measured by the ratio of thicknesses on the low and high-speed sides, is shown to increase with M_c and λ.