Compressible mixing layer: linear theory and direct simulation

Results from linear stability analysis are presented for a wide variety of mixing layers, including low-speed layers with variable density and high Mach number mixing layers. The linear amplification predicts correctly the experimentally observed trends in growth rate that are due to velocity ratio, density ratio, and Mach number, provided that the spatial theory is used and the mean flow is a computed solution of the compressible boundary-layer equations. It is found that three-dimensional modes are dominant in the high-speed mixing layer above a convective Mach number of 0.6, and a simple relationship is proposed that approximately describes the orientation of these waves. Direct numerical simulations of the compressible Navier-Stokes equations are used to show the reduced growth rate that is due to increasing Mach number. From consideration of the compressible vorticity equation, it is found that the dominant physics controlling the nonlinear roll-up of vortices in the high-speed mixing layer is contained in an elementary form in the linear eigenfunctions. It is concluded that the linear theory can be very useful for investigating the physics of free shear layers and predicting the growth rate of the developed plane mixing laye