Sandham, N.D. and Reynolds, W.C.
Compressible mixing layer: linear theory and direct simulation.
AIAA Journal, 28, (4), .
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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 layer
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