Non-linear instability of compressible mixing layers

In this paper, we study the non-linear spatial stability behavior of compressible mising layers, based on Landau's pert, urbation series and Tollmien-Schlichting waves. It is wellknown from linear theory that, for spatially-developing perturbation waves, whether the disturbance is amplified, neutral, or damped is dependent on the imaginary part of the complex wavenumber, which could be negative, zero, or positive. The non-linear theory goes further and predicts the possibility for amplified wave to develop into supercritical equilibrium state and the possibility for damped waves to diverge into subcritical instability. The present study deals with the first of these possible situations since the non-linear behavior of the most amplified wave is being studied. It is found that the constants in Landau's series determine the existence of supercritical equilibrium state. If it exists, the constants will also determine the value of the equilibrium amplitude. If it does not exist, the constants will give the location of the singularity. We carry out a study of the influence of compressibility on the existence of supercritical equilibrium. The resutls show that supercritical equilibrium exists at relatively low Mach numbers, while singularity is more likely at high Mach numbers.