A numerical study of inviscid, supersonic mixing layers

The purpose of this research is to understand the physical processes associated with turbulent mixing in supersonic shear layers. Specifically, the evolution of instabilities in two and three-dimensional, confined and unconfined, temporal shear layers are studied. Both linear stability theory and direct numerical simulation are used. For the two-dimensional, supersonic, confined layer, two distinct modes of instability are found, a symmetric and an asymmetric mode. In both cases the instability grows nonlinearly with large amplitude disturbances that never roll up like the classical Kelvin-Helmholtz instability. Another mode of instability is found for the confined, transonic layer where a higher mode is excited from a nonlinear interaction of the walls with the fundamental mode. The most unstable modes for the three-dimensional layer at supersonic relative Mach numbers is purely three-dimensional, i.e. oblique to the flow direction