A study of the stability of the compressible single-stream shear mixing layers is performed by using parabolized stability equations (PSE). Associated high accuracy numerical methods are adopted and developed for the free shear layer to solve the parabolized stability equations effectively, including a sixth order compact scheme, algebraic transformation, gradual boundary conditions, etc. Similar boundary layer equations are solved to obtain more accurate basic flow in the shear layers; initial conditions of disturbances are achieved by solving equations of linear stability theory (LST); the spatial stability of disturbances are resolved through streamwise marching methods. The linear evolutions of disturbances with different frequencies and wave numbers at different Mach numbers and temperature ratios are computed and analyzed. The results demonstrate that, 2D disturbances are most unstable under weak compressibility conditions; 3D disturbances become more unstable than 2D ones with the increase of compressibility and dominate the flow instability; temperature ratio has a stabilizing effect at the upstream area, but destabilizing effect downstream; the streamwise instable area becomes smaller when the frequency becomes higher or when the wave angle becomes larger. The study proves that the PSE methods are effective for the stability analysis of single-stream shear mixing layers.

Key words：

single-stream shear mixing layer; compressibility; linear stability theory; parabolized stability equation; compact scheme