Nonlinear stability of subsonic mixing layers with symmetric temperature variations

The nonlinear evolution of stability waves in mixing layers of a perfect gas with a symmetric mean temperature profile is studied for subsonic Mach numbers in the high Reynolds number limit where viscous and thermal diffusion effects enter first and dominate in the critical layer. The linear, neutral eigensolution of the inviscid theory for temperature profiles having either an excess or deficit of mean temperature in the shear layer is used as a basis for the weakly nonlinear, slightly viscous analysis. The coefficients of viscosity and thermal conductivity are assumed to have a power-law dependence on the temperature and the effect of viscous dissipation is included. An analytical expression for the Landau constant, and other constants appearing in the nonlinear evolution equation for the amplitude of the eigenmode, have been obtained. It is found that the temperature excess or deficit at the critical level and the Mach number have a strong nonlinear effect, even to the extent of changing the sign of the Landau constant.