Optimal streamwise vortices intended for supersonic mixing enhancement

The theory of optimal, spatially growing disturbances is applied to a compressible turbulent mixing layer. It is suggested that the weak steady disturbances generated by tiny vortex generators be considered as in the triple decomposition method. The linearized equations for the disturbances are closed via the eddy viscosity model with a turbulent Prandtl number equal to one. The optimization procedure is formulated in terms of Mack's energy norm. As an example, a parallel flow with a hyperbolic tangent velocity profile and a temperature profile following from the Crocco-Busemann relation is analyzed. Theoretical results indicate that the optimization procedure leads to streamwise vortices, and it is consistent with experimental findings. The theory provides the possibility of estimating the spacing of the tiny vortex generators placed on the splitter plate. Results show that an increase in the convective Mach number is accompanied by an increase in the transient growth effect.