Linear stability analysis of interactions between mixing layer and boundary layer flows

The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed. The mixing layers include wake, shear layer and their combination. The mean velocity profile of confluent flow is taken as a superposition of a hyperbolic and exponential function to model a mixing layer and the Blasius similarity solution for a flat plate boundary layer. The stability equation of confluent flow was solved by using the global numerical method. The unstable modes associated with both the mixing and boundary layers were identified. They are the boundary layer mode, mixing layer mode 1 (nearly symmetrical mode) and mode 2 (nearly anti-symmetrical mode). The interactions between the mixing layer stability and the boundary layer stability were examined. As the mixing layer approaches the boundary layer, the neutral curves of the boundary layer mode move to the upper left, the resulting critical Reynolds number decreases, and the growth rate of the most unstable mode increases. The wall tends to stabilize the mixing layer modes at low frequency. In addition, the mode switching behavior of the relative level of the spatial growth rate between the mixing layer mode 1 and mode 2 with the velocity ratio is found to occur at low frequency.