Pressure field, feedback, and global instabilities of subsonic spatially developing mixing layers

Abstract

Two-dimensional numerical simulations of compressible, subsonic, planar shear flows, are used to investigate the role of feedback in the reinitiation of vortex roll-up. The study deals with unforced, spatially evolving mixing layers for which the propagation of acoustic disturbances can be resolved and boundary effects are ensured to be negligible. The calculated pattern of coherent structures shows global self-sustaining instabilities in which new vortex roll-ups are triggered in the initial shear layer by pressure disturbances originating in the fluid accelerations downstream. This reinitiation mechanism, absent in the linear treatments of stability, is demonstrated conclusively here and examined as a function of Mach number and free-stream velocity ratio. The global instability becomes less efficient in reinitiating vortex roll-up in the initial shear layer when the acoustic propagation velocities on the sides of the mixing layer approach each other, i.e., as the incompressible regime is approached, and as the free-stream velocity ratios approach unity.