Interaction of Stationary Disturbances with Tollmien—Schlichting Waves in a Supersonic Boundary Layer

Abstract

The possibility of controlling unsteady disturbances, traveling Tollmien—Schlichting waves, and stationary streamwise structures is studied. The investigation is performed for the flat-plate boundary layer at the freestream Mach number M = 2. The possible enhancement and suppression of the growth of these waves by stationary streaky structures of the stability eigenproblem of supersonic boundary layer is studied. The problem is solved in the local-parallel approximation within the framework of the three-wave resonance interaction. The pumping wave is a stationary, near-streaky formation. It is shown that even in the stability domain Tollmien—Schlichting waves grow under the influence of the streamwise structures. It is established that under certain conditions the effect of stationary disturbances on these waves can be considerable also in the instability domain and the Reynolds number ranges in which the steady disturbances suppress traveling waves are determined.