VORTEX WAVE INTERACTION IN SEPARATING FLOWS

The wide-vortex/Tollmien-Schlichting-wave three-dimensional interactio n equations are considered in a region of finite adverse pressure grad ient driving an incompressible boundary-layer flow. The asymptotic str ucture that emerges enables simplification of the equations and result s in a partial differential equation governing directly the three-dime nsional skin-friction field coupled with the effects of the wave forci ng. The initial linear development of the interaction is described by an analytic solution and then numerical solutions of the three-dimensi onal nonlinear interaction equations are presented. The results sugges t the formation of a finite-distance singularity in the wave pressure at a location upstream of the point where a Goldstein singularity woul d occur in the absence of an interaction. A singularity structure is p roposed which is in agreement with the numerical results and the possi ble flow development beyond this terminal form is discussed, along wit h other types of interaction.