On the Interaction of Görtler Vortices and Tollmien-Schlichting Waves in Boundary Layer Flows

Abstract

Here we are concerned with the interaction of short wavelength Görtler vortices and lower branch Tollmien-Schlichting waves within general two-dimensional boundary layer flows. The vortices are fully nonlinear in the sense that they are large enough so as to drive the mean flow state at leading order. Such vortices are described by the asymptotic structure proposed by Hall & Lakin (1988) in which the vortex activity is confined to a finite zone concentrated in the main part of the boundary layer. The Tollmien-Schlichting waves are chosen so as to be large enough to also drive the mean flow profile within this vortex activity zone. In order to do this it is found that the Tollmien-Schlichting waves are of surprisingly small size. Some preliminary calculations of steady vortex/wave states are discussed and we demonstrate how our formulation may be used as a springboard for physically more realistic computations corresponding to spatially and/or temporally varying boundary layer flows.