The stability of boundary layers on curved heated plates

Abstract

We consider the effect the competing mechanisms of buoyancy-driven acceleration (arising from heating a surface) and streamline curvature (due to curvature of a surface) have on the stability of boundary-layer flows. We confine our attention to vortex type instabilities (commonly referred to as Gortler vortices) which have been identified as one of the dominant mechanisms of instability in both centrifugally and buoyancy driven boundary layers. The particular model we consider consists of the boundary-layer flow over a heated (or cooled) curved rigid body. In the absence of buoyancy forcing the flow is centrifugally unstable to counter-rotating vortices aligned with the direction of the flow when the curvature is concave (in the fluid domain) and stable otherwise. Heating the rigid plate to a level sufficiently above the fluid's ambient (free-stream) temperature can also serve to render the flow unstable. We determine the level of heating required to render an otherwise centrifugally stable flow unstable and likewise, the level of body cooling that is required to render a centrifugally unstable flow stable.