Görtler instability of boundary layers over concave and convex walls

Abstract

The stability analysis of boundary layers over curved surfaces is presented. A simple inviscid stability criterion is developed and used to identify shear layers which are potentially unstable with respect to the Görtler-type disturbances. A flow is stable if the velocity magnitude increases with distance away from the wall in the case of convex surfaces and decreases in the case of concave surfaces. The flows with nonmonotonic velocity distributions are therefore always potentially unstable regardless of the type of surface being considered. When viscous stability theory is applied to selected boundary layers the results confirm conclusions based on the inviscid theory. Detailed calculations are carried out for the Blasius boundary layer (monotonic velocity distribution) and a wall jet (nonmonotonic velocity distribution). Results suggest that flows with monotonic velocity distributions become unstable earlier than flows with nonmonotonic velocity distributions.