Effects of curvature variations on the nonlinear evolution of Goertler vortices

Abstract

The nonlinear development of Goertler vortices over walls of variable curvature is studied. The parabolized disturbance equations governing the problem for small curvature, high Reynolds number, and order unity Goertler number are integrated numerically. Cases with concave, convex, and zero curvatures are analyzed. The ‘‘mushroom-shaped’’ distributions of low-momentum fluid riding above high-momentum fluid that are subject to secondary instability are predicted. The results show significant stabilization of disturbances introduced from a concave into a convex region, where new sets of vortices are successively created with opposite rotation to the preceding set. The convex curvature tends to eliminate the inflection points from the spanwise and normal profiles of the streamwise velocity and, hence, suppresses the oscillatory secondary instability that leads to turbulence. Decay of Goertler vortices in a flat region is found to be less rapid than in a convex region.