NONLINEAR SPATIALLY DEVELOPING GORTLER VORTICES IN CURVED WALL-JET FLOW

Linear and nonlinear spatial developments of two-dimensional wall jets on curved surfaces are computed using pseudospectral-finite differenc e methods. Inviscid analysis shows that the instability originates fro m the inner/outer region on a concave/convex wall; the shear layer is thus always unstable regardless of the curvature. This primary instabi lity is a steady spanwise vortex structure similar to Gortler instabil ity in a Blasius flow. In the present study, a perturbation of prescri bed wave number ct is assumed. In the limit of high Reynolds number (R e) and small curvature (E), a parabolic set of nonlinear equations des cribes the spatial evolution of the disturbance. Direct marching simul ation of the perturbation and a parabolic stability approach are emplo yed. Both give the same results with different computational efficienc ies. For the concave case at low Gortler numbers (G(2) = epsilon root Re), perturbations are unstable for small alpha. Their energy reaches a maximum and then decays. At high G, the most unstable disturbance oc curring at larger alpha will grow exponentially and reach saturation. The convex case is the most unstable situation. But as for the concave case, the most dangerous disturbance moves from small to larger alpha as G increases. The numerical results are able to capture the primary instability as observed in the experiment of Matsson [Phys. Fluids 7, 3048 (1995)]. (C) 1996 American Institute of Physics.