The onset of Görtler vortices in laminar boundary layer flow over a slightly concave wall

Abstract

The onset of convective instability in the laminar boundary layer over the slightly curved wall is analyzed theoretically and compared with the existing experimental data. A new set of stability equations are derived by the propagation theory considering the relative instability under the linear stability theory. In this analysis the disturbances are assumed to have the form of longitudinal vortices and also to grow themselves in streamwise direction. The critical position to mark the onset of Görtler instability is obtained as a function of the Görtler number, where disturbances at the critical state are mainly confined to the hydrodynamic boundary layer. Comparing the theoretical predictions with available experimental and other theoretical results, the present predictions follow experimental trends fairly well with slightly higher critical Görtler numbers than those from the local stability theory. The propagation theory commanding the local eigenvalue analysis is successful to obtain stability conditions reasonably in Görtler vortex problems, relaxing the limitations by the conventional analyses.