Separated flows near the nose of a body of revolution
The solution of the Navier-Stokes equations for the problem of cross-flow separataion about a deforming cylinder was achieved by iteration. It was shown that the separation starts at the rear stagnation point and the point of primary separation moves upstram along the cylinder surface. A general method of linear stability analysis for nonparallel external flows was constructed, which consists of representing the eigenfunctions with complete orthogonal sets and forms characteristic equations with the Galerkin method. The method was applied to the Kovasznay flow which is an exact solution of the Navier-Stokes equation. The results show that when the critical parameter is exceeded, there are only a few isolated unstable eigen-frequencies. Another exact solution is shown to be absolutely and monotonically stable with respect to infinitesimal disturbances of all frequencies. The flow is also globally, asymptotically, and monotonically stable in the mean with respect o three-dimensional disturbances. This result forms the sound foundation of rigorous stability analysis for nonparallel flows, and provides an invaluable test ground for future studies of nonparallel flows in which the basic states do not posses exact solutions. The application of this method to the study of the formation of spiral vorticies near the nose of a rotating body of revolution is underway. The same method will be applied to the stability analysis of reversed flow over a plate with suction.