Streamline-Curvature Instability of the Flow on a Rotating Disk with Uniform Suction

Abstract

Linear stability analysis of the rotating-disk flow is made with a very simple model of disturbance equations consisting of the parallel-flow approximation and an additional term associated with the curvature of flow field. Numerical solutions of the resulting eigenvalue problem indicate the existence of two instabilities and reveal their entirely different mechanisms. One is the well-known cross-flow instability and the other is the instability due to the curvature of external streamlines, which was recently predicted to occur in three-dimensional boundary layers on a swept wing. The streamline-curvature mode is in fact identical with the classical one called `parallel' or `type 2' instability in atomospheric literature.