Stability of Rotating Viscous and Inviscid flows

Abstract

Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction and that in transverse direction, if there is no work input. In this note, it is shown based on the energy gradient theory that inviscid non-uniform flow is unstable if the energy in transverse direction is not constant. This new finding breaks the classical linear theory from Rayleigh that inviscid flow is unstable if the velocity profile has an inflection point in parallel flows and inviscid flow is stable if the velocity profile has no inflection point in parallel flow. Then, stability of rotating viscous and inviscid flows is studied, and two examples of rotating flows (rotating rigid body motion and free vortex motion) are shown, respectively.