Stability of Taylor-Dean flow in an annulus with arbitrary gap spacing

Abstract

A linear stability analysis based on three-dimensional disturbances is implemented for the Taylor-Dean flow, a viscous flow driven simultaneously by a rotating inner cylinder and an azimuthal pressure gradient within an annulus with an arbitrary gap spacing. It is found that nonaxisymmetric instability modes prevail for a wide variety of basic flows. The most stable state is always associated with the smallest critical axial wavelength as well as with the onset of instability being largely confined to a small portion within the gap. The flow reaches the most stable state either when the corresponding instability is about to change from a nonaxisymmetric mode into an axisymmetric mode, as the pumping velocity is increasing, or when a nonaxisymmetric mode changes both its azimuthal wavelength and its direction of traveling. The nonaxisymmetric mode with smaller azimuthal wave number becomes increasingly significant as the gap increases in width. From both the present calculated results and previous experimental observations, it is inferred that nonlinear interactions between different instability modes may occur when the basic flow is near the most stable state.