Three-dimensionality in the wake of a rapidly rotating cylinder in uniform flow

Abstract

AbstractThe flow around an isolated cylinder spinning at high rotation rates in free stream is investigated. The existence of two steady two-dimensional states is confirmed, as is the existence of a secondary mode of vortex shedding. The stability of the two steady states to three-dimensional perturbations is established using linear stability analysis. At lower rotation rates on the first steady state, two three-dimensional modes are confirmed, and their structure and curves of marginal stability as a function of rotation rate and Reynolds number are determined. One mode (named mode $E$) appears consistent with a hyperbolic instability in the wake, while the second (named mode $F$) appears to be a centrifugal instability of the flow very close to the cylinder surface. At higher rotation rates on the second steady state, a single three-dimensional mode due to centrifugal instability (named mode ${F}^{\prime } $) is found. This mode becomes increasingly difficult to excite as the rotation rate is increased.