Instability of Taylor-Couette Flow Subjected to a Coriolis Force

Abstract

Taylor-Couette flow subjected to a Coriolis force is a rich pattern-forming system.1–5 The Coriolis force is applied by rotating a Couette apparatus so that the axis of rotation for the system is. orthogonal to the common axis of the cylinders (see figure 1). This orientation produces a nonaxisymmetric Coriolis force through the interaction of the rotation of the system with the (primarily) azimuthal base flow. Experimentally, a small Coriolis force is found to stabilize the base flow against Taylor vortex formation. In other words, the Coriolis force increases the critical value of the Reynolds number R c for the onset of instability in the base flow. At the transition to secondary flow, the Taylor vortices are tilted out of the plane normal to the cylinders’ axis. But the flow is still time-independent. This tilted Taylor vortex flow is an example of a novel pattern which arises as a result of the nonaxisymmetric Coriolis force. Several other novel patterns also arise. At somewhat large system rotation rates, there is a direct transition from the base flow to strong spatiotemporal turbulence. At small values of Ω (where Ω is a dimensionless measure of the angular frequency of the rotating system) there is nonhysteretic re-emergent order at Reynolds numbers not far from the threshold for instability.3 In a medium gap system, there is a Hopf bifurcation from the base flow to axially travelling tilted Taylor vortices.4 KeywordsHopf BifurcationSecondary FlowBase FlowCoriolis ForceRadius RatioThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.