Bifurcation phenomena in Taylor–Couette flow in a very short annulus with radial through-flow

Abstract

AbstractIn this study, the non-linear dynamics of Taylor–Couette flow in a very small-aspect-ratio wide-gap annulus in a counter-rotating regime under the influence of radial through-flow are investigated by solving its full three-dimensional Navier-Stokes equations. Depending on the intensity of the radial flow, either an axisymmetric (pure $$m=0$$ m = 0 mode) pulsating flow structure or an axisymmetric axially propagating vortex will appear subcritical, i.e. below the centrifugal instability threshold of the circular Couette flow. We show that the propagating vortices can be stably existed in two separate parameter regions, which feature different underlying dynamics. Although in one regime, the flow appears only as a limit cycle solution upon which saddle-node-invariant-circle bifurcation occurs, but in the other regime, it shows more complex dynamics with richer Hopf bifurcation sequences. That is, by presence of incommensurate frequencies, it can be appeared as 1-, 2- and 3-torus solutions, which is known as the Ruelle–Takens–Newhouse route to chaos. Therefore, the observed bifurcation scenario is the Ruelle-Takens-Newhouse route to chaos and the period doubling bifurcation, which exhibit rich and complex dynamics.