Author:
Altmeyer Sebastian,Sankar M.,Do Younghae
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.
Funder
Spanish Government grant
National Research Foundation of Korea
Publisher
Springer Science and Business Media LLC
Reference46 articles.
1. Taylor, G. I. Stability of a viscous liquid contained between two rotating cylinders. Philos. Trans. R. Soc. Lond. A 223, 289 (1923).
2. Chandrasekhar, S. Hydrodynamic and Hydromagnetic Stability (Dover, 1961).
3. DiPrima, R. C. & Swinney, H. L. Instabilities and transition in flow between concentric rotating cylinders. In Hydrodynamic Instabilities and the Transition to Turbulence, Number 45 in Topics in Applied Physics (eds Swinney, H. L. & Gollub, J. G.) (Springer, 1985).
4. Tagg, R. The Couette–Taylor problem. Nonlinear Sci. Today 4, 1 (1994).
5. Barcilon, V. & Berg, H. C. Forced axial flow between rotating concentric cylinders. J. Fluid Mech. 47, 469 (1987).
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献