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Direction reversal of a rotating wave in Taylor–Couette flow

Published online by Cambridge University Press:  30 June 2008

J. ABSHAGEN ,
M. HEISE ,
Ch. HOFFMANN  and
G. PFISTER
J. ABSHAGEN
Affiliation:
Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel, Germany
M. HEISE
Affiliation:
Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel, Germany
Ch. HOFFMANN
Affiliation:
Institute for Theoretical Physics, Saarland University, 66123 Saarbrücken, Germany
G. PFISTER
Affiliation:
Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel, Germany
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Abstract

In Taylor–Couette systems, waves, e.g. spirals and wavy vortex flow, typically rotate in the same direction as the azimuthal mean flow of the basic flow which is mainly determined by the rotation of the inner cylinder. In a combined experimental and numerical study we analysed a rotating wave of a one-vortex state in small-aspect-ratio Taylor–Couette flow which propagates either progradely or retrogradely in the inertial (laboratory) frame, i.e. in the same or opposite direction as the inner cylinder. The direction reversal from prograde to retrograde can occur at a distinct parameter value where the propagation speed vanishes. Owing to small imperfections of the rotational invariance, the curves of vanishing rotation speed can broaden to ribbons caused by coupling between the end plates and the rotating wave. The bifurcation event underlying the direction reversal is of higher codimension and is unfolded experimentally by three control parameters, i.e. the Reynolds number, the aspect ratio, and the rotation rate of the end plates.

JFM classification

Instability: Taylor-Couette flow Nonlinear Dynamical Systems: Bifurcation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 607 , 25 July 2008 , pp. 199 - 208
Copyright
Copyright © Cambridge University Press 2008

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References

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Abshagen supplementary movie

Movie 1. The movies display a numerical simulation of the direction reversal of a rotating wave for the case of stationary end plates, stationary outer cylinder (R2=0) and L/d=1.25. The inner cylinder Reynolds number R1 is increased during these movies. The four movies down the left-hand side depict the intensity of the radial velocity in the azimuthal and axial directions at four different radial positions. The movie on the right shows the vector field of the flow in the radial and axial directions at one azimuthal position, with the inner cylinder located on the left. The isolines of the azimuthal velocty are also included in this plot. In the first part of the movie the wave rotates prograd, i.e. in the same direction as the inner cylinder. At R1 = 1160 the wave stops and then starts to rotate in the opposite, i.e. retrograde, direction.

Download Abshagen supplementary movie(Video)
Video 5.6 MB