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Wave speeds in wavy Taylor-vortex flow

Published online by Cambridge University Press:  20 April 2006

Gregory P. King ,
Y. Li, W. Lee ,
Harry L. Swinney  and
Philip S. Marcus
Gregory P. King
Affiliation:
Department of Physics, University of Texas, Austin TX 78712 Present address: Royal Signals and Radar Establishment, Great Malvern, WR 14 3PS, England.
Y. Li, W. Lee
Affiliation:
Department of Physics, University of Texas, Austin TX 78712
Harry L. Swinney
Affiliation:
Department of Physics, University of Texas, Austin TX 78712
Philip S. Marcus
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 Present address: Division of Applied Sciences, Aiken Hall, Harvard University, Cambridge, MA 02138.
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Abstract

The speed of travelling azimuthal waves on Taylor vortices in a circular Couette system (with the inner cylinder rotating and the outer cylinder at rest) has been determined in laboratory experiments conducted as a function of Reynolds number R, radius ratio of the cylinders η, average axial wavelength $\overline{\lambda}$, number of waves m1 and the aspect ratio Γ (the ratio of the fluid height to the gap between the cylinders). Wave speeds have also been determined numerically for axially periodic flows in infinite-length cylinders by solving the Navier-Stokes equation with a pseudospectral technique where each Taylor-vortex pair is represented with 32 axial modes, 32 azimuthal modes (in an azimuthal angle of 2π/m1) and 33 radial modes. Above the onset of wavy-vortex flow the wave speed for a given η decreases with increasing R until it reaches a plateau that persists for some range in R. In the radius-ratio range examined in our experiments we find that the wave speed in the plateau region increases monotonically from 0.14Ω at η = 0.630 to 0.45Ω at η = 0.950 (where the wave speed is expressed in terms of the rotation frequency Ω of the inner cylinder). There is a much weaker dependence of the wave speed on $\overline{\lambda}$, m1 and Γ. For three sets of parameter values (R, $\overline{\lambda}$, η and m1) the wave speeds have been measured, extrapolated to infinite aspect ratio, and compared with the numerically computed values. For each of these three cases the agreement is within 0.1 %.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 141 , April 1984 , pp. 365 - 390
Copyright
© 1984 Cambridge University Press

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