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Marginal instability in Taylor–Couette flows at a very high Taylor number

Published online by Cambridge University Press:  19 April 2006

A. Barcilon ,
J. Brindley ,
M. Lessen  and
F. R. Mobbs
A. Barcilon
Affiliation:
Geophysical Fluid Dynamics Institute, Florida State University
J. Brindley
Affiliation:
Department of Applied Mathematical Studies, University of Leeds
M. Lessen
Affiliation:
Department of Mechanical and Aerospace Sciences, University of Rochester
F. R. Mobbs
Affiliation:
Department of Mechanical Engineering, University of Leeds
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Abstract

We report on a set of turbulent flow experiments of the Taylor type in which the fluid is contained between a rotating inner circular cylinder and a fixed concentric outer cylinder, focusing our attention on very large Taylor number values, i.e. \[ 10^3 \leqslant T/T_c \leqslant 10^5, \] where Tc is the critical value of the Taylor number T for onset of Taylor vortices. At such large values of T, the turbulent vortex flow structure is similar to the one observed when T – Tc is small and this structure is apparently insensitive to further increases in T. These flows are characterized by two widely separated length scales: the scale of the gap width which characterizes the Taylor vortex flow and a much smaller scale which is made visible by streaks in the form of a ‘herring-bone’-like pattern visible at the walls. These are conjectured to be Görtler vortices which arise as a result of centrifugal instability in the wall boundary layers. Ideas of marginal instability by which we postulate that both the Taylor and Görtler vortex structures are marginally unstable on their own scale seem to provide good quantitative agreement between predicted and observed Görtler vortex spacings.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 94 , Issue 3 , 16 October 1979 , pp. 453 - 463
Copyright
© 1979 Cambridge University Press

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