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Bifurcations in Couette flow between almost corotating cylinders

Published online by Cambridge University Press:  21 April 2006

M. Nagata
M. Nagata
Affiliation:
School of Mathematics, The University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, UK Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK.
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Abstract

Transition to turbulence in a circular Couette system is followed numerically up to the state beyond the second bifurcation in the limit of the narrow gap between coaxial cylinders which rotate with almost equal speeds in the same direction. Taylor-vortex flow, which emerges after the Taylor number T exceeds its critical value Tc = 1708, becomes unstable to two different types of non-axisymmetric disturbances, depending on [Rscr ] (the Reynolds number) and Ω, which measure the velocity difference between the cylinders and the mean angular velocity respectively. Finite-amplitude calculations show that one part of the bifurcating flow is characterized by the vortices winding out of phase in the axial direction but still keeping the boundaries between vortices unaffected. The other is distinguished by the vortex dislocation. The inflow as well as the outflow boundaries between vortices are wavy. Both types of solutions are stationary in the frame of reference rotating with the angular velocity Ω.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 169 , August 1986 , pp. 229 - 250
Copyright
© 1986 Cambridge University Press

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