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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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References

Andereck, D. D., Dickman, R. & Swinney, H. L. 1983 New flows in a circular Couette system with co-rotating cylinders. Phys. Fluids 26, 1395–1401.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Clever, R. M. & Busse, F. H. 1974 Transition to time-dependent convection. J. Fluid Mech. 65, 625–645.Google Scholar
Diprima, R. C. & Swinney, H. L. 1981 Instabilities and transition in flow between concentric rotating cylinders. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub), pp. 139–180. Springer.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Eagles, P. M. 1974 On the torque of wavy vortices. J. Fluid Mech. 62, 1–9.Google Scholar
Jones, C. A. 1981 Nonlinear Taylor vortices and their stability. J. Fluid Mech. 102, 249–261.Google Scholar
Nagata, M. & Busse, F. H. 1983 Three-dimensional tertiary motions in a plane shear layer. J. Fluid Mech. 135, 1–26.Google Scholar
Rayleigh, Lord 1880 On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc. 11, 57–70.Google Scholar
Taylor, G. I. 1921 Experiments with rotating fluids. Proc. Camb. Phil. Soc. 20, 326–329.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. Roy. Soc. Lond. A 223, 289–343.Google Scholar