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Twist vortices and their instabilities in the Taylor–Couette system

Published online by Cambridge University Press:  26 April 2006

E. Weisshaar ,
F. H. Busse  and
M. Nagata
E. Weisshaar
Affiliation:
Institute of Physics, University of Bayreuth, 858 Bayreuth, Germany
F. H. Busse
Affiliation:
Institute of Physics, University of Bayreuth, 858 Bayreuth, Germany
M. Nagata
Affiliation:
Institute of Physics, University of Bayreuth, 858 Bayreuth, Germany Present address: Department of Mathematics, The University of Birmingham, Birmingham B15 2TT, UK.
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Abstract

The problem of three-dimensional flows arising from the twist instability of Taylor vortices is investigated numerically in the narrow gap limit of the Taylor–Couette system with nearly corotating cylinders. There are two types of twist vortices: those that do not deform the in– and outflow boundaries of the Taylor vortices and those that do. The latter type are called wavy twist vortices and correspond to class II of Nagata (1986). The stability of the twist vortices with respect to arbitrary infinitesimal disturbances is analysed with the result that the twist solutions are unstable within a large part of the parameter space with respect to Eckhaus and skewed-varicose-type instabilities. An analytical model is described which fits the numerical results on the transition from axisymmetric vortices to unstable twist solutions. The theoretical findings are compared with experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 226 , May 1991 , pp. 549 - 564
Copyright
© 1991 Cambridge University Press

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References

Andereck, C. D. & Baxter, G. W., 1988 An overview of the flow regimes in a circular Couette system. In Propagation in Systems Far From Equilibrium, Proc. Workshop, Les Houches, France. March 10–18, 1987, pp. 315–324. Springer.
Andereck, C. D., Dickman, R. & Swinney, H. L., 1983 New flows in a circular Couette system with co-lrotating cylinders. Phys. Fluids 26, 1395–1401.Google Scholar
Andereck, C. D., Liu, S. S. & Swinney, H. L., 1986 Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Much. 164, 155–183.Google Scholar
Baxter, G. W. & Andereck, C. D., 1986 Formation of dynamical domains in a circular Couette system. Phys. Rev. Lett. 57, 3046–3049.Google Scholar
Chandrasekhar, S.: 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Iooss, G.: 1986 Secondary bifurcations of Taylor vortices into wavy inflow or outflow boundaries. J. Fluid Mech. 173, 273–288.Google Scholar
Marcus, P. S.: 1984 Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy vortex flow with one travelling wave. J. Fluid Mech. 146, 65–113.Google Scholar
Moser, R. D., Moin, P. & Leoniiard, A., 1983 A spectral numerical method for the Navier-Stokes equation with applications to Taylor-Couette flow. J. Comput. Phys. 52, 524–544.Google Scholar
Nagata, M.: 1986 Bifurcations in Couette flow between almost corotating cylinders. J. Fluid Mech. 169, 229–250.Google Scholar
Nagata, M.: 1988 On wavy instabilities of the Taylor-vortex flow between corotating cylinders. J. Fluid Mech. 188, 585–598.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
Weisshaar, E., Busse, F. H. & Nagata, M., 1990 Instabilities of tertiary flow in the Taylor—Couette system. In Topological Fluid Dynamics, Proc. IUTAM Symp., Cambridge UK 13–18 August 1989 (ed. H. K. Moffatt & A. Tsinober), pp. 709–716. Cambridge University Press.