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A shear-flow instability in a circular geometry

Published online by Cambridge University Press:  20 April 2006

M. Rabaud  and
Y. Couder
M. Rabaud
Affiliation:
Groupe de Physique des Solides de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
Y. Couder
Affiliation:
Groupe de Physique des Solides de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
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Abstract

A circular shear zone is created in a thin layer of fluid. The Kelvin-Helmholtz instability induces regular, steady patterns of m vortices. The experimental conditions are such that neither the centrifugal nor the Coriolis forces play a role in the motion. The state of the flow is defined by a Reynolds number, the value of which is controlled by the imposed velocities. The pattern of vortices can be characterized by its wavevector k or by m, the order of its symmetry. As k is quantized, its evolution, due to an increase or a decrease of the controlled stress, leads to transitions between patterns of different m. The transitory states between different symmetries are investigated. The experiments are performed with a soap film which provides a new type of visualization of an air flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 136 , November 1983 , pp. 291 - 319
Copyright
© 1983 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics, pp. 177, 178. Cambridge University Press.
Busse, F. H. 1968 J. Fluid Mech. 33, 577.
Chabert D'Hieres, G. 1982 In Proc. European Geophys. Soc., Leeds (to be published).
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability, p. 481. Clarendon.
Coles, D. 1965 J. Fluid. Mech. 21, 385.
Couder, Y. 1981 J. Physique Lett. 42, L429.
Hénon, M. 1969 Q. Appl. Maths 27, 291.
Hide, R. & Titman, C. W. 1967 J. Fluid Mech. 29, 39.
Kober, K. 1957 Dictionary of Conformal Representation, p. 99. Dover.
Moore, D. W. & Saffman, P. G. 1969 Phil. Trans. R. Soc. Lond. A, 264, 597.
Moore, D. W. & Saffman, P. G. 1975 J. Fluid Mech. 69, 465.
Mysels, K. J., Shinoda, K. & Frankel, S. 1959 Soap Films, Studies of Their Thinning. Pergamon.
Pierrehumbert, R. T. & Widnall, S. E. 1981 J. Fluid Mech. 102, 301.
Pierrehumbert, R. T. & Widnall, S. E. 1982 J. Fluid Mech. 114, 59.
Rand, D. 1982 Arch. Rat. Mech. Anal. 59, 1.
Roshko, A. 1976 AIAA J. 14, 1349.
Siegmann, W. L. 1974 J. Fluid Mech. 64, 289.
Stewartson, K. 1957 J. Fluid Mech. 3, 17.
Trapeznikov, A. A. 1957 In Proc. 2nd Intl Congress on Surface Activity, vol. 1, p. 242.
Weske, J. R. & Rankin, T. M. 1963 Phys. Fluids 6, 1397.
Winant, C. D. & Browand, F. K. 1974 J. Fluid Mech. 63, 237.