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Turbulence and waves in a rotating tank

Published online by Cambridge University Press:  20 April 2006

E. J. Hopfinger ,
F. K. Browand  and
Y. Gagne
E. J. Hopfinger
Affiliation:
Institut de Mécanique, Université de Grenoble, Grenoble, France
F. K. Browand
Affiliation:
Institut de Mécanique, Université de Grenoble, Grenoble, France Present address: Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90007.
Y. Gagne
Affiliation:
Institut de Mécanique, Université de Grenoble, Grenoble, France
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Abstract

A turbulent field is produced with an oscillating grid in a deep, rotating tank. Near the grid, the Rossby number is kept large, 0(3-33), and the turbulence is locally unaffected by rotation. Away from the grid, the scale of the turbulence increases, the r.m.s. turbulent velocity decreases, and rotation becomes increasingly important. The flow field changes dramatically at a local Rossby number of about 0.20, and thereafter remains independent of depth. The flow consists of concentrated vortices having axes approximately parallel to the rotation axis, and extending throughout the depth of the fluid above the turbulent Ekman layer. The number of vortices per unit area is a function of the grid Rossby number. The local vorticity within cores can be a factor of 50 larger than the tank vorticity 2Ω. The total relative circulation contained in the vortices remains, however, a small fraction of the tank circulation.

The concentrated vortex cores support waves consisting of helical distortions, which travel along the axes of individual vortices. Isolated, travelling waves seem well-described by the vortex-soliton theory of Hasimoto (1972). The nonlinear waves transport mass, momentum and energy from the vigorously turbulent region near the grid to the rotation-dominated flow above. Interactions between waves, which are frequent occurrences, almost always result in a local breakdown of the vortex core, and small-scale turbulence production. Usually the portions of broken core reform within ½−1 rotation periods, but occasionally cores are destroyed and reformed on a much longer timescale.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 125 , December 1982 , pp. 505 - 534
Copyright
© 1982 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bretherton, F. P. & Turner, J. S. 1968 On the mixing of angular momentum in a stirred rotating fluid. J. Fluid Mech. 32, 449–464.Google Scholar
Burgers, J. M. 1948 A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1, 171–199.Google Scholar
Colin De Verdiere, A. 1980 Quasi-geostrophic turbulence in a rotating homogeneous fluid. Geophys. Astrophys. Fluid Dyn. 15, 213–251.Google Scholar
Dickinson, S. C. & Long, R. R. 1982 Oscillating grid turbulence including effects of rotation. Submitted to J. Fluid Mech. (in the press).Google Scholar
Escudier, M. P. 1979 Estimation of pressure loss in ring-type exit chambers. Trans. A.S.M.E. I: J. Fluids Engng 101, 511–516Google Scholar
Escudier, M. P., Bornstein, J. & Maxworthy, T. 1982 The dynamics of confined vortices. Proc. R. Soc. Lond. 383, 335–360.Google Scholar
Escudier, M. P. & Zehnder, N. 1982 Vortex-flow regimes. J. Fluid Mech. 115, 105–121.Google Scholar
Faler, J. & Leibovich, S. 1977 Disrupted states of vortex flow and vortex breakdown. Phys. Fluids 20, 1385–1400.Google Scholar
Gough, D. O. & Lynden-Bell, D. 1968 Vorticity expulsion by turbulence: astrophysical implications of an Alka-Seltzer experiment. J. Fluid Mech. 32, 437–447.Google Scholar
Hasimoto, H. 1972 A soliton on a vortex filament. J. Fluid Mech. 51, p. 477–485.Google Scholar
Hopfinger, E. J. & Browand, F. K. 1981 Intense vortex generation by turbulence in a rotating fluid. In Proc. IUTAM-IUGG Symp. on Concentrated Atmospheric Vortices, Reading.
Hopfinger, E. J. & Browand, F. K. 1982 Vortex solitary waves in a rotating, turbulent flow. Nature 295, 393–396.Google Scholar
Hopfinger, E. J. & Toly, A.-J. 1976 Spatially decaying turbulence and its relation to mixing across density interfaces. J. Fluid Mech. 78, 155–175.Google Scholar
Ibbetson, A. & Tritton, D. Y. 1975 Experiments on turbulence in a rotating fluid. J. Fluid Mech. 68, 639–672.Google Scholar
Kida, S. 1981 A vortex filament moving without change of form. J. Fluid Mech. 112, 397–409.Google Scholar
Lambourne, N. C. & Bryer, D. W. 1961 The bursting of leading-edge vortices: some observations and discussion of the phenomenon, Aero. Res. Counc. R. no. 3282.
Mcewan, A. D. 1976 Angular momentum diffusion and the initiation of cyclones. Nature 260, 126–128.Google Scholar
Sarpkaya, T. 1971 On stationary and travelling vortex breakdowns. J. Fluid Mech. 45, 545–559.Google Scholar
Scorer, R. S. 1966 Origin of cyclones. Sci. J. 2, 46–52.Google Scholar