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Trapped vortices in rotating flow

Published online by Cambridge University Press:  12 April 2006

E. R. Johnson
E. R. Johnson
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge Present address: Department of Mathematics, University of British Columbia, Vancouver, Canada.
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Abstract

A variational principle is presented which characterizes steady motions, at finite Rossby number, of rotating inviscid homogeneous fluids in which horizontal velocities are independent of depth. This is used to construct nonlinear solutions corresponding to stationary patches of distributed vorticity above topography of finite height in a uniform stream. Numerical results are presented for the specific case of a right circular cylinder and are interpreted using a series expansion, derived by analogy with a deformable self-gravitating body. The results show that below a critical free-stream velocity a trapped circular vortex is present above the cylinder and a smaller patch of more concentrated vorticity, of the opposite sign, maintains a position to the right (looking downstream) of the cylinder. An extension to finite Rossby number and finite obstacle height of Huppert's (1975) criterion for the formation of a Taylor column is presented in an appendix.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 2 , 29 May 1978 , pp. 209 - 224
Copyright
© 1978 Cambridge University Press

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References

Benjamin, T. B. 1975 The alliance of practical and analytical insights into the nonlinear problems of fluid mechanics. In Lecture Notes in Mathematics, vol. 503. pp. 8–29. Springer.
Bretherton, F. P. & Haidvogel, D. B. 1976 Two-dimensional turbulence above topography. J. Fluid Mech. 78, 129–154.Google Scholar
Fraenkel, L. E. & Berger, M. S. 1974 A global theory of steady vortex rings in an ideal fluid. Acta Mathematica 132, 13–51.Google Scholar
Grace, S. F. 1927 On the motion of a sphere in a rotating liquid. Proc. Roy. Soc. A 113, 46–77.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Greenspan, H. P. & Howard, L. N. 1963 On non-linear spin-up of a rotating fluid. J. Math. Phys. 44, 66–85.Google Scholar
Hide, R. 1961 Origin of Jupiter's Great Red Spot. Nature 190, 895–896.Google Scholar
Hide, R. & Ibbetson, A. 1966 An experimental study of ‘Taylor Columns’. Icarus 5, 279–290.Google Scholar
Hide, R. & Ibbetson, A. 1968 On slow transverse flow past obstacles in a rapidly rotating fluid. J. Fluid Mech. 32, 251–272.Google Scholar
Huppert, H. E. 1975 Some remarks on the initiation of inertial Taylor columns. J. Fluid Mech. 67, 397–412.Google Scholar
Huppert, H. E. & Bryan, K. 1976 Topographically generated eddies. Deep-Sea Res. 23, 655–679.Google Scholar
Huppert, H. E. & Stern, M. E. 1974 Ageostrophic effects in rotating stratified flow. J. Fluid Mech. 62, 369–385.Google Scholar
Ingersoll, A. P. 1969 Inertial Taylor columns and Jupiter's Great Red Spot. J. Atmos. Sci. 26, 744–752.Google Scholar
Jacobs, S. J. 1964 The Taylor column problem. J. Fluid Mech. 20, 581–91.Google Scholar
Proudman, J. 1916 On the motion of solids in a liquid possessing vorticity. Proc. Roy. Soc. A 92, 408–424.Google Scholar
Stern, M. E. 1975 Minimal properties of planetary eddies. J. Mar. Res. 33, 1–13.Google Scholar
Stewartson, K. 1952 On the slow motion of a sphere along the axis of a rotating fluid. Proc. Camb. Phil. Soc. 48, 168–177.Google Scholar
Stewartson, K. 1953 On the slow motion of an ellipsoid in a rotating fluid. Quart. J. Mech. Appl. Math. 6, 141–162.Google Scholar
Stewartson, K. 1967 On slow transverse motion of a sphere through rotating fluid. J. Fluid Mech. 30, 357–370.Google Scholar
Stommel, H. 1955 Direct measurements of sub-surface currents. Deep-Sea Res. 2, 284–5Google Scholar
Swallow, J. C. & Hamon, B. V. 1960 Some measurements of deep currents in the eastern North-Atlantic. Deep-Sea Res. 6, 155–68.Google Scholar
Taylor, G. I. 1917 Motion of solids in fluids when the flow is not irrotational. Proc. Roy. Soc. A 93, 99–113.Google Scholar
Taylor, G. I. 1923 Experiments on the motion of solid bodies in rotating fluids. Proc. Roy. Soc. A 104, 213–218.Google Scholar