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The effects of obstacle shape and viscosity in deep rotating flow over finite-height topography

Published online by Cambridge University Press:  20 April 2006

E. R. Johnson
E. R. Johnson
Affiliation:
Department of Mathematics, University College London
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Abstract

The limiting process introduced by Stewartson & Cheng (1979) is used to obtain solutions in the limit of vanishing Rossby number for deep rotating flows at arbitrary Reynolds number over cross-stream ridges of finite slope. Examination of inviscid solutions for infinite-depth flow shows strong dependence on obstacle shape of not only the magnitudes but also the positions of disturbances in the far field. In finite-depth flow there is present the Stewartson & Cheng inertial wave wake, which may be expressed as a sum of vertical modes whose amplitudes depend on the obstacle shape but are independent of distance downstream; the smoother the topography and the shallower the flow, the fewer the number of modes required to describe the motion. For abrupt topography the strength of the wake does not, however, decrease monoton- ically with decreasing container depth (or Rossby number). In very deep flows viscosity causes the wake to decay on a length scale of order the Reynolds number times the ridge width. In shallower flows, where only a few modes are present, the decay of the wake is more rapid. For Reynolds numbers and depths of the order of those in the experiments of Hide, Ibbetson & Lighthill (1968)) viscosity causes the disturbance to take on the appearance of a leaning column.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 120 , July 1982 , pp. 359 - 383
Copyright
© 1982 Cambridge University Press

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References

Boyer, D. L. 1971a Rotating flow over long shallow ridges. Geophys. Fluid Dyn. 2, 165–184.Google Scholar
Boyer, D. L. 1971b Rotating flow over a step. J. Fluid Mech. 50, 675–687.Google Scholar
Cheng, H. K. 1977 On inertial wave and flow structure at low Rossby number. Z. angew. Math. Phys. 28, 753–769.Google Scholar
Cheng, H. K. & Johnson, E. R. 1982 Inertial waves above topography in an unbounded, rapidly rotating fluid. Proc. R. Soc. Lond. (in press).
Hide, R. 1961 Origin of Jupiter's Great Red Spot. Nature 190, 213–218.Google Scholar
Hide, R., Ibbetson, A. & Lighthill, M. J. 1968 On slow transverse flow past obstacles in a rapidly rotating fluid. J. Fluid Mech. 32, 251–272.Google Scholar
Hocking, L. M., Moore, D. W. & Walton, I. C. 1979 The drag on a sphere moving axially in a long rotating container. J. Fluid Mech. 90, 781–793.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. & 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
Lighthill, M. J. 1967 On waves generated in dispersive systems by travelling forcing effects, with applications to the dynamics of rotating fluids. J. Fluid Mech. 27, 725–752.Google Scholar
Mason, P. J. 1975 Forces on bodies moving transversely through a rotating fluid. J. Fluid Mech. 71, 577–599.Google Scholar
Mason, P. J. & Sykes, R. I. 1981 A numerical study of rapidly rotating flow over surface-mounted obstacles. J. Fluid Mech. 111, 175–195.Google Scholar
Moore, D. W. & Saffman, P. G. 1968 The rise of a body through a rotating fluid in a container of finite length. J. Fluid Mech. 31, 635–642.Google Scholar
Moore, D. W. & Saffman, P. G. 1969 The structure of free vertical shear layers in a rotating fluid and the motion produced by a slowly rising body. Phil. Trans. R. Soc. Lond A 264, 597–634.Google Scholar
Queney, P. 1947 The problem of air flow over mountains: a summary of theoretical studies. Bull. Am. Met. Soc. 29, 16–26.Google Scholar
Smith, R. B. 1979 Some aspects of quasi-geostrophic flow over mountains. J. Atmos. Sci. 36, 2385.Google Scholar
Stewartson, K. & Cheng, H. K. 1979 On the structure of inertial waves produced by an obstacle in a deep, rotating container. J. Fluid Mech. 91, 415–432.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves, chap. 11. Wiley.