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On the stratified Taylor column

Published online by Cambridge University Press:  29 March 2006

Nelson G. Hogg
Nelson G. Hogg
Affiliation:
National Institute of Oceanography, Wormley, Godahing, Surrey Present address: Department of Earth and Planetary Sciences, Massachusetts Institute of Technology.
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Abstract

We analyse the effects of small, circularly symmetric topography on the slow flow of an inviscid, incompressible, diffusionless, horizontally uniform, baroclinic current and show that the vertical influence depends primarily on three parameters: a stratification measure S (the square of the ratio of buoyancy frequency times height scale to Coriolis parameter times length scale), a topographic parameter β (ratio of scaled topographic height multiplied by scaled bottom current to Rossby number ε) and the scaled upstream shear u′0(z) (the dimensional upstream shear divided by the ratio of the r.m.s. upstream flow speed to height scale).

Investigating a linear stratification model we find that the topographic effect is depth independent if S [lsim ] ε and a Taylor column, as indicated by the appearance of closed streamlines above the bump, exists when β > 2. Moderate stratification (S ∼ 1) causes the flow to be fully three-dimensional and the Taylor column to be a conical vortex whose height depends on β S and u′0). The results are compared with Davies's (1971, 1972) experiments.

Our results tend to support the Taylor column theory of Jupiter's Great Red Spot but effects due to variations in the Coriolis parameter with latitude have been (unjustifiably) ne glected. Using typical values for the earths oceans we find that Taylor columns of significant height could be found there. Some pertinent observations from the ocean are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 3 , 8 May 1973 , pp. 517 - 537
Copyright
© 1973 Cambridge University Press

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References

Buzyna, C. & Veronis, G. 1971 Spin-up of a stratified fluid: theory and experiment. J. Fluid Mech. 50, 579–608.Google Scholar
Davies, P. A. 1971 Experiments on Taylor columns in rotating, stratified fluids. Ph.D. Thesis, University of Newcastle-upon-Tyne.
Davies, P. A. 1972 Experiments on Taylor columns in rotating stratified fluids. J. Fluid Mech. 54, 691–718.Google Scholar
Defant, A. 1961 Physical Oceanography, vol. 1. Pergamon.
Eady, F. T. 1949 Long waves and cyclone waves. Tellus, 1, 33–52.Google Scholar
Fuglister, F. C. 1963 Gulf Stream '60. Progress in Oceanography, vol. 1 (ed. M. Sears), pp. 265–373. Pergamon.
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Table of Integrals Series and Products, 4th edn. Academic.
Hide, R. 1961 Origin of Jupiter's Great Red Spot. Nature, 190, 895–896.Google Scholar
Hide, It. 1963 On the hydrodynamics of Jupiter's atmosphere. Mem. Soc. Roy. Sci. Liége, V7, 481–505.Google Scholar
Hide, R. 1969 Dynamics of the atmospheres of the major planets with an appendix on the viscous boundary layer at the rigid bounding surface of an electricallyconducting rotating fluid in tho presence of a magnetic field. J. Atmos. Sci. 26, 841–853.Google Scholar
Hide, R. 1971 On geostrophic motion of a non-homogeneous fluid. J. Fluid Mech. 49, 745–751.Google Scholar
Hide, R. & Ibbetson, A. 1966 An experimental study of ‘Taylor columns’. Icarus, 5, 279–290.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
Hogg, N. G. 1973 The preconditioning phase of Medoc 1969-II. Topographic effects. Deep Sea Res. (in press).Google Scholar
Ingersoll, A. P. 1969 Inertial Taylor columns and Jupiter's Great Red Spot. J. Atmos. Sci. 26. 744–752Google Scholar
Jacobs, S. J. 1964 The Taylor column problem. J. Pluid Mech. 20, 581–591.Google Scholar
Johnson, G. L., Vogt, P. R. & Schneider, E. D. 1971 Morphology of the Northeastern Atlantic and Labrador Sea. Deut. Hydrograph. 24, 49–73.Google Scholar
Lowrie, A. & Heezen, B. C. 1967 Knoll and sediment drift near Hudson Canyon. Science, 157, 1552–1553.Google Scholar
Meincke, J. 1971 Observation of an anticyclonic vortex trapped above a seamount. J. Geophys. Res. 76, 7432–7440.Google Scholar
Proudman, J. 1916 On the motion of solids in a liquid possessing vorticity. Proc. Roy. Soc. A 92, 408–424.Google Scholar
Roberts, D. G., Hogg, N. G., Bishop, D. G. & Flewellen, C. G. 1973 Sediment distribution around moated seamounts in the Rockall Trough. (To appear.)
Stone, P. H. & Baker, D. J. 1968 Concerning the existence of Taylor columns in atom spheres. Quart. J. Roy. Met. Soc. 94, 576–580.Google Scholar
Swallow, J. C. & Caston, G. F. 1973 The preconditioning phase of Medoc 1969-1. Observations. Deep Sea Res. (in press).Google Scholar
Taylor, G. I. 1917 Motion of solids in fluids when the flow is not irrotational. Proc. Roy. Soc. 93, 99–113.Google Scholar
Taylor, G. I. 1923 Experiments on the motion of solid bodies in rotating fluids. Proc. Roy. Soc. 104, 213–218.Google Scholar
Vawri, A. & Boyer, D. L. 1971 Rotating flow over shallow topographies. J. Fluid Mech. 50, 79–95.Google Scholar
Walin, O. 1969 Some aspects of time-dependent motion of a stratified rotating fluid. J. Fluid Mech. 36, 289–307.Google Scholar