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Inertial Taylor columns on a beta plane

Published online by Cambridge University Press:  29 March 2006

Michael S. McCartney
Michael S. McCartney
Affiliation:
Woods Hole Oceanographic Institution
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Abstract

The effect of variable Coriolis parameter on the formation of inertial Taylor columns is determined for the case of a two-layer fluid with moderate stratification. Analytic solutions of the inertial, quasi-geostrophic, β-plane equations are obtained. As a special case, sohtions corresponding to a single-layer, homo-geneous fluid are also obtained. When both layer velocities are retrograde (westward), the effect of β is to limit the horizontal extent of the disturbance due to the bump. When both layer velocities are prograde (eastward), an extensive meandering wake is found downstream of the bump. Associated with this wake can be large stationary cyclonic and anti-cyclonic eddies. The meander amplitudes in the two layers are typically nearly the same. I n both the retrograde and prograde cases, the strength of the disturbance to the flow above the bump is less in the upper layer compared with the lower, indicating an attenuation in the vertical due to stratification. For a counter-flow situation, the solutions are complicated by the possibility of a stationary baroclinic wave, one that would exist even for β = 0. In all the situations in which a meandering wake is formed, there is a wave-drag force on the bump. Some laboratory experiments corres- ponding to the single-layer solutions are described.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 1 , 11 March 1975 , pp. 71 - 95
Copyright
© 1975 Cambridge University Press

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References

Baker, D. J. 1966 A technique for the precise measurement of small fluid velocities. J. Fluid Mech. 26, 573–575.Google Scholar
Frenzen, P. 1955 Westerly flow past an obstacle in a rotating hemispherical shell. Bull. Am. Met. Soc. 36, 204–210.Google Scholar
Fuglister, F. C. 1963 Gulf stream'60. Prog. in Oceanogmphy, 1, 265–383.Google Scholar
Fuglister, F. C. 1972 Cyclonic rings formed by the Gulf Stream 1965-66. Studies in Physical Oceanography: a Tribute to Gieorg Wust on his 80th Birthday, pp. 137–168. Gordon & Breach.
Fuglister, F. C. & Voorhis, A. D. 1965 A new method of tracking the Gulf Stream. Limnol. Oceanog. S.uppl., 10, R115–R124.Google Scholar
Fuglister, F. C. & Worthington, L. V. 1951 Some results of a multiple ship survey of the Gulf Stream. Tellus, 3, 1–14.Google Scholar
Fultz, D. & Frenzen, P. 1955 A note on certain interesting ageostrophic motions in a rotating hemispherical shell. J. Meteor. 12, 332–338.Google Scholar
Fultz, D. & Long, R. R. 1951 Two-dimensional flow around a circular barrier in a rotating spherical shell. Tellus, 3, 61–68.Google Scholar
Gill, A. E. 1968 A linear model of the Antarctic circumpolar current. J. Fluid Mech. 32, 465–488.Google Scholar
Gordon, A. L. & Bye, J. A. T. 1972 Surface dynamic topography of Antarctic Waters. J. Geophys. Res. 77, 5993–5999.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
Hansen, D. V. 1970 Gulf Stream meanders between Cape Hatteras and the Grand Banks. Deep Sea Res. 17, 495–511.Google Scholar
Hide, R. 1961 Origin of Jupiter's Great Red Spot. Nature, 190, 895–896.Google Scholar
Hogg, N. G. 1973 On the stratified Taylor column. J. Fluid Mech. 58, 517–537.Google Scholar
Huppert, H. E. 1975 Some remarks on the initiation of inertial Taylor columns. J. Fluid Mech. 67, 397–414.Google Scholar
Ingersoll, A. P. 1969 Inertial Taylor columns and Jupiter's Great Red Spot. J. Atnzos. Sci. 26, 744–752.Google Scholar
Jacobs, S. J. 1964 The Taylor column problem. J. Fluid Mech. 29, 581–591.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
Long, R. R. 1952 The flow of a, liquid past a barrier in a rotating spherical shell. J. Meteor. 9, 187–199.Google Scholar
Mccartney, M. S. 1972 Taylor columns and Rossby wakes generated by isolated topographic features on a beta-plane. Notes on the 1972 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanograph, IC Institution, Whoi Ref. 72–79, 60–81.
Miles, J. W. & Huppert, H. E. 1968 Lee waves in a stratified flow. Part 2. Semi-circular obstacle. J. Fluid Mech. 33, 803–814.Google Scholar
Munk, W. H. & Palmén, E. 1951 Note on the dynamics of the Antarctic Circumpolar Current. Tellus, 3, 53–56.Google Scholar
Pedlosky, J. 1964 The stability of currents in the atmosphere and the ocean. Part 1. J. Atmos. Sci. 21, 201–219.Google Scholar
Robinson, A.R., Luyten, J. R. & Fuglister, F. C. 1974 Transient Gulf Stream meandering. Part 1. An observational experiment. J. Phys. Oceanog. 4, 237–255.Google Scholar
Stewartson, K. 1953 On the slow motion of an ellipsoid in a rotating fluid. Quart. J. Mech. Appl. Moth. 6, 141–162.Google Scholar
Stewartson, I. 1967 On slow transverse motion of a sphere through a rotating fluid. J. Fluid Mech. 30, 357–369.Google Scholar
Vaziri, A. & Boyer, D. L. 1971 Rotating flow over shallow topographies. J. Fluid Mech. 5, 79–95.Google Scholar