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Dynamics of ventilated coherent cold eddies on a sloping bottom

Published online by Cambridge University Press:  26 April 2006

Gordon E. Swaters  and
Glenn R. Flierl
Gordon E. Swaters
Affiliation:
Applied Mathematics Institute, Department of Mathematics and Institute of Earth and Planetary Physics, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
Glenn R. Flierl
Affiliation:
Center for Meteorology and Physical Oceanography, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

A theory is presented to describe the propagation and structure of coherent cold-core (mesoscale) eddies on a sloping bottom including dynamical and thermodynamical interaction with the surrounding fluid. Based on parameter values suggested by oceanographic and rotating-tank experimental data, the evolution of the baroclinic eddy is modelled with nonlinear ‘intermediate lengthscale’ geostrophic dynamics which is coupled to the surrounding fluid. The process of ventilation is modelled with a simple cross-interfacial mass flux parameterization. The surrounding fluid is governed by nonlinear quasi-geostrophic dynamics including eddy-induced vortex-tube compression. Assuming a relatively weak ventilation rate, a multiple-scale asymptotic theory is constructed to describe the propagation of an initially isolated or coherent baroclinic eddy. Throughout the evolution the eddy is assumed to be interacting strongly with the surrounding fluid. To leading order, the eddy and surrounding fluid satisfy the Stern isolation constraint. The magnitude of the Eulerian velocity field in the surrounding fluid above the eddy is shown to be larger than the swirl velocities in the eddy interior as suggested by experimental data. Also, to leading order, the along-shelf translation speed is given by the Nof formula. The process of ventilation is shown to induce a slowly decaying upslope translation in the propagating eddy, and acts to stimulate a weak slowly decaying topographic Rossby wave field in the surrounding fluid. The important features of the theory are illustrated with a simple example calculation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 565 - 587
Copyright
© 1991 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A., 1965 Handbook of Mathematical Functions. Dover.
Armi, L. & D'Asaro, E. 1980 Flow structures of the benthic ocean. J. Geophys. Res. 85, (C1), 469–483.Google Scholar
Chapman, R. & Nof, D., 1988 The sinking of warm-core rings. J. Phys. Oceanogr. 18, 565–583.Google Scholar
Charney, J. G. & Flierl, G. R., 1981 Oceanic analogues of large-scale atmospheric motions. In Evolution of Physical Oceanography - Scientific Surveys in Honor of Henry Stommel (ed. B. A. Warren & C. Wunsch), pp. 504–548. MIT Press.
Dewar, W. K.: 1987 Ventilating warm rings: theory and energetics. J. Phys. Oceanogr. 17, 2219–2231.Google Scholar
Dewar, W. K.: 1988a Ventilating warm rings: structure and model evaluation. J. Phys. Oceanogr. 18, 552–564.Google Scholar
Dewar, W. K.: 1988b Ventilating β-plane lenses. J. Phys. Oceanogr. 18, 1193–1201.Google Scholar
Flierl, G. R.: 1984a Model of the structure and motion of a warm-core ring. Austral. J. Mar. Freshw. Res. 35, 9–23.Google Scholar
Flierl, G. R.: 1984b Rossby wave radiation from a strongly nonlinear warm eddy. J. Phys. Oceanogr. 14, 47–58.Google Scholar
Griffiths, R. W., Killworth, P. D. & Stern, M. E., 1982 Ageostrophic instability of ocean currents. J. Fluid Mech. 117, 343–377.Google Scholar
Houghton, R. W., Schlitz, R., Beardsley, R. C., Butman, B. & Chamberlin, J. L., 1982 The middle Atlantic bight cool pool: evolution of the temperature structure during summer 1979. J. Phys. Oceanogr. 12, 1019–1029.Google Scholar
Kilworth, P. D.: 1983 On the motion of isolated lenses on a β-plane. J. Phys. Oceanogr. 13, 368–376.Google Scholar
McCartney, M. S.: 1975 Inertial Taylor columns on a beta plane. J. Fluid Mech. 68, 71–95.Google Scholar
McKee, W. W.: 1971 Comments on 'A Rossby wake due to an island in an eastward current. J. Phys. Oceanogr. 1, 287–289.Google Scholar
Miles, J. W.: 1968 Lee waves in a stratified flow. Part 2. Semi-circular obstacle. J. Fluid Mech. 33, 803–814.Google Scholar
Mory, M.: 1983 Theory and experiment of isolated baroclinic vortices. Tech. Rep. WHOI-83–41, pp. 114–132. Woods Hole Oceanographic Institute.
Mory, M.: 1985 Integral constraints on bottom and surface isolated eddies. J. Phys. Oceanogr. 15, 1433–1438.Google Scholar
Mory, M., Stern, M. E. & Griffiths, R. W., 1987 Coherent baroclinic eddies on a sloping bottom. J. Fluid Mech. 183, 45–62.Google Scholar
Nof, D.: 1983 The translation of isolated cold eddies on a sloping bottom. Deep-Sea Res. 30, 171–182.Google Scholar
Nof, D.: 1984 Oscillatory drift of deep cold eddies. Deep-Sea Res. 31, 1395–1414.Google Scholar
Ou, H. W. & Houghton, R., 1982 A model of the summer progression of the cold-pool temperature in the middle Atlantic bight. J. Phys. Oceanogr. 12, 1030–1036.Google Scholar
Pedlosky, J.: 1987 Geophysical Fluid Dynamics, 2nd edn. Springer.
Shaw, P. T. & Csanady, G. T., 1983 Self-advection of density perturbations on a sloping continental shelf. J. Phys. Oceanogr. 13, 769–782.Google Scholar
Smith, P. C.: 1976 Baroclinic instability in the Denmark strait overflow. J. Phys. Oceanogr. 6, 355–371.Google Scholar
Swaters, G. E.: 1991 On the baroclinic instability of cold-core coupled density fronts on a sloping continental shelf. J. Fluid Mech. 224, 361–382.Google Scholar
Whitehead, J. A., Stern, M. E., Flierl, G. R. & Klinger, B., 1990 Experimental observations of a baroclinic eddy on a sloping bottom. J. Geophys. Res. 95, 9585–9610.Google Scholar