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A series solution of the nonlinear wind-driven ocean circulation and its inertial limit

Published online by Cambridge University Press:  26 April 2006

W. T. M. Verkley  and
J. T. F. Zimmerman
W. T. M. Verkley
Affiliation:
Netherlands Institute for Sea Research, Den Burg (Texel), The Netherlands Present address and address for correspondence: Royal Netherlands Meteorological Institute, PO Box 201, 3730 AE De Bilt, The Netherlands.
J. T. F. Zimmerman
Affiliation:
Netherlands Institute for Sea Research, Den Burg (Texel), The Netherlands Institute of Marine and Atmospheric Sciences, University of Utrecht, The Netherlands
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Abstract

A series solution approach to the forced and damped quasi-geostrophic barotropic vorticity equation is considered in order to examine the strongly forced and inertial limits of ocean gyre dynamics. The strongly forced limit is the limit investigated numerically by Veronis (1966b). It is shown that this limit, although superficially having the same symmetry properties as the inertial limit, is distinguishably different from the latter. After isolating the inertial limit in an appropriate way it is shown that our series solution method is able to find the ‘free mode’ and its ‘almost free correction’, that the ‘free mode’ obeys the integral criteria of Niiler (1966) and Pierrehumbert & Malguzzi (1984) and that the relationship between the streamfunction and the absolute vorticity is in general a nonlinear one.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 295 , 25 July 1995 , pp. 61 - 89
Copyright
© 1995 Cambridge University Press

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References

Beardsley, R. C. 1969 A laboratory model of the wind-driven ocean circulation. J. Fluid Mech. 38, 255–271.Google Scholar
Fofonoff, N. P. 1954 Steady flow in a frictionless homogeneous ocean. J. Mar. Res. 13, 254–262.Google Scholar
Fofonoff, N. P. 1962 Dynamics of ocean currents. In The Sea, vol. 1: Physical Oceanography (ed. M. N. Hill), pp. 3–30. Interscience.
Greatbatch, R. J. 1987 A model for the inertial recirculation of a gyre. J. Mar. Res. 45, 601–634.Google Scholar
Harrison, D. E. & Stalos, J. 1982 On the wind-driven ocean circulation. J. Mar. Res. 40, 773–791.Google Scholar
Høiland, E. 1950 On horizontal motion in a rotating fluid. Geofys. Publik. 17, 1–26.Google Scholar
Holloway, G. 1986 Comment on Fofonoff's mode. Geophys. Astrophys. Fluid Dyn. 37, 165–169.Google Scholar
Marshall, J. & Nurser, G. 1986 Steady, free circulation in a stratified quasi-geostrophic ocean. J. Phys. Oceanogr. 16, 1799–1813.Google Scholar
Merkine, L.-O., Mo, K. C. & Kalnay, E. 1985 On Fofonoff's mode. Geophys. Astrophys. Fluid Dyn. 32, 175–196.Google Scholar
Miller, J., Weichman, P. B. & Cross, M. C. 1992 Statistical mechanics, Euler's equations and Jupiter's red spot. Phys. Rev. A 45, 2328–2359.Google Scholar
Niiler, P. P. 1966 On the theory of wind-driven ocean circulation. Deep-Sea Res. 13, 597–606.Google Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics. Springer.
Pierrehumbert, R. T. & Malguzzi, P. 1984 Forced coherent structures and local multiple equilibria in a barotropic atmosphere. J. Atmos. Sci. 41, 246–257.Google Scholar
Robert, R. & Sommeria, J. 1991 Statistical equilibrium states for two-dimensional flows. J. Fluid Mech. 229, 291–310.Google Scholar
Rudin, W. 1964 Principles of Mathematical Analysis. McGraw-Hill.
Salmon, R., Holloway, G. & Hendershott, M. C. 1976 The equilibrium statistical mechanics of simple quasi-geostrophic models. J. Fluid Mech. 75, 691–703.Google Scholar
Stommel, H. 1948 The westward intensification of wind-driven ocean currents. Trans. Am. Geophys. Union 99, 202–206.Google Scholar
Swart, H. E. de & Zimmerman, J. T. F. 1993 Rectification of the wind-driven ocean circulation on the β plane. Geophys. Astrophys. Fluid Dyn. 71, 17–41.Google Scholar
Veronis, G. 1966a Wind-driven ocean circulation – part I: linear theory and perturbation analysis. Deep-Sea Res. 13, 17–29.Google Scholar
Veronis, G. 1966b Wind-driven ocean circulation – part II: numerical solution of the nonlinear problem. Deep-Sea Res. 13, 31–55.Google Scholar
Zimmerman, J. T. F. 1993 A simple model for the symmetry properties of nonlinear wind-driven ocean circulation. Geophys. Astrophys. Fluid Dyn. 71, 1–15.Google Scholar
Zimmerman, J. T. F. & Maas, L. R. M. 1989 Renormalized Green's function for nonlinear circulation on the beta plane. Phys. Rev. A 39, 3575–3590.Google Scholar