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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 2, issue 3/4
Nonlin. Processes Geophys., 2, 186–193, 1995
https://doi.org/10.5194/npg-2-186-1995
© Author(s) 1995. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Complex space-time geophysical structures

Nonlin. Processes Geophys., 2, 186–193, 1995
https://doi.org/10.5194/npg-2-186-1995
© Author(s) 1995. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  31 Dec 1995

31 Dec 1995

What can asymptotic expansions tell us about large-scale quasi-geostrophic anticyclonic vortices?

A. Stegner and V. Zeitlin A. Stegner and V. Zeitlin
  • LMD, B.P.99, Université P.et M. Curie, 4, pl. Jussieu, 75252 Paris Cedex 05, France

Abstract. The problem of the large-scale quasi-geostrophic anticyclonic vortices is studied in the framework of the baratropic rotating shallow- water equations on the β-plane. A systematic approach based on the multiplescale asymptotic expansions is used leading to a hierarchy of governing equations for the large-scale vortices depending on their characteristic size, velocity and a free surface elevation. Among them are the Charney-Obukhov equation, the intermediate geostrophic model equation, the frontal dynamics equation and some new nonlinear quasi-geostrophic equation. We are looking for steady-drifting axisymmetric anticyclonic solutions and find them in a consistent way only in this last equation. These solutions are soliton-like in the sense that the effects of weak non-linearity and dispersion balance each other. The same regimes on the paraboloidal β-plane are studied, all giving a negative result in what concerns the axisymmetric steady solutions, except for a strong elevation case where any circular profile is found to be steadily propagating within the accuracy of the approximation.

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