Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 2 3/4 1995 10.5194/npg-2-186-1995 http://www.nonlin-processes-geophys.net/2/186/1995/ http://www.nonlin-processes-geophys.net/2/186/1995/npg-2-186-1995.html http://www.nonlin-processes-geophys.net/2/186/1995/npg-2-186-1995.pdf 186 193 0000-00-00 What can asymptotic expansions tell us about large-scale quasi-geostrophic anticyclonic vortices? A. Stegner V. Zeitlin LMD, B.P.99, Université P.et M. Curie, 4, pl. Jussieu, 75252 Paris Cedex 05, France 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.