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A Numerical Investigation of the Stability of Isolated Shallow Water Vortices

A. StegnerLaboratoire de Météorologie Dynamique, École Normale-Supérieure, Paris, France

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D. G. DritschelMathematical Institute, University of St. Andrews, North Haugh, St. Andrews, United Kingdom

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Print Publication:
01 Oct 2000
DOI:
https://doi.org/10.1175/1520-0485(2000)030<2562:ANIOTS>2.0.CO;2
Page(s):
2562–2573
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Abstract

Motivated by observational data and recent numerical simulations showing that ageostrophic effects may play an important role in the dynamics and transport of large-scale vortices in the atmosphere and the oceans, the authors examine the stability of a family of isolated vortices, numerically, using the contour-advective semi-Lagrangian algorithm. The full shallow-water equations (1½-layer model) are integrated in order to investigate vortices over a wide range of parameters. In order to characterize the cyclone–anticyclone asymmetry, the stability of a couple of vortices having velocity profiles of opposite sign is compared. It is found that ageostrophic effects (finite Rossby number) tend to stabilize anticyclones but destabilize cyclones. On the other hand, large-scale effects (small Burger number) are shown to stabilize all vortices for this reduced-gravity model. Here again, the anticyclones tend to be favored in this restabilization process. These results are compared with a linear stability analysis performed in the framework of the standard quasigeostrophic model that predicts a symmetric evolution for cyclones and anticyclones. The authors have shown that a significant departure from QG dynamics, due to ageostrophic and large-scale effects, appears in a range of parameters relevant to large-scale coherent structures in nature.

Corresponding author address: Dr. Alexandre Stegner, Laboratoire de Météorologie Dynamique, École Normale Supérieure, 24, rue Lhomond, 75005 Paris Cedex, France.

Email: stegner@lmd.ens.fr

Abstract

Motivated by observational data and recent numerical simulations showing that ageostrophic effects may play an important role in the dynamics and transport of large-scale vortices in the atmosphere and the oceans, the authors examine the stability of a family of isolated vortices, numerically, using the contour-advective semi-Lagrangian algorithm. The full shallow-water equations (1½-layer model) are integrated in order to investigate vortices over a wide range of parameters. In order to characterize the cyclone–anticyclone asymmetry, the stability of a couple of vortices having velocity profiles of opposite sign is compared. It is found that ageostrophic effects (finite Rossby number) tend to stabilize anticyclones but destabilize cyclones. On the other hand, large-scale effects (small Burger number) are shown to stabilize all vortices for this reduced-gravity model. Here again, the anticyclones tend to be favored in this restabilization process. These results are compared with a linear stability analysis performed in the framework of the standard quasigeostrophic model that predicts a symmetric evolution for cyclones and anticyclones. The authors have shown that a significant departure from QG dynamics, due to ageostrophic and large-scale effects, appears in a range of parameters relevant to large-scale coherent structures in nature.

Corresponding author address: Dr. Alexandre Stegner, Laboratoire de Météorologie Dynamique, École Normale Supérieure, 24, rue Lhomond, 75005 Paris Cedex, France.

Email: stegner@lmd.ens.fr

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