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Instability of coupled geostrophic density fronts and its nonlinear evolution

Published online by Cambridge University Press:  01 October 2008

EMILIE SCHERER  and
VLADIMIR ZEITLIN
EMILIE SCHERER
Affiliation:
Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure / Université Paris VI, 24 rue Lhomond, 75231 Paris Cedex 5, [email protected]
VLADIMIR ZEITLIN
Affiliation:
Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure / Université Paris VI, 24 rue Lhomond, 75231 Paris Cedex 5, [email protected]
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Abstract

Instability of coupled density fronts, and its fully nonlinear evolution are studied within the idealized reduced-gravity rotating shallow-water model. By using the collocation method, we benchmark the classical stability results on zero potential vorticity (PV) fronts and generalize them to non-zero PV fronts. In both cases, we find a series of instability zones intertwined with the stability regions along the along-front wavenumber axis, the most unstable modes being long wave. We then study the nonlinear evolution of the unstable modes with the help of a high-resolution well-balanced finite-volume numerical scheme by initializing it with the unstable modes found from the linear stability analysis. The most unstable long-wave mode evolves as follows: after a couple of inertial periods, the coupled fronts are pinched at some location and a series of weakly connected co-rotating elliptic anticyclonic vortices is formed, thus totally changing the character of the flow. The characteristics of these vortices are close to known rodon lens solutions. The shorter-wave unstable modes from the next instability zones are strongly concentrated in the frontal regions, have sharp gradients, and are saturated owing to dissipation without qualitatively changing the flow pattern.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 613 , 25 October 2008 , pp. 309 - 327
Copyright
Copyright © Cambridge University Press 2008

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