HR: 14:40h
AN: OS53B-05    [Abstracts]
TI: Stability and nonlinear evolution of coupled density fronts
AU: * Scherer, E
EM: scherer@lmd.ens.fr
AF: Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure 24 rue Lhomond, Paris Cedex 5, 75231, France
AU: Zeitlin, V
EM: zeitlin@lmd.ens.fr
AF: Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure 24 rue Lhomond, Paris Cedex 5, 75231, France
AB: We study the linear stability of coupled density fronts with the help of the collocation method, which enables us to treat flows with arbitrary potential vorticity (PV).
In their classical work, Griffiths, Killworth and Stern (1982) have shown that coupled density fronts are unstable to perturbations with small wavenumbers and that flows with zero PV are, more precisely, unstable over an interval of finite width of small wavenumbers. Paldor and Ghil (1990) have shown that coupled density fronts with zero PV are unstable to perturbations with finite wavenumbers on finite intervals separated by intervals of stability, and when the wavenumber increases the maximum growth rate in each interval of unstability decreases. We have reproduced the results of Griffiths, Killworth and Stern (1982) and of Paldor and Ghil (1990), and we found, for zero PV flows, a new instability interval. For flows with non-zero PV the picture is qualitatively the same: we find several instability intervals, separated by stability zones in the wavenumber space. Each unstable interval has a maximum growth rate inferior to those of unstable intervals with smaller wavenumbers. We then study the nonlinear stage of evolution of the instability with the help of the high-resolution finite-volume numerical scheme by Bouchut (2007). The simulations are initialized with the most unstable eigenmode recovered from the linear analysis. We observe that as the instability develops the flow is reorganized into a series of rotating anticyclonic elliptic vortices connected by thin filaments of fluid. The parameters of vortices are close to those of rodons (Cushman-Roisin, Heil and Nof 1985), the exact lens-like solutions of the nonlinear shallow water equations. References:
B. Cushman-Roisin, W.H. Heil and D. Nof, Journal of Geophysical Research, 1985.
F. Bouchut in: V. Zeitlin et al, Edited Series on Advances in Nonlinear Science and Complexity, 2007.
R.W. Griffiths, P. D. Killworth and M.E. Stern, Journal of Fluid Mechanics, 1982.
N. Paldor and M. Ghil, Journal of Physical Oceanography, 1990.
DE: 3215 Instability analysis
DE: 4512 Currents
DE: 4520 Eddies and mesoscale processes
DE: 4528 Fronts and jets
SC: Ocean Sciences [OS]
MN: 2007 Fall Meeting