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Generalized Ginzburg-Landau Equations for Four Unstable Baroclinic Waves

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  • 1 Institut für Theoretische Physik und Synergetik, Universität Stuttgart, Germany
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Abstract

The critical surface of the quasigeostrophic two-layer equations (Phillips model) on the β plane is examined for finite dissipation. Some points in the parameter space lead to four pairs of marginally stable wave modes. The generalized Ginzburg–Landau equations are derived in order to describe the nonlinear dynamics of the system near the threshold of instability of the axisymmetric state. It is shown that the form of the generalized Ginzburg–Landau equations is completely determined by the symmetry properties of the system and does not depend on the details of the quasigeostrophic two-layer equations. The numerical solutions of the four-mode–order parameter equations show that for the specific coefficients of the Phillips model chaos occurs for arbitrary weak supercriticality in a particular part of the supercritical domain.

Abstract

The critical surface of the quasigeostrophic two-layer equations (Phillips model) on the β plane is examined for finite dissipation. Some points in the parameter space lead to four pairs of marginally stable wave modes. The generalized Ginzburg–Landau equations are derived in order to describe the nonlinear dynamics of the system near the threshold of instability of the axisymmetric state. It is shown that the form of the generalized Ginzburg–Landau equations is completely determined by the symmetry properties of the system and does not depend on the details of the quasigeostrophic two-layer equations. The numerical solutions of the four-mode–order parameter equations show that for the specific coefficients of the Phillips model chaos occurs for arbitrary weak supercriticality in a particular part of the supercritical domain.

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