GENERALIZED GINZBURG-LANDAU EQUATIONS FOR 4 UNSTABLE BAROCLINIC WAVES

The critical surface of the quasigeostrophic two-layer equations (Phil lips model) on the beta-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 thresh old of instability of the axisymmetric state. It is shown that the for m of the generalized Ginzburg-Landau equations is completely determine d by the symmetry properties of the system and does not depend on the details of the quasigeostrophic two-layer equations. The numerical sol utions of the four-mode-order parameter equations show that for the sp ecific coefficients of the Phillips model chaos occurs for arbitrary w eak supercriticality in a particular part of the supercritical domain.