Chaotic Behavior and Subcritical Formation of Flow Patterns of Baroclinic Waves for Finite Dissipation

Abstract

The nonlinear dynamics of the quasi-geostrophic two-layer model on the β-plane is examined for finite dissipation near the threshold of instability by analyzing the generalized Ginzburg-Landau equations. According to the choice of the external parameters, there are one, two, three, or four pairs of simultaneously unstable modes. The order parameter equations are derived and analyzed in each case up to three pairs of unstable modes. For one pair of modes a Hopf-bifurcation and a monotonous equilibration to a limit cycle results, for two pairs of modes we find two Hopf-bifurcations, quasi-periodicity with frequency and amplitude vacillation, frequency locking, and transient chaotic behavior, depending on the symmetry properties of the interacting modes. For three unstable pairs of modes a first-order nonequilibrium phase transition is possible if the involved modes satisfy some symmetry conditions. In this case hysteresis, subcritical pattern formation, and permanent chaotic attractors are found.