Nonlinear Interactions in a Two-layer, Quasi-geostrophic, Low-order Model with Topography

Part I: Zonal Flow-Forced Wave Interactions

Abstract

A two-layer, quasi-geostrophic, low-order model is constructed to investigate the nonlinear interactions between the zonal flow, topographically forced waves and free baroclinic waves. In Part I free baroclinic waves are excluded to direct our attention to the zonal flow-forced wave interactions.
In the conservative case, without external thermal forcing and dissipation, equilibrium solutions are obtained and the resonance condition in the present two-layer model is examined. Multiple flow equilibria are also obtained in the non-conservative case. However, unlike the barotropic model of Charney and DeVore (1979), there do not exist two stable equilibria. A multiplicity of the time-dependent solutions is found in a certain range of the external parameters. There exist two or more stable periodic (or aperiodic) solutions for the same external conditions. The selection of a solution depends on the initial condition.
As the external thermal forcing parameter increases or decreases by bits, the period of a stable periodic solution can become doubled, quadrupled, and so on. Finally aperiodic solutions appear through the period-doubling sequence phenomenon.