A model for the transition to baroclinic chaos

The transition to chaos in a 2-layer baroclinic fluid with a slightly different viscosity in each layer is investigated. A low-order model is constructed by truncating the quasi-geostrophic partial differential equations to include one azimuthal wave in each layer while retaining a general zonal-flow correction. When the viscosities are equal the model reduces to a modified form of the Lorenz equations and displays a cusped return map. For slightly different viscosities the transition to chaos follows the Feigenbaum scenario. The return map in the chaotic regime is nearly parabolic and highly contracted. Multiple attractors are found for the same control parameters. The predicted route to chaos is similar to that observed in laboratory experiments, although significant quantitative differences remain.