Oscillatory convection and chaos in a Lorenz-type model of a rotating fluid

A four-mode model of convection in a rotating fluid layer is studied. The model is an extension of the Lorenz model of Rayleigh-Bénard convection, the extra mode accounting for the regeneration of vorticity by rotation. Perturbation theory is applied to show that the Hopf bifurcations from conductive and steady convective solutions can be either supercritical or subcritical. Perturbation theory is also used at large Rayleigh numbersr to predict novel behavior. Supercritical oscillatory convection of finite amplitude is found by numerical integration of the governing equations. The general picture is of a series of oscillatory solutions stable over larger intervals, interspersed by short bursts of chaos.