A quasi-geostrophic numerical model of a rotating internally heated fluid

A quasi-geostrophic numerical model of flow in a rotating channel is integrated under conditions typical of laboratory experiments with an internally heated annulus system. Compared to a laboratory experiment, or a full Navier-Stokes simulation, the quasi geostrophic numerical model is a simple system. It includes nonlinear interactions, dissipation via conventional parameterizations of Ekman layers and internal diffusion, and a steady forcing term which represents heating near the centre of the channel and cooling near both sides. Explicit boundary layers, cylindrical geometry effects, horizontal variations in static stability and variations in conductivity and diffusivity with temperature are all absent, and ageostrophic advection is incompletely represented. Nevertheless, over a range of parameters, flows are produced which strongly resemble those seen in the laboratory thus suggesting that the most important physical processes are represented. The numerical model is used to map out a regime diagram which includes examples of steady flows, flows with periodic time dependence (wavenumber vacillations) and flows which are irregularly time dependent.