On the effect of laterally varying boundary heat flux on rapidly rotating spherical shell convection

The onset of convection in a rotating spherical shell subject to laterally varying heat flux at the outer boundary is considered in this paper. The focus is on the geophysically relevant regime of rapid rotation (low Ekman number) where the natural length scale of convection is significantly smaller than the length scale imposed by the boundary heat flux pattern. Contrary to earlier studies at a higher Ekman number, we find a substantial reduction in the onset Rayleigh number Ra_c with increasing lateral variation. The decrease in Ra_c is shown to be closely correlated to the equatorial heat flux surplus in the steady, basic state solution. The consistency of such a correlation makes the estimation of Ra_c possible without solving the full stability problem. The steady baroclinic flow has a strong cyclone–anticyclone asymmetry in the kinetic helicity only for equatorially symmetric lateral variations, with possible implications for dynamo action. Equatorially antisymmetric variations, on the other hand, break the symmetry of the mean flow, in turn negating its helicity. Analysis of the perturbation solution reveals strongly localized clusters through which convection rolls drift in and out at a frequency higher than that for the reference case with homogeneous boundary heat flux. Large lateral variations produce a marked decrease in the azimuthal length scale of columns, which indicates that small-scale motions are essential to the transport of heat in rapidly rotating, localized convection. With an equatorially antisymmetric heat flux pattern, convection in individual clusters goes through an asynchronous wax-wane cycle whose frequency is much lower than the drift rate of the columns. These continual variations in convection intensity may in turn result in fluctuations in the magnetic field intensity, an effect that needs to be considered in dynamo models. Finally, there is a notable analogy between the role of a laterally varying boundary heat flux and the role of a laterally varying magnetic field in confining small-scale convection.