Titre/Title : Revisiting the equatorial beta-plane: a local model for convection in rapidly rotating spherical shells

Contact : Joel Sommeria (Equipe MEIGE)

Résumé/Abstract : Motivated by the recent discovery of subsurface oceans on planetary moons (Enceladus, Europa, Titan, etc.) and the interest they have generated, I will present an exploration of convective flows in shallow spherical shells in the rapid rotation limit. The convective flows in these oceans are believed to have far-reaching consequences for each moon including the active shaping of the outer crust topography and magnetic field generation via the dynamo effect. However, as many other geo- and astrophysical systems, these flows are usually in a regime characterized by the dominance of the Coriolis and pressure forces in the Navier-Stokes equations: the geostrophic balance. As a result of this balance, the flow develops a strong anisotropy between the scales along and perpendicular to the axis of rotation (the Proudman-Taylor theorem). Generally, this anisotropy severely hinders our ability to find analytical solutions, or the numerical approximations thereof, to the equations of motion.

I will present an approach that leverages the presence of a leading order balance and provides a local model for convective motions in the equatorial region of a shallow layer of fluid driven by a temperature difference between the inner and the outer shell. Coined the non-hydrostatic equatorial beta-plane, this fully nonlinear model has been studied semi-analytically and numerically [1]. Robust predictions for the variation of the equatorial heat flux with the latitude have been obtained at a much more modest numerical cost than standard DNS. In our model, the heat flux is found to be maximum at the equator. The decay of the heat flux with latitude is found to be controlled by a trapping parameter that can be understood as the local rate of change of the Coriolis force.

[1] Benjamin Miquel, Jin-Han Xie, Nicholas Featherstone, Keith Julien and Edgar Knobloch