Experimental and numerical studies of convection in a rapidly rotating spherical shell

Abstract

Thermal convection in a rapidly rotating spherical shell is investigated experimentally and numerically. The experiments are performed in water (Prandtl number P=7) and in gallium (P=0.025), at Rayleigh numbers R up to 80 times the critical value in water (up to 6 times critical in gallium) and at Ekman numbers E∼10−6. The measurements of fluid velocities by ultrasonic Doppler velocimetry are quantitatively compared with quasi-geostrophic numerical simulations incorporating a varying β-effect and boundary friction (Ekman pumping). In water, unsteady multiple zonal jets, weaker in amplitude than the non-axisymmetric flow, are experimentally observed and numerically reproduced at moderate forcings (R/Rc<40). In this regime, zonal flows and vortices share the same length scale. Gallium experiments and strongly supercritical convection experiments in water correspond to another regime. In these turbulent flows, the zonal motion amplitude U dominates the non-axisymmetric motion amplitude Ũ. As a result of the reverse cascade of kinetic energy, the characteristic Rhines length scale $\ell_{\beta} \,{\sim}\, \sqrt{\overline{U}/\beta}$ of zonal jets emerges, and the boundary friction becomes the main brake on the growth of the zonal flow. A scaling law U ∼ Ũ4/3 is then derived and verified both numerically and experimentally.