Chaotic thermal convection in a rapidly rotating spherical shell: consequences for flow in the outer core

Abstract

Results of a combined laboratory and numerical study of fully developed thermal convection in a rapidly rotating spherical shell are presented. We determine the effects of rotation and a solid inner core on high Reynolds number buoyancy-driven flow in a fluid with the geometry of the Earth's liquid outer core. Centrifugal acceleration is used as a substitute for the spherical gravity field of the core. Experiments are made with Prandtl number Pr = 7, Ekman numbers E ⩾ 2 × 10 −6 and Rayleigh numbers Ra T ⩽ 3 × 10 9. Numerical calculations of finite-amplitude convection are made using a quasi-geostrophic flow model with the same Prandtl number, and with Ra T ⩽ 5 × 10 7 and E ⩾ 2 × 10 −5. Near the onset of convection, the motion consists of periodic columnar cells aligned parallel to the rotation axis and arrayed around the axial cylinder tangent to the inner sphere. The cells spiral and propagate in the direction of rotation, the platform in the equatorial plane resembling a drifting pinwheel. At Rayleigh numbers greater than a few times critical, the periodic pinwheel planform is replaced by chaotic, time-dependent convection consisting of numerous columnar vortices that fill the spherical shell. The vortices are driven by ribbon-shaped plumes concentrated near the equatorial plane. Reynolds stresses derived from the vortices and large-scale temperature gradients produced by the plumes generate a large-scale zonal flow that is retrograde (westward) near the inner boundary tangent cylinder, and prograde (eastward) in an equatorial band near the outer boundary. Our results suggest that convection in the Earth's core consists of irregularly distributed columnar vortices plus a secondary zonal flow.