Penetration of columnar convection into an outer stably stratified layer in rapidly rotating spherical fluid shells

Penetration of columnar convection in a rapidly rotating spherical shell in to a stably stratified fluid layer near the outer boundary is investigated. An analytical expression for the penetration thickness is derived by consi dering perturbations to a stably stratified rotating Boussinesq fluid in a semi-infinite region with the rotation axis tilted relative to the gravity axis. Solutions for the response to vortical motion applied at the bottom b oundary show that the penetration thickness is proportional to the angular velocity of the system and to the horizontal scale of the vortices, and inv ersely proportional to the Brunt-Vaisala frequency in the stratified layer. Thus the stratification acts as a lowpass filter to forcing from below. Th e analytic expression for the penetration thickness gives good agreement wi th numerical results for critical convection in a rotating spherical shell with a stably stratified outer layer. The results suggest that if deep conv ection is to penetrate the stratified layer observed by the Galileo probe t hen the horizontal scale needs to be more than several thousand kilometers. Parameter values from recent studies of the thermal history of the Earth's core also suggest that any convection columns with horizontal scale larger than several hundred kilometers would be expected to penetrate into any st able layer in the outer part of the Earth's fluid outer core when the Loren tz force plays a subdominant role. (C) 2001 Elsevier Science B.V. All right s reserved.