Numerical models of the onset of yield strength in crystal¯melt suspensions

Penetration of columnar convection in a rapidly rotating spherical shell into a stably stratified fluid layer near the outer boundary is investigated. An analytical expression for the penetration thickness is derived by considering 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 boundary show that the penetration thickness is proportional to the angular velocity of the system and to the horizontal scale of the vortices, and inversely proportional to the Brunt¯V?is?l? frequency in the stratified layer. Thus the stratification acts as a low-pass filter to forcing from below. The analytic expression for the penetration thickness gives good agreement with numerical results for critical convection in a rotating spherical shell with a stably stratified outer layer. The results suggest that if deep convection is to penetrate the stratified layer observed by the Galileo probe then the horizontal scale needs to be more than several thousand kilometers. Parameter values from recent studies of the thermal history of the Earthʹs core also suggest that any convection columns with horizontal scale larger than several hundred kilometers would be expected to penetrate into any stable layer in the outer part of the Earthʹs fluid outer core when the Lorentz force plays a subdominant role.