[MIS18-P04] A comparison between top-down and bottom-up type convective flows in a rotating spherical shell with stress-free boundaries
Keywords:compositional convection, linear stability analysis
For this purpose, onsets of top-down and bottom-up compositional convection in a rotating spherical shell are studied as a linear stability problem. We consider the Boussinesq fluid contained in the rotating spherical shell, of which radius ratio is 0.2. The linearized governing equations, that is, conservation equations of the momentum and mass, and the transport equation of composition, are solved as an eigenvalue problem. The adopted values of the Ekman number, Ek range from 10-4 to 10-3. Boundary conditions are stress-free and impermeable for the velocity field, and fixed flux for composition. It is found that the critical Rayleigh numbers Rac shows an Ekman-number-dependence of Rac∝Ek-1.26 for the top-down case and Rac∝Ek-1.09 for the bottom-up one. The flows at the onsets for both the types have columnar convection owing to the effect of rotation. Motion in the top-down case is dominated by the convection outside the tangent cylinder, which is an imaginary cylinder co-axial with the rotation axis touching the inner sphere at the equator. On the other hand, the axially elongated flow structure around the surface of the tangent cylinder is formed in the bottom-up case as well as columnar flows outside the tangent cylinder. In decreasing the Ekman number, it repeats that the structure inside the cylinder appears and vanishes, and depends on the transition of critical horizontal wavenumber.