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Session 69 - The Solar Dynamo and Helioseismology.
Display session, Thursday, June 13
We consider the dynamics of compressible convection within a curved local segment of a rotating spherical shell, aiming to resolve the disparity between the differential rotation profiles predicted by previous laminar simulations (angular velocity constant on cylinders) and those deduced from helioseismic inversion of the observed frequency splitting of p modes. By limiting the horizontal extent of the domain under study, we can utilize the available spatial degrees of freedom on current supercomputers to attain more turbulent flows than in the full shell. Our previous study of three-dimensional convection within a slab geometry of an f-plane neglected the effects of curvature, and thus did not admit the generation of Rossby waves. These waves propagate in the longitudinal direction and thus produce rather different spectral characteristics and mean flows in the north-south and east-west directions. By considering motions in a curvilinear geometry in which the Coriolis parameter varies with latitude, we admit the possibility of Rossby waves which couple to the turbulent convection. Here we present simulations with Rayleigh numbers in excess of 10^6, and Prandtl numbers less than 0.1 in such a curved local segment of a spherical shell using a newly developed code based on compact finite differences. This computational domain takes the form of a curved, periodic channel in longitude with stress-free sidewalls in latitude and radius. Despite the differences in geometry and boundary conditions, the flows maintain similarities with those of our previous f-plane simulations. The surface flows form broad, laminar networks which mask the much more turbulent flows of the interior. The dynamics within this turbulent region is controlled by the interactions of a tangled web of strong vortex tubes. These interactions are further complicated by the effects of curvature. The differential rotation generated by the turbulent convection typically increases with depth and attains a maximum at the base of the layer of about 10 % over the imposed rotation rate.
Program listing for Thursday