CONSISTENT SCALING LAWS IN ANELASTIC SPHERICAL SHELL DYNAMOS

Abstract

Numerical dynamo models always employ parameter values that differ by orders\nof magnitude from the values expected in natural objects. However, such models\nhave been successful in qualitatively reproducing properties of planetary and\nstellar dynamos. This qualitative agreement fuels the idea that both numerical\nmodels and astrophysical objects may operate in the same asymptotic regime of\ndynamics. This can be tested by exploring the scaling behavior of the models.\nFor convection-driven incompressible spherical shell dynamos with constant\nmaterial properties, scaling laws had been established previously that relate\nflow velocity and magnetic field strength to the available power. Here we\nanalyze 273 direct numerical simulations using the anelastic approximation,\ninvolving also cases with radius-dependent magnetic, thermal and viscous\ndiffusivities. These better represent conditions in gas giant planets and\nlow-mass stars compared to Boussinesq models. Our study provides strong support\nfor the hypothesis that both mean velocity and mean magnetic field strength\nscale as a function of power generated by buoyancy forces in the same way for a\nwide range of conditions.\n