Abstract
AbstractNumerical simulations of convection-driven dynamos in rotating spherical shells are employed to better understand the observed strength and geometry of planetary magnetic fields. The model computations cannot be performed for realistic values of several of the control parameters. By varying parameters within the accessible range, it is possible to derive scaling laws for the magnetic field strength and the flow velocity in the dynamo region and for the dipole moment. Our scaling laws suggest that, even though diffusivities are far too large in the models, diffusive processes do not play an important role, just as in planetary cores. Extrapolating the scaling laws to planetary values of the control parameters leads to reasonable predictions for the field strength in the dynamo region and fits the observed dipole moments decently, in particular in the cases of Earth and Jupiter. For Mercury, which does not fit well when applying the scaling laws in a straightforward way, a model is proposed in which the upper part of the fluid core is stably stratified and the dynamo operates only in its deep regions. The time-varying dynamo field must diffuse through the stable region and is attenuated by the skin effect. The model explains why Mercury has a very weak but probably dipole-dominated magnetic field.
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