The Non-Negligible Effect of Viscosity Diffusion on the Geodynamo Process

Abstract

Exploring geodynamo's scaling laws is of great importance when a tremendous gap still lies between realistic physics and estimated model parameters. Existing scaling laws need to be tested by numerical simulations. To boost these, taking the outer core viscosity (Formula presented.), we studied its impacts on weak and strong field geodynamo outputs by varying (Formula presented.) in two orders of magnitudes. In the weak field mode, the fluid velocity (Formula presented.) varies with (Formula presented.) by a scaling law of (Formula presented.). While in the strong field mode, (Formula presented.) varies very slowly by a scaling law of (Formula presented.). The magnetic field (Formula presented.) does not change much with (Formula presented.) when the driving force is not too strong ((Formula presented.)) but decreases with (Formula presented.) by a scaling law of (Formula presented.) when geodynamo operates in a very vigorous mode ((Formula presented.)). The reason that (Formula presented.) increases with (Formula presented.) is essential that increasing (Formula presented.) breaks the Taylor-Proudman constraint and drops the critical Rayleigh number, but this kind of increase of (Formula presented.) does not give a stronger (Formula presented.). Furthermore, we conducted a local force balance analysis and demonstrated that the balance shifts under different (Formula presented.). In a quasi-MAC regime, the Lorentz force instead of the inertial force enters into the first-order agostrophic force balance, though the viscous force still plays a role. Comparing with other scaling laws previous wisdom holds, we propose that the effect of viscosity diffusion is non-negligible for both existing weak and strong dynamo regimes. Still, appropriate assumptions can be made to take this variation into account.