** Progress in Earth and Planetary Science is the official journal of the Japan Geoscience Union, published in collaboration with its 50 society members.

** Progress in Earth and Planetary Science is partly financially supported by a Grant-in-Aid for Publication of Scientific Research Results to enhance dissemination of information of scientific research.

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Solid earth sciences

201509201509

### The competition between Lorentz and Coriolis forces in planetary dynamos

#### Soderlund K M, Sheyko A, King E M, Aurnou J M

Planetary dynamos, Core convection, Magnetic fields, Rotation, Magnetostrophic force balance

Lorentz to Coriolis force ratio predictions for planetary cores. Modified dynamic Elsasser number as a function of imposed Elsasser number and magnetic Reynolds number across a range of values that may be relevant to planets in our solar system as well as exoplanets. The approximate ranges of anticipated Λ_{i} and Rm values are given for planets with active dynamos. Barred line ends for Λ_{i} denote the observed magnetic field strength; arrowed line ends denote upper bounds. Barred line ends for Rm denote constrained bounds; arrowed line ends denote a larger range of uncertainties. Black circles denote the most probable Λ_{i} and Rm values.

Fluid motions within planetary cores generate magnetic fields through dynamo action. These core processes are driven by thermo-compositional convection subject to the competing influences of rotation, which tends to organize the flow into axial columns, and the Lorentz force, which tends to inhibit the relative movement of the magnetic field and the fluid. It is often argued that these forces are predominant and approximately equal in planetary cores; we test this hypothesis using a suite of numerical geodynamo models to calculate the Lorentz to Coriolis force ratio directly. Our results show that this ratio can be estimated by (Λ _{i} is the traditionally defined Elsasser number for imposed magnetic fields and Rm is the system-scale ratio of magnetic induction to magnetic diffusion). Best estimates of core flow speeds and magnetic field strengths predict the geodynamo to be in magnetostrophic balance where the Lorentz and Coriolis forces are comparable. The Lorentz force may also be significant, i.e., within an order of magnitude of the Coriolis force, in the Jovian interior. In contrast, the Lorentz force is likely to be relatively weak in the cores of Saturn, Uranus, Neptune, Ganymede, and Mercury.