### Abstract

Earth sustains its magnetic field by a dynamo process driven by
convection in the liquid outer core. Geodynamo simulations have been
successful in reproducing many observed properties of the geomagnetic
field. However, although theoretical considerations suggest that flow in
the core is governed by a balance between Lorentz force, rotational
force, and buoyancy (called MAC balance for Magnetic, Archimedean,
Coriolis) with only minute roles for viscous and inertial forces, dynamo
simulations must use viscosity values that are many orders of magnitude
larger than in the core, due to computational constraints. In typical
geodynamo models, viscous and inertial forces are not much smaller than
the Coriolis force, and the Lorentz force plays a subdominant role; this
has led to conclusions that these simulations are viscously controlled
and do not represent the physics of the geodynamo. Here we show, by a
direct analysis of the relevant forces, that a MAC balance can be
achieved when the viscosity is reduced to values close to the current
practical limit. Lorentz force, buoyancy, and the uncompensated (by
pressure) part of the Coriolis force are of very similar strength,
whereas viscous and inertial forces are smaller by a factor of at least
20 in the bulk of the fluid volume. Compared with nonmagnetic convection
at otherwise identical parameters, the dynamo flow is of larger scale
and is less invariant parallel to the rotation axis (less geostrophic),
and convection transports twice as much heat, all of which is expected
when the Lorentz force strongly influences the convection properties.

Original language | English |
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Pages (from-to) | 12065-12070 |

Number of pages | 6 |

Journal | Proceedings of the National Academy of Sciences |

Volume | 113 |

Issue number | 43 |

DOIs | |

Publication status | Published - 25 Oct 2016 |

### Keywords

- geodynamo
- magnetohydrodynamics
- planetary dynamos
- turbulence
- rotating convection

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## Cite this

Yadav, R. K., Gastine, T., Christensen, U. R., Wolk, S. J., & Poppenhaeger, K. (2016). Approaching a realistic force balance in geodynamo simulations.

*Proceedings of the National Academy of Sciences*,*113*(43), 12065-12070. https://doi.org/10.1073/pnas.1608998113