Approaching a realistic force balance in geodynamo simulations
Significance Flow in Earth's liquid core is expected to be primarily governed by the Coriolis force due to Earth's rotation, the buoyancy force driving the convection, and the Lorentz force due to the geomagnetic field. A relevant geodynamo model has to be in such a force balance. Contemporaneous simulations invoke high viscosities to suppress flow turbulence to keep the computational costs manageable. The unrealistically large viscosity in these simulations is a major concern. Here we show that the state of the art simulations with a viscosity that is lower than in most simulations, but still much larger than in Earth's core, can approach a realistic force balance. Our simulations produce many properties that have been theoretically predicted in the past. 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.
Proceedings of the National Academy of Sciences