Combined dynamical and morphological characterisation of geodynamo simulations

Numerical dynamo simulations cannot operate at the physical conditions of Earth's core, yet they often produce fields that appear morphologically similar to the present geomagnetic field. A key issue is therefore to decipher under what conditions “Earth-like” simulations can be achieved. Recent work has shown that a set of simulations undertaken along a specific path in parameter space smoothly approach the QG-MAC dynamics that are expected in Earth's core, whereby the leading order force balance is Quasi-Geostrophic with Magnetic, Archimedean and Coriolis forces equilibrating at first order. However, a systematic link between QG-MAC balance and morphological features of the simulated fields has yet to be established. Here we assess a suite of 67 simulations using established compliance criteria for the field morphology and scale-dependent force balances to quantify the internal dynamics. Morphological compliance with the modern geomagnetic field does not imply a single underlying force balance or vice versa; however, the majority of compliant simulations, including all those approaching a realistic value of the magnetic Reynolds number Rm, are in QG-MAC balance. Simulations that simultaneously achieve excellent morphological compliance with Earth's modern field, QG-MAC balance, and high Rm, are confined to an intermediate range of dipolarity (the ratio of energy in the dipole field to the energy truncated at degree 12 at the outer boundary). Reversing simulations in this dipolarity range maintain dominant QG-MAC balance during polarity transition, though inertia makes a non-negligible contribution to the force balance.