The influence of magnetic fields in planetary dynamo models

The magnetic fields of planets and stars are thought to play an important role in the fluid motions responsible for their field generation, as magnetic energy is ultimately derived from kinetic energy. We investigate the influence of magnetic fields on convective dynamo models by contrasting them with non-magnetic, but otherwise identical, simulations. This survey considers models with Prandtl number Pr=1; magnetic Prandtl numbers up to Pm=5; Ekman numbers in the range 10−3≥E≥10−5; and Rayleigh numbers from near onset to more than 1000 times critical.Two major points are addressed in this letter. First, we find that the characteristics of convection, including convective flow structures and speeds as well as heat transfer efficiency, are not strongly affected by the presence of magnetic fields in most of our models. While Lorentz forces must alter the flow to limit the amplitude of magnetic field growth, we find that dynamo action does not necessitate a significant change to the overall flow field. By directly calculating the forces in each of our simulations, we show that the traditionally defined Elsasser number, Λi, overestimates the role of the Lorentz force in dynamos. The Coriolis force remains greater than the Lorentz force even in cases with Λi≃100, explaining the persistence of columnar flows in Λi>1 dynamo simulations. We argue that a dynamic Elsasser number, Λd, better represents the Lorentz to Coriolis force ratio. By applying the Λd parametrization to planetary settings, we predict that the convective dynamics (excluding zonal flows) in planetary interiors are only weakly influenced by their large-scale magnetic fields.The second major point addressed here is the observed transition between dynamos with dipolar and multipolar magnetic fields. We find that the breakdown of dipolar field generation is due to the degradation of helicity in the flow. This helicity change does not coincide with the destruction of columnar convection and is not strongly influenced by the presence of magnetic fields. Force calculations suggest that this transition may be related to a competition between inertial and viscous forces. If viscosity is indeed important for large-scale field generation, such moderate Ekman number models may not adequately simulate the dynamics of planetary dynamos, where viscous effects are expected to be negligible.

► We quantify the dynamical influence of magnetic fields in planetary dynamo models. ► Magnetic fields tend to weakly modify convection at moderate Ekman numbers. ► Our models call into question the importance of Lorentz forces in planets. ► Magnetic field morphology changes may be linked to inertial/viscous force ratio. ► Moderate Ekman number models may not correctly simulate planetary dynamos.