Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers

Abstract

Most large-scale planetary magnetic fields are thought to be driven by low Rossby number convection of a low magnetic Prandtl number fluid. Here kinematic dynamo action is investigated with an asymptotic, rapidly rotating dynamo model for the plane layer geometry that is intrinsically low magnetic Prandtl number. The thermal Prandtl number and Rayleigh number are varied to illustrate fundamental changes in flow regime, ranging from laminar cellular convection to geostrophic turbulence in which an inverse energy cascade is present. A decrease in the efficiency of the convection to generate a dynamo, as determined by an increase in the critical magnetic Reynolds number, is observed as the buoyancy forcing is increased. This decreased efficiency may result from both the loss of correlations associated with the increasingly disordered states of flow that are generated, and boundary layer behavior that enhances magnetic diffusion locally. We find that the spatial characteristics of α, and thus the large-scale magnetic field, is dependent only weakly on changes in flow behavior. In contrast to the large-scale magnetic field, the behavior of the small-scale magnetic field is directly dependent on, and therefore shows significant variations with, the small-scale convective flow field. However, our results are limited to the linear, kinematic dynamo regime; future simulations that include the Lorentz force are therefore necessary to assess the robustness of these results.

Oscillatory thermal–inertial flows in liquid metal rotating convection

“…The DNS flow field analyses support the idea of a fully self-consistent dynamo in the oscillatory regime, as has also been proposed by Calkins et al. (2015, 2016 b ); Davidson & Ranjan (2018). Helicity is an important ingredient in many dynamo systems (e.g.…”

“…Rapidly rotating, kinematic plane layer dynamo models have now demonstrated that low oscillatory convective modes are actually capable of generating dynamo action at lower and in lower electrical conductivity fluids than in moderate cases (Calkins et al. 2016 a , b ).…”

Self-consistent single mode investigations of the quasi-geostrophic convection-driven dynamo model

“…Moffatt 1978). For sufficiently long simulation times, it is expected, and observed by Calkins et al (2016b), that α ij will become symmetric; it was further observed that α 12 ≈ α 21 ≈ 0 as t → ∞.…”

Magnetic quenching of the inverse cascade in rapidly rotating convective turbulence

“…However, rapid rotation alone is sufficient for generating large-scale magnetic fields [13], even for laminar, small-Reynolds-number flows that lack an inverse cascade [14][15][16]. In the asymptotic limit of rapid rotation, LSVs are unimportant for the onset of dynamo action [16]. However, the influence of magnetic field on the inverse cascade remains poorly understood due, in large part, to the limited parameter range of previous DNS studies.…”