Convective Heat Transport Asymptotic Law in an $α^2$ dynamo model
Giuseppina Nigro
TL;DR
The paper tackles how convective heat transport behaves in magnetized, rotating plasmas relevant to stellar and planetary dynamos under extreme parameter values. It introduces a computationally inexpensive thermally driven shell model of magnetoconvection that encodes an $\alpha^2$ dynamo and magnetic polarity reversals via a pitchfork bifurcation, enabling exploration beyond current DNS. The key finding is a power-law scaling of the Nusselt number $Nu$ with $Ra$ and $Pr$ that is steeper than in non-magnetic convection, with magnetic fields enhancing heat transport and higher turbulence correlating with more frequent polarity reversals. The study provides a practical framework to understand interior heat transport in astrophysical objects and to guide interpretation of more complex, higher-fidelity simulations and observations.
Abstract
Stellar activity and planetary magnetospheres are powered by an underlying dynamo mechanism generated by magnetoconvection coupled with rotation. In astrophysical contexts, magnetoconvection typically occurs in parameter regimes that are currently inaccessible to direct numerical simulations (DNS). We investigate convective heat transfer in a magneto-convection and dynamo model under extreme parameter conditions, specifically high Rayleigh and Prandtl numbers, in a plasma flow with maximum kinetic helicity compatible with fast-rotating objects. Our approach to studying magneto-convection and dynamo mechanisms employs a simplified thermally driven shell model. Magnetic polarity reversals are obtained by including a pitchfork bifurcation term in the large-scale magnetic field equation, while nonlinear dynamics are described by a shell model formulation. The low computational cost of the model allows us to explore the asymptotic behavior of convective heat transfer in regimes beyond those reached by current DNS. Our results reveal that the Nusselt number $Nu$ -- a dimensionless measure of convective heat transport -- generally increases with turbulence, following a power-law scaling and showing a strong correlation with Ra and Pr. This relationship appears to be more pronounced than that observed in non-magnetized fluids, suggesting that magnetic fields may significantly enhance convective heat transfer. Despite the assumption to neglect spatial information such as density stratification -- an assumption that is necessary in the shell model approach -- our model captures the gross dynamical features of turbulent magnetoconvection in asymptotic regimes. It allows for a broad exploration of parameter space, indicating that magnetic fields may play a central role in modulating heat transport in stellar and planetary interiors.