Asymptotic law of convective heat transport in an α² dynamo model

Dipartimento di Fisica, Università degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica 1, Roma, 00133, Italy

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Received: 6 November 2025
Accepted: 17 June 2026

Abstract

Context. 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 (DNSs).

Aims. We investigated convective heat transfer in a magnetoconvection and dynamo model under extreme parameter conditions, specifically at high Rayleigh and Prandtl numbers (Ra and Pr), in a plasma flow with maximum kinetic helicity consistent with rapidly rotating objects.

Methods. Our approach to studying magnetoconvection and dynamo mechanisms employs a simplified thermally driven shell model. Magnetic polarity reversals were 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 allowed us to explore the asymptotic behavior of convective heat transfer in regimes beyond those reached by current DNSs.

Results. Our results reveal that the Nusselt number (Nu), a dimensionless measure of convective heat transport, generally increases with Ra and Pr, following a power-law scaling. Compared to the hydrodynamic version, the dynamo-active shell model exhibits a steeper asymptotic scaling, Nu(Ra), indicating that magnetic-field dynamics can modify convective heat transport. However, at a fixed Ra in the dynamo regime, Nu systematically decreases as the magnetic coupling increases, revealing that the system exhibits anisotropic behavior in the parameter space.

Conclusions. Despite neglecting spatial information such as density stratification – an assumption that is necessary in the shell model approach – our model captures some of the gross dynamical features of turbulent magnetoconvection in asymptotic regimes. It allows for a broad exploration of parameter space, complementing and extending results previously reported for strongly magnetized convection in other settings. Our main finding is that, within the present dynamo shell-model in which the magnetic field is generated self-consistently by a fully developed turbulent flow, magnetic field dynamics can play an important role in modulating heat transport and shaping the asymptotic law in stellar and planetary interiors.