Magnetic energy cascade in spherical geometry: I. The stellar convective dynamo case

TL;DR

This paper introduces a spectral transfer analysis method for magnetic energy in stellar dynamo simulations, revealing non-local energy transfers and the role of large-scale interactions in magnetic field saturation.

Contribution

The paper develops a novel spectral transfer function method using spherical harmonics and applies it to both mean field and turbulent stellar dynamo models, highlighting non-local energy cascades.

Findings

Magnetic energy growth is primarily non-local and mirrors convection scales.

Two types of direct magnetic energy cascades are identified during saturation.

Large-scale magnetic field saturation involves non-local interactions with the most energetic scales.

Abstract

We present a method to characterize the spectral transfers of magnetic energy between scales in simulations of stellar convective dynamos. The full triadic transfer functions are computed thanks to analytical coupling relations of spherical harmonics based on the Clebsch-Gordan coefficients. The method is applied to mean field $\alpha\Omega$ dynamo models as benchmark tests. From the physical standpoint, the decomposition of the dynamo field into primary and secondary dynamo families proves very instructive in the $\alpha\Omega$ case. The same method is then applied to a fully turbulent dynamo in a solar convection zone, modeled with the 3D MHD ASH code. The initial growth of the magnetic energy spectrum is shown to be non-local. It mainly reproduces the kinetic energy spectrum of convection at intermediate scales. During the saturation phase, two kinds of direct magnetic energy cascades are observed in regions encompassing the smallest scales involved in the simulation. The first cascade is obtained through the shearing of magnetic field by the large scale differential rotation that effectively cascades magnetic energy. The second is a generalized cascade that involves a range of local magnetic and velocity scales. Non-local transfers appear to be significant, such that the net transfers cannot be reduced to the dynamics of a small set of modes. The saturation of the large scale axisymmetric dipole and quadrupole are detailed. In particular, the dipole is saturated by a non-local interaction involving the most energetic scale of the magnetic energy spectrum, which points out the importance of the magnetic Prandtl number for large-scale dynamos.