Magnetic Energy Cascade in Spherical Geometry. I. The Stellar Convective Dynamo Case
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 αΩ dynamo models as benchmark tests. From a physical standpoint, the decomposition of the dynamo field into primary and secondary dynamo families proves very instructive in the αΩ case. The same method is then applied to a fully turbulent dynamo in a solar convection zone, modeled with the three-dimensional MHD Anelastic Spherical Harmonics 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 the 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 is detailed. In particular, the dipole is saturated by a non-local interaction involving the most energetic scale of the magnetic energy spectrum, which points to the importance of the magnetic Prandtl number for large-scale dynamos.