Turbulent dynamos in spherical shell segments of varying geometrical extent

TL;DR

This study uses numerical simulations to explore how the size and shape of spherical shell segments influence the growth and structure of large-scale magnetic fields in turbulent dynamo processes.

Contribution

It demonstrates the impact of domain geometry on magnetic field organization and saturation in spherical shell segments, extending understanding from Cartesian to spherical geometries.

Findings

Magnetic energy surpasses kinetic energy during saturation.

Large domains develop cellular magnetic structures with aspect ratios near unity.

Domain size influences the scale and organization of magnetic structures.

Abstract

We use three-dimensional direct numerical simulations of the helically forced magnetohydrodynamic equations in spherical shell segments in order to study the effects of changes in the geometrical shape and size of the domain on the growth and saturation of large-scale magnetic fields. We inject kinetic energy along with kinetic helicity in spherical domains via helical forcing using Chandrasekhar-Kendall functions. We take perfect conductor boundary conditions for the magnetic field to ensure that no magnetic helicity escapes the domain boundaries. We find dynamo action giving rise to magnetic fields at scales larger than the characteristic scale of the forcing. The magnetic energy exceeds the kinetic energy over dissipative time scales, similar to that seen earlier in Cartesian simulations in periodic boxes. As we increase the size of the domain in the azimuthal direction we find that the nonlinearly saturated magnetic field organizes itself in long-lived cellular structures with aspect ratios close to unity. These structures tile the domain along the azimuthal direction, thus resulting in very small longitudinally averaged magnetic fields for large domain sizes. The scales of these structures are determined by the smallest scales of the domain, which in our simulations is usually the radial scale. We also find that increasing the meridional extent of the domains produces little qualitative change, except a marginal increase in the large-scale field. We obtain qualitatively similar results in Cartesian domains with similar aspect ratios.