Scaling laws in spherical shell dynamos with free-slip boundaries

TL;DR

This study uses 57 numerical simulations to compare how free-slip versus rigid boundary conditions affect the scaling laws of heat flow, flow velocity, and magnetic field strength in spherical shell dynamos, relevant for astrophysical objects.

Contribution

It provides the first systematic comparison of free-slip and rigid boundary effects on dynamo scaling laws using extensive numerical simulations.

Findings

Boundary condition has minor influence on scaling laws.

Dipolar and multipolar dynamos share similar scaling exponents.

Offset in scaling pre-factors is linked to zonal flow differences.

Abstract

Numerical simulations of convection driven rotating spherical shell dynamos have often been performed with rigid boundary conditions, as is appropriate for the metallic cores of terrestrial planets. Free-slip boundaries are more appropriate for dynamos in other astrophysical objects, such as gas-giants or stars. Using a set of 57 direct numerical simulations, we investigate the effect of free-slip boundary conditions on the scaling properties of heat flow, flow velocity and magnetic field strength and compare it with earlier results for rigid boundaries. We find that the nature of the mechanical boundary condition has only a minor influence on the scaling laws. We also find that although dipolar and multipolar dynamos exhibit approximately the same scaling exponents, there is an offset in the scaling pre-factors for velocity and magnetic field strength. We argue that the offset can be attributed to the differences in the zonal flow contribution between dipolar and multipolar dynamos.