Self-consistent simulations of a von K\'arm\'an type dynamo in a spherical domain with metallic walls

TL;DR

This study uses 3D magnetohydrodynamical simulations to explore how metallic walls influence the self-sustaining dynamo process in a spherical shell with von Kármán flow, highlighting the importance of wall properties.

Contribution

It provides a detailed analysis of how conducting wall parameters affect dynamo generation, emphasizing the role of wall conductivity and permeability in a self-consistent simulation framework.

Findings

Conducting walls are essential for dynamo existence.

Wall conductivity and permeability have distinct effects on dynamo efficiency.

Dynamo features include an axisymmetric toroidal field and an axial dipole.

Abstract

We have performed numerical simulations of boundary-driven dynamos using a three-dimensional non-linear magnetohydrodynamical model in a spherical shell geometry. A conducting fluid of magnetic Prandtl number Pm=0.01 is driven into motion by the counter-rotation of the two hemispheric walls. The resulting flow is of von K\'arm\'an type, consisting of a layer of zonal velocity close to the outer wall and a secondary meridional circulation. Above a certain forcing threshold, the mean flow is unstable to non-axisymmetric motions within an equatorial belt. For fixed forcing above this threshold, we have studied the dynamo properties of this flow. The presence of a conducting outer wall is essential to the existence of a dynamo at these parameters. We have therefore studied the effect of changing the material parameters of the wall (magnetic permeability, electrical conductivity, and thickness) on the dynamo. In common with previous studies, we find that dynamos are obtained only when either the conductivity or the permeability is sufficiently large. However, we find that the effect of these two parameters on the dynamo process are different and can even compete to the detriment of the dynamo. Our self-consistent approach allow us to analyze in detail the dynamo feedback loop. The dynamos we obtain are typically dominated by an axisymmetric toroidal magnetic field and an axial dipole component. We show that the ability of the outer shear layer to produce a strong toroidal field depends critically on the presence of a conducting outer wall, which shields the fluid from the vacuum outside. The generation of the axisymmetric poloidal field, on the other hand, occurs in the equatorial belt and does not depend on the wall properties.