Kinematic dynamos in triaxial ellipsoids

TL;DR

This paper develops a spectral algorithm to study magnetic dynamos in triaxial ellipsoids, providing new benchmarks and insights into boundary effects on dynamo onset beyond spherical models.

Contribution

It introduces a spectral method for solving the dynamo problem in ellipsoids with various boundary conditions, advancing non-spherical planetary magnetic field modeling.

Findings

Dynamo magnetic fields can be generated at low magnetic Reynolds numbers in ellipsoids.

Boundary conditions significantly influence the dynamo onset, with perfectly conducting boundaries weakening dynamo action.

The method provides accurate benchmarks for future dynamo studies in non-spherical geometries.

Abstract

Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magnetic field in triaxial ellipsoids to solve the induction equation with local boundary conditions (i.e. pseudo-vacuum or perfectly conducting boundaries). We use the method to compute the free-decay magnetic modes and to solve the kinematic dynamo problem for prescribed flows. The new method is thoroughly compared with analytical solutions and standard finite-element computations, which are also used to model an insulating exterior. We obtain dynamo magnetic fields at low magnetic Reynolds numbers in ellipsoids, which could be used as simple benchmarks for future dynamo studies in such geometries. We finally discuss how the magnetic boundary conditions can modify the dynamo onset, showing that a perfectly conducting boundary can strongly weaken dynamo action, whereas pseudo-vacuum and insulating boundaries often give similar results.