Kinematic dynamos in triaxial ellipsoids. (arXiv:2109.03232v1 [astro-ph.EP])

<a href="http://arxiv.org/find/astro-ph/1/au:+Vidal_J/0/1/0/all/0/1">Jérémie Vidal</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Cebron_D/0/1/0/all/0/1">David Cébron</a>

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.

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.

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