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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