On the toroidal‑velocity antidynamo theorem under the presence of nonuniform electric conductivity
Abstract
Laminar electrically conducting Couette flows with the hydrodynamically stable quasiKeplerian rotation profile and nonuniform conductivity are probed for dynamo instability. In spherical geometry the equations for the poloidal and the toroidal field components completely decouple, resulting in free decay, regardless of the spatial distribution of the electric conductivity. In cylindrical geometry the poloidal and toroidal components do not decouple, but here also we do not find dynamo excitations for the cases that the electric conductivity only depends on the radius or  much more complex  that it only depends on the azimuthal or the axial coordinate. The transformation of the planeflow dynamo model of Busse \& Wicht (1992) to cylindrical or spherical geometry therefore fails. It is also shown that even the inclusion of axial flows of both directions does {\em not} support the dynamo mechanism. The Elsasser toroidalvelocity antidynamo theorem, according to which dynamos without any radial velocity component cannot work, is thus not softened by nonuniform conductivity distributions.
 Publication:

Astronomische Nachrichten
 Pub Date:
 June 2022
 DOI:
 10.1002/asna.20224011
 arXiv:
 arXiv:2110.02309
 Bibcode:
 2022AN....34324011R
 Keywords:

 Physics  Fluid Dynamics;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 8 pages, 6 figures