http://arxiv.org/abs/2110.02309
Laminar electrically conducting Couette flows with quasi-Keplerian rotation law 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 independent of the spatial distribution of the electric conductivity. For cylindric flows the decoupling vanishes but also here we do not find dynamo excitations for the two cases that the electric conductivity only depends on the radius or — much more complex — that it only depends on the azimuth. The transformation of the plane-flow dynamo model of Busse & Wicht (1992) to cylindric or spherical geometry, therefore, fails. It is also shown that even the inclusion of axial flows of both signs does not support the dynamo mechanism. The Elsasser toroidal-velocity antidynamo theorem, after which dynamos without any radial velocity component cannot work, is thus not softed by nonuniform conductivity distributions.
G. Rüdiger and M. Schultz
Thu, 7 Oct 21
12/51
Comments: 8 pages, 6 figures