bei Google ScholarTitelangaben
Kaiser, Ralf:
Approximately axisymmetric antidynamo theorems.
In: SIAM Journal on Applied Mathematics.
Bd. 78
(2018)
Heft 6
.
- S. 3188-3212.
ISSN 1095-712X
DOI: https://doi.org/10.1137/18M1173174
| Rez.: |
Abstract
The axisymmetric antidynamo theorem rules out dynamo action by the motion of a conducting fluid in a bounded domain surrounded by vacuum, provided that magnetic field, flow field, magnetic diffusivity distribution, and the shape of the domain are axisymmetric. We present in this paper three versions of a generalized axisymmetric antidynamo theorem, which establishes decay of the magnetic field even in the presence of small amounts of nonaxisymmetry in the magnetic field, the flow field, and the diffusivity distribution. The first two versions hold only in the case of weak variations of compressibility and diffusivity of the fluid, whereas the third version is not subject to such a restriction. By proper choice of the diffusivity distribution modeling the conducting domain the third version allows even small deviations from axisymmetry of this domain. However the smallness requirements of the third version are not as explicit as in the other versions and they are generally more severe. The first version refers only to the meridional part of the axisymmetric magnetic field and proves monotonic decay to zero of the corresponding scalar in the energy norm, whereas the other two versions demonstrate decay of functionals that involve both the meridional as well as the azimuthal scalars and the magnetic field itself. The smallness of the nonaxisymmetric part of the magnetic field is controlled by the ratio of energies of the nonaxisymmetric over the axisymmetric part, whereas the nonaxisymmetric parts of flow field and diffusivity distribution are controlled by their maximum values.