1210.7122 (Ralf Kaiser)

The axisymmetric antidynamo theorem revisited    [PDF]

Ralf Kaiser

The axisymmetric kinematic dynamo problem is reconsidered and a number of open questions are answered. Apart from axisymmetry and smoothness of data and solution we deal with this problem under quite general conditions, i.e. we assume a compressible fluid of variable (in space and time) conductivity moving in an arbitrary (axisymmetric) domain. We prove unconditional, pointwise and exponential decay of magnetic field and electric current to zero. The decay rate of the external (meridional) magnetic field can become very small (compared to free decay) for special flow fields and large magnetic Reynolds numbers. We give an example of that. On the other hand, we show for incompressible fluids of constant conductivity in balls that the meridional and azimuthal decay rates coincide with the well-known poloidal and toroidal free decay rates, respectively.

View original: http://arxiv.org/abs/1210.7122