Asymptotic properties of dynamo waves

D. D. Sokoloff - M. Fioc - E. Nesme-Ribes

Joint Institute for Earth Physics, Russian Academy of Sciences, Moscow, Russia

Abstract
We discuss the properties of a dynamo wave in a solar convective shell that is produced by an aw-dynamo. A nonlinear aw-dynamo with a-quenching, is considered. We use the approximation of very large dynamo numbers, |D| >> 1, and construct the asymptotic solution of the nonlinear dynamo equations. This solution depends crucially on whether or not the mean helicity a, as a function of B, has a positive root (here B is the mean magnetic field). When such a root exists, the field value is of order Bo, the level of magnetic field at which the nonlinear effects are essential. Otherwise, the strength of the magnetic field in the dynamo wave is much larger than Bo. We demonstrate the possibility of two types of solution, with zero and nonzero mean levels of magnetic field in the dynamo wave and consider the bifurcation between these types of solutions. We compare our results with the results of computer simulations of a solar dynamo and observations of the solar magnetic field. Figs 9, Refs 27.