The macrodynamics of α-effect dynamos in rotating fluids

Abstract

Past study of the large-scale consequences of forced small-scale motions in electrically conducting fluids has led to the ‘α-effect’ dynamos. Various linear kinematic aspects of these dynamos have been explored, suggesting their value in the interpretation of observed planetary and stellar magnetic fields. However, large-scale magnetic fields with global boundary conditions can not be force free and in general will cause large-scale motions as they grow. I n this paper the finite amplitude behaviour of global magnetic fields and the large-scale flows induced by them in rotating systems is investigated. In general, viscous and ohmic dissipative mechanisms both play a role in determining the amplitude and structure of the flows and magnetic fields which evolve. In circumstances where ohmic loss is the principal dissipation, it is found that determination of a geo- strophic flow is an essential part of the solution of the basic stability problem. Nonlinear aspects of the theory include flow amplitudes which are independent of the rotation and a total magnetic energy which is directly proportional to the rotation. Constant a is the simplest example exhibiting the various dynamic balances of this stabilizing mechanism for planetary dynamos. A detailed analysis is made for this case to determine the initial equilibrium of fields and flows in a rotating sphere.