A convection-driven dynamo I. The weak field case

• DOI: 10.1098/rsta.1974.0003
• Publication Date: 2006-12-15T22:43:50Z
• Authors: A. M. Soward
• Keywords: Lorentz force; Solar dynamo; Induction equation

A hydromagnetic dynamo model is considered. Boussinesq, electrically conducting fluid confined between two horizontal planes and heated from below. The system rotates rapidly about the vertical axis with constant angular velocity. It supposed that instability first sets in as stationary convection characterized by a small length scale. In preliminary calculations Lorentz force neglected so magnetic induction equation of motion are decoupled. possibility motions occurring at onset may sustain fields thus reduced to kinematic problem. Moreover, existence scales introduces simplifications which enable problem be studied well-known techniques. effect on finite amplitude dynamics investigated also. Since only weak considered kinetic energy fixed other considerations it fine structure flow influenced field. set nonlinear equations, govern evolution dynamo, derived an asymptotic analysis. equations detail both analytically numerically. spite serious doubts concerning sufficiently complex stable motions, periodic dynamos shown exist. An interesting analytic solution these pertinent problems arising finite-amplitude Benard convection, presented final section.