Nonlinear laminar `dynamos' linear in one coordinate

Abstract

We consider two self-similar flow fields, for which the Navier--Stokes equations reduce to ODEs. If the magnetic field has a similar structure, then the induction equation also reduces to ODEs. The coupled system can be regarded as a kinematic dynamo problem, but also the fields grow until they saturate as exact solutions of the nonlinear system. The extent to which these solutions can be regarded as genuine dynamos is discussed. Figs 6, Refs 13.