The fast kinematic magnetic dynamo and the dissipationless limit

This paper investigates the possibility of utilizing the equation for the magnetic field in a perfectly conducting fluid to obtain information on the kinematic magnetic dynamo in the limit where the magnetic Reynolds number Rm (equivalently, the conductivity) approaches infinity. Since the limit Rm→∞ is highly singular, it is not immediately clear that such an approach is possible. Recently, however, it has been proposed that the growth rate for the fastest growing mode at finite Rm, γmax(Rm), has a limit, γ∞=limRm→∞γmax (Rm), which can be obtained directly from the flux through a macroscopic area, using the equation for the magnetic field in a perfectly conducting fluid. The utility of this is that it reduces the problem to one of investigating the chaotic dynamics of the trajectories of fluid elements convected by the flow. Numerical experiments with finite Rm on a simple class of models will be presented. These numerical experiments support the idea that γ∞ can be obtained from the perfect conductivity equation and elucidate the nature of the singular limiting process yielding this result