Dynamo efficiency and Beltrami flows in rectangular cells

Abstract

Numerical simulations are performed for a kinematic dynamo problem in a rectangular cell geometry having dynamo laboratory experiments in mind. It is shown that the maximum growth rate of the magnetic field is given by a Beltrami flow with extremum flow helicity. This relation is so accurate that a slight change of the flow always gives a lower growth rate, at least in the low magnetic Reynolds number limit. It is also pointed out that two Beltrami flows with exactly the same kinetic energy and the helicity give very different dynamo growth rates. This indicates that the helicity extremum or the Beltrami condition alone is not sufficient to tell the most efficient dynamo flow.