Dynamo action in the Taylor–Green vortex near threshold

Abstract

Dynamo action is demonstrated numerically in the forced Taylor–Green (TG) vortex made up of a confined swirling flow composed of a shear layer between two counter-rotating eddies, corresponding to a standard experimental setup in the study of turbulence. The critical magnetic Reynolds number above which the dynamo sets in depends crucially on the fundamental symmetries of the TG vortex. These symmetries can be broken by introducing a scale separation in the flow, or by letting develop a small non-symmetric perturbation which can be either kinetic and magnetic, or only magnetic. The nature of the boundary conditions for the magnetic field (either conducting or insulating) is essential in selecting the fastest growing mode; implications of these results to a planned laboratory experiment are briefly discussed.