Stretch-twist-fold and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ABC</mml:mi></mml:math>nonlinear dynamos: Restricted chaos

Abstract

We present direct numerical simulations for nonlinear dynamos, based on a Lagrangian approach that allows us to compute for relatively high effective magnetic Reynolds numbers, ${R}_{m}$\ensuremath{\sim}(1--3)\ifmmode\times\else\texttimes\fi{}${10}^{4}$. The particular systems we study and contrast are the stretch-twist-fold (STF) and the $\mathrm{ABC}$ flow dynamos. In the case of the STF dynamo, we show that whereas small-scale magnetic fluctuations are suppressed in the nonlinear regime, they still remain sufficiently large so that the STF dynamo still cannot be considered (in this nonlinear regime) a paradigm for a fast dynamo. Our numerical study of the $\mathrm{ABC}$ flow dynamo indicates, first, that during the period of kinematic behavior, there is no growth of a large-scale magnetic field, and that any large-scale field components are subject to classical turbulent diffusion; second, we show that if back reactions (due to magnetic tension) are taken into account this diffusion is highly restricted. We refer to this behavior as ``restricted chaos.''