Fractal properties of the stretch-twist-fold magnetic dynamo

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Abstract
This paper presents direct numerical simulations of the stretch-twist-fold (STF) dynamo. For more than two decades, this dynamo has been viewed as the prototype of the fast dynamo process; and because of its apparently conceptual simplicity, it was generally not thought to be necessary to investigate its quantitative properties in detail via numerical simulations. Furthermore, it has been generally assumed that the STF dynamo is not characterized by small-scale fluctuations, as is usually the case for many other dynamo processes. Numerical simulations show, however, that the STF dynamo process is accompanied by the generation of small-scale fluctuations in the magnetic field. Therefore, it cannot be taken as an a priori given that the STF dynamo is a large-scale dynamo; however, our results suggest that the STF dynamo does generate large-scale magnetic fields. In any eventuality, the magnetic fields generated by the STF process do not behave as was previously expected: As we show, these fields become chaotic, first, in the sense that magnetic field lines acquire multifractal properties; and, second, because the field itself becomes chaotic [i.e., the (intermittency) fractal dimensions are no longer trivial].