The dynamo action of a time-periodic two-dimensional flow close to integrability is analyzed. At fixed Reynolds numberRMand frequency #x3C9;, magnetic structures develop in the form of both eddies and filaments. The growth rate of the eddies appears to be the same for all frequencies and decreases withRM, while the growth rate of the filaments displays a strong co-dependence and, except in the limit of zero or infinite frequencies, converges to a non-zero value asRM#x2192; #x221E;. Magnetic filaments develop in the widest chaotic zones located near the homoclinic or heteroclinic tangles, and their growth rate is strongly influenced by the width of these zones which is estimated using Melnikov formalism. This study illustrates quantitatively that not only a local stretching but also a sizable chaotic zone is required for fast dynamo action.
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