Writhe in the stretch-twist-fold dynamo

This article looks at the influence of writhe in the stretch-twist-fold dynamo. We consider a thin flux tube distorted by simple stretch, twist, and fold motions and calculate the helicity and energy spectra. The writhe number assists in the calculations, as it tells us how much the internal twist changes as the tube is distorted. In addition it provides a valuable diagnostic for the degree of distortion. Non mirror-symmetric dynamos typically generate magnetic helicity of one sign on large-scales and the opposite sign on small scales. The calculations presented here confirm the hypothesis that the large-scale helicity corresponds to writhe and the small scale corresponds to twist. In addition, the writhe helicity spectrum exhibits an interesting oscillatory behavior. The technique of calculating Fourier spectra for the writhe helicity may be useful in other areas of research, for example, the study of highly coiled molecules.