Intermittency assessed through a model of kurtosis–skewness relation in MHD in fast dynamo regimes

Intermittency as it occurs in fast dynamos in the magnetohydrodynamics (MHD) framework is evaluated through the examination of relations between normalized moments at third order (skewness $S$ ) and fourth order (kurtosis $K$ ) for both the velocity and magnetic field, and for their local dissipations. As investigated by several authors in various physical contexts such as fusion plasmas (Krommes 2008 Phys. Plasmas 15 , 030703), climate evolution (Sura & Sardeshmukh 2008 J. Phys. Oceano. 38 , 639-647), fluid turbulence or rotating stratified flows (Pouquet et al. 2023 Atmosphere 14 , 01375), approximate parabolic $K(S)\sim S^\alpha$ laws emerge whose origin may be related to the applicability of intermittency models to their dynamics. The results analyzed herein are obtained through direct numerical simulations of MHD flows for both Taylor–Green and Arnold–Beltrami–Childress forcing at moderate Reynolds numbers, and for up to $3.14 \times 10^5$ turn-over times. We observe for the dissipation $0.2 \lesssim \alpha \lesssim 3.0$ , an evaluation that varies with the field, the forcing and when filtering for high-skewness intermittent structures. When using the She & Lévêque (1994) Phys. Rev. Lett. 72 , 336-339 intermittency model, one can compute $\alpha$ analytically; we then find $\alpha \approx 2.5$ , clearly differing from a (strict) parabolic scaling, a result consistent with the numerical data.