Inverse and direct energy cascades in 3D MHD turbulence at low-Rm

Abstract

This experimental study analyzes the relationship between the dimensionality of turbulence and the upscale or downscale nature of its energy transfers. We do so by forcing low-$Rm$ magnetohydrodynamic (MHD) turbulence in a confined channel, while precisely controlling its dimensionality by means of an externally applied magnetic field. We first identify a specific lengthscale ${\hat{l}}_{\perp }^c$ that separates smaller three-dimensional structures from larger quasi-two-dimensional ones. We then show that an inverse energy cascade of horizontal kinetic energy along horizontal scales is always observable at large scales, but that it extends well into the region of 3D structures. At the same time, a direct energy cascade confined to the smallest and strongly 3D scales is observed. These dynamics therefore appear not to be simply determined by the dimensionality of individual scales, nor by the forcing scale, unlike in other studies. In fact, our findings suggest that the relationship between kinematics and dynamics is not universal and may strongly depend on the forcing and dissipating mechanisms at play.

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