Inverse and Direct Energy Cascades in Three-Dimensional Magnetohydrodynamic Turbulence at Low Magnetic Reynolds Number

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 turbulence in a confined channel, while precisely controlling its dimensionality by means of an externally applied magnetic field. We first identify a specific length scale l[over ^]_{⊥}^{c} that separates smaller 3D structures from larger quasi-2D ones. We then show that an inverse energy cascade of horizontal kinetic energy along horizontal scales is always observable at large scales, and 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.

From three-dimensional to quasi-two-dimensional: transient growth in magnetohydrodynamic duct flows

“…Thus, although the point where bulk dissipation drops below the level of Hartmann layer dissipation is an unmistakable signature of a transition to quasi-two-dimensional MHD dynamics, the optimal mode retains noticeable threedimensional features at values of Ha well beyond this transition (Pothérat & Klein 2014). Though somewhat counter-intuitive, the occurrence of two-dimensional dynamics has been recently observed in three-dimensional MHD turbulence by Baker et al (2018), and underlines that the link between topological and dynamical dimensionality is anything but obvious.…”

“…Nevertheless, despite the important role of the Shercliff layers at high Hartmann number, none of the regimes investigated showed Q2D turbulence, and even less of a mechanism leading up to it. This is most likely because a sufficiently high Hartmann number could not be reached, where previous experiments have suggested values of O(10 3 -10 4 ) are needed (Pothérat & Klein 2014;Baker et al 2018).…”

Direct numerical simulation of quasi-two-dimensional MHD turbulent shear flows

“…Conversely, away from the shear layers, the mean flow does not inject energy into the small scales. Since the recent experiments on MHD turbulence without a strong mean flow of Baker et al (2018) suggest that even in the presence of moderate three-dimensionality, the energy cascades upscale, the flow is dominated by larger vortices for which two-dimensionalisation is more efficient. Unlike in these experiments, however, the presence of vorticity streaks in the wake of these vortices suggests that an additional transfer mechanism less favourable to large scales may be at play in the outer region of MATUR.…”

“…Combining it with finite-element simulations (based on a two-dimensional (2-D) axisymmetric model), they studied the instabilities of the free shear layer and identified several flow regimes characterised by the nature of the instabilities of the Kelvin-Helmholtz type (Stelzer et al 2015a). Based on the FLOWCUBE platform, a more homogeneous type of turbulence between Hartmann walls was produced from the destabilisation of vortex arrays (Klein & Pothérat 2010;Pothérat & Klein 2014;Baker et al 2018). These authors focused on the transition between 3-D and Q2-D turbulence.…”

Transition between advection and inertial wave propagation in rotating turbulence

“…Finally, while the mechanisms found here do not exclude the possibility that triadic interaction may participate in the build-up of large quasi-two dimensional structures, they illustrate that linear inertial waves govern transport mechanisms at the large scales, as shown by Davidson et al [2006], but they also dominate down to the level of smaller scales as long as the local balance of Coriolis force and advection favours the former. More generally, it is not unusual that turbulence dynamics be controlled at the scale level by linear processes, as illustrated in magnetohydrodynamic turbulence at low magnetic Reynolds number, where the anisotropy of individual scales is controlled by the balance between inertia and momentum diffusion by the Lorentz force [Sommeria and Moreau, 1982, Pothérat and Klein, 2014, Baker et al, 2018.…”