Magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number is experimentally investigated by studying a liquid metal flow in a cubic domain. We focus on the mechanisms that determine whether the flow is quasi-two-dimensional, three-dimensional or in any intermediate state. To this end, forcing is applied by injecting a DC current I through one wall of the cube only, to drive vortices spinning along the magnetic field. Depending on the intensity of the externally applied magnetic field, these vortices extend part or all of the way through the cube. Driving the flow in this way allows us to precisely control not only the forcing intensity but also its dimensionality. A comparison with the theoretical analysis of this configuration singles out the influences of the walls and of the forcing on the flow dimensionality. Flow dimensionality is characterised in several ways. First, we show that when inertia drives three-dimensionality, the velocity near the wall where current is injected scales as U b ∼ I 2/3 . Second, we show that when the distance l z over which momentum diffuses under the action of the Lorentz force (Sommeria & Moreau, J. Fluid Mech., vol. 118, 1982, pp. 507-518) reaches the channel width h, the velocity near the opposite wall U t follows a similar law with a correction factor (1 − h/l z ) that measures three-dimensionality. When l z < h, by contrast, the opposite wall has less influence on the flow and U t ∼ I 1/2 . The central role played by the ratio l z /h is confirmed by experimentally verifying the scaling l z ∼ N 1/2 put forward by Sommeria & Moreau (N is the interaction parameter) and, finally, the nature of the three-dimensionality involved is further clarified by distinguishing weak and strong three-dimensionalities previously introduced by Klein & Pothérat (Phys. Rev. Lett., vol. 104 (3), 2010, 034502). It is found that both types vanish only asymptotically in the limit N → ∞. This provides evidence that because of the no-slip walls, (i) the transition between quasi-two-dimensional and three-dimensional turbulence does not result from a global instability of the flow, unlike in domains with non-dissipative boundaries (Boeck et al. Phys. Rev. Lett., vol. 101, 2008, 244501), and (ii) it does not occur simultaneously at all scales.

We characterize experimentally how three dimensionality appears in wall-bounded magnetohydrodynamic flows. Our analysis of the breakdown of a square array of vortices in a cubic container singles out two mechanisms: first, a form of three dimensionality we call weak appears through differential rotation in individual 2D vortices. Second, strong three dimensionality characterized by vortex disruption leads on the one hand to a remarkable vortex array that is both steady and 3D, and, on the other hand, to scale-selective breakdown of two dimensionality in chaotic flows. Most importantly, these phenomena are entirely driven by inertia, so they are relevant to other flows with a tendency to two dimensionality, such as rotating, or stratified flows in geophysics and astrophysics.

Imposing a magnetic field on a turbulent flow of electrically conducting fluid incurs the Joule effect. A current paradigm is that the corresponding dissipation increases with the intensity of the magnetic field, and as a result turbulent fluctuations are all the more damped as the magnetic field is strong. While this idea finds apparent support in the phenomenology of decaying turbulence, measurements of turbulence in duct flows and other, more complex configurations have produced seemingly contradicting results. The root of the controversy is that magnetic fields promote sufficient scale-dependent anisotropy to profoundly reorganise the structure of turbulence, so their net effect cannot be understood in terms of the additional dissipation only. Here we show that when turbulence is forced in a magnetic field that acts on turbulence itself rather than on the mechanisms that generate it, the field promotes large, nearly 2D structures capturing sufficient energy to offset the loss due to Joule dissipation, with the net effect of increasing the intensity of turbulent fluctuations. This change of paradigm potentially carries important consequences for systems as diverse as the liquid cores of planets, accretion disks and a wide range of metallurgical and nuclear engineering applications.

An experimental study of the transition to turbulence in a confined quasi-two-dimensional magnetohydrodynamic flow is presented. A pair of counterrotating vortice is electrically driven in the center of a thin horizontal liquid metal layer, enclosed in a cylindrical container and subject to a homogeneous vertical magnetic field. When the forcing is increased, the pair is displaced away from the center. Boundary layer separations from the circular wall appear that trigger a sequence of supercritical bifurcations. These are singled out in numerical calculations based on our previously developed shallow water model as well as in the experiment, and these bifurcations are shown to resemble those observed in flows past a cylindrical obstacle. For the highest forcing, the flow then ends up in a turbulent regime where the dissipation increases drastically, which we could relate to a possible transition from a laminar to a turbulent Hartmann boundary layer. Finally we show the first experimental evidence of a transition to three-dimensionality in liquid metal magnetohydrodynamics (MHD) by comparing velocity measurements on either horizontal sides of the layer as we find that columnar vortice wobble for a high enough forcing.

This paper introduces an experimental apparatus, which drives turbulence electrically in a liquid metal pervaded by a high magnetic field. Unlike past magnetohydrodynamic (MHD) setups involving a shallow confinement, the experiment presented here drives turbulence whose dimensionality can be set anywhere between three-dimensional and quasi two-dimensional. In particular, we show that the dimensionality and componentality of the turbulence thus generated are in fact completely fixed by the single parameter lz(li)/h, which quantifies the competition between the solenoidal component of the Lorentz force and inertia acting on a turbulent structure of the size of the forcing scale li. This parameter is fully tunable thanks to the three operating settings at hand: the injection scale, the intensity of the electric forcing and the magnitude of the magnetic field. Thanks to the very high number of measuring probes and fast acquisition rate implemented in this experiment, it is possible to reliably measure the finest features of the inertial range on a scale-wise basis