Controlling the dimensionality of low-Rm MHD turbulence experimentally

Abstract

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

Cascades and transitions in turbulent flows

“…(1) for two paradigmatic examples of a fast rotating flow (left panel) and flow constrained in a thin layer (right panel), where structures at both large and small scales coexist. Split cascades have been shown to exist in different physical situations, in numerical simulations and experiments of thin/thick layers [32][33][34][35][36], in rotating and stratified turbulence and in MHD turbulence [66][67][68][69][70][71][72][73][74][75][76]. They have been observed in geophysical flows, e.g.…”

PIV mapping of pressure and velocity fields in the plane magnetohydrodynamic Couette flow

“…The main advantage of this setup is to provide access to 2D velocity and pressure fields in planes containing the streamwise direction and one spanwise direction. This was made possible by using electrolytes in high magnetic fields, but at the cost of several limitations: the low conductivity of the electrolyte (sulphuric acid) leaves the sort of high Hartmann numbers accessible in liquid metal experiments (such as 4×10 4 in [15]) out of reach. The problem is exacerbated by the large size of the experiment that precludes fitting it in the bore of high field solenoidal magnets.…”

“…Secondly, MHD experiments require electrically conducting fluids such as liquid metals, whose opacity make direct flow visualisation impossible. While indirect methods based on electric potential velocimetry provide partial visualisations, their application to the MHD Couette flow would be extremely difficult [15]. Despite these challenges, the plane configuration makes it possible to align an external magnetic field with velocity gradients rather than with the flow (as in most MHD TC experiments).…”

Do magnetic fields enhance turbulence at low magnetic Reynolds number?

“…The metal is Gallinstan, an eutectic alloy of gallium, indium and tin that is liquid a room temperature. Full details and validation of the experimental setup are provided in [3,24]. An electrically generated force of lengthscale L f keeps turbulence in a statistically steady state as follows: Electric current I locally injected through one of the channel walls (arbitrarily the bottom wall) forces horizontally divergent currents through the bulk and the Hartmann layers.…”