Why, how and when MHD turbulence at low becomes three-dimensional

Abstract

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.

The decay of wall-bounded MHD turbulence at low

“…Ongoing experiments on decaying turbulence conducted on the FLOWCUBE setup (Pothérat & Klein 2014) show that reliable quantitative laws require ensemble averaging on a large number of initial conditions, which cannot be done numerically. Nevertheless, we shall now estimate the impact of the domain size in the x-y directions, and of the particular set of initial conditions used on the mechanisms found, by examining the result of two simulations in a channel four times bigger (dimensions 2L × 2L × L), with different random initial conditions (albeit with the same statistical properties as in the cases where energy has not been boosted), and slightly smaller initial Reynolds number (see table 1).…”

“…The main question concerning the later stages of the decay becomes to find to which extent quasi-two-dimensionality is achieved. (2) Turbulence between Hartmann walls can be reproduced experimentally (for example using the FLOWCUBE platform (Klein & Pothérat 2010;Pothérat & Klein 2014)) so (1) can be answered both numerically and experimentally. (3) In decaying turbulence, physical mechanisms can be more easily be identified through their characteristic time scales than in forced turbulence in a statistically steady state.…”

Spatial evolution of a quasi-two-dimensional Kármán vortex street subjected to a strong uniform magnetic field

“…15 Current injection has been used as a source of vorticity too, as in the experiments of Sommeria, 16 Alboussière, Uspenski, and Moreau, 17 and Pothérat and Klein. 18 In the present investigation, the vortices are generated using a circular cylinder aligned with the magnetic field. In the absence of a magnetic field, flow around a circular cylinder is steady, attached, and nearly symmetrical upstream and downstream at very low Reynolds numbers.…”

Secondary optimal energy growth and magnetic damping of turbulence in Hartmann channel flow

“…We note parenthetically that the suppression of gradients along the field does not necessarily imply that turbulent fluctuations are eliminated since strong two-dimensional flow structures can be amplified in forced MHD turbulence. The interplay between two-and three-dimensional structures in such flows is an active field of research [4,5].…”