arXiv subjects

A. Pothérat

Publications and source records attributed to A. Pothérat.

3 recordsLinked to original sources

arXiv2018

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

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.

physics.flu-dyn↗

arXiv2015

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

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-2D, 3D 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, which is characterised in several ways. First, when inertia drives three-dimensionality, the velocity near the wall where current is injected scales as $U_b\sim I^{2/3}$. Second, when the distance $l_z$ over which momentum diffuses under the action of the Lorentz force reaches the channel width $h$, the velocity near the opposite wall $U_t$ follows a similar law with a correction factor $(1-h/l_z)$. When $l_z<h$, by contrast, the opposite wall has less influence on the flow and $U_t\sim I^{1/2}$. The central role played by the ratio $l_z/h$ is confirmed by experimentally verifying Sommeria & Moreau (1982)'s scaling $l_z\sim N^{1/2}$ ($N$ is the interaction parameter) and finally, the nature of the three-dimensionality is further clarified by distinguishing weak and strong three-dimensionalities. It is found that both vanish only asymptotically in the limit $N\rightarrow\infty$. This provides evidence that because of the no-slip walls, 1) the transition between quasi-2D and 3D turbulence does not result from a global instability of the flow, and 2) it doesn't occur simultaneously at all scales.

physics.flu-dyn↗

arXiv2013

Direct and inverse pumping in flows with homogeneous and non-homogeneous swirl

The conditions in which meridional recirculations appear in swirling flows above a fixed wall are analysed. In the classical Bodewädt problem, where the swirl tends towards an aysmptotic value away from the wall, the well-known "tea-cup effect" drives a flow away from the plate at the centre of the vortex. Simple dimensional arguments applied to a single vortex show that if the intensity of the swirl decreases away from the wall, the sense of the recirculation can be inverted, and that the associated flow rate scales with the swirl gradient. Only if the flow is quasi-2D, does the classical tea-cup effect take place. This basic theory is confirmed by numerical simulations of a square array of steady, electrically driven vortices. Experiments in the turbulent regimes of the same configuration reveal that these mechanisms are active in the average flow and in its fluctuating part. The mechanisms singled out in this letter provide an explanation for previously observed phenomena in electrolyte flows. They also put forward a possible mechanism for the generation of helicity in flows close to two-dimensionality, which plays a key role in the transition between 2D and 3D turbulence.

physics.flu-dyn↗