  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.
