  A scenario is put forward for the appearance of three-dimensionality both in
quasi-2D rotating flows and quasi-2D magnetohydrodynamic (MHD) flows. We show
that 3D recirculating flows and currents originate in wall boundary layers and
that, unlike in ordinary hydrodynamic flows, they cannot be ignited by
confinement alone. They also induce a second form of three-dimensionality with
quadratic variations of velocities and current across the channel. This
scenario explains both the common tendency of these flows to two-dimensionality
and the mechanisms of the recirculations through a single formal analogy
covering a wide class of flow including rotating and MHD flows. These
trans-disciplinary effects are thus active in atmospheres, oceans or the
cooling blankets of nuclear fusion reactors.
