  The conditions in which meridional recirculations appear in swirling flows
above a fixed wall are analysed. In the classical Bodew\"adt 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.
