THE ROLE OF EKMAN PUMPING IN CONFINED, ELECTROMAGNETICALLY-DRIVEN FLOWS

Our primary thesis is that Ekman pumping is an essential component of many confined, MHD flows. It occurs whenever the axis of a forced, col umnar vortex intersects a solid boundary. The weak recirculation assoc iated with Ekman pumping is important for two reasons. First, the reci rculation provides an efficient mechanism of removing the energy suppl ied by the Lorentz force, by hushing ail streamlines through a boundar y layer. Second, the Coriolis acceleration associated with the seconda ry flow can be used to balance the azimuthal component of the Lorentz force. We illustrate these points by looking at both axisymmetric and three-dimensional flows. We start with forced swirl in an axisymmetric cavity. Here we extend Davidson's [1992] model and compare its predic tions with laboratory and numerical experiments. The experiments were performed in both cones and hemispheres and broadly support the model' s predictions. In particular, they show the dominance of Ekman pumping and the resulting independence of angular momentum with depth. Next w e note that axial symmetry, although mathematically convenient, is not a physical prerequisite for Ekman pumping. The same structure emerges in rectangular domains, and when the body force possesses no axial sy mmetry. We merely require that the axis of a vortex intersects with a solid boundary. This is illustrated through a sequence of numerical ex periments of swirling flow in a rectangular box.