The role of Ekman pumping and the dominance of swirl in confined flows driven by Lorentz forces

We are concerned here with confined, axisymmetric flours of smalt viscosity driven by a prescribed Lorentz force. In a previous paper we examined the case where the body force is purely azimuthal, generating a swirling motion . We showed that, in such cases, Ekman pumping provides the means by which the flow establishes a steady state. In this paper we examine a problem whi ch, superficially, looks rather different. That is, we consider the case wh ere the dominant Lorentz force is poloidal (F-r, 0, F-z) in (r, theta, z) c oordinates, while the azimuthal component of force is taken to be small but finite. This characterizes many important industrial processes and it is w ell known that such flows exhibit a curious phenomenon. That is, provided t he azimuthal forcing exceeds a relatively low threshold (about one percent of the poloidal force), the flow is dominated, not by poloidal motion, but by swirl. Previous explanations of this phenomenon are inconsistent-with th e experimental evidence. Here we offer an alternative view. We show that, o nce again, the poor dynamics are controlled by Ekman pumping, and that the dominance of swirl is a direct consequence of the suppression of the poloid al motion by the radial stratification of angular momentum. (C) Elsevier, P aris.