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

We are concerned here with confined, axisymmetric flows of small 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 which, superficially, looks rather different. That is, we consider the case where the dominant Lorentz force is poloidal (Fr ,0,Fz) in (r, θ, z) coordinates, while the azimuthal component of force is taken to be small but finite. This characterizes many important industrial processes and it is well known that such flows exhibit a curious phenomenon. That is, provided the 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 the experimental evidence. Here we offer an alternative view. We show that, once again, the pool dynamics are controlled by Ekman pumping, and that the dominance of swirl is a direct consequence of the suppression of the poloidal motion by the radial stratification of angular momentum.  Elsevier, Paris