Fluid motion induced by electromagnetic forces on free surfaces

We study the shaping, by a MHD process applied to liquid metals, of cruciform section cylinders. The two-dimensional problem comes from the equilibrium between the magnetic pressure forces created by a quadripolar inductor and the surface tension stress. We summarize first calculation of the equilibrium shape, with a variational method where the function of energy of the system is minimized. Then we study the effect of the electromagnetic forces, which gives the fluid a recirculating motion, by a finite element analysis.