  Let S be a finite union of (pairwise disjoint but possibly knotted and
linked) closed curves and tubes in the round sphere S^3 or in the flat torus
T^3. In the case of the torus, S is further assumed to be contained in a
contractible subset of T^3. In this paper we show that for any sufficiently
large odd integer \lambda there exists a Beltrami field on S^3 or T^3
satisfying curl u = \lambda u and with a collection of vortex lines and vortex
tubes given by S, up to an ambient diffeomorphism.
