Knotted structures in high-energy Beltrami fields on the torus and the sphere

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Let S be a finite union of (pairwise disjoint but possibly knotted and linked) closed curves and tubes in the round sphere S³ or in the flat torus T³. In the case of the torus, S is further assumed to be contained in a contractible subset of T³. In this paper we show that for any sufficiently large odd integer λthere exists a Beltrami field on S³ or T³ satisfying curl u = λu and with a collection of vortex lines and vortex tubes given by S, up to an ambient diffeomorphism.