Contact topology and hydrodynamics III: knotted orbits

We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct a steady nonsingular solution to the Euler equations on a Riemannian whose flowlines trace out closed curves of all possible knot and link types. Using careful contact-topological controls, we can make such vector fields real-analytic and transverse to the tight contact structure on . Sufficient review of concepts is included to make this paper independent of the previous works in this series.