  We employ the relationship between contact structures and Beltrami fields
derived in part I of this series to construct steady nonsingular solutions to
the Euler equations on a Riemannian $S^3$ whose flowlines trace out closed
curves of all possible knot and link types simultaneously. Using careful
contact-topological controls, we can make such vector fields real-analytic and
transverse to the tight contact structure on $S^3$.
