  We prove the existence of periodic orbits for steady $C^\omega$ Euler flows
on all Riemannian solid tori. By using the correspondence theorem from part I
of this series, we reduce the problem to the Weinstein Conjecture for solid
tori. We prove the Weinstein Conjecture on the solid torus via a combination of
results due to Hofer et al. and a careful analysis of tight contact structures
on solid tori.
