  In this paper we study the existence of periodic orbits in the flow of
non-singular steady Euler fields $X$ on closed 3-manifolds, that is $X$ is a
solution of time independent Euler equations. We show, that when $X$ is $C^2$
the flow always posses a periodic orbit unless the manifold is a torus bundle
over the circle. This result generalizes preavious result of J. Etnyre and R.
Ghrist by weakening the real analytic hypothesis to $C^2$.
