  Link invariants of long pieces of orbits of a volume-preserving flow can be
used to define diffeomorphism invariants of the flow. In this paper, we extend
the notions of wrapping number and trunk and define invariants of links with
respect to a fibration on a 3-manifold. Extending work of Dehornoy and
Rechtman, we apply this to define diffeomorphism invariants wrappingness and
trunkenness of volume-preserving flows on 3-manifolds and interpret these
invariants as obstructions to the existence of a global surface of section for
the flow. Finally, we construct flows and show that wrappingness and
trunkenness are not functions of the helicity of a flow.
