  We extend the notion of "coupling with a foliation" from Poisson to Dirac
structures and get the corresponding generalization of the Vorobiev
characterization of coupling Poisson structures. We show that any Dirac
structure is coupling with the fibers of a tubular neighborhood of an embedded
presymplectic leaf, give new proofs of the results of Dufour and Wade on the
transversal Poisson structure, and compute the Vorobiev structure of the total
space of a normal bundle of the leaf. Finally, we use the coupling condition
along a submanifold, instead of a foliation, in order to discuss submanifolds
of a Dirac manifold which have a differentiable, induced Dirac structure. In
particular, we get an invariant that reminds the second fundamental form of a
submanifold of a Riemannian manifold.
