  We use cotangent bundles of spaces of smooth embeddings to construct
symplectic dual pairs involving the group of volume preserving diffeomorphisms.
Via symplectic reduction we obtain descriptions of coadjoint orbits of this
group in terms of nonlinear Grassmannians of augmented submanifolds. For
codimension one embeddings these submanifolds are further constrained to the
leaves of isodrastic foliations with finite codimensions.
