  A formal symplectic structure on RxM is constructed for the unsteady flow of
an incompressible viscous fluid on a three dimensional domain M. The evolution
equation for the helicity density is expressed via the divergence of the
Liouville vector field that generates symplectic dilation. For an inviscid
fluid this equation reduces to a conservation law. As an application the
symplectic dilation is used to generate Hamiltonian automorphisms of the
symplectic structure which are then related to the symmetries of the velocity
field.
