  The Euler equation for an inviscid, incompressible fluid in a
three-dimensional domain M implies that the vorticity is a frozen-in field.
This can be used to construct a symplectic structure on RxM. The normalized
vorticity and the suspended velocity fields are Hamiltonian with the function t
and the Bernoulli function, respectively. The symplectic structure incorporates
the helicity conservation law as an identity. The infinitesimal dilation for
the symplectic two-form can be interpreted as a current vector for the
helicity. The symplectic dilation implies the existence of contact
hypersurfaces. In particular, these include contact structures on the space of
streamlines and the Bernoulli surfaces. The symplectic structure on RxM can be
realized as symplectisations of these through the Euler equation.
