  We construct multisymplectic formulations of fluid dynamics using the inverse
of the Lagrangian path map. This inverse map -- the ``back-to-labels'' map --
gives the initial Lagrangian label of the fluid particle that currently
occupies each Eulerian position. Explicitly enforcing the condition that the
fluid particles carry their labels with the flow in Hamilton's principle leads
to our multisymplectic formulation. We use the multisymplectic one-form to
obtain conservation laws for energy, momentum and an infinite set of
conservation laws arising from the particle-relabelling symmetry and leading to
Kelvin's circulation theorem. We discuss how multisymplectic numerical
integrators naturally arise in this approach.
