  We present a variational principle for relativistic hydrodynamics with
gauge-anomaly terms for a fluid coupled to an Abelian background gauge field.
For this we utilize the Clebsch parametrization of the velocity field. We also
set up the Hamiltonian formulation and the canonical framework for the theory.
While the equations of motion only involve the density and velocity fields,
i.e., the Clebsch potentials only appear in the combination which is the
velocity field, the generators of symmetry transformations (including the
Hamiltonian) depend explicitly on one of the Clebsch potentials, if the
background field is time-dependent. For the special case of time-independent
background fields, this feature is absent.
