  We study flows of barotropic perfect fluid under the simultaneous action of
the electromagnetic field and the axial-vector potential, the external field
conjugate to the fluid helicity. We obtain the deformation of the Euler
equation by the axial-vector potential and the deformations of various currents
by two external fields. We show that the divergence of the vector and axial
currents are controlled by the chiral anomaly known in quantum field theories
with Dirac fermions. We obtain these results by extending the variational
principle for barotropic flows of a perfect fluid by coupling with the external
axial-vector potential.
