  We discuss both the anomalous Cartan currents and the energy-momentum tensor
in a left chiral theory with flavour anomalies as an effective theory for
flavored chiral phonons in a chiral superfluid with the gauged
Wess-Zumino-Witten term. In the mean-field (leading tadpole) approximation the
anomalous Cartan currents and the energy momentum tensor take the form of
constitutive currents in the chiral superfluid state. The pertinence of higher
order corrections and the Adler-Bardeen theorem is briefly noted.
