  Recently, a Lagrangian description of superfluids attracted some interest
from the fluid/gravity-correspondence viewpoint. In this respect, the work of
Dubovksy et al. has proposed a new field theoretical description of fluids,
which has several interesting aspects. On another side, we have provided in
arXiv:1304.2206 a supersymmetric extension of the original works. In the
analysis of the Lagrangian structures a new invariant appeared which, although
related to known invariants, provides, in our opinion, a better parametrisation
of the fluid dynamics in order to describe the fluid/superfluid phases.
