  We study weakly interacting Bose gases using the functional renormalization
group with a hydrodynamic effective action. We use a scale-dependent
parametrization of the boson fields that interpolates between a Cartesian
representation at high momenta and an amplitude-phase one for low momenta. We
apply this to Bose gases in two and three dimensions near the superfluid phase
transition where they can be described by statistical O(2) models. We are able
to give consistent physical descriptions of the infrared regime in both two and
three dimensions. In particular, and in contrast to previous studies using the
functional renormalization group, we find a stable superfluid phase at finite
temperatures in two dimensions. We compare our results for the superfluid and
boson densities with Monte-Carlo simulations, and we find they are in
reasonable agreement.
