  This article is a detailed version of our short letter `On equilibrium
partition function for non-relativistic fluid' [arXiv:1505.05677] extended to
include an anomalous $U(1)$ symmetry. We construct a relativistic system, which
we call null fluid and show that it is in one-to-one correspondence with a
Galilean fluid living in one lower dimension. The correspondence is based on
light cone reduction, which is known to reduce the Poincare symmetry of a
theory to Galilean in one lower dimension. We show that the proposed null fluid
and the corresponding Galilean fluid have exactly same symmetries,
thermodynamics, constitutive relations, and equilibrium partition to all orders
in derivative expansion. We also devise a mechanism to introduce $U(1)$ anomaly
in even dimensional Galilean theories using light cone reduction, and study its
effect on the constitutive relations of a Galilean Fluid.
