  We construct the non-relativistic parity-violating hydrodynamic description
of a two-dimensional dissipative, normal fluid in presence of small U(1)
background fields and vorticity. This is achieved by taking the
non-relativistic limit of the recently developed relativistic hydrodynamics in
2+1 dimensions. We identify and interpret the resulting parity-violating
contributions to the non-relativistic constitutive relations, which include the
Hall current flowing perpendicular to the temperature gradient, the Hall
viscosity and the Leduc-Righi energy current. Also a comparison of our findings
is made with the non-relativistic parity-violating hydrodynamics obtained from
a light-cone dimensional reduction.
