Nonrelativistic parity-violating hydrodynamics in two spatial dimensions

We construct the nonrelativistic parity-violating hydrodynamic description of a two-dimensional dissipative, normal fluid in the presence of small $U(1)$ background fields and vorticity. This is achieved by taking the nonrelativistic limit of the recently developed relativistic hydrodynamics in $2+1$ dimensions. We identify and interpret the resulting parity-violating contributions to the nonrelativistic 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 nonrelativistic parity-violating hydrodynamics obtained from a light-cone dimensional reduction.