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In this paper, we discuss relativistic hydrodynamics for a massless Diracfermion in $(2+1)$ dimensions, which has the parity anomaly -- a global 'tHooft anomaly between $\mathrm{U}(1)$ and parity symmetries. We investigate howhydrodynamics implements the party anomaly, particularly focusing on thetransport phenomena at the boundary. Based on the parity anomaly matching andthe second law of local thermodynamics, we find $\mathrm{U}(1)$ and entropycurrents localized at the boundary as well as the bulk anomalous current withvanishing divergence. These edge currents are similar to the$(1+1)$-dimensional chiral transports, but the coefficients are given by halfof theirs. We also generalize our discussion to more general anomalies amongmultiple $\mathrm{U}(1)$ symmetries and single $\mathbb{Z}_2$ symmetry.

Anomaly-induced edge currents in hydrodynamics with parity anomaly