Chern-Simons modification of Fluid Mechanics

We show that the hydrodynamics of a perfect fluid admits a natural modification that incorporates a chiral gravitational anomaly (also known as a mixed gauge-gravity anomaly) alongside the chiral current anomaly. This modification introduces in parallel a gravitational and gauge Chern-Simons terms in a manner analogous to the Jackiw-Pi Chern-Simons modification of gravity, and features an axion in fluid mechanics. As a result, flows of a spinless perfect fluid acquire spin through motion, with the spin being equal to the fluid helicity. Furthermore, spacetime curvature induces an analogue of the Mathisson-Papapetrou force and a geometric counterpart of the chiral magnetic effect.