  We present a consistent scheme of quantization of chiral flows (flows with
extensive vorticity) in ideal hydrodynamics in two dimensions. Chiral flows
occur in rotating superfluid, rotating turbulence and also in electronic
systems in the magnetic field in the regime of a fractional Hall effect. The
quantization is based on a geometric relation of chiral flows to
two-dimensional quantum gravity and is implemented by the gravitational
anomaly. The effect of the gravitational anomaly violates the major property of
classical hydrodynamics, the Helmholtz law: vortices are no longer frozen into
the flow. Effects of quantization could be cast in the form of quantum stress.
We show that the quantum stress generates Virasoro algebra, the centrally
extended algebra of holomorphic diffeomorphisms.
