  We study holographic three-dimensional fluids with vorticity in local
equilibrium and discuss their relevance to analogue gravity systems. The
Fefferman-Graham expansion leads to the fluid's description in terms of a
comoving and rotating Papapetrou-Randers frame. A suitable Lorentz
transformation brings the fluid to the non-inertial Zermelo frame, which
clarifies its interpretation as moving media for light/sound propagation. We
apply our general results to the Lorentzian Kerr-AdS_4 and Taub-NUT-AdS_4
geometries that describe fluids in cyclonic and vortex flows respectively. In
the latter case we associate the appearance of closed timelike curves to
analogue optical horizons. In addition, we derive the classical rotational Hall
viscosity of three-dimensional fluids with vorticity. Our formula remarkably
resembles the corresponding result in magnetized plasmas.
