  Fluid analog models for gravity are based on the idea that any spacetime
geometry admits a reinterpretation in which space is thought of as a fluid
flowing with a prescribed velocity. This fluid picture is a restatement of the
ADM decomposition of the metric. Most of the literature has focused on flat
spatial geometries and physical fluid flows, with a view toward possible
laboratory realizations. Here we relax these conditions and consider fluid
flows on curved and time-dependent spatial geometries, as a way of
understanding and visualizing solutions to general relativity. We illustrate
the utility of the approach with rotating black holes. For the Kerr black hole
we develop a fluid description based on Doran coordinates. For spinning BTZ
black holes we develop two different fluid descriptions. One involves static
conical spatial slices, with the fluid orbiting the tip of the cone. The other
resembles a cosmology, with the fluid flowing on a time-dependent cylindrical
geometry.
