Oh that reminded me, in terms of cheating, you can use curl of a noise field to get completely fake incompressible flow. I used this in a Siggraph course once, and in some shots for a CG movie, but Bridson made it useful and way better by showing how to make it flow around objects.
https://www.cs.ubc.ca/~rbridson/docs/bridson-siggraph2007-cu...The main issue with it is that computing curl of a noise field is a ton more compute than Navier stokes. :P
