I'm looking for analytic solutions to time dependent fluid flow problems (can be compressible or incompressible, Euler or Navier-Stokes equations). The main thing though is that I'd like there to be 'interesting' physics going on and for this 'interesting' physics to develop as time proceeds. I'm fine with having source terms to force the solution to be 'interesting'.

To give an idea of what I mean by interesting -- I'm thinking along the lines of something that appears like transitioning to turbulence, developing shocks and/or vortex shedding.