Is there a test case for 3D incompressible Navier Stokes Equations like the Taylor vortex in two dimensions?
I know, I can easily construct 3D manufactured solutions but I would like to have something more physical.
Chapter 7 of the (free in PDF form) book "I do like CFD, Vol. 1" collects many different known solutions for multidimensional flows that can be used for benchmarking.
There are several benchmarks, like the flow around a cylinder, which is described in details at the FEATFLOW web page here. It is a well defined configuration of a flow passing by a cylinder obstacle and values such as the drag and lift can be compared with values obtained with different softwares (a file containing the data is provided).
Otherwise there are "less physical" flows, like the Ethier-Steinman problem described here, which however has a known exact solution.
Let me add, the cavity flow in three dimensions. A very good reference is R. Glowinski, Handbook of Numerical Analysis, Numerical Methods for Fluids, Chapter 9, Section 44.3. Here the test is very well detailed.