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Numerical model for a Air core Vortex; is this succesfully been done? (plughole vortex CFD)

I mean this every day phenomenon;

enter image description here

It's so easily reproducible, that it must be able to been solved with an exact solution.

But I can't find it from this list; Exact Solutions to the Navier-Stokes Equations

Short google didn't help me either.

The reason why i am asking is, that if the numerical model (Navier Stokes) can't solve this rather simple experiment, it must be wrong.