the big deal

Exact numerical solutions of Navier-Stokes are pretty amazing:

Velocity field is varying all over, indistinguishable from a snapshot of a turbulent fluid,

but solutions are stationary - they do not change under Navier-Stokes evolution.

The next set of exact solutions is more amazing still:

movies are indistinguishable from the turbulent ones, but
they return exactly to the initial state after a given period.