Given a solution $S$ of the Navier-Stokes equations, is there a way to make mathematically precise a statement like: "$S$ is turbulent in the spacetime region $U$"?

And if such a definition exists, are there any known exact solutions of Navier-Stokes exhibiting turbulence?

Reading Wikipedia makes me also want to ask the following related questions:

- Does a single vortex count as turbulence?
- Is the appearance of vortices a necessary feature of turbulence?
- What's the difference between a vortex and an eddy?

Pointers to (mathematically rigorous) literature are much appreciated.