TITLE: Is there a mathematically precise definition of turbulence for solutions of Navier-Stokes?
QUESTION [28 upvotes]: 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.

REPLY [4 votes]: I understand turbulence to be defined as a chaotic patch of vorticity. This definition comes from http://books.google.co.uk/books?id=rkOmKzujZB4C&lpg=PP1&dq=davidson%20turbulence&pg=PP1#v=onepage&q=davidson%20turbulence&f=false 
This definition implies that vorticity is a necessary feature of turbulence. I suppose the vortex patch would tend towards a stable structure such as a vortex.
A vortex often refers to a mathematically definable point vortex. An eddy is a less rigorous term for an overturning motion that often implies a vortex.