I was thinking about the non-linear Navier-Stokes equation this morning and was briefly browsing a text on the subject. I'm aware that one popular approach to dealing with turbulence is to take averages and look at correlators (which, in turn, can be related to field theory.) Now, one thing which strikes me as odd about this statistical approach to dealing with turbulence is that the Navier-Stokes equation is fully deterministic; given some set of initial and boundary conditions, the entire time evolution of the system is determined. So, I have a question about the Navier-Stokes equation: is it known that the solutions are psuedo-random for high Reynold's number? Of course, one can extend this more generally to dynamical systems with positive Lyapunov exponents -- are the solutions to such systems (e.g., chaotic differential equations) known to be psuedo-random? If so, it would appear to be natural to attack them statistically since they would pass tests for randomness.