Turbulent Flow - Solved or Unsolved?

I think your last sentence answers your question perfectly.
From a design point of view, I suppose the answer is to either utilse turbulent flow by designing empirically or to laminarize the flow.
Del

I think the practical thing to do is to allow the turbulence where you can allow it and minimize it at places where you need minimal turbulence (such as before flowmeters).

regards,

Vulcan

I do believe that the reasons for the difficulty in solving the Navier-Stokes Equations are two: The equations are very nonlinear as becomes obvious with the reformulation of the equations in the vector curl representation, The assumption of uniform continuity creates mathematical problem of lack of Internal Self-consistency.The first reason is obvious, but the second is somewhat subtle.

Regarding the second reason, the entire concept depends on the adoption of continuum fluid mechanics, implying that there is a minimum fluid particle size on which the derivations are based; however, the use of Reimann Daboux Integration or Reiman Stieltjes Integration clearly violates the continuum principle of a minimum fluid particle size as those integration techniques are based on the intervals -> 0, or infinitesimally small intervals, which clearly are smaller than the minimum continuum fluid particle size. Both techniques integrates along the distance coordinates. However, in "Introduction to Fluid Dynamics" by G K Batchelor, the author introduced an approach that was rather interesting and not so explicitly explained in the book; actually I never really understood it until I want into mathematics, the author, Batchelor, integrated along the volume coordinate using a different integration techniques - the name of hich escapes me right now. this approach captures the concept just right while preserving the continuum principle assumption.

Even more interesting about the approach of Batchelor is that it fits in nicely with the concepts guiding The principle of Point-Particle Interchangeability. I firmly believe that the solution of the Turbulence will obtain only through a mastery of the Point-particle Interchangeability Principle. this principle allows the representation of every point with a particle and every particle with a point. Now this really becomes interesting when one uses augmented geometric space for the derivation of the Navier-Stokes equations using Lie Algebra - by this approach the fixed point of exterior derivative associated with a continuum particle lies on the flowpath of that particle and every flowpath in a fluid is also the fixed point of a continuum particle.

So then in the case of Turbulent flow, then turbulence is then simply described by the chaotic motion of the continuum particles, which motions may be better understood through the use of Chaos Theory an innovative treatment of Chaos Theory I suppose is being extensively studied at Los Alamos. Therefore there is hope, methinks.

Just my thought.

Because of the chaos theory?

I haven't run into much that is "solved" in my brief engineering career. Almost everything becomes an approximation at some point, but that is what makes engineering so much fun.

Interesting