Is it possible to make a theoretical model to describe the statistics of a turbulent flow (in particular, its internal structures)?Also, under what conditions do smooth solutions to the Navier–Stokes equations exist?
Nice but difficult subject needing fluid mechanics and mathematics on stochastic processes. The book by Tenekes can give some answers. Many other books have been written during the last 30 years.
Ram,
There are already so many models and methods to calculate turbulent statistics. It might be helpful to understand those models from Reynolds Average Navier Stokes (RANS) viewpoint and Large Eddy Simulation (LES) viewpoint. RANS models will give you average stats and LES models will give you 1st and 2nd order stats mostly. If you are interested in learning the RANS methods I would recommend Wilcox's masterpiece ''Turbulence Modeling for CFD' and chapter 3-6 of Roland B. Stull's classic An Introduction to Boundary Layer meteoroogy. It's always a good idea to begib learing turbulence modeling from RANS perspective. Hope this will help you.
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