Conclusion/Close

The problem of turbulence is not just to find more accurate formulae for various physical quantities associated with a turbulent fluid, but also to obtain a conceptually satisfactory theory based on first principles … In spite of satisfaction which one may have in writing rigorous inequalities originating from nontrivial linear theory, it must be said that the great difficulty which remains is to understand the nonlinear objects of turbulence (Ruelle, 1990). In spite of a huge number of papers and a large amount of research on turbulence, it remains an unsolved problem left for future generations (Sinai, 1999). … with all due respect for the coherent structures of the seventies, the insight gained from the chaos theory in the eighties, the achievements of Direct Numerical Simulations (DNS) and Large Eddy Simulation in the nineties, we all hope in our heart of hearts to see the great breakthrough in turbulence, stirring Sir Horace Lamb in his eternal sleep to bring him the long awaited revelation (Wijngaarden, 2000).