Application of an Integral Fluctuation Theorem to Turbulent Flows

There is a long lasting discussion on universal properties of turbulence. The following questions arise: do turbulent properties change with the Reynolds number, or are they even dependent on the large scale properties of turbulence? An important feature would be that turbulence could be taken as universal below some scales. In this case, even for turbulent flows which are generated on a large scale by different processes, the same subgrid models can be used, an important aspect for numerical simulations. For large eddy simulations, it is essential to know the connections between larger scales and the unresolved subgrid turbulence. From this aspect it is important to get a profound understanding of the turbulent cascade, relating turbulent structures on different scales. Rigorous results on the turbulent cascade are still missing.