The vortex filament model and velocity structure functions of well-developed hydrodynamical turbulence

We present a further elaboration of a vortex filament theory which was developed in our previous papers. A representative example of a cylindrical vortex filament is considered in detail. It is shown that contraction and stretching of a filament provide an energy flux from larger to smaller scales. A connection between velocity scaling exponents and moments of vorticity is clarified. Lagrangian and Eulerian transversal scaling exponents are derived based on the concept of vortex filament evolution. Arguments hypothesizing that Lagrangian scaling exponents tend to a constant for n -> infinity and an upper constraint for lim(n ->infinity) xi(n)/n are presented.