Lagrangian statistical theory of fully developed hydrodynamical turbulence.

The Lagrangian velocity structure functions in the inertial range of fully developed fluid turbulence are for the first time derived based on the Navier-Stokes equation. For time T much smaller than the correlation time, the structure functions are shown to obey the scaling relations K n (τ) α T ξn . The scaling exponents ξ n are calculated analytically without any fitting parameters. The obtained values are in amazing agreement with the experimental results of the Bodenschatz group. A new relation connecting the Lagrangian structure functions of different orders analogously to the extended self-similarity ansatz is found.