Lagrangian Structure Functions in Turbulence: Scaling Exponents and Universality

In this paper, the approach for investigation of asymptotic ($Re\to \mathrm{\infty }$) scaling exponents of Eulerian structure functions (J. Schumacher et al, New. J. of Physics {\bf 9}, 89 (2007)) is generalized to studies of Lagrangian structure functions in turbulence. The novel “bridging relation” based on the derived expression for the fluctuating, moment-order - dependent dissipation time ${\tau }_{\eta ,n}$ enabled us to calculate scaling exponents (${\kappa }_n$) of the moments of Lagrangian velocity differences $S_{n,L}(\tau )=\overline{(u(t+\tau )-u(t){)}^n}\propto {\tau }^{{\kappa }_n}$ in a good agreement with experimental and numerical data.