Lagrangian Structure Functions in Turbulence: Scaling Exponents and Universality

Abstract

In this paper, the approach for investigation of asymptotic ($Re\to \infty$) 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 $S_{n,L}(\tau)=\bar{(u(t+\tau)-u(t))^{n}}\propto \tau^{\kappa_{n}}$ in a good agreement with experimental and numerical data.