Lagrangian Structure Functions in Turbulence: Scaling Exponents and Universality

In this paper, the approach for investigation of asymptotic (Re→∞) scaling exponents of Eulerian structure functions (J. Schumacher et al, New. J. of Physics 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 τη,n, led to analytic expression for scaling exponents (κn ) of the moments of Lagrangian velocity differences Sn,L(τ) = (u(t+ τ)− u(t))n ∝ τn in a good agreement with experimental and numerical data.