Lagrangian Structure Functions in Turbulence: Scaling Exponents and Universality

TL;DR

This paper extends the analysis of turbulence scaling laws from Eulerian to Lagrangian frameworks, introducing a novel bridging relation that accurately predicts Lagrangian velocity structure function exponents and aligns well with experimental and numerical data.

Contribution

It generalizes the approach for asymptotic scaling exponents to Lagrangian turbulence and introduces a new bridging relation for dissipation time, enabling precise calculation of scaling exponents.

Findings

Calculated Lagrangian structure function exponents match experimental data.

Introduced a new bridging relation based on dissipation time.

Extended turbulence scaling analysis to Lagrangian framework.

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.