Saturation and multifractality of Lagrangian and Eulerian scaling exponents in 3D isotropic turbulence

TL;DR

This study uses direct numerical simulations to analyze the saturation and multifractality of Lagrangian and Eulerian scaling exponents in 3D isotropic turbulence, revealing distinct saturation behaviors and their interrelations.

Contribution

It provides new insights into the saturation of scaling exponents in turbulence and links Lagrangian and Eulerian multifractal spectra through the frozen hypothesis.

Findings

Transverse Eulerian exponents saturate at ~2.1 for p ≥ 10.

Lagrangian exponents saturate at ~2 for p ≥ 8.

Different multifractal spectra suggest Lagrangian intermittency is characterized by transverse Eulerian intermittency.

Abstract

Inertial range scaling exponents for both Lagrangian and Eulerian structure functions are obtained from direct numerical simulations of isotropic turbulence in triply periodic domains at Taylor-scale Reynolds number up to 1300. We reaffirm that transverse Eulerian scaling exponents saturate at $\approx 2.1$ for moment orders $p \ge 10$, significantly differing from the longitudinal exponents (which are predicted to saturate at $\approx 7.3$ for $p \ge 30$ from a recent theory). The Lagrangian scaling exponents likewise saturate at $\approx 2$ for $p \ge 8$. The saturation of Lagrangian exponents and transverse Eulerian exponents is related by the same multifractal spectrum by utilizing the well known frozen hypothesis to relate spatial and temporal scales. Furthermore, this spectrum is different from the known spectra for Eulerian longitudinal exponents, suggesting that that Lagrangian intermittency is characterized solely by transverse Eulerian intermittency. We discuss possible implication of this outlook when extending multifractal predictions to the dissipation range, especially for Lagrangian acceleration.