Analysis of the Lagrangian path structures in fluid turbulence

Abstract

Because in the Lagrangian frame the time scale separation has a stronger Reynolds number dependence than the length scale case in the Eulerian frame, it is more difficult to reveal inertial range scaling laws, as predicted from dimensional arguments. The present work introduces a newly defined trajectory segment structure to tentatively understand Lagrangian statistics. When a fluid particle evolves in space, its Lagrangian trajectory encounters regions of different dynamics, which can be characterized by the magnitude of material acceleration, i.e., \documentclass[12pt]{minimal}\begin{document}$|\vec{a}|$\end{document}|a⃗|, in certain time span. The extrema of \documentclass[12pt]{minimal}\begin{document}$|\vec{a}|$\end{document}|a⃗| are considered as the representative markers along the Lagrangian trajectories. A trajectory segment is defined as the part bounded by two adjacent extrema of \documentclass[12pt]{minimal}\begin{document}$|\vec{a}|$\end{document}|a⃗|. The time difference and magnitude of the velocity difference at the two ends of each segment are chosen as the characteristic parameters. It shows that such structure reveals interesting turbulence physics, such as the scaling of the structure function and the quantitative description of the time scale. The corresponding explanation and analysis of flow physics are provided as well to improve the understanding of some remaining challenging issues.