Introduction of longitudinal and transverse Lagrangian velocity increments in homogeneous and isotropic turbulence

TL;DR

This paper introduces longitudinal and transverse Lagrangian velocity increments in turbulence, revealing their distinct roles in probing flow stretching and spinning, and analyzing their statistical properties through simulations.

Contribution

It defines new Lagrangian velocity increments based on geometric considerations and compares their statistical features with traditional increments in turbulence.

Findings

Longitudinal increments are negatively skewed, indicating turbulence irreversibility.

Transverse increments are more intermittent than longitudinal ones.

Standard Lagrangian increments show similar scaling to transverse increments.

Abstract

Based on geometric considerations, longitudinal and transverse Lagrangian velocity increments are introduced as components along, and perpendicular to, the displacement of fluid particles during a time scale {\tau}. It is argued that these two increments probe preferentially the stretching and spinning of material fluid elements, respectively. This property is confirmed (in the limit of vanishing {\tau}) by examining the variances of these increments conditioned on the local topology of the flow. Interestingly, these longitudinal and transverse Lagrangian increments are found to share some qualitative features with their Eulerian counterparts. In particular, direct numerical simulations at turbulent Reynolds number up to 300 show that the distributions of the longitudinal increment are negatively skewed at all {\tau}, which is a signature of time irreversibility of turbulence in the Lagrangian framework. Transverse increments are found more intermittent than longitudinal increments, as quantified by the comparison of their respective flatnesses and scaling laws. Although different in nature, standard Lagrangian increments (projected on fixed axis) exhibit scaling properties that are very close to transverse Lagrangian increments.