# Laboratoire de Mécanique des Fluides et d’Acoustique - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

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Article dans Europhys. Lett. (2014)

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

Emmanuel Lévêque & Aurore Naso

Based on geometric considerations, longitudinal $(\delta u_\parallel^{(L)}(\tau))$ and transverse $(\delta u_\perp^{(L)}(\tau))$ 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. These longitudinal and transverse Lagrangian increments are found to share some qualitative features with their Eulerian counterparts. In particular, direct numerical simulations at $R_\lambda$ up to 300 show that the distributions of $\delta u_\parallel^{(L)}(\tau)$ are negatively skewed at all τ, which is a signature of time irreversibility 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 Cartesian Lagrangian increments (projected on fixed axis) exhibit scaling properties that are very close to transverse Lagrangian increments.

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