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Journal Articles EPL - Europhysics Letters Year : 2014

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

Abstract

Based on geometric considerations, longitudinal (δu (L) (τ)) and trans-verse (δu (L) ⊥ (τ)) Lagrangian velocity increments are introduced as com-ponents along, and perpendicular to, the displacement of fluid particles during a time scale τ . It is argued that these two increments probe pref-erentially the stretching and spinning of material fluid elements, respec-tively. This property is confirmed (in the limit of vanishing τ) by exam-ining 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 λ up to 300 show that the distributions of δu (L) (τ) 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 incre-ments (projected on fixed axis) exhibit scaling properties that are very close to transverse Lagrangian increments.
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Dates and versions

hal-01091613 , version 1 (05-12-2014)

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Emmanuel Lévêque, Aurore Naso. Introduction of longitudinal and transverse Lagrangian velocity increments in homogeneous and isotropic turbulence. EPL - Europhysics Letters, 2014, 108, pp.54004. ⟨10.1209/0295-5075/108/54004⟩. ⟨hal-01091613⟩
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