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

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 τ. 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 τ) 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 τ, 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.

References in corpus (8)

• Particles and fields in fluid turbulence
• Universal intermittent properties of particle trajectories in highly turbulent flows
• Lagrangian dynamics and statistical geometric structure of turbulence
• Acceleration statistics of finite-sized particles in turbulent flow: the role of Faxen forces
• Lagrangian Structure Functions in Turbulence: A Quantitative Comparison between Experiment and Direct Numerical Simulation
• A phenomenological theory of Eulerian and Lagrangian velocity fluctuations in turbulent flows
• An exact relation between Eulerian and Lagrangian velocity increment statistics
• A new assessment of the second order moment of Lagrangian velocity increments in turbulence

Cited by in corpus (4)

• Lagrangian Statistics for Navier-Stokes Turbulence under Fourier-mode reduction: Fractal and Homogeneous Decimations
• Heavy inertial particles in turbulent flows gain energy slowly but lose it rapidly
• Time-irreversibility of the statistics of a single particle in a compressible turbulence
• Transport, flow topology and Lagrangian conditional statistics in edge plasma turbulence