Longitudinal and transverse Lagrangian velocity increments

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Longitudinal and transverse Lagrangian velocity increments are introduced as components along, and perpendicular to, the displacement of fluid particles during a time scale $\tau$. These increments provide a new path to the characterization of Lagrangian statistics in homogeneous and isotropic turbulence, and allows us to establish some bridge with Eulerian statistics. From direct numerical simulations, it is shown that the probability distributions of the longitudinal Lagrangian increment are negatively skewed at all time scales, which is a signature of time irreversibility in the Lagrangian framework. Transverse increments are found more intermittent than longitudinal increments. Eventually, transverse Lagrangian increments exhibit scaling properties that are very close to those of standard Cartesian Lagrangian increments.