An exact relation between Eulerian and Lagrangian velocity increment statistics

TL;DR

This paper establishes a formal link between Eulerian and Lagrangian velocity increment statistics in turbulence, supported by numerical estimates in 2D turbulence, revealing processes behind non-Gaussian behaviors.

Contribution

It introduces a general formal connection applicable across turbulent systems and numerically investigates transition probabilities in 2D turbulence.

Findings

Identifies processes leading to non-Gaussian Lagrangian velocity statistics

Provides a numerical estimate of transition probabilities in 2D turbulence

Establishes a formal relation between Eulerian and Lagrangian velocity increments

Abstract

We present a formal connection between Lagrangian and Eulerian velocity increment distributions which is applicable to a wide range of turbulent systems ranging from turbulence in incompressible fluids to magnetohydrodynamic turbulence. For the case of the inverse cascade regime of two-dimensional turbulence we numerically estimate the transition probabilities involved in this connection. In this context we are able to directly identify the processes leading to strongly non-Gaussian statistics for the Lagrangian velocity increments.