Eulerian and Lagrangian Statistics from high resolution Numerical Simulations of weakly compressible turbulence

TL;DR

This study provides high-resolution Eulerian and Lagrangian statistics from simulations of weakly compressible turbulence, revealing differences from previous results and linking them through multifractal theory.

Contribution

It offers new high-resolution data on turbulence statistics and demonstrates the applicability of a multifractal bridge relation to connect Eulerian and Lagrangian scaling properties.

Findings

Eulerian statistics align with previous data.

Lagrangian statistics differ for moments of sixth order and higher.

A multifractal bridge relation effectively connects Eulerian and Lagrangian scalings.

Abstract

We report a detailed study of Eulerian and Lagrangian statistics from high resolution Direct Numerical Simulations of isotropic weakly compressible turbulence. Reynolds number at the Taylor microscale is estimated to be around 600. Eulerian and Lagrangian statistics is evaluated over a huge data set, made by $1856^3$ spatial collocation points and by 16 million particles, followed for about one large-scale eddy turn over time. We present data for Eulerian and Lagrangian Structure functions up to ten order. We analyse the local scaling properties in the inertial range and in the viscous range. Eulerian results show a good superposition with previous data. Lagrangian statistics is different from existing experimental and numerical results, for moments of sixth order and higher. We interpret this in terms of a possible contamination from viscous scale affecting the estimate of the scaling properties in previous studies. We show that a simple bridge relation based on Multifractal theory is able to connect scaling properties of both Eulerian and Lagrangian observables, provided that the small differences between intermittency of transverse and longitudinal Eulerian structure functions are properly considered.