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.