On the velocity distribution in homogeneous isotropic turbulence: correlations and deviations from Gaussianity

TL;DR

This paper explores the velocity distribution in homogeneous isotropic turbulence, combining theoretical analysis with numerical simulations to understand deviations from Gaussian behavior and the underlying statistical factors.

Contribution

It introduces a framework using the Lundgren-Monin-Novikov hierarchy with conditional averaging to analyze the velocity PDF in turbulence.

Findings

Conditional averages influence the shape of the velocity PDF.

Deviations from Gaussianity are quantified through simulations.

Theoretical insights identify key statistical quantities affecting turbulence velocity distribution.

Abstract

We investigate the single-point probability density function of the velocity in three-dimensional stationary and decaying homogeneous isotropic turbulence. To this end we apply the statistical framework of the Lundgren-Monin-Novikov hierarchy combined with conditional averaging, identifying the quantities that determine the shape of the probability density function. In this framework the conditional averages of the rate of energy dissipation, the velocity diffusion and the pressure gradient with respect to velocity play a key role. Direct numerical simulations of the Navier-Stokes equation are used to complement the theoretical results and assess deviations from Gaussianity.