Statistics of velocity gradients in wall-bounded shear flow turbulence

TL;DR

This paper analyzes the statistical properties of velocity gradients in wall-bounded turbulence using direct numerical simulations, revealing how these properties vary with distance from the wall and highlighting the significance of the logarithmic layer.

Contribution

It provides detailed statistical analysis of velocity gradients and enstrophy in wall turbulence, emphasizing the impact of spectral resolution and spatial location.

Findings

Largest velocity gradient fluctuations occur in the logarithmic layer.

Probability density functions vary significantly with distance from the wall.

Spectral resolution affects the amplitude of velocity gradient tails.

Abstract

The statistical properties of velocity gradients in a wall-bounded turbulent channel flow are discussed on the basis of three-dimensional direct numerical simulations. Our analysis is concentrated on the trend of the statistical properties of the local enstrophy ${\bm \omega}^2({\bm x},t)$ and the energy dissipation rate $\epsilon({\bm x},t)$ with increasing distance from the wall. We detect a sensitive dependence of the largest amplitudes of both fields (which correspond with the tail of the distribution) on the spectral resolution. The probability density functions of each single field as well as their joint distribution vary significantly with increasing distance from the wall. The largest fluctuations of the velocity gradients are found in the logarithmic layer. This is in agreement with recent experiments which observe a bursting of hairpin vortex packets into the logarithmic region.