The dissipation tensor $\varepsilon_{ij}$ in wall turbulence

TL;DR

This paper analyzes the dissipation tensor in wall turbulence, comparing its anisotropy with Reynolds-stresses, and studies its transport equations and Reynolds number effects using detailed DNS data.

Contribution

It provides new insights into the anisotropy and transport mechanisms of the dissipation tensor in wall turbulence through detailed DNS analysis.

Findings

Differences in anisotropy between $oldsymbol{ au}_{ij}$ and $r_{ij}$ are illustrated.

Transport budgets of $oldsymbol{ au}_{ij}$ are characterized with high-resolution DNS.

Reynolds number influences on $oldsymbol{ au}_{ij}$ components are quantified.

Abstract

The paper investigates the dissipation tensor $\varepsilon_{ij}$ in wall turbulence. Available DNS data are examined to illustrate the differences in the anisotropy of the dissipation tensor $\varepsilon_{ij}$ with respect to the anisotropy of the Reynolds-stresses $r_{ij}$. The budgets of the transport equations of the dissipation tensor $\varepsilon_{ij}$ are studied using novel DNS data of low-Reynolds-number turbulent plane channel flow with spatial resolution sufficiently fine to accurately determine the correlations of products of 2-derivatives of fluctuating velocities $u_i'$ and pressure $p'$ which appear in various terms. Finally, the influence of the Reynolds number on the diagonal components of $\varepsilon_{ij}$ ($\varepsilon_{xx}$, $\varepsilon_{yy}$, $\varepsilon_{zz}$) and on the various terms in their transport equations is studied using available DNS data of Vreman and Kuerten (Phys. Fluids 26 (2014) 085103).