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

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).