  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).
