Similarities between statistically-stationary homogeneous shear turbulence and the logarithmic layer in channels

The rough independence of the logarithmic layer (LL) of wall-bounded turbulence from the details of the buffer and outer layers, suggests that the interaction of the turbulent fluctuations with the mean shear may be mimicked by statistically-stationary homogeneous shear turbulence(SS-HST) in a finite box. We study SS-HST in boxes for which the statistics best agree with those of the LL. Both flows share similar Corrsin shear parameters, and Reynolds-stress and vorticity anisotropies. Two-point correlation functions show that $u$ and $w$ are constrained by the simulation box and are respectively shorter and narrower for SS-HST than for the LL, but $v$ and the vorticity are roughly of the same size in both flows when $Re_{\lambda}$ is similar. The transient bursting of $v$ in both flows is quite similar to the linear Orr mechanism, with time scales that are of the same order in both flows. In both cases, a streamwise velocity streak forms and breaks down quasi periodically, and the break down is accompanied by an enhanced flux of momentum, in the form of large-scale ejections and sweeps.