Energy production and self-sustained turbulence at the Kolmogorov scale in Couette flow

Several recent studies have reported that there exists a self-similar form of invariant solutions down to the Kolmogorov microscale in the bulk region of turbulent Couette flow. While their role in a fully-developed turbulent flow is yet to be identified, here we report that there exists a related mechanism of turbulence production at the Kolmogorov microscale in the bulk region of turbulent Couette flow by performing a set of minimalspan direct numerical simulations up to friction Reynolds number Reτ ≃ 800. This mechanism is found to essentially originate from the non-zero mean shear in the bulk region of the Couette flow, and involves the eddy turn-over dynamics remarkably similar to the so-called self-sustaining process (SSP) and/or vortex-wave interaction (VWI). A numerical experiment that removes all the other motions except in the core region is also performed, which demonstrates that the eddies at a given wall-normal location in the bulk region are sustained in the absence of other motions at different wall-normal locations. It is proposed that the self-sustaining eddies at the Kolmogorov microscale correspond to those in uniform shear turbulence at transitional Reynolds numbers, and a quantitative comparison between the eddies in uniform shear and near-wall turbulence is subsequently made. Finally, it is shown that the turbulence production by the selfsustaining eddies at the Kolmogorov microscale is much smaller than that of full-scale simulations, and that the difference between the two increases with Reynolds number.