Extreme-scale motions in turbulent plane Couette flows

We study the large-scale motions in turbulent plane Couette flows at moderate friction Reynolds number up to $Re_{\unicode[STIX]{x1D70F}}=500$ . Direct numerical simulation (DNS) domains were as large as $100\unicode[STIX]{x03C0}\unicode[STIX]{x1D6FF}\times 2\unicode[STIX]{x1D6FF}\times 5\unicode[STIX]{x03C0}\unicode[STIX]{x1D6FF}$ , where $\unicode[STIX]{x1D6FF}$ is half the distance between the walls. The results indicate that there are streamwise vortices filling the space between the walls that remain correlated over distances in the streamwise direction and that increase strongly with the Reynolds number, so that for the largest Reynolds number studied here, they are correlated across the entire $100\unicode[STIX]{x03C0}\unicode[STIX]{x1D6FF}$ length of the domain. The presence of these very long structures is apparent in the spectra of all three velocity components and the Reynolds stress. In DNS using a smaller domain, the large structures are constrained, eliminating the streamwise variations present in the larger domain. Near the centre of the domain, these large-scale structures contribute as much as half of the Reynolds shear stress.