On the self-sustained nature of large-scale motions in turbulent Couette flow

Abstract

Large-scale motions in wall-bounded turbulent flows are frequently interpreted as resulting from an aggregation process of smaller-scale structures. Here, we explore the alternative possibility that such large-scale motions are themselves self-sustained and do not draw their energy from smaller-scale turbulent motions activated in buffer layers. To this end, it is first shown that large-scale motions in turbulent Couette flow at $Re=2150$ self-sustain, even when active processes at smaller scales are artificially quenched by increasing the Smagorinsky constant $C_{s}$ in large-eddy simulations (LES). These results are in agreement with earlier results on pressure-driven turbulent channel flows. We further investigate the nature of the large-scale coherent motions by computing upper- and lower-branch nonlinear steady solutions of the filtered (LES) equations with a Newton–Krylov solver, and find that they are connected by a saddle–node bifurcation at large values of $C_{s}$. Upper-branch solutions for the filtered large-scale motions are computed for Reynolds numbers up to $Re=2187$ using specific paths in the $Re{-}C_{s}$ parameter plane and compared to large-scale coherent motions. Continuation to $C_{s}=0$ reveals that these large-scale steady solutions of the filtered equations are connected to the Nagata–Clever–Busse–Waleffe branch of steady solutions of the Navier–Stokes equations. In contrast, we find it impossible to connect the latter to buffer-layer motions through a continuation to higher Reynolds numbers in minimal flow units.