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

TL;DR

This study demonstrates that large-scale motions in turbulent Couette flow are self-sustained entities, independent of smaller-scale turbulence, and are connected to known steady solutions of the Navier-Stokes equations.

Contribution

It provides evidence that large-scale motions can self-sustain without energy transfer from smaller scales, supported by simulations and bifurcation analysis.

Findings

Large-scale motions self-sustain at Re=2150 even when small-scale activity is suppressed.

Large-scale steady solutions are connected to classical Navier-Stokes solutions via bifurcation.

Impossible to connect buffer layer motions to large-scale solutions through Reynolds number continuation.

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 Cs in large eddy simulations. These results are in agreement with earlier results on pressure driven turbulent channels. 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 Cs. Upper branch solutions for the filtered large scale motions are computed for Reynolds numbers up to Re=2187 using specific paths in the Re-Cs parameter plane and compared to large-scale coherent motions. Continuation to Cs = 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.