Large-eddy simulation of turbulent plane-Couette flow *

We describe DNS, wall-resolved and wall-modeled LES of plane Couette (PC) flow.  Subgrid-scale (SGS) motion is represented using the stretched-spiral vortex SGS model while the virtual-wall model is utilized for wall-modeling.  Cases studied include DNS at  friction Reynolds numbers Re_τ = 220, wall-resolved LES at  Re_{τ =}  500- 3,600 and wall-modeled LES at  Re_t = 3,600-2.85x10⁵.  All LES performed show the presence of approximately span-wise periodic sets of stream-wise rolls. Averaged wall-normal profiles of the mean stream-wise velocity  show a consistent log region across all Reynolds numbers. Both the mean-flow roll energy and circulation, scaled with outer variables, decrease monotonically for Re_t > 500. At lower  Re_t the mean stream-wise zero-velocity line follows a wavy form in the span-wise direction, while at larger Re_τ, a mushroom shape emerges which could  potentially enhance local momentum transport in the span-wise direction and be responsible for the weakening of the span-wise rolls.