Evidence that uniform momentum zones originate from roughness sublayer structure interactions in fully rough channel turbulence

Abstract

Fully rough wall-sheared turbulence is composed of an inner and outer layer, the former occupied by sinuous structures sustained by the well-known autonomous inner cycle, the latter occupied by inclined parcels of momentum deviations relative to the average. The outer-layer structures are also known as uniform momentum zones (UMZs), where the presence of successive UMZs manifests instantaneously with a distinct ‘staircase’ pattern in streamwise velocity. Direct numerical simulation (DNS) of fully rough channel turbulence was recently used to interpret UMZs as wakes originating from antecedent bluff-body-like interactions within the inner layer (Anderson & Salesky, J. Fluid Mech., vol. 906, 2020, A8). Wake-scaling arguments agreed precisely with instantaneous results from DNS. Foremost among these results was evidence that the instantaneous wall-normal gradient of streamwise velocity exhibited scaling of ${\sim }x_3^{-1/2}$ , where $x_3$ is wall-normal location; this is in contrast to logarithmic scaling, which requires the wall-normal gradient of streamwise velocity to scale as ${\sim }x_3^{-1}$ . Herein, wake-scaling arguments have been advanced and compared against results from wall-modelled large-eddy simulation (LES). New results from the ‘bottom up’ wake-scaling arguments agree with LES results, such that the shear associated with the instantaneous staircase-like streamwise velocity follows a clear trend. We have leveraged conditional sampling during LES – predicated upon instantaneous low-frequency, high-magnitude surface stress values known to correspond to large-scale inertial-layer coherence – to further assess the predictive value of the wake-scaling arguments. Model results compare favourably.