Roughness and Reynolds Number Effects on the Flow Past a Rough-to-Smooth Step Change

Abstract

We report direct numerical simulations (DNSs) of open-channel flow with a step change from three-dimensional sinusoidal rough surface to smooth surface. We investigate the persistence of non-equilibrium behaviour beyond this step change (i.e. departures from the equilibrium smooth open-channel flow) and how this depends on (1) roughness virtual origin \(\epsilon /h\)? (scaled by the channel height h), (2) roughness size k / h?, (3) roughness shape? and (4) Reynolds number \(Re_\tau \)? To study (1), the roughness origin was placed aligned with, below (step-up) and above (step-down) the smooth patch. To study (2), the equivalent sand-grain roughness of the aligned case was decreased from \(k^+_s \simeq \) 160 to \(k^+_s \simeq 106\). To study (3) and (4) the step-down case at \(Re_\tau \simeq 395\) was compared with a backward-facing step case at \(Re_\tau \simeq 527\), and DNS of square rib rough-to-smooth case at \(Re_\tau \simeq 1160\) (Ismail et al., J. Fluid Mech., vol. 843, 2018, pp. 419–449). Results showed that \(\epsilon /h\) affects the departure from equilibrium by a large extent, while k / h, roughness shape and \(Re_\tau \) have a marginal influence. The departure from equilibrium was found to be related to the near-wall amplification of Reynolds shear stress, which in turn depends on \(\epsilon /h\), i.e. higher \(\epsilon /h\) leads to higher amplification.