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.