Secondary currents in smooth-wall open channel flow

Secondary currents of Prandtl's second kind in straight channels play an important role in the distribution of the bed shear-stress, affecting sediment transport and morphodynamics, mixing and channel flow capacity. Smooth open-channels form the cornerstone of understanding of these complex flows (e.g., Nezu and Nakagawa, 1993) and have been a reference for numerical simulations, more recently via direct numerical simulations (e.g., Sakai, 2019). However, since the Laser-Doppler-Anemometry (LDA) study of Nezu and Rodi (1985), discussed in the seminal book of Nezu & Nakagawa (1993), there have been no further experimental studies on secondary currents in smooth-wall open channels to the authors' knowledge. In this exploratory work, the effect of aspect ratio on the formation of secondary currents in a smooth-walled rectangular open-channel is studied via stereoscopic particle image velocimetry (PIV) in a vertical cross-plane. The measurements were conducted for aspect ratios AR = 2b/h = 4, 6 and 10, where h is the flow depth and b is the half-width of the channel. The mean streamwise-velocity iso-contours as well as the contours of signed swirling strength indicate the presence of secondary circulations close to the channel sidewalls, while they become nearly inexistent in the region beyond 2.5h from the side-wall, consistent with Nezu and Rodi (1985). However, contrary to Nezu & Rodi (1985), who identified different topologies for different aspect ratios, the pattern of the secondary currents is the same for the three aspect ratios measured here. It consists of three main cells: a "bottom vortex" and a "surface vortex" as identified by Nezu & Rodi (1985), and a third vortex away from the wall and spanning the hole water depth.