Development of very-large-scale motions and secondary currents in rough-bed open-channel flow

This study examines the streamwise development of secondary currents (SCs) and very-large-scale motions (VLSMs) in a rough-bed open-channel flume. We used long-duration stereoscopic particle image velocimetry at six cross-sections, extending up to 300 flow depths downstream from the flume entrance, to obtain detailed velocity fields, stress distributions and spectra. SCs were initially observed with a transverse spacing of approximately one flow depth, which increased downstream as adjacent cells merged. VLSMs became clearly identifiable by 100 flow depths from the flume entrance and continued to develop further downstream. The total transverse spectra of the streamwise velocity remained nearly constant downstream, as diminishing dispersive contributions from SCs were compensated by increasing turbulent contributions from VLSMs. A new phase-based analysis was used to quantify the lateral meandering of VLSMs. This revealed a linear relationship between meandering amplitude and streamwise VLSM wavelength, suggesting self-similarity of their spatial pattern. The results provide experimental evidence supporting the interpretation that SCs and VLSMs originate from a system of counter-rotating vortices, with SCs representing their time-averaged footprint and VLSMs arising through their temporal meandering. The findings highlight a mechanistic link between SC decay and VLSM growth, offering new insights into large-scale organisation in open-channel turbulence and its evolution along the channel.