Secondary currents and very-large-scale motions in open-channel flows: effect of flow aspect ratio

Large-eddy simulations of open-channel flow are conducted to investigate how the channel aspect ratio ( mathematical equation ), defined as the width ( upper B B $B$ ) to depth ( h h $h$ ) ratio ( mathematical equation ), affects secondary currents (SCs), large-scale motions (LSMs) and very-large-scale motions (VLSMs). Four cases spanning mathematical equation are considered. For wide-channel flows ( mathematical equation ), certain flow features dominate depending on the distance from the sidewall, which are: (i) secondary current instability (SCI) within tilde 0.6 h ∼ 0.6 h ${\sim} 0.6h$ of the sidewalls; (ii) VLSMs and LSMs from distance 2.4 h 2.4 h $2.4h$ onwards from the sidewalls; and (iii) prevalence of LSMs between (i) and (ii). In the SCI-dominated region (i), two time-averaged SC cells appear, one near the bottom wall–bed corner (BV) and another near the surface (SV). The size and position of the BV and SV oscillate quasi-periodically with a wavelength tilde 6 h ∼ 6 h ${\sim} 6h$ , reflecting the instability of the secondary currents. In the VLSM/LSM-dominated region (ii), pre-multiplied spectra of the streamwise velocity fluctuations peak at tilde 3 h ∼ 3 h ${\sim} 3h$ and tilde 20 h