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 (

) 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 ∼ 20 h ${\sim} 20h$

, consistent with the presence of LSMs and VLSMs. In the LSM-dominated region (iii), velocity spectra exhibit a LSM prevalent peak at

tilde 3 h ∼ 3 h ${\sim} 3h$

. The near-sidewall SCI region (i) and central VLSM/LSM region (ii) are phase independent in their oscillations, likely due to a barrier effect of LSM-dominated region (iii) between them. For mathematical equation , the VLSM/LSM region (ii) disappears, while the other two regions exhibit distinct alterations. At mathematical equation , the SCI-dominated region resembles that for mathematical equation , while VLSMs in the LSM-dominated region have a remarkably shorter wavelength (

tilde 10 h ∼ 10 h ${\sim} 10h$

). At a lower mathematical equation ( mathematical equation ), VLSMs are completely absent in the LSM-dominated region. Based on these results, a schematic framework of the interrelations between SCs and VLSMs across different channel mathematical equation is proposed.