It is widely acknowledged that streamwise ridges on the bed of open-channel flows generate secondary currents (SCs). A recent discovery of meandering long streamwise counter-rotating vortices in open-channel flows, known as very-large-scale motions (VLSMs), raises a question regarding the interrelations between VLSMs and SCs in flows over ridge-covered fully rough beds. To address it, we conducted long-duration experiments using stereoscopic particle image velocimetry, covering a range of ridge spacings ( $s$ ) from ${\approx}0.4$ to ${\approx}4$ flow depths ( $H$ ). For a benchmark no-ridge case, the flow is quasi-two-dimensional in the central part of the channel, exhibiting a strong spectral signature of VLSMs, as expected. With ridges on the bed at $s\lessapprox 2H$ , two SC cells are formed between neighbouring ridges and VLSMs are entirely suppressed, suggesting that ridge-induced SCs prevent the formation of VLSMs by absorbing their energy or overpowering their formation. At the same time, velocity auto- and cross-spectra reveal a new feature that can be explained by low-amplitude meandering of the alternating low- and high-momentum flow regions associated with instantaneous manifestations of SCs. Two-point velocity correlations and smooth velocity field reconstructions using proper orthogonal decomposition further support the validity of this effect. Its origin is probably due to the instability related to the presence of inflection points in the spanwise distribution of the streamwise velocity within the SC cells. These results have implications for bed friction in open channels, where the friction factor may increase if depth-scale SCs are present, or decrease under conditions of sub-depth-scale SCs and suppressed VLSMs.

中文翻译：

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流经山脊的明渠流中的二次流和超大规模运动

众所周知，明渠流床上的流向脊会产生二次电流 (SC)。最近在明渠流中发现蜿蜒的长流向反向旋转涡流，称为超大规模运动 (VLSMs)，提出了一个问题，即 VLSMs 和 SCs 之间的相互关系在山脊覆盖的完全粗糙床上的流动中。为了解决这个问题，我们使用立体粒子图像测速法进行了长时间的实验，覆盖了从 ${\approx}0.4$ 到 ${\approx}4$ 流动深度（$H$）的一系列脊间距（$s$） . 对于基准无脊情况，通道中央部分的流动是准二维的，正如预期的那样，表现出强烈的 VLSM 光谱特征。床上有山脊 $s\lessapprox 2H$ ，在相邻的脊之间形成两个 SC 细胞并且 VLSM 被完全抑制，这表明脊诱导的 SC 通过吸收它们的能量或压制它们的形成来阻止 VLSM 的形成。同时，速度自动谱和交叉谱揭示了一个新特征，可以通过与 SCs 的瞬时表现相关的交替低动量和高动量流区域的低幅度曲折来解释。两点速度相关性和使用适当正交分解的平滑速度场重建进一步支持这种效果的有效性。它的起源可能是由于与 SC 单元内流向速度的展向分布中拐点的存在相关的不稳定性。这些结果对明渠中的床摩擦有影响，