Large and very large scale motions in open-channel flows over rough bed in the presence and absence of a mixing layer

Abstract This study examines shallow uniform flow and spanwise-sheared flow behind a vertical splitter plate over a uniformly rough bed. The primary objective is to assess the presence of Large Scale Motions (LSMs) and Very Large Scale Motions (VLSMs) in these flow types, as well as the potential effects of horizontal Kelvin–Helmholtz Coherent Structures (KHCS) on LSMs and VLSMs. The presence of LSMs and VLSMs is investigated using pre-multiplied velocity spectra derived from long-term Acoustic Doppler Velocimeter measurements. A comparative analysis revealed that strong KHCSs inhibit the emergence of VLSMs. Although LSMs do appear in spanwise-sheared flow, they are less discernible in the pre-multiplied spectra. As the strength of KHCSs diminishes downstream, VLSMs begin to emerge. Established LSMs and VLSMs exhibit longitudinal wavelengths of $$\lambda _x \sim$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> </mml:mrow> </mml:math> 3–4h and $$\lambda _x \sim$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> </mml:mrow> </mml:math> 25 h respectively, for both flow types ( h is water depth), closely matching those reported for uniform open-channel flows. VLSMs contribute approximately 40% to the streamwise velocity variance and about 30% to the vertical Reynolds shear stress. For both flow types, the spectral correlation coefficient between longitudinal and vertical velocity fluctuations indicates a higher correlation at the VLSMs scale than at the LSMs scale, suggesting a greater organization of VLSMs. Our results also suggest that the VLSMs wavelength may be independent of the friction Reynolds number. Supplementing our measurements with published data, we suggest that VLSMs longitudinal wavelength is likely dependent on the relative submergence and/or flow aspect ratio.