Shallow mixing layers over hydraulically smooth bottom in a tilted open channel

Shallow mixing layers (SMLs) behind a splitter plate were studied in a tilted rectangular open-channel flume for a range of flow depths and the initial shear parameter λ = (U₂ - U₁)/(U₂ + U₁), where U₁ and U₂ are streamwise velocities of the slow and fast streams, respectively. The main focus of the study is on (i) key parameters controlling the time-averaged SMLs; and (ii) the emergence and spatial development of Kelvin-Helmholtz coherent structures (KHCSs) and large- and very-large-scale motions (LSMs and VLSMs) and associated turbulence statistics. The time-averaged flow features of the SMLs are mostly controlled by bed-friction length scale h/c_f and shear parameter λ as well as by time-averaged spanwise velocities V and momentum fluxes UV, where h and c_f are flow depth and bed-friction coefficient, respectively. For all studied cases, the effect of shear layer turbulence on the SML growth is comparatively weak, as the fluxes UV dominate over the spanwise turbulent fluxes. Initially, the emergence of KHCSs and their length scales largely depend on λ. The KHCSs cannot form if λ (Equation presented) 0.3 and the turbulence behind the splitter plate resembles that of free mixing layers. Further downstream, shear layer turbulence becomes dependent on the bed-friction number S = c_fδ_v/(4hλ), where δ_v is vorticity thickness. When S (Equation presented) 0.01, the KHCSs are longitudinally stretched and the scaled transverse turbulent fluxes decrease with increasing S. The presence and streamwise development of LSMs/VLSMs away from the splitter plate depends on the λ-value, particularly when λ > 0.3, resembling LSMs/VLSMs in conventional open-channel flows when λ is small.