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

• DOI: 10.1017/jfm.2022.818
• Publication Date: 2022-11-08T10:25:42Z
• Authors: Sébastien Proust; Céline Berni; Vladimir I. Nikora
• Keywords: shear layer turbulence; Supplementary Data; Mechanical Engineering; Applied Mathematics; 0208 environmental biotechnology; 0207 environmental engineering; 610; river dynamics; 02 engineering and technology; Condensed Matter Physics; QC Physics; Mechanics of Materials; [PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]; QC; shallow water flows

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

${\lambda = (U_{2}-U_{1})/(U_{2}+U_{1})}$

, where

$U_1$

and

$U_2$

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

$\lambda$

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

$\lambda$

. The KHCSs cannot form if

${\lambda \lessapprox 0.3}$

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

$S = c_f \delta _v /(4 h \lambda )$

, where

$\delta _v$

is vorticity thickness. When

$S \gtrapprox 0.01$

, 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

$\lambda$

-value, particularly when

$\lambda > 0.3$

, resembling LSMs/VLSMs in conventional open-channel flows when

$\lambda$

is small.