Predicting Transverse Mixing Efficiency Downstream of a River Confluence

Abstract

Predicting mixing processes, especially transverse mixing, downstream of river confluences, is necessary for assessing and modeling the fate of pollutants transported in river networks, but it is still challenging. Typically, there is a lack of transverse mixing solutions implemented in 1-D hydrodynamical models widely used in river engineering applications. To investigate the mixing processes developing downstream of a medium-sized river confluence, three high-resolution in situ surveys are conducted at the Rhône-Saône confluence in France, based on geolocated specific conductivity and hydroacoustic measurements. Contrasting mixing situations are observed depending on hydrological conditions. In some cases, the two flows mix slowly due to turbulent shear at their vertical interface. This can be modeled by an analytical solution of the advection-diffusion equation. In other cases, the waters from one of the two tributaries move under the waters of the other tributary. The induced local circulation enhances transverse mixing but not vertical mixing and the flow remains stratified vertically, which may be missed when surface or satellite images are analyzed qualitatively. Stratification may be predicted by comparing the time scales for shear and density-driven adjustment. Shear-dominated transverse mixing of depth-averaged concentrations can be predicted analytically and implemented in 1-D hydrodynamical models. However, the initiation of apparently rapid transverse mixing due to density-driven circulation remains to be better understood and quantified. Plain Language Summary Predicting how waters mix downstream of river confluences is necessary for assessing and modeling the fate of pollutants transported in river networks, but it is still challenging. Typically, there is a lack of transverse mixing solutions implemented in models widely used in river engineering applications. To investigate the mixing processes developing downstream of a medium-sized river confluence, three high-resolution in situ surveys are conducted at the Rhône-Saône confluence in France. Contrasting slow or rapid mixing situations are observed depending on hydrological conditions. The transverse mixing of depth-averaged concentrations can be predicted analytically and implemented in 1-D hydrodynamical models. However, the initiation of rapid transverse mixing due to difference in fluid density remains to be better understood and quantified.

Analysis of Storage Effects in the Recirculation Zone Based on the Junction Angle of Channel Confluence

“…Lewis et al [16] and Lewis and Rhoads [41] reported that transverse mixing increases with M r . Additionally, the results presented by Pouchoulin et al [30] support the positive correlation between transverse mixing and M r based on field measurements, where D T /hu * was 1.34, M r = 1.15 and 2.21, and M r = 1.54. However, analysis of the transverse dispersion associated with flow structures by junction angle has been limited in previous studies.…”

“…When the concentration changes are less than 5% throughout the channel width, transverse mixing is considered to be complete [40]. When the distance between the solute input source and transverse mixing completion point (L m ) is five to 10 times the width of the channel, it is considered to be rapid mixing [30]. In the case of slow mixing, the distance between the source and completion point is 100 times the channel width [31,41].…”

“…The discharge of the main and tributary channels was set to Fr d = 0.37 for a discharge ratio (Q r ) of 0.25, such that the numerical simulations would have a separation zone downstream of the junction. Based on these hydraulic conditions, the momentum flux ratio (M r ) in this study was 1.62, which is included in the range for previous studies (0.29-2.52) [16,30]. The free-slip condition was employed for the wall boundary.…”

“…The junction angle influences near-field mixing by creating a recirculation zone and helical cells downstream of the confluence. Near-field mixing at confluences can be divided into rapid mixing, where transverse mixing is completed within a short distance, and slow mixing, where transverse mixing is maintained further downstream [30]. Lane et al [31] found that the presence of channel-scale circulation at a confluence transforms slow mixing into rapid mixing.…”

Evaluating longitudinal dispersion of scalars in rural channels of agro-urban environments

“…of ≈ 50% For the sake of clarity, only the name of the first author of the study is reported in the first column. For more details about the formulas, see Table 4 in cross-sections [5], river confluences [70] and riparian vegetation [58,64,80]-in a sort of universal formula for natural streams. Furthermore, Table 4 in "Appendix" shows that almost all the formulas have been developed by using field data taken from the same few works [10,21,31,37,38,56,62,74,86,100], i.e.…”