To generate electricity, prevent floods, supply water, and provide irrigation capacity, a huge number of large reservoirs have been constructed worldwide. For reservoirs built on rivers carrying high sediment loads, subaerial sediment-laden flows from the main channel and/or tributaries may plunge into less dense ambient fluid, and convert into subaqueous sediment-laden flows called turbidity currents. The hydrological and morphological impacts of large reservoirs with high sediment loads can be enormous, as exemplified by the Yellow River, China. In long-term hydro-sediment-morphodynamic processes, confluent flows with high sediment loads may cause severe bed aggradation. One of the most telling cases concerns the Sanmenxia reservoir on the Yellow River, where severe bed aggradation occurred inside its tributary, the Weihe River, driven by the intrusion of turbidity currents from the Yellow River in August 1967 (Fan, 2011). Severe bed aggradation caused by a turbidity current at the confluence of a reservoir and tributary can adversely affect flood control and hydropower functions. Notably, disparate vertically layered flow structures are often generated at these confluences, which exert a major influence on local sediment transport and morphological evolution processes. Enhanced understanding of such layered flow structures is essential for the management of large rivers with confluences carrying sediment-laden flows.

The hydro-sediment-morphodynamics of river confluences have been investigated for more than half a century. Field investigations (Rhoads and Sukhodolov, 2001; Sukhodolov and Rhoads, 2001; Biron et al., 2002; Riley and Rhoads, 2012; Ramón et al., 2013; Rhoads and Johnson, 2018; Zhang et al., 2020; Yuan et al., 2021), laboratory experiments (Taylor, 1944; Webber and Greated, 1966; Weber et al., 2001; Ribeiro et al., 2012; Yuan et al., 2018), and mathematical modelling studies (Bradbrook et al., 2001; Biron et al., 2004; Constantinescu et al., 2012; Lyubimova et al., 2014; Yang et al., 2014) have improved the understanding of the hydrodynamic characteristics, mixing, sediment transport, and bed morphology near river confluences. Generally, it has been revealed that the flow structure at river channel confluences can be divided into six major zones, i.e., flow stagnation, flow deflection, flow separation, maximum velocity, flow recovery, and distinct shear zones (Best, 1987). Accordingly, bed morphology at channel confluences is characterized by three elements: avalanche faces at the mouth, a deep central scour and a bar within the separation zone (Best, 1988), depending on width-to-depth ratio (Parsons et al., 2007; Szupiany et al., 2009), confluence angle (Mosley, 1976; Ghobadian and Bajestan, 2007) and momentum flux ratio between tributary and main channel (Rhoads and Johnson, 2018). Such studies have, however, almost exclusively been confined to confluent flows with low sediment loads or clear water, where sediment entrainment and scouring at the confluence are fundamentally controlled by downwelling and upwelling flows of helical motions (Yuan et al., 2018; Yuan et al., 2021). By contrast, fluvial processes of highly concentrated sediment-laden confluent flows can be distinct as characterized by much more significant sediment deposition without obvious scour hollow at the junction. To date, only a few experimental and computational studies have focused on river confluences with hyperconcentrated tributary flows (Zhang et al., 2015; Zhang and Wang, 2017; Wang et al., 2019). Increased sediment deposition and more prominent bars occur at confluences with high sediment loads than at those starved of sediment (Zhang and Wang, 2017). A number of investigations have been carried out on flows at river confluences, but little attention has been paid to reservoir-tributary confluences. Reservoir-tributary confluent flows carrying high sediment loads exhibit constantly changing and complex hydro-sediment-morphological processes. A thorough investigation of such processes can only be obtained when flow structures at reservoir-tributary confluences are properly understood. However, the understanding of flow structures at the confluences of reservoirs and tributaries carrying high sediment loads is presently far from clear.

Under appropriate inflow and sediment input conditions, especially when there is sufficiently high sediment load from either the main channel or a tributary, a turbidity current may develop at the river confluence and lead to a vertically layered flow structure, featuring complicated fluid-particle interactions that are not yet fully understood (Armanini, 2013; Cantero-Chinchilla et al., 2015). Over the past few decades, computational simulations have facilitated resolution of turbidity currents in reservoirs (Ford and Johnson, 1983; Hu et al., 2012; Cao et al., 2015; Xia, 2019). Full 3D models (Georgoulas et al., 2010; An and Julien, 2014) incur excessively high computational overheads and so are not viable for large-scale, long-duration applications. Based on an empirical plunging criterion, Wang et al. (2016) proposed a 1D model for open channel flows with turbidity currents, which ignored the differences between incipient and stable plunging criteria that have been revealed by theoretical analysis (Dai and Garcia, 2009; Li et al., 2011) and flume experiments (Lee and Yu, 1997). 2D layer-averaged models are significantly more efficient than 3D and so are more commonly used for turbidity current propagation (Hu et al., 2012; Lai et al., 2015). For the first time, Cao et al. (2015) developed a 2D double layer-averaged model to resolve the whole processes of reservoir turbidity currents, from formation and propagation to recession, as well as bed evolution. This model, along with its recently extended double layer-averaged two-phase flow version, has been applied to resolve landslide-generated waves, and barrier lake formation and breach processes (Li et al., 2019; Li et al., 2020; Li et al., 2021).

This study aims to unravel the vertically layered flow structure at a river confluence under a wide range of inflow and sediment input conditions. The coupled 2D double layer-averaged model proposed by Cao et al. (2015) is used to investigate a series of idealized laboratory-scale tests and a large-scale prototype case study concerning the Guxian Reservoir on the Middle Yellow River, China. The computational results are evaluated in accordance with the corresponding physical controls to ascertain the layered flow structure patterns at a reservoir-tributary confluence under different conditions in the main channel and tributary.

The 2D double layer-averaged model is detailed in Cao et al. (2015) and outlined in Supplementary Text S1 in the Support Information online. Briefly, the governing equations in the 2D double layer-averaged model (Cao et al., 2015) are derived from fundamental conservation laws for shallow water-sediment flow dynamics. These include mass and momentum conservation equations for the upper clear-water flow layer and the lower sediment-laden flow layer (e.g., turbidity current), a mass conservation equation for sediment carried by the turbidity current, and a mass conservation equation for bed sediment. For the upper layer, η is water surface elevation, h w denotes clear-water flow layer thickness, u w and v w are the layer-averaged velocity components in the x- and y-directions. For the lower layer, η s is the elevation of the interface between the clear-water layer and turbidity current layer, h s denotes sediment-laden flow layer thickness, u s and v s are the layer-averaged velocity components in the x- and y-directions, and c s is the total volumetric sediment concentration. Bed elevation is denoted by z b . A set of relationships is introduced to determine bed resistance, interface shear stress and water entrainment, and net sediment exchange flux (i.e., entrainment minus deposition). Manning’s formula is used to calculate bed shear stresses. Shear stresses at the interface between the upper and lower layers are estimated in a similar fashion. Water entrainment at the interface is calculated using the Richardson number, following Parker et al. (1986). Sediment deposition is determined using the sediment particle settling velocity and near-bed concentration. Bed entrainment flux is estimated using Zhang and Xie’s formula for suspended sediment transport capacity (Zhang and Xie, 1993).

The model governing equations (Cao et al., 2015) are synchronously solved as two hyperbolic systems, one for the upper layer, the other for the lower layer. Each hyperbolic system is solved by a quasi-well-balanced numerical algorithm involving drying and wetting, using an accurate finite volume Godunov-type approach in conjunction with the HLLC (Harten-Lax-van Leer Contact Wave) approximate Riemann solver on a fixed rectangular mesh. The numerical algorithm is second-order accurate, explicit, and its time step is controlled by the Courant-Friedrichs-Lewy condition.

An earlier version of the aforementioned 2D double layer-averaged model was applied to dam break flows over erodible bed (Li et al., 2013), and gave numerical predictions that agreed well with observed data involving shock waves and contact discontinuity. To date, the 2D double layer-averaged model (Cao et al., 2015) has remained to the authors’ knowledge the only 2D model that can resolve the whole process of formation, propagation, and recession of turbidity currents. It has been extensively calibrated and validated using a series of experimental turbidity currents related to lock-exchange (Bonnecaze et al., 1995) and sustained inflows (Lee and Yu, 1997), and also successfully applied to the whole process of turbidity currents in the Xiaolangdi Reservoir in the Middle Yellow River, China. Recently, it has been tested against a suite of flume experiments of turbidity currents in a main channel-tributary system (Wang et al., 2020), with the tributary joining the main channel at an angle of 90° or 60°, as displayed in Text S2 in the Support Information online. Further, the model has been further extended to resolve landslide-generated waves and barrier lake formation and breach processes (Li et al., 2019; Li et al., 2020; Li et al., 2021). Here it is applied to resolve the flow at a reservoir-tributary confluence, noting that its extended two-phase flow version (Li et al., 2020; Li et al., 2021) produces equivalent results for reservoir turbidity currents.

It is interesting to probe into the physical controls on the distinct layered flow structures at a reservoir-tributary confluence, as described above. Given that the upstream boundary discharge and sediment concentration are steady in the laboratory-scale cases, the vertically layered flow structure at the confluence evolves to a steady regime. In contrast to the unsteady discharge and sediment input from the upstream reach of the Yellow River and its tributary Wuding River, the vertically layered flow structure at the confluence evolves in time and eventually falls into one of the primary patterns identified.

As shown in Figure 2, for Case C7, single sediment-laden flows are generated upstream of the main channel and tributary, respectively, while the tributary with higher sediment concentration sufficiently intrudes into the main channel. Sediment-laden flows from the main channel and tributary are well mixed vertically at the confluence, thus producing a vertically layered flow structure SL MC^SF—SL TR^SF. By contrast, as shown in Figure 4, for Case B5, there is a single layer sediment-laden flow upstream in the main channel and clear-water flow upstream in the tributary. The tributary flow with smaller discharge does not suffice to block the intrusion of the sediment-laden flow from the main channel. Therefore, a vertically layered flow structure SL MC^SF—DL TR^CW is formed at the confluence in the laboratory-scale case (Figure 4A), in accordance with the field-scale results of the Guxian Reservoir at t = 120 h (Figure 11). In a long term, the upper clear-water flow layer inside the tributary mouth diminishes, and thus the SL MC^SF—DL TR^CW is less discernible (Figure 4B). Comparison between Figures 2, 4 shows that when the main channel features a single layer (i.e., SL MC^SF), the formation of a single layer or double layer in the tributary (i.e., SL TR^SF or DL TR^CW) mainly depends on whether the main channel sediment-laden flow could intrude into the tributary or not.

As illustrated in Figure 3, for Case C12, a double layer flow exists upstream of the confluence in the main channel, and a single sediment-laden flow layer exists upstream in the tributary, featuring no intrusion between the main channel and tributary. Thus, a vertically layered flow structure DL MC^SF—SL TR^SF is produced at the confluence. By contrast, as shown in Figure 6, for Case C16, a double layer flow exists upstream of the confluence in the main channel and in the tributary, leading to the formation of DL MC^SF—DL TR^SF at the confluence. Figures 3, 6 illustrate that when the main channel features a double layer (i.e., DL MC^SF), the formation of a single layer or double layer in the tributary (i.e., SL TR^SF or DL TR^SF) at the confluence depends on whether a turbidity current could form upstream in the tributary.

As illustrated by Figure 5, for Case B1, there is a double layer upstream of the confluence in the main channel and a single clear-water flow layer upstream in the tributary. The main channel turbidity current intrudes into the tributary at the confluence and thus produces a vertically layered flow structure DL MC^SF—DL TR^CW, similar to the field-scale results of the Guxian Reservoir at t = 24 h in Figure 10. By contrast, as displayed in Figure 7, for Case D4, there is a single clear-water flow layer upstream in the main channel and a double layer upstream of the confluence in the tributary. With intrusion of turbidity current from the tributary into the main channel, a vertically layered flow structure DL MC^CW—DL TR^SF occurs at the confluence. In short, it is the intrusion of turbidity current from the main channel (or tributary) into clear-water flow in the tributary (or main channel) that leads to the formation of a double layer at the confluence.

Physically, bed evolution at a reservoir-tributary confluence carrying high sediment load depends strongly on the pattern of vertically layered flow structure that develops. More specifically, with intrusion of the reservoir turbidity current from main channel to tributary, a vertically layered flow structure SL MC^SF—DL TR^CW with bed aggradation inside the tributary mouth appears to occur at the confluence (Figures 4B,C). For high-concentration, sediment-laden flows in both the main channel and tributary, a vertically layered flow structure SL MC^SF—SL TR^SF causes bed aggradation inside the tributary mouth and below the downstream junction corner (Figures 2B,C), whereas a vertically layered flow structure DL MC^SF—DL TR^SF leads to severe bed aggradation within the confluence (Figures 6B,C). For a high-concentration, sediment-laden flow arising solely from the tributary, the resulting DL MC^CW—DL TR^SF structure leads to bed aggradation at the confluence and more sediment deposition upstream of the junction along the main channel (Figures 7B,C). By contrast, for high-concentration, sediment-laden flow in the main channel and low-concentration sediment-laden flow in the tributary, a vertically layered flow structure DL MC^SF—SL TR^SF develops at the confluence with bed aggradation upstream of the junction and below the opposite tributary side (Figures 3B,C). These findings contrast with the scour hollow observed in previous studies (Herrero et al., 2017; Sambrook Smith et al., 2019) of river confluences with low sediment loads or clear water. It is implied that sediment transport and morphological evolution at such reservoir-tributary confluences may vary drastically under the influences of distinct layer flow structures identified above. Further studies along this line are certainly warranted.

The present 2D double layer-averaged model does not explicitly consider the effect of velocity discrepancy between sediment particles and the fluid phase. Although this effect is negligible in the present computational cases with essentially fine sediment, future studies should be conducted using two-phase flow models (Li et al., 2020; Li et al., 2021). Moreover, the effect of sediment on the turbulence model is neglected in the 2D double layer-averaged model. In practice, this effect remains far from clear, even for steady, uniform sediment-laden flows in open channels (Cao et al., 2015). Furthermore, when the sediment concentration is sufficiently high, the water-sediment mixture may behave as a non-Newtonian fluid, and the present model would have to be extended accordingly. Computational cost is also of major concern in the present work, particularly when the model is used to simulate natural large-scale fluvial processes. Therefore, the present model could be improved to incorporate an unstructured mesh, local time step, and parallel computing following e.g., (Hu et al., 2019; Ni et al., 2020). To better represent the vertically layered flow structure in complicated domains, it is also recommended that the present model be boundary fitted, perhaps using cut-cell methods on an adaptive grid (see e.g., Liang et al. (2007), for an application to shallow flow hydrodynamics) and using sophisticated wetting and drying algorithms (Liang and Borthwick, 2009).

The vertically layered flow structure at a confluence of a reservoir and tributary carrying high sediment loads was investigated computationally using a coupled 2D double layer-averaged model (Cao et al., 2015). The following conclusions are drawn from the numerical results for laboratory-scale confluences and a field porotype-scale case concerning the Guxian Reservoir on the Middle Yellow River, China.

At a reservoir-tributary confluence, four primary patterns of vertically layered flow structure at such confluences are identified (Table 3). Vertically layered flow structures at such confluences are primarily controlled by the interaction between hydro-sediment factors in both the main channel and tributary:

(i) Formation of SL MC^SF—SL TR^SF and SL MC^SF—DL TR^CW mainly depends on whether the tributary flow could intrude into the main channel sediment-laden flow.

In response to unsteady discharge and sediment inputs from upstream, the vertically layered flow structure at such a reservoir-tributary confluence evolves in time. Yet it remains to fall into one of the primary patterns identified. Concurrent bed aggradation may considerably modify the confluent flow, yet the vertically layered flow pattern remains unchanged so far as the computational cases at both laboratory- and prototype scales considered herein are concerned.

The present study is limited to the vertically layered flow structure at the confluence of a reservoir and tributary carrying high sediment loads. The findings have implications for sediment transport and morphological evolution at river confluences, for which further investigations are warranted in order to facilitate optimization of reservoir operation schemes to mitigate sedimentation and accordingly alleviate capacity loss.