## 1. Introduction

Reservoir sedimentation is an increasingly important challenge that operators worldwide are facing [

1,

2,

3,

4]. Storage capacity lost results in a decrease of energy production [

5]. Moreover the interruption of sediment continuity impacts the downstream river morphology causing ecological problems. Thus efficient sediment management is important for economical, technical and environmental reasons [

1,

6].

Turbidity currents are the main transport mechanisms for fine sediments in reservoirs. They can even redistribute the material inside the reservoir [

7]. In literature turbidity currents are also referred to as particle-driven gravity currents. They represent a group of density currents in which density differences result from the spatial distribution of concentration of a particulate substance. In contrast to other density currents where density differences are caused by e.g., concentration variations of a diluted substance or by temperature variations there occurs a relative velocity between the dispersed phase and the ambient phase [

8]. This relative velocity is a result of gravitational (settling) and inertia forces [

9].

Field observations of turbidity currents are difficult to accomplish due to their rare occurrence, for example during floods [

9,

10]. In addition turbidity currents usually form on the bottom of large and deep reservoirs [

7] which are difficult to reach. Thus the analysis of such currents in real reservoirs is often limited to time series of point measurements of flow properties at different locations. Some studies focus on the analysis of the consequences of turbidity currents such as bottom elevation changes [

7,

11]. The use of satellite imaginary for turbidity measurements over larger areas (e.g., [

12]) is not considered applicable for the study of turbidity currents, because this method provides turbidity data only for the near surface region of the reservoir. In addition, in most cases the spatial resolution of the available images will not be high enough.

Physical laboratory experiments have been undertaken to enhance process understanding of density currents in general (e.g., [

13,

14,

15,

16]) and also particle-driven gravity currents in particular (e.g., [

17,

18,

19,

20,

21,

22,

23]). Lock exchange experiments are a common approach of studying gravity currents. They feature a certain volume of sediment laden fluid which is released into still ambient fluid by removing a lock which is initially separating two compartments [

13,

15,

16,

18,

19,

20]. The main parameter studied in these experiments is the flow front advance of the gravity current with time. In addition, the current height and sediment deposition are often recorded.

Huppert and Simpson [

13] discuss several theoretical concepts describing gravity currents and study their efficiency in the laboratory on lock exchange experiments. They categorize the temporal development of the turbidity current into three regimes: (i) Right after the release of the suspension the gravity current passes through the slumping phase, in which the buoyant force is in balance with the counterflow of the ambient fluid; (ii) After this initial phase, in which the velocity is fairly constant, the gravity current is in the inertia-buoyancy phase in which it is balanced by forces of inertia; (iii) The final stage of a gravity current is the viscous-buoyancy regime where it is balanced by viscous forces [

13].

Experiments with constant inflow and sediment supply have been carried out (amongst others) by Baas et al. [

21] and Sequeiros et al. [

22,

23]. The former studied the expansion of high-concentration turbidity currents on a horizontal plate and the following deposition of sediments on that plate [

21]. The latter carried out experiments with constant inflow and sediment supply studying self acceleration of turbidity currents due to sediment uptake [

22].

Venting of turbidity currents has the potential of enabling highly efficient sediment management in reservoirs, satisfying economical as well as ecological needs [

3,

10,

17,

24]. The aim of this sediment management strategy is to route turbid water through bottom outlets as soon as it reaches the dam [

3]. Water losses through venting are generally lower than the amount of water lost by flushing. In addition, sediment continuity can be maintained to a high degree [

3,

24]. As for any sediment management strategy for reservoirs, a detailed process understanding of the driving sediment transport processes is particularly crucial for efficient venting of turbidity currents [

1,

24].

Laboratory studies investigating particularly the formation and evolution of turbidity currents in a reservoir during venting have been performed by Fan and Chamoun et al., The former gathered general knowledge on turbidity currents and their development during venting [

17]. The latter elaborated optimum conditions for venting in terms of bed slope of the reservoir [

25], venting degree [

24] and timing of venting [

26]. With the advance of computational fluid dynamics (CFD), the experimental set-up of lock exchange experiments has been taken up for numerical studies [

8,

9,

14,

27,

28,

29,

30,

31]. Flow in these models is purely driven by gradients in the spatial distribution of density. Thus they provide an efficient test case for the validation of solvers for models of density currents. In models particularly for the simulation of fluid flow in reservoirs the set-up of lock exchange experiments imitates the inflow of turbid water during a short term storm event.

Sediment transport in these models is implemented in different detail. One-way coupling of momentum exchange between the ambient and the dispersed phase can be achieved using advection-diffusion equations [

8,

29,

32]. In these models the particle velocity equals the sum of the fluid velocity and the fall velocity. Hence forces of inertia are neglected [

8,

29]. In addition, the dispersed phase is neglected in the mass conservation equation. Buoyant forces are accounted for through a source term in the momentum equation and neglected for all other terms rather than gravitational terms (Boussinesq approximation) [

8,

29,

33]. This limits the applicability of such models to small mass loadings [

8,

29].

An et al. [

29] simulated different kinds of gravity currents including particle driven gravity currents produced by lock exchange experiments from Gladstone et al. [

19]. The focus of this study was on the differences in large eddy simulations and Reynolds averaged simulations of gravity currents. Similarly, Stancanelli et al. [

30] studied the differences of LES and RANS numerically but using the setup of Musumeci et al. [

15] and Stancanelli et al. [

16], where the high density fluid was released into an oscillating ambient fluid [

30]. Both models ([

29,

30]) were solved using the commercial FLOW-3D CFD code.

On the basis of their results An et al. [

29] classify particle-driven gravity currents into three regimes with respect to the deposition rate of the sediment. When particles are small (e.g.,

$d$ < 16 µm) and hence fall velocity is low deposition has only little influence on the propagation of the gravity current (suspended regime). When suspended particles are larger (e.g., 16 µm <

$d$ < 40 µm), the propagation of the gravity current is highly influenced by the fall velocity (mixed regime). Particle-driven gravity currents with larger particles (e.g.,

$d$ > 40 µm) rapidly loose momentum due to deposition (deposition regime). Exemplary particle sizes mentioned above apply to particles with a relative density of

${\rho}_{\mathrm{rel}}$ = 3.22. [

29].

Necker et al. [

8] studied the development of a particle-driven gravity current in several further aspects. The numerical data is compared to experimental data of DeRooij and Dalziel [

20]. Additional data is retrieved from a high resolution numerical model as well as laboratory experiments carried out by Bonnecaze et al. [

18]. Main points studied by Necker et al. were (i) the structure of the flow front, (ii) conversion of potential energy to kinematic energy and (iii) dissipation of energy due to particle settling. In addition the difference between 2D and 3D models of turbidity currents is discussed. Resuspension of particles is considered to the point that the authors show using Shields critical velocities [

34] that resuspension is unlikely to occur in the studied flows [

8].

Two-way coupling is necessary for higher mass loads and to account for inertial effects [

9,

31,

35]. A model treating water and sediment as separate continua has been set up using the commercial code FLUENT by Georgoulas et al. [

9]. With this model they reproduced the lock exchange experiments of Gladstone et al. [

19] and simulated the expansion of high concentration turbidity currents on a horizontal plane as physically investigated by Baas et al. [

21]. Cantero et al. [

31,

35] accounted for inertial effects using an Eulerian equilibrium approach. They carried out a direct numerical simulation of turbidity currents on a 2D Eulerian-Eulerian model.

A simplified approach for modelling the two-phase flow of a water-sediment suspension including buoyant forces has been proposed by LaRocca et al. [

14,

27] using the two-layer shallow water equations. Their approach is based on the assumption that the upper layer of lighter fluid remains flat during the motion. In addition to the commercial codes mentioned above, also the freeware Delft3D-FLOW model [

33] developed by Deltares provides the capability of modelling particle-driven gravity currents for river applications.

Despite this large number of studies on investigating the basic process of the formation and development of turbidity currents in test cases physically and numerically, only a reduced number of works on turbidity currents in operational reservoirs has been found in literature. Exemplary, simulations of turbidity currents in reservoirs during flood events have been carried out for the Luzzone Lake, Switzerland [

7], the Lugano Lake, Switzerland/Italy [

36] and the Imha Reservoir, South Korea [

32]. The former two models were solved using the CFX-4 code, while the latter was solved with the FLOW-3D model presented in an earlier study by the same authors [

29].

Hillebrand et al. [

37] simulated the flow field and sediment transport including bottom elevation changes in the Iffezheim hydropower reservoir. They used the freeware SSIIM developed at the Norwegian University of Science and Technology (NTNU) [

38] for their model. This code accounts for the effects of density changes on turbulence but not for buoyant forces [

39].

A two-dimensional simulation of turbidity currents in the Shimen Reservoir, Taiwan, has been carried out by Huang et al. [

10], using the 2D layer-averaged turbidity current model SRH2D [

40]. The method used to model turbidity currents in this model is similar to what has been proposed by LaRocca et al. [

14,

27]. For the study of venting Huang et al. applied a two stage approach using the empirical Rouse equation [

41] for the estimation of the sediment released through the outlets at the dam.

The model set up by Lee et al. [

11] simulating turbidity currents in Tsengwen Reservoir in Taiwan during typhoon-induced food events is the only model found in literature in which venting is included. The model based on the CFX-12.0 code was validated against a laboratory experiment with a setup similar to the experiments carried out by Chamoun et al. [

24,

25,

26]. Additionally, the model of the real reservoir was validated using concentration measurements at different elevations near the dam. Based on their results, Lee et al., developed a formula for the estimation of the concentration of the vented suspension [

11].

Apart from the study by Lee et al. [

11] no other 3D model applications particularly studying venting of turbidity currents have been found in literature. On the one hand, such a numerical tool can provide the basis for the design of an efficient venting system for reservoirs Lee et al., Numerical models are more flexible for geometry adaptions than physical models. They are free of scaling errors and allow an analysis of the entire flow field in high detail. They can be used to study the development of a turbidity current at the actual site of a reservoir which is usually difficult to rebuild in every detail in a laboratory. On the other hand, Lee et al. pointed out that the required fine discretization and thus long computation times make it impractical to run such a model on a normal desktop computer in real time [

11].

Hence this study aims to develop a numerical model allowing to study turbidity currents in real reservoirs. The basic hydrodynamic model used is RSim-3D [

42,

43,

44]. This model is adopted for the simulation of turbidity currents through a source term in the momentum equations. Basic model verification and validation is carried out reproducing the lock exchange experiments by Gladstone et al. [

19]. Moreover, results of the experiments by Chamoun et al. [

24,

25,

26] were used for further optimization of the tool to study the development of turbidity currents in reservoirs. Thus, in a second step, these experiments are reproduced with the developed model.