Study of Dam-Break Flow Over a Vegetated Channel With and Without a Drop

The effects of a drop in a vegetated channel on the flow characteristics during a dam failure were investigated using a numerical approach. A CFD package was used for all dam failure simulations. After performing validation tests, the model was used to predict the flow characteristics during a dam failure over a vegetated channel with positive, negative, or no drop. A positive drop resulted in a backflow into the reservoir with a negative discharge of Qbackflow = − 0.01 m3/s. Even in the channel with no drop, backflow into the reservoir occurred in the last stage due to the drag effect of the vegetation. The maximum discharge occurred at the peak time tpeak = 2.5 s above the drop for all models. The peak discharge decreased from Qpeak = 0.037 m3/s to Qpeak = 0.032 m3/s with increasing positive drop height. However, a negative drop had no significant effect on peak discharge values. In most cases, the maximum flow velocity was around um = 2 m/s. The maximum eddy values decreased by Δωmax = 500 1/s for the positive drops and increased by Δωmax = 700 1/s for negative drops at the middle stage.


Introduction
Floods caused by dam failure can have an immensely destructive impact on downstream areas, with substantial loss of property and human life. River morphology, infrastructure, and vegetation can significantly affect flood development by increasing the resistance or driving forces in the event of dam failure (Tsakiris and Spiliotis 2013;Tsakiris and Bellos 2014;He et al. 2020;Issakhov and Zhandaulet 2020b;Oguzhan and Aksoy 2020;He et al. 2020;Issakhov et al. 2022).
River morphology can change significantly throughout the downstream channel. Downstream infrastructure can create discontinuities in the main channel and affect flood evolution by altering kinetic energy, leading to the development of hydraulic jumps, secondary flows, and flow disturbances (Fraccarollo and Toro 1995;Soares-Frazão and Zech 2007;Kocaman and Güzel 2011;Kocaman and Ozmen-Cagatay 2012;Kocaman et al. 2020;Khoshkonesh et al. 2021;Sarkhosh et al. 2021). These phenomena can significantly affect flood discharge and velocity during a dam failure.
Vegetation in the main channel or floodplain increases resistance to flow development during a dam failure. This can lead to a significant change in the velocity field and deformation of the free surface in the downstream channel (Acker et al. 2008;Uotani et al. 2014;Kasiteropoulou et al. 2017;Mavrommatis and Christodoulou 2022).
A review of previous studies shows that the evolution of a free surface over a mixed discontinuity caused by both downstream channel elevation and vegetation has not been studied experimentally or numerically. In this case, the free surface discontinuity may coincide in the front, wave body, and wave end. It is a complex three-dimensional phenomenon that can occur throughout the dam failure wave. The development of the free surface could be influenced by inconsistencies in the channel, the splitting of the flow acceleration into components, and mixed flow. The dam break flow can be divided into different regions relative to a drop within the vegetated channel: upstream of the drop, above the drop, and downstream of the drop. In these regions, the velocity field could be significantly affected by shallow and deep turbulence structures, the drop direction, and vegetation drag. This is a complex wave behaviour in a dam failure that requires further investigation and a threedimensional modelling approach.
Few studies have addressed the effects of positive or negative downstream drop on flow characteristics during dam failure (Ostapenko 2012;Khoshkonesh et al. 2022). Studies addressing the effects of the presence or absence of a downstream drop, and its direction, elevation, and vegetation, on the discharge hydrograph, velocity, and flow disturbance during a dam failure are even more sparse.
Therefore, this study focuses on investigating the effects of the presence or absence of a drop in a downstream channel covered by dense, rigid vegetation, and different drop directions and heights, on the flow dynamics during a dam failure using a CFD package, namely Flow-3D. Accordingly, the volume of fluid (VOF) method was used to track advection at the free surface. Then, the model was used to predict the flow characteristics during a dam failure in seven different cases, including vegetated channels with and without a drop. Dam failure calculations included the discharge hydrograph, flow velocity, locations of inflection points, and eddy evolution.

Governing Equations
The continuity and momentum conservation equations were solved in three-dimensional Cartesian coordinates to reproduce the flow field of the dam break (Hirt and Nichols 1981).
The turbulence structures were captured and modelled using the standard k-ε model, renormalization groups (RNG), the k-ω model, and the large eddy simulation (LES) method, as shown in Eq. (1) to (7) (Lee and Wahab 2019). After validation tests, the LES model was used for all simulations in this study.
The equations of the turbulence models including k-ε (Eq. (1) to (4)), k-ω (Eqs. (5) and (6)), and RNG and LES (Eq. (7)) in generic form are as follows: The variables c p , c ε , c b , DF k , DF ε , υ ε , υ T , N c , and ε T, min represent the production, decay, and buoyancy empirical coefficients (with values of 1.44, 0.2, and 1.92, respectively), turbulent kinetic energy diffusion and dissipation, turbulent viscosity induced by dissipation, turbulent kinetic viscosity, constant equal to 0.09. The RNG model includes (a) the additional term in Eq. (2), (b) the turbulence, and (c) an analytical approach to calculate the coefficients (c p = 1.42, N c = 0.085). The turbulence frequency ω ≡ ε / k improves the ability of the transport model to predict turbulent properties near wall boundaries, jet flows, and rotational flows, including the evolution of vortices in the flow field. The closure coefficients of the model are α = 5/9, β = 3/40, β* = 9/100, σ = 1/2, and σ* = 1/2. In the LES model, the turbulent structures that are resolvable within the computational domain are computed directly, while the structures that are too small for direct resolution are computed approximately, as in Eq. (7) (Khoshkonesh et al. 2021).

Sensitivity Analysis of Fluid Cells size and Turbulence Models
A sensitivity analysis was performed for the primary modelling parameters: the size of the fluid cells (FC) in the computational domain and the turbulence models (TM). The results are listed in Table 1. The experimental results of previous studies were used for validation tests, specifically, the study of Fraccarollo and Toro (1995) was used to evaluate the model's ability to reproduce the velocity field, the studies by Kocaman and Guzel (2011) and Kocaman et al. (2020) were used to evaluate the model's ability to reproduce the flow evolution during a dam failure in a channel with a rigid obstacle, and the work of Kocaman and Ozmen-Cagatay (2012) was used to evaluate the model's ability to reproduce backflow evolution, jumps, 1D and local 3D flows. The model's performance was acceptable in all cases.
All simulations in this study were performed with an Intel Core i7-1165G7 2.80 GHz processor, which has eight threads, and 16.0 GB of RAM. The maximum and minimum run times for about 5 260 000 cells in the RNG model and 62 000 cells in the LES model were approximately 113 000 and 270 s, respectively. The LES model had the lowest run time among the turbulence models. The size of the fluid cells in these cases was d = 0.75 cm (Table 1).

Model's Performance in Reproducing the dam-break flow Against an Obstacle
The evolution of the free surface after impact with an obstacle was studied at two control points, P1 inside the reservoir and P5 behind the obstacle, for four different fluid cell sizes (listed in Table 1).
In all cases except d = 1.1 cm, there was good agreement between the experimental and numerical results ( Fig. 1a and d). The finest mesh d = 0.5 cm resulted in the highest accuracy in reproducing the stage hydrograph downstream of the obstacle (Fig. 1i). The other models underestimated the stage hydrograph from t = 4 s to t = 10 s (Fig. 1j L).
The model accurately predicted the free surface deformation after the mushroom-shaped jet hit the obstacle (Fig. 2 g to 2 L). Subsequently, the flow rising over the side walls was higher in the numerical results due to the higher momentum values. The flow disturbance behind the obstacle was significant in both the numerical and experimental results (Fig. 2j  L).

Effect of Turbulence Models and Fluid Cells size on dam-break flow mean Velocity
The maximum mean velocity was about U max = 1.1 m/s in both experimental and numerical models ( Fig. 3a and f). There was good agreement between the experimental and numerical results at t < 2s. In contrast, the model overestimated the mean velocity at the dam site, especially between t = 2s and t = 10s. The best consistency was observed for LES and a cell size of d = 0.75 mm.

Effect of Turbulence Models and Fluid Cells size on dam-break Transitional flow
The numerical model successfully reproduced the development of a transitional flow at the constriction site. The model was able to efficiently predict the evolution of the moving hydraulic jump towards the reservoir (see Fig. 4). However, the fluctuations of the free surface over the moving jump decreased as the cell size was increased from d = 0.5 cm to d = 1.1 cm.
The results of the validation test showed that this model reliably reproduced the flow depth and discharge hydrograph in the event of a dam failure. Since the drop and dense vegetation act as physical obstructions, the validation results were generalizable to these cases with significant flow disturbance in the downstream channel.
The model could also reliably predict the velocity field and velocity gradients during dam failure. Subsequently, the model could reliably predict the secondary events of a dam failure, such as the evolution of backflow into the reservoir and the effects of a drop as the cross-section changes with the elevation of the free surface.   The length of the reservoir was 200 cm, and the depth of the static water column in the reservoir was 30 cm. The height of the drops was Hw0/15, 2Hw0/15, and 3Hw0/15 in two opposite directions, upwards (positive drop) and downwards (negative drop). The vegetation elements were rigid and dense, while the downstream channel was dry (Fig. 5).
The dimensions, density, and spacing between vegetation were selected based on the studies of Uotani et al. (2014). The vegetation elements' radius, height, and spacing were 1.2 cm, 10 cm, and 3 cm, respectively. The duration of the dam break phenomenon was 10 s in all simulations. The boundary conditions included free slip or symmetry at the intersections of the mesh blocks and the upper boundary of the computational domain.
The physics of the modeling included the assumptions of a fluid and a free surface under atmospheric pressure. At the beginning of the simulation the water is assumed to be at rest (U = 0). The endpoint of the channel was considered the outlet. Free-slip conditions were assumed at the channel's left wall, side walls, and bottom. The channel bed and vegetation elements were defined as fixed geometric elements.
In addition, six control points (control points 0 to 5) were adopted in the dam site, above the drop, in the beginning, middle, and end of the vegetated area, and downstream of the vegetation. At these control points, the flow characteristics of the dam break were predicted.

Fig. 1 Temporal variation of the free surface height in (a-d) point P1 and (i-l) point P5
A positive correlation between the number of fluid cells and the run time was observed in all cases except Case 1. The run time of Tr = 40 855 s in case wd (without drop) was shorter than that of the other cases, with a negative drop for the lower number of fluid cells. Thus, a drop in the downstream channel led to a significant change in the computational cost.

Outflow Hydrograph of the Reservoir
At the early stage, t < 0.1 s, a rapid and immediate increase in discharge to the peak value Q p = 0.05 m 3 /s was observed in all cases. However, the discharge decreased after 0.2 s and reached the equilibrium value Q e = 0.043 m 3 /s at some time between t = 0.2 s and t = 2 s in all cases (Fig. 6a h).
Wave damping, free surface deformation due to reflection from the positive drop, and vegetation drag effects caused a significant decrease in discharge values at t > 2 s (Fig. 6a  and c). The backflow into the reservoir resulted in a negative discharge Q p < − 0.01 m 3 /s.  (Kocaman and Guzel 2011) and in (g-l) the numerical results of this study A significant increase in negative discharge was observed with an increase in drop height from 0.02 to 0.06 cm between t = 0.06 s and t = 0.08 s. The negative discharge was observed in the case wd at t > 7.4 s (Fig. 6h).

Inflow Hydrograph Across the Downstream Channel
In all cases, the maximum discharge was observed at control point 1 at t p = 2.5s and at control point 5 at t p = 3.7s. Thus, the presence of a drop and its direction had a negligible effect on t p (Fig. 7a and n). Variations in the rising limb of the hydrograph increased due to an increase in the height of the positive drops. At the same time, peak discharge values decreased from Q p = 0.037 m 3 /s in dp1 to Q p = 0.032 m 3 /s in dp3 due to an increase in drop height from 0.02 to 0.06 m at control point 1 (Fig. 7a and f). In contrast, for models dn1 to dn3, the drop height had no significant effect on the inflow hydrograph (Fig. 7 g to 7 L). The maximum peak discharges at control points 1 and 5 were Q p = 0.043 m 3 /s in case wd and Q p = 0.036 m 3 /s in case dn3, respectively.  Fraccarollo and Toro (1995) and the numerical results of this study; (a-d) fluid cell size, and (c-f) turbulence models

Streamwise Velocity in the Vertical Direction Within Vegetation
The streamwise velocity in the vertical direction decreased significantly during the development of the dam break from t = 3 s to t = 7 s. The flow velocity fluctuation in the vertical direction was significant due to the development of turbulence structures around the vegetation. The maximum flow velocity was about 2 m/s in all cases except for dn1 and occurred in the middle of the vegetation elements at t = 3 s (Fig. 8a h). However, the flow velocity decreased significantly near the free surface. Several inflection points formed at various  flow depths at t = 3 s and t = 5 s. This indicated significant resistance to dam-break flow development due to eddy formation and transitional flow throughout the vegetated area. However, the number of inflection points decreased due to wave damping at t = 7 s. For the dp1 to dp3, and wd models, there was a significant difference between the velocity values at t = 3 s and t = 5 s (Fig. 8a and c h). This difference was not observed for models dn1 to dn3 ( Fig. 8d and f).
Therefore, the velocity profile in models dp1 to dp3 and wd was approximately smoothed at t = 7s. Flow condition in these models was indeed subcritical as flow in the upstream channel returned to the reservoir.

Development of the Turbulence Structures
Turbulence structures were observed due to the flow rotation and separation over the drop and vegetation (see Fig. 9). In all cases, the maximum clockwise (positive) and anticlockwise (negative) vorticities were observed near the surface and the bottom of the channel, respectively. The pattern of vorticity evolution was approximately the same in the cases dp and wd, especially at t = 1 s. The vorticity values decreased from t = 1 s to t = 5 s, but the vorticity density in the vegetated area increased with the development of the dam-break flow during this time. The maximum clockwise vorticity values decreased from ω max = 1 544 s − 1 to ω max = 987 s − 1 at t = 1 s and from ω max = 808 s -1 to ω max = 668 s − 1 at t = 5 s in models dp1 to dp3, but this decreasing trend was not observed in model dp3 at t = 5 s.
In contrast, the maximum clockwise vorticity values increased from ω max = 1 297 s − 1 to ω max = 1 361 s − 1 at t = 1 s and from ω max = 844 s − 1 to ω max = 1 540 s − 1 at t = 5 s in models dn1 to dn3. The lowest values for clockwise vorticity were observed in the model wd at t = 5 s.  Hydrographs of inflow in cases (a-f) dp1 to dp3, (g-l) dn1 to dn3, (m-n) wd

Discussion
The numerical model accurately reproduced the temporal variation of the free surface height in the reservoir and behind the obstacle. However, some inconsistency was found between the experimental and numerical results when the size of the cells increased from the middle to the last stages: the flow velocity in the model was higher than in the experiments. In addition, the model accurately reproduced the reflection of the flow at an obstacle and the side walls, as well as the return after impact at the lateral transitions. The strong performance of the VOF method in tracking the deformation of a free surface after impact with an obsta- Fig. 8 Streamwise velocity in the vertical direction in (a-c) dp1 to dp3, (d-f) np1 to np3, (g) wd Fig. 9 Iso-surface of vorticity in the x direction from up to down in models with a positive drop dp1, dp2, dp3 and without a drop wd in the downstream channel at (a-g) t = 1s, (h-n) t = 5s cle and transitions has previously been reported by Kocaman and Ozmen-Cagatay (2012), Kocaman et al. (2020), Issakhov and Zhandaulet (2020a), and Issakhov et al. (2022).
The reservoir discharge and inflow hydrographs are affected by the boundary conditions (Tsakiris and Spiliotis 2013;Tsakiris and Bellos 2014). In this study, backflow returning to the reservoir caused negative discharge in models with a positive drop or no drop. A significant increase in negative discharge was observed with increasing drop height. Although the fluctuations of the rising limb of the inflow hydrograph increased, the peak discharge values decreased due to an increase in the height of the positive drops. In most cases, the maximum streamwise flow velocity was about 2 m/s, while in the middle stage, several inflection points were formed at different flow depths. This was due to velocity reduction and significant resistance to the dam-break flow caused by eddy formation and transitional flow throughout the vegetated area, as previously shown by Acker et al. (2008) and Uotani et al. (2014). There was a significant difference between the velocity values in the middle stage for the positive-drop and no-drop models. This difference was not observed in the negative-drop models. Possible reasons for this were the great distance between the reservoir and the vegetated channel with a drop, the high density and thickness of vegetation, and the presence of a drop in the downstream channel.
The maximum vorticity values were observed near the free surface and the bottom of the channel due to kinetic energy dissipation (Kasiteropoulou et al. 2017;Mavrommatis and Christodoulou 2022). The pattern of vorticity evolution was approximately the same in the cases with a negative drop or no drop at the initial stage. The maximum clockwise vorticity values decreased in the models with a positive drop at the middle stage. In contrast, the maximum clockwise vorticity values increased in the negative-drop models. The lowest values for clockwise vorticity were observed in the no-drop model.

Conclusion
In this study, a CFD package, Flow-3D, was used to reproduce a dam break's flow characteristics and mean velocity under the effects of an obstacle and transitions. The results showed that the model accurately reproduced the flow field and mean velocity. Then, the model was used to predict flow characteristics during dam break, with and without a drop across a vegetated channel in a lower reach. The results showed that complex topographic features and vegetation significantly affected discharge from the reservoir and inflow downstream. Flood discharge was reduced in the cases with a positive or no drop and dense vegetation due to the development of backflow towards the reservoir. Flood discharge and depth could be significantly affected under complex topographic conditions in which the bed elevation increased in the river's main channel. Accordingly, the resistant effects of dense vegetation in the downstream channel were dominated by the development of local three-dimensional flows, flow separation, and cross-flows on flood development. The height and direction of the drop, as well as the density of vegetation, significantly increased the deformation of the free surface and the fluctuations, and thus the flood velocity. The flood velocity changed significantly in the vertical direction near the channel bottom and on the free surface above the vegetation. This led to the development of turbulence structures of various scales throughout the vegetated area and over drops. They could significantly reduce a flood's kinetic energy and downstream propagation.