# Experimental Investigation of Flood Energy Dissipation by Single and Hybrid Defense System

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}land area was affected as a result of 23 major flood events from 1947 to 2015 in Pakistan [8]. The extreme flood events in India resulted in the death of several thousand people in Uttarakhand 2013, in Chennai 2015, and in Kerala 2018 [9,10]. Almost 38 districts were affected by a continuous spell of heavy rainfall in Bangladesh in 2017 [11]. Similarly, Indonesia is also vulnerable to flood damages [12,13].

## 2. Materials and Methods

#### 2.1. Experimental Apparatus and Procedures

#### 2.1.1. Flume Characteristics

_{o}= V/(gh)

^{0.5}, where V = depth-averaged velocity (m/s), g = gravitational acceleration (m/s

^{2}), and h = water depth (m)). The initial Froude number (Fr

_{o}) was estimated with the velocity and water depth without any obstruction placed in the channel. The calculated range of Froude number at Jinnah barrage was 0.17–0.59 and at Taunsa barrage was 0.10–0.59. The flow was subcritical (Fr

_{o}< 1) in all the cases. Froude similarity was used to set the model scale of the laboratory experiments. For creating subcritical conditions, the water depths without any obstruction (h

_{o}) selected in the experiments were 4.5, 5.3, 6.8, 7.3, 7.7, 8.2, and 8.5 cm, setting the initial Fr

_{o}approximately equal to 0.40, 0.44, 0.50, 0.57, 0.60, 0.63, and 0.65. The scale for all the cases of the current experimental models was 1/100.

#### 2.1.2. Experimental Conditions

_{v}) (Figure 2c) were selected by considering the thickness of vegetation d

_{n}= 180 No.cm, where d

_{n}= $\frac{2}{{D}^{2}\sqrt{3\text{}}}{W}_{v}{d\text{}\times \text{}10}^{2}$. The d

_{n}represents the cumulative diameter of trees at breast height and is defined as the product of tree diameter and the number of trees in a rectangle with a frontage of unit length along the shoreline and depth equal to the width of the forest (W

_{v}) [37].

_{n}= 180 No.cm was selected for both the intermediate and sparse vegetation cases. The water level was measured by using a point gauge at the interval of 2–3 cm. Without placing any obstruction in the flume, the discharge was measured using a flow meter against each selected initial water depth (h

_{o}). The depth-averaged velocity was computed using the relationship between measured water depth and discharge. The dike and the moat were modeled at a scale of 1/100. The recommended height of embankment (dike) on Indus river in Pakistan is in the range of about 4–7 m high with addition to 1.2–1.8 m freeboard [38]. In the current study, the selected height of embankment (including the freeboard) was 5.5 m. Therefore, by using the scale of 1/100, the height of the embankment model was kept 5.5 cm. The dimensions of dike and moat are already mentioned in Table 1. In case of flooding, water flows from the embankment towards the floodplain in an oblique direction with respect to flow in the main channel. However, the direction of flow of water towards the weir-like obstacles/embankments in the floodplains of the river can be encountered in various orientations i.e., oblique or perpendicular depending upon the angle of placement of the obstruction [39,40,41,42]. In this study, it is assumed that the obstruction in the field will be constructed in such a way that the direction of flow of water towards the obstruction will be perpendicular. It was also considered that the slope of the floodplain was negligible provided that the banks of the river were already limited by defense work. However, it is worth mentioning here that if the obstruction is placed as per usual cases then the flow will approach the obstruction in an oblique manner and the results of this study will have to be reduced by a reduction factor depending upon the angle of obliqueness of flow. This angle will be different for different situations, and the reduction factor developed by [42,43,44] may be used to modify our results for real-life designs.

#### 2.1.3. Non-Dimensional Pi Groups

_{1}= backwater rise at the upstream of dike, h

_{o}= initial water depth without any model, v

_{o}= velocity at h

_{o}, Fr

_{o}= Froude number at h

_{o}, Fr

_{1}= Froude number on the upstream side of dike against water depth h

_{1}and velocity v

_{1}, Fr

_{2}= Froude number in front of vegetation patch against water depth h

_{2}and velocity v

_{2}, Fr

_{3}= Froude number on the downstream side of the vegetation patch against water depth h

_{3}and velocity v

_{3}, g = gravitational acceleration, ρ

_{w}= density of water, μ = viscosity of water, d

_{n}′ = dn/D is non-dimensional vegetation width, y

_{1}= minimum water depth during the jump on the downstream of vegetation, L

_{j}= length of hydraulic jump on the downstream of vegetation, HGL = hydraulic grade line, EGL = energy grade line, E

_{1}, E

_{2}, E

_{3}= specific energies at respective points, ΔE

_{1}= total energy loss (E

_{1}− E

_{3}), ΔE

_{2}= total energy loss (E

_{2}− E

_{3}), d

_{n}, d and B are already defined in Section 2.1.2. To minimize the sidewall effects on the flow structure the ratio between the flume width and the cylinder diameter should be greater than five [4,45]. In this study, this ratio was kept greater than 5 to minimize the sidewall effect. The backwater rise, i.e., Δh

_{1}/h

_{o}, Δh

_{2}/h

_{o}and total energy loss (ΔE

_{1}/E

_{1}) and (ΔE

_{2}/E

_{2}) are the function of the initial Froude number Fr

_{o}, vegetation density (B/d) and d

_{n}′. Froude number is commonly used in free-surface flows, so the Reynolds number was not considered here.

#### 2.1.4. Description of Energy Dissipation

_{j}

_{2}/y

_{1}) and (ΔE

_{j}

_{3}/y

_{1}), where, $\mathsf{\Delta}{E}_{j2},\text{}\mathsf{\Delta}{E}_{j3}=\text{}{\frac{\left({y}_{2}-{y}_{1}\right)}{4{y}_{1}{y}_{2}}}^{3}$, y

_{1}is the minimum depth at the toe of the hydraulic jump, y

_{2}is the average water depth after the hydraulic jump [43]. The specific energy is defined as the energy per unit volume of water at any section of a channel with respect to the channel bed [46,47]. Therefore,

_{1}is the relative energy loss, E

_{1}= energy on the upstream side of dike in DV and DMV models, E

_{2}= energy on the upstream side of vegetation and E

_{3}= energy on the downstream side of vegetation.

#### 2.1.5. Delay Time Analysis

_{WM}) required to reach the water from inlet to the crest level of the crump weir was noted without placing any model in the channel and compared with the time required in SDS and HDS models.

## 3. Results

#### 3.1. Backwater Rise

_{o}) was raised upstream of the vegetation model, and the water surface slope was increased inside the vegetation due to the resistance offered by it. It was found that by increasing the density of vegetation from sparse to intermediate, the backwater rise increases to 26% and the surface slope inside the vegetation was also increased. The backwater rise and relative backwater rise varied linearly with increasing Froude number as shown in Figure 5a,b. However, the relative backwater rise was only slightly increased for different Froude number values as the range of the values on y-axis was lower as shown in Figure 5b. A similar trend was observed in the literature [48]. This shows that the initial flow depth had very little effect on the relative backwater rise for a given Froude number. In these figures, Δh and h

_{o}are the water depths on the upstream side of vegetation and initial water depth without any model placed in the channel respectively.

_{o}= 0.40 and 0.44, the backwater rise was slightly higher in SDS than that in HDS and for the remaining values of Froude number the backwater rise in the case of HDS was comparatively higher. It happened, because in HDS, for lower values of Fr

_{o}the depth of water overtopping the dike was low so the depth achieved in front of vegetation was also low. However, for higher values of Fr

_{o}the overtopping depth was high, due to which higher depth was achieved on the upstream side of vegetation.

#### 3.2. Hydraulic Jump and Water Surface Profile Classification

#### 3.2.1. Hydraulic Jump Classification in SDS

_{o}= 0.40, 0.44, 0.50, 0.57, and 0.60, only backwater rise and small undulations on the downstream side of vegetation with no hydraulic jump were observed while the flow was found to have higher slope inside the vegetation patch. However, for remaining Froude numbers i.e., Fr

_{o}= 0.63 and 0.65 an undulated jump (UJ) (1 < Fr < 1.7 [51]) was developed on the downstream side of vegetation patch (Type I) as shown in Figure 6a. Similarly, in the case of intermediate vegetation (OVI) there was no jump formed against the lower values of Fr

_{o}= 0.40, 0.44, 0.50 and 0.57, however, for Fr

_{o}= 0.60, 0.63 and 0.65 undulated jump was formed on the downstream side of vegetation patch (Type I). The classification of the hydraulic jump of SDS is also elaborated in Table 2. A higher backwater rise, larger undulations, and a larger undulated jump were observed in OVI as compared to OVS. The relative length of the hydraulic jump L

_{j}/y

_{1}was maximum against Fr

_{o}= 0.65 in OVI case. In Figure 6a h

_{1}and h

_{2}are the average depths of water on the upstream and downstream side of vegetation after the jump, y

_{1}= minimum depth of water in hydraulic jump, L

_{j}= length of hydraulic jump, h

_{c}= critical depth, V

_{1}, V

_{2}are the average velocities on the upstream and downstream side of vegetation patch respectively and V

_{c}= critical velocity against critical depth.

#### 3.2.2. Hydraulic Jump Classification in HDS

_{1}, h

_{2}and h

_{3}are the average water depths in front of dike, in front of vegetation, and downstream of vegetation patch, respectively, h

_{d}= the average depth of water in the middle of L

_{dv}, L

_{o}= the length of start of hydraulic jump on the downstream slope of dike from the toe of dike towards the crest, L

_{dv}= distance between dike and vegetation, Fr

_{1}= Froude number on the upstream of dike, Fr

_{o}, h

_{o}, V

_{o}, V

_{1}, V

_{2}, V

_{c,}and L

_{j}are already define previously. In Type II, a hydraulic jump developed in Section 2 with no jump in Section 3. However, in Type III no jump formed in Section 2 with the only jump developed in Section 3. The classification of the hydraulic jump of HDS is described below and summarized in Table 2.

_{o}= 0.40 and 0.44 weak jump (WJ) (1.7 < Fr < 2.5 [51]) was formed in only Section 2 (Type II) with small undulations in Section 3 as shown in Figure 6b. For the initial values of Froude number (Fr

_{o}= 0.40) the jump initiated on the bed in Section 2, however, for Fr

_{o}= 0.44 jumpstarted from the downstream slope of the trapezoidal shape dike. Air bubbles were also formed in Section 2, and water surface slope also increases inside the vegetation model. For Fr

_{o}= 0.50 undulated jump of Type II was formed in Section 2. However, for higher values of Froude numbers, i.e., Fr

_{o}= 0.57, 0.60, 0.63 and 0.65 an undulated hydraulic jump of Type III was formed as shown in Figure 6c.

_{o}= 0.40 and 0.44 weak jump of Type II and for Fr

_{o}= 0.50 and 0.57 undulated jump of Type II was developed starting from the downstream slope of dike (L

_{o}increases with Froude number), as shown in Figure 6c. For Fr

_{o}= 0.60, 0.60 and 0.65 undular jump of Type III was developed in Section 3 with surface oscillations in Section 2 as shown in Figure 6c. In DTMVS, DTMVI and DRMVI cases, the formation of hydraulic jumps was classified as Type IV, V and VI. The classification is based on the location of the formation of a hydraulic jump either in Section 2 (Type IV), in both Section 2 and Section 3 (Type V) or in Section 3 (Type VI). In DTMVS model for the lower values of Froude number, i.e., Fr

_{o}= 0.40, 0.44 undulated jump of Type IV was observed as shown in Figure 6d. Air bubbles were also formed in Section 2, and water surface slope also increased inside the vegetation model. There was no jump (NJ) for Fr

_{o}= 0.50, 0.57, and 0.60 because the hydraulic jump shifted its position from Section 2 to Section 3 from lower to higher Froude numbers. In this range, the hydraulic jump was in the transition state. For the remaining values of Fr

_{o}= 0.63 and 0.65 an undulated hydraulic jump of Type VI was developed, as shown in Figure 6e. The graphical representation of experimental results of DTMVS against all the values of the selected range of initial Froude number (Fr

_{o}) are shown in Figure 8a.

_{o}= 0.40, 0.44, and 0.50 jump of Type IV was observed (Figure 6d). The jump against Fr

_{o}= 0.40 was weak and for Fr

_{o}= 0.44 and 0.50 was undulated in nature. For Fr

_{o}= 0.57 undulated jump was observed in both Section 2 and Section 3 classified as Type V as shown in Figure 6e and for Fr

_{o}= 0.60, 0.63 and 0.65 undulated jump developed was classified as Type VI. The graphical representation of experimental results of DTMVI against all the values of the selected range of initial Froude number (Fr

_{o}) is shown in Figure 8b.

_{o}= 0.40 weak jump of Type IV, for Fr

_{o}= 0.44 and 0.50 undulated jump of Type IV, for Fr

_{o}= 0.57 undulated jump of Type V was observed. For the remaining values of Fr

_{o}= 0.60, 0.63 and 0.65 undulated jump Type VI was developed as shown in Figure 6f. The graphical representation of experimental results of DRMVI against all the values of the selected range of initial Froude number (Fr

_{o}) is shown in Figure 8c. The variation of length of the hydraulic jump can be represented by the relative length of the hydraulic jump (L

_{j}/y

_{1}) [48]. In these cases, the relative length of the hydraulic jump (L

_{j}/y

_{1}) increased by increasing Fr

_{o}and the maximum relative jump was noted in the case of DTMVI as compared to DTMVS and DRMVS, as shown in Figure 9.

#### 3.3. Evaluation of Energy Dissipation

#### 3.3.1. Energy Dissipation in Single Defense System (SDS)

_{o}= 0.40–0.65. In this study, the total energy loss for all the cases of SDS and HDS was determined, however, the energy loss due to a hydraulic jump is explained only for HDS. For SDS, the maximum energy reduction in OVS and OVI was 28% and 36.34%, respectively, against Fr

_{o}= 0.40 and it decreased with higher values of Fr

_{o}. While increasing the values of Fr

_{o}from 0.40 to 0.65 the energy dissipation rate decreased by about 14.25% and 33.86% in OVS and OVI, respectively. The average energy loss was 25.32% and 31.49% for OVS and OVI, respectively. The results of energy dissipation show that initial Froude number and the density of vegetation (B/d) were the factors affecting the total energy loss. Based on these two important factors regression equations were developed for all the cases of SDS and HDS. In this paper, the Equations (4)–(6) were developed using EXCEL spreadsheet and graph to get the exponent type functions. The best fit curve and 95% confidence bands were computed and plotted (Figure 10a–c) for each of Equations (4)–(6) by software built in EXCEL. Equation (4), as given below, was developed to calculate the relative percentage energy loss in the case of OVS and OVI.

#### 3.3.2. Energy Dissipation in Hybrid Defense System (HDS)

_{o}= 0.40. While increasing the values of Fr

_{o}from 0.40 to 0.65 the energy reduction rate decreased by about 44% and 37.13% and the average energy loss was 36.63% and 41%, respectively. Equation (5) given below was developed by regression analysis as described above in Section 3.2.1, to compute the relative percentage energy reduction within the selected range of Fr

_{o}. The computed values of energy loss using Equation (5) for a certain range of Fr

_{o}are shown in Figure 11b.

_{j}

_{2}), in Section 3 (ΔE

_{j}

_{3}), maximum overall energy dissipation and average energy dissipation were calculated (summary is shown in Table 3) In all these cases, DTMVI performed better than DTMVS and DRMVI regarding energy dissipation. In the case of DTMVI, maximum ΔE

_{j}

_{2}= 27% and ΔE

_{j}

_{3}= 4%. The maximum total energy reduced in this case was 60% and the average energy reduced was 46%.

#### 3.3.3. Delay in Floodwater Arrival Time and Water Level Rise

_{WM}was computed without placing any obstruction model in the flume. Similarly, the delay times for a single defense system and a hybrid defense system were computed. The values of T

_{WM}were in the range of 28–80 s, against the different values of initial Froude number, whereas it was 29–115 s for OVS, 30–118 s for OVI, 32–129 s for DVS and 34–132 s for DVI. Similarly, the delay time for DTMVS, DTMVI, and DRMVI was 33–137 s, 37–140 s and 36–139 s respectively. The maximum delay time was 2 min 20 s for DTMVI against Fr

_{o}= 0.40. In all the cases, the delay time decreases by increasing Fr

_{o}. The relative time with respect to T

_{WM}was also maximum in the case of DTVMI, which will result in a maximum delay in flood arrival. To examine the relationship between the relative delay time for different cases of SDS and HDS, a pairwise comparison method namely least significant difference (LSD) method explained in the literature [52] was used. The calculated critical value of LSD was 0.21. So, the minimum difference between a pair of means (µ1–µ2) necessary for statistical significance was 0.21. There were 21 pairwise groups (G1 to G21). It was observed that for the difference of means of pairs G5–G6, G10–G11, and G14–G15 were greater than 0.21 means that there is a significant difference between the means of these pairs exist. OVI and DTMVI. It is concluded from G5, G6, G10, and G11 that the relative delay time of HDS (DTMVI and DRMVI) is higher than SDS (OVS and OVI). The results of G14 and G15 indicated that the relative time of delay increased by placing the moat in between the dike and vegetation of higher density. The complete pairwise comparison list is shown in Table A1 (Appendix A).

## 4. Discussion

#### 4.1. Hydraulic Jump Formation and Energy Dissipation in SDS

_{o}/L [48], where b = width of the channel, y

_{1}= depth of water at the toe of a hydraulic jump, h

_{o}= initial water depth and L = wavelength. In the current study, for OVS and OVI undulated hydraulic jump was observed only for the higher values of Fr

_{o}(0.60, 0.63, and 0.65) and no jump was observed for lower values of Fr

_{o}. The similar results were found in the literature [48]. The relative energy dissipation for a vegetation thickness of dn-180 No. cm calculated by Pasha and Tanaka (2017) was 26–28% and 29–32% in sparse and intermediate vegetation, respectively [48]. However, in the current research, the relative energy dissipated was in the range of 24–28% and 24–36% in sparse and intermediate vegetation respectively. The range of Fr

_{o}used by Pasha and Tanaka (2017) was 0.57 to 0.73 [48] and in this study, it was 0.40 to 0.65. The back-water rise increases by increasing the density of vegetation [47]. The back-water rise was observed higher in OVI than OVS as shown in Figure 5a.

#### 4.2. Hydraulic Jump Formation and Energy Dissipation in HDS

_{o}, Type A jump was formed on the bed of the channel in between embankment and vegetation while Type B jump was observed for the higher values of Fr

_{o}. The maximum energy dissipated due to jump was 39%, and the maximum total energy reduction was in between 27% and 54% [4]. The hydraulic jump based on the values of Froude number was also classified by 2-D numerical analysis in the previous study [67].

_{o}(0.40–0.57). However, for higher values (i.e., Fr

_{o}= 0.60, 0.63 and 0.65) the jump formed was only on the downstream of vegetation and no jump was observed between dike and vegetation. The total relative energy reduction for DVS and DVI was between 28% and 57% and the average relative energy dissipation was 37% and 41% in DVS and DVI, respectively.

_{j}

_{3}in Table 3). The maximum total relative energy dissipation and maximum average energy dissipation by hybrid defense system was 60% and 46% in DTMVI model. The arrival time was also highest in the DTMVI case. Contrarily, the hybrid defense system in the order of vegetation, moat and dike (where vegetation was in front) performed best in the previous study [32]. However, in this combination, in the case of a devastating flood event, the water may overtop the embankment and it will be difficult to connect this water to the river. Secondly, in that study, there was no space considered between the moat and embankment. In case of the breaching or erosion of embankment, the moat may be filled with erodible material and will not serve as a moat after its filling.

_{dv}) was kept 15 cm to ensure the safety of the moat structure in case of breaching of dike. The rectangular moat was less effective than the trapezoidal moat based on the total energy loss and the arrival time. The sides of a rectangular hydraulic structure are also not stable. The tree breaking phenomena also occurred in some regions of Japan due to the large wave thrust of tsunami [29]. However, the floodwater has less capacity to break trees and other components of hybrid defense system [70]. Therefore, the defense system proposed in the current study will be more effective in the river environment. In the light of the results obtained in this study, a hybrid defense system in the order of dike, trapezoidal moat, and intermediate vegetation is highly recommended. The limitation of the proposed system is the space available to construct the defense system. In case of non-availability of the space, a single defense system will be preferred.

## 5. Conclusions

_{o}= 0.40–0.65) around single defense system (SDS) and the hybrid defense system (HDS) was investigated experimentally in a flume. The main conclusions of the study are as follows:

- The backwater rise is maximum for OVI and DTMVI in SDS and HDS, respectively. The backwater rise is directly proportional to the density of vegetation and the value of initial Froude number. The water surface slope also increases by increasing vegetation density. The denser and wider the vegetation, the larger is the total energy dissipation in both SDS and HDS cases.
- In SDS only undulated hydraulic jump was observed in both OVS and OVI, resulting in a significant energy loss. In HDS both weak and undulated hydraulic jumps were formed and in the case of DTMVI, the maximum energy loss due to hydraulic jump formed in between the dike and vegetation was 27% and 4% energy was dissipated due to the formation of jump on the downstream side of vegetation. The maximum total energy reduced in this case was 60% and the average energy reduced was 46%. Similarly, in the case of DRMVI, the maximum value of energy loss due to hydraulic jump between dike and vegetation was 22% and 3% energy was dissipated due to the formation of hydraulic jump on the downstream side of vegetation. The maximum total energy reduction and average energy reduction were 60% and 43.75%, respectively. In all these cases, the rate of energy reduction due to the hydraulic jump decreases by increasing Fr
_{o}. - The performance of the DTMVI model to delay the arrival time of floodwater is the highest among all the models investigated in this paper
- The “moat” can serve as floodwater harvesting and increasing the response time of flash floods generated from hill torrents. The shape of the moat affects the reduction of energy in general. However, its trapezoidal shape performs better than rectangular shape.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Group No. | Pairs | µ1–µ2 | Critical Value (LSD) | Remarks | |
---|---|---|---|---|---|

1 | T_{OVS}/T_{WM} | T_{OVI}/T_{WM} | 0.050 | 0.21 | No significant difference |

2 | T_{OVS}/T_{WM} | T_{DVS}/T_{WM} | 0.060 | 0.21 | No significant difference |

3 | T_{OVS}/T_{WM} | T_{DVI}/T_{WM} | 0.130 | 0.21 | No significant difference |

4 | T_{OVS}/T_{WM} | T_{DTMVS}/T_{WM} | 0.202 | 0.21 | No significant difference |

5 | T_{OVS}/T_{WM} | T_{DTMVI}/T_{WM} | 0.281 | 0.21 | significant difference |

6 | T_{OVS}/T_{WM} | T_{DRMVI}/T_{WM} | 0.281 | 0.21 | significant difference |

7 | T_{OVI}/T_{WM} | T_{DVS}/T_{WM} | 0.010 | 0.21 | No significant difference |

8 | T_{OVI}/T_{WM} | T_{DVI}/T_{WM} | 0.080 | 0.21 | No significant difference |

9 | T_{OVI}/T_{WM} | T_{DTMVS}/T_{WM} | 0.152 | 0.21 | No significant difference |

10 | T_{OVI}/T_{WM} | T_{DTMVI}/T_{WM} | 0.239 | 0.21 | significant difference |

11 | T_{OVI}/T_{WM} | T_{DRMVI}/T_{WM} | 0.231 | 0.21 | significant difference |

12 | T_{DVS}/T_{WM} | T_{DVI}/T_{WM} | 0.069 | 0.21 | No significant difference |

13 | T_{DVS}/T_{WM} | T_{DTMVS}/T_{WM} | 0.142 | 0.21 | No significant difference |

14 | T_{DVS}/T_{WM} | T_{DTMVI}/T_{WM} | 0.228 | 0.21 | significant difference |

15 | T_{DVS}/T_{WM} | T_{DRMVI}/T_{WM} | 0.220 | 0.21 | significant difference |

16 | T_{DVI}/T_{WM} | T_{DTMVS}/T_{WM} | 0.072 | 0.21 | No significant difference |

17 | T_{DVI}/T_{WM} | T_{DTMVI}/T_{WM} | 0.158 | 0.21 | No significant difference |

18 | T_{DVI}/T_{WM} | T_{DRMVI}/T_{WM} | 0.150 | 0.21 | No significant difference |

19 | T_{DTMVS}/T_{WM} | T_{DTMVI}/T_{WM} | 0.086 | 0.21 | No significant difference |

20 | T_{DTMVS}/T_{WM} | T_{DRMVI}/T_{WM} | 0.078 | 0.21 | No significant difference |

21 | T_{DTMVI}/T_{WM} | T_{DRMVI}/T_{WM} | 0.0079 | 0.21 | No significant difference |

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**Figure 1.**Pictorial views of the floodplain of Indus River near Taunsa Barrage. (

**a**) Unprotected and scoured embankment. (

**b**) Stone embankment protection. (

**c**) Existing dike and level gauge. (

**d**) Imagery of proposed hybrid defense system (HDS) at River Indus near Taunsa Barrage.

**Figure 2.**Experimental setup: (

**a**) Schematic of the channel with models, (

**b**) experimental setup of the hybrid defense system in the laboratory, (

**c**) vegetation arrangement details of staggered strips (SS).

**Figure 5.**(

**a**) Backwater rise (Δh) of single defense system (SDS) and HDS, (

**b**) relative backwater rise (Δh/h

_{o}) of SDS and HDS.

**Figure 6.**Hydraulic jump and water surface classifications: (OV model: (

**a**) Jump on the downstream of vegetation (Type I)), (DV model: (

**b**) Jump in Section 2 only (Type II) (

**c**) Jump in Section 3 only (Type III)), (DVM model: (

**d**) Jump in Section 2 only (Type IV) (

**e**) Jump in both Section 2 and Section 3 (Type V)) (

**f**) Jump in Section 3 only (Type VI).

**Figure 7.**Experimental photographs: (

**a**) only vegetation (OV) model (

**b**) dike and vegetation (DV) model and (

**c**) dike, moat and vegetation (DMV) model, (

**d**) crump weir model for delay time analysis.

**Figure 8.**Experimental observations of water surface profiles (

**a**) dike, trapezoidal moat and sparse vegetation (DTMVS), (

**b**) dike, trapezoidal moat, and intermediate vegetation (DTMVI) and (

**c**) dike, rectangular moat and intermediate vegetation (DRMVI).

**Figure 10.**Percentage energy loss for different obstruction types and 95% confidence bands for: (

**a**) sparse vegetation (OVS) and intermediate vegetation (OVI), (

**b**) DVS and DVI and (

**c**) DTMVS, DTMVI and DRMVI.

**Figure 11.**Experimental and computed results comparison: (

**a**) OVS and OVI, (

**b**) DVS and DVI, and (

**c**) DTMVS, DTMVI, and DRMVI.

Case ID | Initial Froude No. (Fr_{o}) | Dike | Moat | Vegetation Density (B/d) | D (cm) | W_{v} (cm) | * Vegetation Thickness “dn” (No.cm) | Vegetation Type |
---|---|---|---|---|---|---|---|---|

OVS | 0.40, 0.44, 0.50, 0.57, 0.60, 0.63, 0.65 | No dike | No moat | 2.13 | 1.88 | 18.36 | 181.67 | Sparse |

OVI | 0.40, 0.44, 0.50, 0.57, 0.60, 0.63, 0.65 | No dike | No moat | 1.09 | 1.254 | 8.17 | 198.31 | Intermediate |

DVS | 0.40, 0.44, 0.50, 0.57, 0.60, 0.63, 0.65 | No moat | 2.13 | 1.88 | 18.36 | 181.67 | Sparse | |

DVI | 0.40, 0.44, 0.50, 0.57, 0.60, 0.63, 0.65 | No moat | 1.09 | 1.254 | 8.17 | 198.31 | Intermediate | |

DTMVS | 0.40, 0.44, 0.50, 0.57, 0.60, 0.63, 0.65 | 2.13 | 1.88 | 18.36 | 181.67 | Sparse | ||

DTMVI | 0.40, 0.44, 0.50, 0.57, 0.60, 0.63, 0.65 | 1.09 | 1.254 | 8.17 | 198.31 | Intermediate | ||

DRMVI | 0.40, 0.44, 0.50, 0.57, 0.60, 0.63, 0.65 | 1.09 | 1.254 | 8.17 | 198.31 | Intermediate |

Classification of Hydraulic Jump | |||||||
---|---|---|---|---|---|---|---|

Froude Numbers | |||||||

Case ID | 0.40 | 0.44 | 0.50 | 0.57 | 0.60 | 0.63 | 0.65 |

OVS | NJ | NJ | NJ | NJ | NJ | UJ, Type I | UJ, Type I |

OVI | NJ | NJ | NJ | NJ | UJ, Type I | UJ, Type I | UJ, Type I |

DVS | WJ, Type II | WJ, Type II | UJ, Type II | UJ, Type III | UJ, Type III | UJ, Type III | UJ, Type III |

DVI | WJ, Type II | WJ, Type II | UJ, Type II | UJ, Type II | UJ, Type III | UJ, Type III | UJ, Type III |

DTMVS | UJ, Type IV | UJ, Type IV | NJ | NJ | NJ | UJ, Type VI | UJ, Type VI |

DTMVI | WJ, Type IV | UJ, Type IV | UJ, Type IV | UJ, Type V | UJ, Type VI | UJ, Type VI | UJ, Type VI |

DRMVI | WJ, Type IV | UJ, Type IV | UJ, Type IV | UJ, Type V | UJ, Type VI | UJ, Type VI | UJ, Type VI |

Case ID | Energy Loss Due to Hydraulic Jump | Average Energy Loss (%) | Maximum Energy Loss (%) | |
---|---|---|---|---|

ΔE_{j}_{2} (%) | ΔE_{j}_{3} (%) | |||

DTMVS | 24 | 2.84 | 38.52 | 53.26 |

DTMVI | 27 | 4 | 46 | 60 |

DRMVI | 22 | 3 | 43.75 | 60 |

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**MDPI and ACS Style**

Ahmed, A.; Ghumman, A.R.
Experimental Investigation of Flood Energy Dissipation by Single and Hybrid Defense System. *Water* **2019**, *11*, 1971.
https://doi.org/10.3390/w11101971

**AMA Style**

Ahmed A, Ghumman AR.
Experimental Investigation of Flood Energy Dissipation by Single and Hybrid Defense System. *Water*. 2019; 11(10):1971.
https://doi.org/10.3390/w11101971

**Chicago/Turabian Style**

Ahmed, Afzal, and Abdul Razzaq Ghumman.
2019. "Experimental Investigation of Flood Energy Dissipation by Single and Hybrid Defense System" *Water* 11, no. 10: 1971.
https://doi.org/10.3390/w11101971