# Roughness Effect of Submerged Groyne Fields with Varying Length, Groyne Distance, and Groyne Types

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## Abstract

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## 1. Introduction

_{k}, which is the ratio of the upstream projected area of an element to the floor area assigned to that element. According to analysis of numerous studies, the maximum flow resistance, i.e., wake interference flow starts to develop at c

_{k}= 0.1 and is maximum at c

_{k}between 0.2 and 0.35, e.g., [23,24]. Comparable results were found using the spatial density of roughness elements [25].

## 2. Materials and Methods

_{G}), resulting in different lengths of the groyne field (l

_{GF}). Two types of groynes (Figure 1) were compared: a simplified model of a groyne made of multiplex plates characterized by sharp edges with no sloping from crest to base and a flat top and a second type made from glued gravel (12–16 mm), which resulted in an irregular surface and a slightly permeable body.

_{m}= 3.64 mm) was glued on the plates to roughen the second floor. A flap gate was installed at the downstream end of the second floor for regulating the water level. The discharge (Q) was controlled by a valve and measured with an inductive discharge meter, and the water depth (h) was measured with a mobile point gauge. The groyne field was located on the left side of the flume always starting at x = 7 m (position of groyne toe), with the origin of the longitudinal coordinate x = 0 at the upstream end of the second floor. The upstream reach of 7 m length was chosen to ensure fully developed flow conditions. The groynes were installed on top of the rough bed. The groyne height (h

_{G}) of both groyne types was 2.5 cm to investigate relative submergence up to 6. The groyne width (w

_{G}) was 6 cm and the projected length of the groyne (l

_{P}) was 20 cm (1/3 of the flume width). The angle of inclination was chosen to 60° against stream direction (Figure 2) as several studies e.g., [13,18,26] recommend this angle for best protection of a bank.

_{N}= 5, 10, and 15 cm were determined by adjusting the flap gate and the discharge until the target water depth was constant along the flume. The resulting relative submergence for the groyne experiments was 2, 4, and 6. The settings of in total 51 experiments are summarized in Table 1. The roughness density (c

_{k}) is calculated as the ratio of the projected area (A’), which is the product of the groyne height and the projected length, and the related ground area of a groyne (A, see Figure 2) (Equation (1)).

_{G}= groyne distance, d

_{G}/l

_{P}= aspect ratio, l

_{GF}= groyne field length, c

_{k}= roghness density, h

_{N}= uniform flow water depth without groynes, Fr = Froude number, and Q = discharge.

_{max}.

_{max}= maximum water depth along the flume, S

_{E}= energy slope, and u

_{m}= mean flow velocity calculated with h

_{max}.

_{m}= 3.64 mm) was placed over a length of 15 m in a 20-m-long flume. A set of ten gravel groynes, with a height of 2.5 cm and l

_{P}= 31 cm (approximately one-third of the flume width), was installed with d

_{G}= 20 cm, 60° angled against flow direction, resulting in c

_{k}= 0.125. The first groyne started at x = 8.35 m, with the origin of x being defined as the beginning of the sediment layer. The water depth at uniform flow conditions (without groynes) was set to 10 cm, which corresponded to incipient motion conditions for the bed material. The experiment ran for 7 hours until only minor changes of the bed topography were observed visually. The resulting bed topography was scanned with a high resolution laser scanner from x = 8 to 10.5 m and across the flume from y = 0.09 to 0.81 m. The resolution of the scan was 0.5 mm in the x-direction and 10 mm in the y-direction. Water levels were measured in three sections in flow direction, relatively related to those in the fixed bed experiments.

## 3. Results and Discussion

_{max}− h

_{N}) was located about 10 cm upstream of the groyne field at x = 6.9 m, which corresponded to the position of the first groyne head. Deviations in the exact longitudinal position of the maximum water depth were due to the wavy water surface, which became more predominant with increasing approach velocity, i.e., increasing h

_{N}, and to the fixed raster for water depth measurements with a distance of 10 cm. However, a difference between the water depth at x = 6.9 m and the maximum water depth was observed in only two experiments and was 3 and 4 mm, respectively. Thus, this position is used for further analysis. Towards the downstream end of the groyne field the water level decreased following a linear trend. As expected, the water level downstream of the last groyne was in general lower than h

_{N}. Despite the scatter due to waves, it is obvious that the backwater increased with increasing water depth h

_{N}. However, the rise of the backwater height at position x = 6.9 m decreased with increasing discharge, i.e., the difference of Δh was always larger from h

_{N}= 5 cm to 10 cm than from h

_{N}= 10 cm to 15 cm, indicating a diminishing effect of the groynes with increasing submergence.

_{N}), measured at x = 6.9 m, which is presented in Figure 4 for the experimental series GF 1 (Table 1). The number of groynes was kept constant, and thus the length of a groyne field grew with the distance between the groynes. Accordingly, the backwater increased with the distance between the groynes; however, approaching a constant backwater height independent of d

_{G}and the groyne field length.

_{N}occurred at d

_{G}= 15 cm for the experiments with larger submergence. The projected width of a groyne (the distance between head and toe along the x-axis) was 11.55 cm. Thus, the head of a downstream groyne overlapped with or was very close to the toe of the upstream groyne for d

_{G}= 10 and 12.5 cm, resp., which can hinder the development of the overtopping flow, and thus result in lower flow resistance. This effect was observed throughout the experiments except for the gravel groynes with h

_{N}= 5 cm in series GF 1. However, this measured water level may be biased as it should match with the water level measured in the corresponding experiment in series GF 2 (see Figure 5).

_{N}= 5 cm) and 15–19% for h

_{N}= 15 cm. The variation is mainly caused by the way of modeling a groyne. The multiplex groynes resulted in higher water depths than the gravel groynes, independent of the level of submergence. The impact was smaller for short distances between the groynes, and the reverse for the shortest groyne distance. The flow field caused by the smooth surface and the sharp edges of the multiplex groynes resulted in higher flow resistances than observed for the irregularly shaped surface and porous body of the gravel groynes. Thus, results from the experiments with strongly simplified substitutes, e.g., the multiplex groynes or plates used by Azinfar and Kells [20] overestimate the groyne influence.

_{G}= 15 cm resulted in the largest hydraulic roughness. With larger groyne distances the relative backwater decreased asymptotically. The minimum backwater can be expected to correspond to the effect of a single groyne.

_{G}= 12.5 and 15 cm, respectively, except for the test run in series GF 1 with gravel groynes and h

_{N}= 5 cm for the aforementioned reason. The multiplex groynes caused larger flow resistance than the gravel groynes. The setup with constant groyne field length (GF 2) resulted in larger friction factors than the setup with variable length (GF 1). However, the friction factors for multiplex and gravel groynes, especially for constant and variable groyne field lengths, followed the same trend. This indicates that the decrease of the energy slope with increasing groyne distance was more distinct for the variable groyne field length than for the constant one. Further investigations require more precise water level measurements to reduce the scatter due to the wavy water surface.

_{k}, which is plotted as second x-axis in Figure 6. The maximum flow resistance corresponded to roughness densities between 0.17 and 0.2 indicating wake interference flow [23,24]. The difference to Canovaro et al. [25], who found maximum flow resistance for spatial densities between 0.2 and 0.4, can be explained with the element height, which is included in c

_{k}, but not in the spatial density.

_{G}= 12.5 cm and h

_{N}= 10 cm with respect to the aspect ratio d

_{G}/l

_{P}and the groyne field length (Table 1). Considering the roughness density, the setup was comparable to GF 1 with d

_{G}= 20 cm. The hydraulic conditions led to incipient motion. Sediment transported from upstream towards the groyne field was deposited in the groyne field, while the bed in the unblocked area eroded. The erosive forces became stronger along the groyne field, resulting in scouring at the groyne heads in the middle of the field as well as at the downstream end of the field towards the middle of the flume (Figure 7). The cross-sectionally averaged backwater height at the beginning of the groyne field was Δh = 0.57 cm, while for the two comparable experiments with fixed bed, the water level was increased by 1.45 cm and 1.9 cm, respectively (Figure 4). Although the blockage effect was even larger due to sediment deposition upstream of and within the groyne field, the roughness of the system was compensated distinctly by the areal erosion of the river bed. The resulting water level only increased by approximately 40% and 30%, respectively, compared to the backwater height of the fixed bed experiments. The reduced roughness of the mobile bed system is reflected by the considerably lower friction factor (Figure 6).

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Example of a groyne field setup section with groyne dimension parameters. The white dots exemplarily indicate positions of water level measurements and the square shows the related ground Area (A) of a single groyne.

**Figure 3.**Water level change (Δh) along the main flow direction (groyne field from x = 7 m to 8.5 m) for gravel groynes with distance d

_{G}= 15 cm (GF 2).

**Figure 4.**Relative increase of the water depth at x = 6.9 m as a function of the distance between groynes d

_{G}and approach flow in series GF 1 (open symbols = multiplex groynes; filled symbols = gravel groynes).

**Figure 5.**Relative increase of the water depth at x = 6.9 m as a function of the distance between groynes d

_{G}and approach flow for gravel groynes with varying field length (GF 1: filled symbols) and constant field length (GF 2: shaded symbols).

**Figure 6.**Friction coefficient f of the groyne fields as a function of groyne distance d

_{G}and roughness density c

_{k}, resp. (open symbols = multiplex groynes in series GF 1; filled symbols = gravel groynes in series GF 1; shaded symbols = gravel groynes in series GF 2; green dot: GF 3).

**Figure 7.**Bed topography at the end of the mobile bed experiment (flow direction from left to right).

Series | Groyne Type | m (-) | d_{G} (cm) | d_{G}/l_{P} (-) | l_{GF} (m) | c_{k} (-) | h_{N} (cm) | Fr (-) | Q (L/s) |
---|---|---|---|---|---|---|---|---|---|

GF 1 | MultiplexGravel | 15 | 10 | 0.5 | 1.4 | 0.25 | 5, 10, 15 | 0.59, 0.65, 0.66 | 11.6, 35.7, 69.7 |

12.5 | 0.625 | 1.75 | 0.2 | ||||||

15* | 0.75 | 2.1* | 0.17* | ||||||

20 | 1 | 2.8 | 0.125 | ||||||

25 | 1.25 | 3.5 | 0.1 | ||||||

35 | 1.75 | 4.9 | 0.07 | ||||||

60** | 3 | 7.8** | 0.04** | ||||||

GF 2 | Gravel | 16 | 10 | 0.5 | 1.5 | 0.25 | 5, 10, 15 | 0.59, 0.65, 0.66 | 11.6, 35.7, 69.7 |

11 | 15 | 0.75 | 0.17 | ||||||

6 | 30 | 1.5 | 0.083 | ||||||

4 | 50 | 2.5 | 0.05 | ||||||

GF 3 | Gravel | 10 | 20 | 0.645 | 1.8 | 0.125 | 10 | 0.59 | 58.6 |

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**MDPI and ACS Style**

Möws, R.; Koll, K.
Roughness Effect of Submerged Groyne Fields with Varying Length, Groyne Distance, and Groyne Types. *Water* **2019**, *11*, 1253.
https://doi.org/10.3390/w11061253

**AMA Style**

Möws R, Koll K.
Roughness Effect of Submerged Groyne Fields with Varying Length, Groyne Distance, and Groyne Types. *Water*. 2019; 11(6):1253.
https://doi.org/10.3390/w11061253

**Chicago/Turabian Style**

Möws, Ronald, and Katinka Koll.
2019. "Roughness Effect of Submerged Groyne Fields with Varying Length, Groyne Distance, and Groyne Types" *Water* 11, no. 6: 1253.
https://doi.org/10.3390/w11061253