# The Impact of Submerged Breakwaters on Sediment Distribution along Marsh Boundaries

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### Model Description

_{por}is the bed porosity, z

_{b}is the bed level (positive up) (m), S

_{x}, S

_{y}are the total sediment transport components per unit width in the x and y directions (m

^{2}/s), and T

_{d}is the deposition or erosion rate of the suspended sediment (m/s).

_{x}and c

_{y}respectively). The fourth term represents shifting of the relative frequency due to variations in depths and currents, the fifth is the depth-induced and current-induced refraction, and lastly, the quantities c

_{σ}and c

_{ϴ}are the propagation velocities in the spectral space. The right-hand side of the equation contains the source/sink term that represents all physical processes, including generation, dissipation, or wave energy redistribution.

_{d}(Figure 1b), while length and width were fixed at 100 m and 10 m, respectively.

_{d}) (50 m, 100 m, 150 m), wave’s height (0.2 m, 0.3 m, 0.5 m, 0.7 m), tide (±0.2 m ±0.4 m), sediment concentration (0.2 kg/m

^{3}0.4 kg/m

^{3}) and the sand fraction diameter D

_{50}(100 µm 150 µm). Non-cohesive sediments were characterized by a specific density of 2650 kg/m

^{3}and dry bed density of 1600 kg/m

^{3}, while characteristics of the cohesive sediment were chosen in agreement with values provided by Berlamont et al. (1993) [42]. Specific density was 2650 kg/m

^{3}, dry bed density was 500 kg/m

^{3}and setting velocity was 0.5 mm/s. Wave parameters (H

_{s}and T

_{p}) were selected to simulate waves generated into the bay, so we analyzed the previously mentioned H

_{s}values with a period T

_{p}of 5s and a direction orthogonal to the shoreline. We imposed these values at the East boundary. Wave reflection was not accounted for in the wave model, so that wave energy was dissipated at the coastline.

_{D}= 60) and one for the breakwater roughness (C

_{D}= 20). The initial condition of the models consisted of an initial water level fixed at 0.4 m. The suspended sediment eddy diffusivities were a function of the fluid eddy diffusivities and were calculated using horizontal large eddy simulation and grain settling velocity. The horizontal eddy diffusivity coefficient was defined as the combination of the subgrid-scale horizontal eddy viscosity, computed from a horizontal large eddy simulation, and the background horizontal viscosity, here set equal to 0.001 m

^{2}/s

^{2}[43,44]. To satisfy the numerical stability criteria of Courant Frederichs–Levy, we used a time step Δt = 3 s [34]. To decrease the simulation time, a morphological scale factor of 50 was used in our models (a user device to multiply the deposition and erosion rate in each Δt). A sensitivity analysis showed that a morphological factor of 50 was acceptable.

## 3. Results

#### 3.1. Hydrodynamic Results

_{d}and proportional to H

_{s}following a power law (R

^{2}= 0.51), while the slope did not affect this specific process. Our results (Figure 2b) were markedly consistent with the wave damping results of Wiberg et al. (2019) [15], who also observed a reduction of between 10–50% of incoming waves in a similar coastal environment at the Virginia Coastal Reserve (VCR).

_{s}) immediately behind waves were dampened on breakwaters (Figure 2a), which were created by the vorticity generated by the breakwater, which made the u velocity component negative (Figure 3b), drawing water back to the breakwater:

_{s}and slope, and proportional to x

_{d}following a power law (Figure 4 0.95 < R

^{2}< 0.98), which described how increasing the waves and distance of the breakwater to the shoreline allowed these vortices to direct water behind the breakwater and raise the wave crests vertically (Figure 4).

_{d}, tide and waves, revealed how the magnitude of the shear stress was proportional to H

_{s}and inversely proportional to x

_{d}and the tide, while the slope increasing effect augmented the erosion at the marsh edge (Figure 5c). Shear stress was correlated with the dimensionless variable for all distinct runs with slope 0.4% (R

^{2}= 0.70) and 0.8% (R

^{2}= 0.67).

#### 3.2. Morphodynamic Results

_{s}. The distance of the breakwater from the shoreline plays an important role on sediment transport. Breakwater distance to shoreline was negatively correlated with the amount of sediment deposited into the marsh (Figure 6a). The volume deposited was proportional to H

_{s}and inversely proportional to x

_{d}and the tide, following a power law correlation (0.50 < R

^{2}< 0.52), while the slope increasing increase the sediment accumulation into the marsh (Figure 6b). Figure 6a also shows how a greater distance of the breakwater from the shore leads to greater erosion of the marsh scarp, an aspect that will be taken up later in the manuscript.

_{d}over the initial value of x

_{d}as function of the tide for all the x

_{d}, wave heights and for the two different values of concentration. We observed the tide to be strongly and positively correlated with the erosion at the marsh boundary. The erosion ratio for the 0.8 m tide condition, which reached the marsh platform at low tide, was greater than the 0.4 m tide condition, as increasing both the breakwater distance to the coastline and the wave height was observed to increase shoreline erosion. Additionally, the lower suspended sediment concentrations lead to higher erosion. It is also possible to observe how wave heights equal to 0.7 do not follow the same behavior as the other wave heights, but only cause deposition in the marsh (Figure 7). This mismatch is due to the great energy that the model develops in the presence of such waves, in environments governed by a very low energy regime.

_{d}* Tide/H

_{s}

^{2}, for the two different slopes and tides, is summarized in Figure 8. A linear correlation between the dimensionless variable and the eroded volume for the slope = 0.4% and tide = ±0.2 m (Figure 8a), slope = 0.4% and tide = ±0.4 m (Figure 8c). Another linear correlation between the dimensionless variable and the eroded volume for the slope = 0.8% and tide = ±0.2 m (Figure 8b), slope = 0.8% and tide = ±0.4 m (Figure 8d). Collectively, these relationships demonstrate how the erosion was proportional to the slope, tide, wave height and the breakwater distance to the shoreline.

_{s}= 0.5 m, slope = 0.8%, Tide = ±0.4 m and x

_{d}= 100 m, for the two sediment concentrations (a) 0.4 kg/m

^{3}and (b) 0.2 kg/m

^{3}(Figure 9). The simulation demonstrated that the higher sediment concentration (Plot a) allows more sedimentation in the area protected by the breakwater and into the marsh.

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

**a**) the longitudinal profile of the domain used in this analysis, highlighting the three different breakwater configurations. (

**b**) An example of wave damping for the case with wave period = 5 s, and (

**c**) linear correlations between wave period and wave height measured at the marsh boundary (x = 200 m) for the three breakwater configurations.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Domain configuration. Plot (

**a**) planimetry of the model with cells dimension and boundary conditions on the North/South side (Neumann condition) and East side (waves, tide and sediment concentration). Transect 1 and 2 will be used later in the paper for making a comparison on breakwater effect on sediment transport. Plot (

**b**) longitudinal profile of the domain with the two different slopes used (blue line = 0.4% and orange line = 0.8%), with three different breakwater positions and two tide conditions (red continuous line = ±0.2 m and cyan dashed line = ±0.4 m).

**Figure 2.**(

**a**) Example of wave damping for the x

_{d}= 100 m configuration. Type of line changes according to the wave height, the color is relative to slope and tide. Red continuous line represents (H

_{s}= 0.2 sl = 0.4% T = 0.4), blue continuous (H

_{s}= 0.2 sl = 0.8% T = 0.4), cyan dashed (H

_{s}= 0.5 sl = 0.8% T = 0.8), and so on. (

**b**) Wave damping for all runs as function of the dimensionless variable x

_{d}*slope/H

_{s}. Wiberg limits define the range within she measured waves damping, which are consistent with our model results.

**Figure 3.**(

**a**) Velocity field around the breakwater related to the configuration with x

_{d}= 100 m, H

_{s}= 0.5 m and sl = 0.8%, during the tidal flood. (

**b**) U velocity component along section A related to all runs with x

_{d}= 100 m (same reading key of Plot 2a).

**Figure 4.**Mean u velocity during one tidal cycle measured at the center of section A, as function of the dimensionless variable x

_{d}* slope/H

_{s}for all simulations with slope = 0.4% (

**a**) and 0.8% (

**b**).

**Figure 5.**Shear stress as function of the x distance for the x

_{d}= 100 m configuration. (

**a**) Shear stress focus on the peak due to the presence of the breakwater (same reading key of Plot 2a). (

**b**) Shear stress zoom on the marsh zone (same reading key of Plot 2a). (

**c**) Shear stress value at the beginning of the marsh (x = 200 m) for the two different slopes, as functions of the dimensionless variable x

_{d}*Tide/H

_{s}

^{2}.

**Figure 6.**(

**a**) Bed level profile after the end of the simulation compared to the initial condition, for the simulation with slope 0.8%, H

_{s}= 0.5 m, Tide = ±0.2 m, C

_{s}= 0.2 kg/m

^{3}and D

_{50}= 100 µm. (

**b**) Sediment deposition into the salt marsh behind the breakwater, as function of breakwater distance from the shoreline, tide and wave height.

**Figure 7.**Ratio between the breakwater distance to the shoreline as function of the tide. The increasing of tide and breakwater distance to the coast increase the erosion at the marsh boundary, except for wave heights equal to 0.7 m, which mainly results in deposition into the marsh.

**Figure 8.**Eroded marsh volume for those configurations which cause erosion (see Figure 7), as function of the dimensionless variable x

_{d}*Tide/H

_{s}

^{2}. (

**a**) slope = 0.4% and Tide = ±0.4 m (

**b**) slope = 0.8% and Tide = ±0.4 m (

**c**) slope = 0.4% and Tide = ±0.8 m (

**d**) slope = 0.8% and Tide = ±0.8 m.

**Figure 9.**Sediment concentration Plot for the run with H

_{s}= 0.5 m, slope = 0.8%, Tide = ±0.4 m and x

_{d}= 100 m. (

**a**) Sediment concentration = 0.4 kg/m

^{3}and (

**b**) Sediment concentration = 0.2 kg/m

^{3}.

**Figure 10.**(

**a**) The 2D bed level at the end of the simulation with slope = 0.8% case, H

_{s}= 0.5 m, x

_{d}= 100 m and Tide = ±0.4 m. (

**b**) Longitudinal profile of transect 1 and 2 for the same simulation. The continuous line represents the initial condition, the dash line the transect 1 final bed level condition and the point line transect 2 final bed level condition. (

**c**) Ratio between the deposited volume on transect 1 and 2 for all runs.

**Figure 11.**Example of failing breakwaters use in Chesapeake Bay, US. (

**A**) Eastern Shore of Maryland, (Hoopers Island), (

**B**) and (

**C**) shows failing coastal structures like breakwaters and submerged Riprap. Signs of erosion are evident in the back-marsh area.

**Figure 12.**Long term simulation for (

**a**) x

_{d}= 50 m, (

**b**) x

_{d}= 100 m and (

**c**) x

_{d}= 150 m. The Figure shows how these morphodynamic structures tend to be less accentuated with an increase in breakwater distance to the shoreline.

H_{s} (m) | x_{d} (m) | sl (%) |
---|---|---|

0.2 0.3 0.5 0.7 | 50 100 150 | 0.4 0.8 |

D_{50} (µm) | T (m) | C (Kg/m^{3}) |

100 150 | ±0.2 ±0.4 | 0.2 0.4 |

**Table 2.**Notation of coefficients of Equations (1)–(5) and Table 1.

C | Mass concentration of sediment fraction, kg/m^{3} | θ | Wave direction |

C_{x} | Propagation velocity in the x-space, m/s | S | Source/sink term for the action Balance equation |

C_{y} | Propagation velocity in the y-space, m/s | S_{x} | Total sediment transport in the x direction, m^{2}/s |

C_{σ} | Propagation velocity in the σ –space, m/s | S_{y} | Total sediment transport in the y direction, m^{2}/s |

C_{θ} | Propagation velocity in the θ –space, m/s | sl | Basin slope, % |

D | Diffusion coefficient | τ | Fluid shear stress tensor |

D_{50} | Median diameter, µm | t | Time, s |

ɛ_{por} | Bed porosity | T_{d} | Deposition or erosion rate, m/s |

g | Gravity acceleration, m/s^{2} | T | Tidal conditions, m |

H_{s} | Wave height, m | V | Velocity field, m/s |

N | Density spectrum | x | Longitudinal direction, m |

p | Fluid pressure, N/m^{2} | x_{d} | Breakwater distance from the coast |

R | Source/sink term for the advection-diffusion equation | y | Transversal direction, m |

ρ | Fluid density, kg/m^{3} | z | Elevation, m |

σ | Frequency | z_{b} | Bed level, m |

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**MDPI and ACS Style**

Vona, I.; Gray, M.W.; Nardin, W.
The Impact of Submerged Breakwaters on Sediment Distribution along Marsh Boundaries. *Water* **2020**, *12*, 1016.
https://doi.org/10.3390/w12041016

**AMA Style**

Vona I, Gray MW, Nardin W.
The Impact of Submerged Breakwaters on Sediment Distribution along Marsh Boundaries. *Water*. 2020; 12(4):1016.
https://doi.org/10.3390/w12041016

**Chicago/Turabian Style**

Vona, Iacopo, Matthew W. Gray, and William Nardin.
2020. "The Impact of Submerged Breakwaters on Sediment Distribution along Marsh Boundaries" *Water* 12, no. 4: 1016.
https://doi.org/10.3390/w12041016