# Long-Term Performance of Mega-Nourishments: Role of Directional Wave Climate and Initial Geometry

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Morphology of the Zm and Prevailing Wave Conditions

#### 2.2. Model Description

#### 2.3. Model Settings

#### 2.4. Metrics for Mega-Nourishment Performance

## 3. Effect of Varying the Wave Angle

#### 3.1. Design and Validation of the Synthetic Wave Climate

#### 3.2. Sensitivity to the Frequency of High-Angle Waves

## 4. Effect of Varying the Mega-Nourishment Geometry

#### 4.1. Sensitivity to the Initial Asymmetry

#### 4.2. Sensitivity to the Initial Aspect Ratio

#### 4.3. Sensitivity to The Volume

## 5. Discussion

#### 5.1. Physical Processes Driving Mega-Nourishment Evolution

#### 5.1.1. Importance of High-Angle Waves

#### 5.1.2. Diffusivity and Feeding Asymmetry

#### 5.2. Design Recommendations

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Design of the Synthetic Mega-Nourishment

**Figure A1.**Simplified Zandmotor bathymetry (SZM) obtained from measurements (17 January 2012) (

**a**) and synthetic mega-nourishment bathymetry (SMN) adjusted from a Gaussian-shape function (

**b**), both with the dry beach set to 2 m; and (

**c**,

**d**) their respective associated bed level perturbations.

**Figure A2.**The 50-year evolution of: (

**a**) diffusivity; (

**b**) feeding asymmetry; and (

**c**) displacement for the Zandmotor (blue lines), simplified Zandmotor (red lines) and synthetic mega-nourishment (yellow lines) predictions.

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**Figure 1.**Aerial pictures of the first concentrated mega-nourishment (ZM, The Netherlands), showing its morphological evolution in the initial six years. Pictures were taken in: (

**a**) July 2011 (shortly after construction); (

**b**) October 2011; (

**c**) January 2012; (

**d**) October 2012; (

**e**) October 2013; (

**f**) September 2014; (

**g**) May 2015; (

**h**) August 2016; and (

**i**) July 2017. Courtesy: Rijkswaterstaat, Joop van der Hout.

**Figure 2.**Sketch of the model simulations, where the y-axis would point into the southwestern direction if this was the real Zandmotor in the Dutch coast. The wave angle $\theta $ indicated has a positive sign and the shown mega-nourishment has a negative orientation. The areas defined to compute the feeding to adjacent beaches are marked with a dashed rectangle.

**Figure 3.**Schematic sketch of wave rose with the five different wave sectors. Sector V represents seaward-directed waves and therefore time periods without morphological changes. The horizontal and vertical line represent the mean coastline and the shore-normal, respectively.

**Figure 4.**Time-averaged shoreline RMSE in the first 30 years and the final 5 years (Years 25–30) for SWCs with a different number of directional sectors (

**a**); and the time evolution of the diffusivity (

**b**), feeding asymmetry (

**c**), and alongshore displacement (

**d**) for the RWC and SWCs with 4 or 64 sectors.

**Figure 5.**Probability of occurrence of each wave sectors for varying high-angle wave frequency, ${p}_{O}$, for: (

**a**) bimodal conditions assuming that both Sectors I and IV are modified proportionally; and (

**b**) unimodal conditions assuming that only the probability of occurrence of Sector I increases. Averaged diffusivity over the last five years of simulations as a function of high-angle wave frequency (

**c**). Shorelines after 50 years of evolution for the indicated simulations (

**d**).

**Figure 6.**Sensitivity of the long-term mega-nourishment evolution to the percentage of high-angle waves in a bimodal wave climate (Set 1 (

**a**,

**c**)) and in a unimodal wave climate (Set 2 (

**b**,

**d**)). Time evolution of: (

**a**,

**b**) the associated feeding asymmetry; and (

**c**,

**d**) the displacement during 50 years.

**Figure 7.**Sketch of the different initial mega-nourishment geometries, including variations on: (

**a**) the orientation or asymmetry; (

**b**) the shape factor; and (

**c**) the volume factor. Notice that the scaling of both axis is not the same.

**Figure 8.**Effect of the initial mega-nourishment orientation on: (

**a**) the final five-year diffusivity, as well as on the 50-year evolution of (

**b**) the FA and (

**c**) the displacement.

**Figure 9.**Effect of the initial mega-nourishment shape factor on: (

**a**) the final five-year diffusivity, as well as on the 50-year evolution of (

**b**) the FA and (

**c**) the displacement.

**Figure 10.**Effect of the initial mega-nourishment volume ratio on: (

**a**) the final five-year diffusivity, as well as on the 50-year evolution of (

**b**) the FA and (

**c**) the displacement.

**Table 1.**Sensitivity to the statistical method that synthesizes the RWC into four directional sectors, where H is the significant wave height, T is the peak wave period, and $\theta $ is the wave direction measured with respect to the shore normal. The frequency of occurrence of each sector is written between brackets. The last column shows the shoreline RMSE (with respect to RWC) at the end of the simulations (average over Years 25–30).

Sector I (33%) | Sector II (11%) | Sector III (27%) | Sector IV (29%) | Shoreline | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Method | H(m) | $\mathbf{\theta}$ (deg) | T (s) | H (m) | $\mathbf{\theta}$ (deg) | T (s) | H (m) | $\mathbf{\theta}$ (deg) | T (s) | H (m) | $\mathbf{\theta}$ (deg) | T (s) | RMSE (m) |

1 | 1.4 | −74.2 | 5.8 | 1.3 | −21.4 | 5.7 | 1.2 | 27.6 | 6.3 | 1.0 | 63.3 | 5.8 | 56 |

2 | 1.8 | −76.5 | 7.0 | 1.7 | −22.0 | 7.2 | 1.5 | 23.9 | 7.4 | 1.2 | 65.5 | 6.5 | 11 |

3 | 1.7 | −72.3 | 6.8 | 1.6 | −21.3 | 7.0 | 1.4 | 24.1 | 7.2 | 1.2 | 62.6 | 6.4 | 17 |

4 | 1.9 | −76.7 | 7.2 | 1.8 | −22.1 | 7.4 | 1.7 | 23.1 | 7.6 | 1.3 | 65.9 | 6.7 | 22 |

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**MDPI and ACS Style**

Arriaga, J.; Ribas, F.; Falqués, A.; Rutten, J.; Ruessink, G. Long-Term Performance of Mega-Nourishments: Role of Directional Wave Climate and Initial Geometry. *J. Mar. Sci. Eng.* **2020**, *8*, 965.
https://doi.org/10.3390/jmse8120965

**AMA Style**

Arriaga J, Ribas F, Falqués A, Rutten J, Ruessink G. Long-Term Performance of Mega-Nourishments: Role of Directional Wave Climate and Initial Geometry. *Journal of Marine Science and Engineering*. 2020; 8(12):965.
https://doi.org/10.3390/jmse8120965

**Chicago/Turabian Style**

Arriaga, Jaime, Francesca Ribas, Albert Falqués, Jantien Rutten, and Gerben Ruessink. 2020. "Long-Term Performance of Mega-Nourishments: Role of Directional Wave Climate and Initial Geometry" *Journal of Marine Science and Engineering* 8, no. 12: 965.
https://doi.org/10.3390/jmse8120965