# Wave Breaker Types on a Smooth and Impermeable 1:10 Slope

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

_{I}and T

_{z}used in the results were the r.m.s. wave height and the mean wave period at the toe of the ramp. Those values were obtained from the statistical analysis of the recorded free surface elevation time series by wave gauges 1, 2 and 3. In the analysis, the zero-upcrossing technique of the time series was applied to obtain the individual wave heights and periods of the signal [16].

## 3. Results

#### 3.1. Log-Transformed Experimental Space

#### 3.2. Breakers Photographs

- −
- ID 15: Surging—weak bore
- −
- ID 16: Weak bore—strong bore
- −
- ID 17: Strong bore—strong plunging
- −
- ID 18: Strong plunging—weak plunging
- −
- ID 19: Weak plunging—spilling

#### 3.3. The Experimental Space and the Types of Wave Breaker

#### 3.4. Influence of the Breaker Types in the Flow Characteristics

^{*}) and the total water excursion [(Ru + |Rd|)/H

_{I}], being R

_{u}and R

_{d}the run-up and run-down respectively, versus the alternate slope similarity parameter $\left(\chi =log\left[h/LH/L\right]\right)$. Those data were calculated numerically using the IH-2VOF numerical model [5] on a smooth impermeable 1:10 slope (further information of the model and the test can be found in Appendix B. The tests are fully described in [14,15]). A sigmoid function was fitted to the numerical data and then, with the $\chi $ value of the experimental tests, the value of the dissipation was obtained from the sigmoid function. The figure highlights the relationships between the types of wave breaker and the flow characteristics and the wave energy transformation on the slope. The relationship with the reflection coefficient can be estimated from the bulk dissipation ${K}_{R}^{2}=1-{D}^{*}$. For impermeable and non-overtoppable slopes, it mimics the wave energy dissipation behavior.

## 4. Discussion

- 1)
- Surging—Weak bore: The wave trains oscillates (like a standing wave), generating no turbulence in the profile. The period of the water rising and falling along the slope is considerably larger than the wave period.
- 2)
- Weak bore—Strong bore: The inclined plane becomes more vertical and collapses in the middle or bottom of the water column.
- 3)
- Strong bore—Strong plunging: There is no volute. There is an inclined plane, mixing water and air bubbles.
- 4)
- Strong plunging—Weak plunging: The wave volute impacts the slope, hits it and bounces back.
- 5)
- Weak plunging—Spilling: The wave volute begins, but disappears in turbulence before it impacts the slope.

## 5. Conclusions

- 1)
- Six types of wave breaker were observed in the flume experiments: surging, weak bore, strong bore, strong plunging, weak plunging and spilling. Four of them were classified as follows [4]: surging, bore (collapsing), plunging, and spilling. The differences between weak—strong bore [13] and strong—weak plunging were explained by [8,12].
- 2)
- 3)
- It was found that the value of the Iribarren number is not sufficient to forecast the expected type of wave breaker on the slope. Except for spilling and early plunging breakers, there is not a biunivocal relationship between Ir and the type of breaker.
- 4)
- A relationship was found between the breaker types and flow characteristics and the wave energy dissipation on the slope. These results could be useful and relevant information for the design of mound breakwaters.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Atmosphere-Ocean Interaction Flume

- 1)
- Wave generation:
- -
- By means of a generation system with paddles and electric actuators, in both directions
- -
- By wind, either in the direction of the swell or in the opposite direction

- 2)
- Generation of currents, in both directions
- 3)
- Wave breakage
- 4)
- Rain generation
- 5)
- Heat exchange processes in the air-water interface
- 6)
- Behavior of different density biphasic fluids: lagoons and reservoirs

- 1)
- Consequences on ABL and OBL of processes such as wave generation or breaking
- 2)
- Heat balances in the boundary layers
- 3)
- Particle dynamics, droplet formation
- 4)
- Wave and wind actions on structures: offshore platforms, wind farms and offshore wind turbines
- 5)
- Wave power generation
- 6)
- Relations between heat exchange and life development: formation of ecosystems

#### Characteristics of the Flume

- 1)
- A wave generation system (wave flume), of 1 m width and 0.70 m water depth design, 15 m length and the possibility of generating waves of a period of 1–5 s and up to 25 cm high.
- 2)
- A closed circuit wind generation system (wind tunnel), 24 m long and capable of generating winds of up to 12 m/s.
- 3)
- A double current generation system, to generate currents at double height, with a maximum generated current speed of 0.75 m/s.

- 1)
- Rain generation system, from 75 to 300 mm/h, with water temperature variation between 10 and 30 °C.
- 2)
- Sediment collector for transport tests.

**Figure A1.**Atmosphere-Ocean Interaction Flume (CIAO) pictures. (

**a**) Inside of the flume with the ramp installed without water; (

**b**) Scheme of the flume provided by the manufacturer (VTI S.L.).

## Appendix B. Numerical Model IH-2VOF

**Figure A2.**Diagram of the wave flume and position of wave gauges (dimensions in meters) in the numerical tests IH-2VOF.

tan(α) | H(m) | T(s) | T_{z}(s) | h/L | H_{I}/L | Ir |
---|---|---|---|---|---|---|

1:10 | 0.002–0.14 | 1–2.2 | 0.8–2.19 | 0.09–0.36 | 0.0008–0.06 | 0.45–4.007 |

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**Figure 1.**Diagram of the Atmosphere-Ocean Interaction Flume (CIAO) and wave gauge position (measured in meters).

**Figure 2.**Experimental data (blue dots) in the log-transformed experimental space (darker dots are the breakers shown in Figure 3), as well as the generation limits (red lines) and Miche’s law for wave breaking (blue line).

**Figure 3.**Types of breaker transitions at the CIAO flume for a 1:10 impermeable slope. ID Numbers are used in Figure 2, Figure 4 and Figure 5 to identify the types of wave breaker in the experimental space. The pairs of figures show the transition between: (

**a**,

**b**) surging and weak bore; (

**c**,

**d**) weak bore and strong bore; (

**e**,

**f**) strong bore and strong plunging; (

**g**,

**h**) strong plunging and weak plunging; and (

**i**,

**j**) weak plunging and spilling.

**Figure 4.**Breaking types (blue lines) vs. Iribarren number (red lines), plotted in the log-transformed experimental space. S: surging, WB: weak bore, SB: strong bore, SP: strong plunging, WP: weak plunging, Sp: spilling.

**Figure 5.**Fitted sigmoid functions to the (

**a**) bulk dissipation and (

**b**) total water excursion versus $\mathrm{log}\left(\chi \right)$. Light blue dots are data from the IH-2VOF, to which the sigmoid function was fitted. Dark blue dots are the tests conducted at the CIAO flume and their value of D

^{*}and [(Ru + |Rd|)/H

_{I}] in the sigmoid. Vertical lines show the transition between breaker types.

**Table 1.**Summarized test conditions. Parameters H and T are input values, namely, the values given to the generation system. T

_{z}, L, H

_{I}and Ir represent the zero-upcrossing mean wave period, wavelength, incident wave height, and Iribarren number, respectively, from the statistical analysis of the surface elevation data.

tan(α) | H(m) | T(s) | T_{z}(s) | h/L | H_{I}/L | Ir |
---|---|---|---|---|---|---|

1:10 | 0.005–0.3 | 0.98–4.8 | 1.1006–5.0114 | 0.0457–0.2804 | 0.0012–0.1002 | 0.367–3.15 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Moragues, M.V.; Clavero, M.; Losada, M.Á.
Wave Breaker Types on a Smooth and Impermeable 1:10 Slope. *J. Mar. Sci. Eng.* **2020**, *8*, 296.
https://doi.org/10.3390/jmse8040296

**AMA Style**

Moragues MV, Clavero M, Losada MÁ.
Wave Breaker Types on a Smooth and Impermeable 1:10 Slope. *Journal of Marine Science and Engineering*. 2020; 8(4):296.
https://doi.org/10.3390/jmse8040296

**Chicago/Turabian Style**

Moragues, María Victoria, María Clavero, and Miguel Á. Losada.
2020. "Wave Breaker Types on a Smooth and Impermeable 1:10 Slope" *Journal of Marine Science and Engineering* 8, no. 4: 296.
https://doi.org/10.3390/jmse8040296