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

Journal of Marine Science and Engineering

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

María Victoria Moragues * , María Clavero and Miguel Á. Losada

Andalusian Institute for Earth System Research, University of Granada, Avda. del Mediterráneo, s/n, 18006 Granada, Spain; [email protected] (M.C.); [email protected] (M.Á.L.) * Correspondence: [email protected]

Received: 31 March 2020; Accepted: 21 April 2020; Published: 23 April 2020

Abstract: This research identified the types of wave breaker on a non-overtoppable, smooth and impermeable 1:10 slope under regular waves. Experimental tests were carried out in the Atmosphere-Ocean Interaction Flume of the Andalusian Institute for Earth System Research (University of Granada). Using the experimental space [log(h/L)–log(H/L)] and the alternate slope similarity parameter [χ = log (h/LH/L)], a complete set of breaker types was identified. Four types of wave breaker were then added to Galvin’s classification. Our results showed that the value of the Iribarren number was not sufficient to predict the expected type of wave breaker on the slope. Except for spilling and early plunging breakers, no biunivocal relationship was found between Ir and the type of breaker. The data obtained in the physical model were further enriched with the results of the flow characteristics and the wave energy transformation coefficients obtained with the IH-2VOF numerical model on a 1:10 impermeable slope. This research study, presented in this paper, showed that the Iribarren number is not a convenient wave breaking similarity parameter.

Keywords: wind waves; breaker type; breakwaters; similarity parameter; experimental tests

1. Introduction Sloping breakwaters are the most common coastal structure for the protection of ports and beaches, because of their capacity to dissipate incident wave energy when interacting with the structure. The transformation of the wave train propagating on an impermeable slope depends, among other things, on the transport of turbulent kinetic energy (TKE) from the following sources: (a) wave breaking causing advection and diffusion of turbulence, generating a vortex dependent on the breaking type; (b) the armor layer whose vortex depends on the characteristic diameter of the armor unit; and (c) the porous core whose turbulence scale depends on the grain size. The research in [1] is based on the hypothesis that the Iribarren number (Ir = tan(α)/ √H/L)[2] helps to address the questions of whether a wave train will break on a slope, by decaying, voluting, collapsing, or oscillating [3,4]. However, surprisingly, in the case of breakwaters, very little attention has been paid to calculating wave dissipation as a function of the type of wave breaking on the slope. In recent decades, several numerical and physical studies have studied the different types of wave breaking on an impermeable slope. References [5–9] developed numerical models based on the volume-averaged Reynolds average Navier–Stokes (VARANS) equations and using the volume of fluid (VOF) method for measuring the free surface. References [7,8] performed an in-depth study of plunging and spilling breakers. On the other hand, using numerical and mathematical models, ref. [9] studied the differences between weak and strong plunging; Ref. [10] investigated the bore type of breakers; Ref. [11] researched breaking waves on steep impermeable slopes for measuring run-up, and ref. [12] studied plunging breakers.

J. Mar. Sci. Eng. 2020, 8, 296; doi:10.3390/jmse8040296 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 2 of 10

These studies provided the spatial-temporal progression of the wave, which is key information to analyze the source of the experimental uncertainty, and to identify the transitions between the types of wave breakers [3,4]. Particularly relevant for this research was the distinction between weak and strong bore [13] and weak and strong plunging [7,12]. J. Mar. Sci.Nowadays, Eng. 2020, 8in, 296coastal engineering, the flow characteristics of the waves (energy transformation,2 of 10 stability, run-up, etc.) are determined by the application of semi-empirical formulas, most of which are based on the Iribarren number [2]. It is implicitly conjectured that the value of the Iribarren numberThese determines studies provided the type the of spatial-temporalwave breaker [1,3,4] progression on the slope. of the wave, which is key information to analyzeFollowing the source [14] of and the [15], experimental the first aim uncertainty, of this pape andr was to identifyto verify the that transitions conjecture. between The second the typeswas ofto wave describe breakers and analyze [3,4]. Particularly the dependence relevant of the for type this of research wave breaker was the on distinction the relative between depth weak(h/L) and and strongwave steepness bore [13] and(H/L weak), while and propagating strong plunging on a smooth, [7,12]. impermeable slope under regular wave train. For Nowadays,this purpose, in a coastalphysical engineering, test was carried the flow out in characteristics the Atmosphere-Ocean of the waves Interaction (energy transformation,Flume (CIAO) stability,of the Andalusian run-up, etc.) Institute are determined for Earth bySystem the application Research (IISTA-University of semi-empirical of formulas, Granada). most of which are basedThe on therest Iribarren of the paper number is organized [2]. It is implicitly as follows. conjectured Firstly, the that experimental the value of set-up the Iribarren and space number are determinesdescribed. theNext, type a series of wave of breakerpictures [1defining,3,4] on thethe slope.types of wave breaker are shown. The types of breakersFollowing are presented [14,15], theas a first function aim of of this the paper relative was depth to verify and thatwave conjecture. steepness. TheIn addition, second wasthese to describeresults are and discussed analyze the and dependence compared ofwith the typethe Iribarren of wave breakernumber. on Finally, the relative the paper depth ends (h/L) andwith wave the steepnessconclusions (H/ Lthat), while can be propagating derived from on athis smooth, research. impermeable slope under regular wave train. For this purpose, a physical test was carried out in the Atmosphere-Ocean Interaction Flume (CIAO) of the Andalusian2. Methodology Institute for Earth System Research (IISTA-University of Granada). TheTo reststudy of thethe paperinfluence is organized of the different as follows. wave Firstly, parameters the experimental and test set-up conditions and space in the are breaking described. Next,processes, a series tests of pictureswere carried defining out the in typesthe Atmo of wavesphere-Ocean breaker are Interaction shown. The Flume types (CIAO) of breakers of the are presentedAndalusian as aInstitute function for of theEarth relative System depth Research and wave (IISTA-University steepness. In addition, of Granada). these results This arewave discussed flume andfacilitates compared the combined with the Iribarrenstudy of number.marine and Finally, atmospheric the paper processes. ends with The the facility conclusions has two that opposing can be derivedpiston-type from generating this research. paddles, equipped with active systems to absorb reflection, and a closed circuit for wind generation. A detailed description of the CIAO facility is given in Appendix 1. 2. MethodologyFor this study, an impermeable ramp made of wood, with a slope angle of 1:10 (in the study area,To Figure study 1) thewas influence used. Regular of the waves different were wavegenerated parameters with paddle and 2. test Two conditions water depths in the were breaking used, processes,h = 0.4 m testsand wereh=0.5 carried m. A out total in theof 19 Atmosphere-Ocean tests were done, of Interaction which the Flume conditions (CIAO) are of summarized the Andalusian in InstituteTable 1. Test for Earth conditions System were Research chosen (IISTA-Universityto cover the maximum of Granada). experimental This space wave [𝑙𝑜𝑔(ℎ/𝐿) flume facilitates 𝑣𝑠 the 𝑙𝑜𝑔(𝐻/ combined𝐿)] to analyze study the of marinemaximum and types atmospheric of breakers, processes. with combinations The facility hasof H two and opposing T, and then piston-type Ir was generatingcalculated. paddles,Pictures equippedof the waves with were active taken systems from the to absorbfirst waves reflection, approaching and a closedthe slope. circuit for wind generation. A detailed description of the CIAO facility is given in AppendixA. ForTable this 1. study,Summarized an impermeable test conditions. ramp Parameters made of H wood, and T withare input a slope values, angle namely, of 1:10 the(in values the given study area, to the generation system. Tz, L, HI and Ir represent the zero-upcrossing mean wave period, Figure1) was used. Regular waves were generated with paddle 2. Two water depths were used, wavelength, incident wave height, and Iribarren number, respectively, from the statistical analysis of h = 0.4 m and h = 0.5 m. A total of 19 tests were done, of which the conditions are summarized in the surface elevation data. Table1. Test conditions were chosen to cover the maximum experimental space [log(h/L) vs. log(H/L)] to analyzetan(α) the maximumH(m) types T(s) of breakers, Tz with(s) combinationsh/L of H and T, andHI/L then Ir was calculated.Ir Pictures1:10 of the 0.005 waves – 0.3 were 0.98 taken – 4.8 from 1.1006- the first 5.0114 waves approaching0.0457-0.2804 the 0.0012-0.1002 slope. 0.367 – 3.15

FigureFigure 1.1. DiagramDiagram ofof thethe Atmosphere-OceanAtmosphere-Ocean Interaction Flume Flume (CIAO) (CIAO) and and wave wave gauge gauge position position (measured(measured in in meters). meters). Table 1. Summarized test conditions. Parameters H and T are input values, namely, the values given to The free surface elevation was measured using four UltraLab ULS 80D acoustic wave gauges the generation system. Tz, L, HI and Ir represent the zero-upcrossing mean wave period, wavelength, placedincident along wave the flume height, before and Iribarren the ramp number, (Figure respectively, 1). These gauges from the have statistical a maximum analysis repetition of the surface rate of elevation data.

tan(α) H(m) T(s) Tz(s) h/LHI/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 J. Mar. Sci.J. Eng. Mar. Sci.2020 Eng., 8, 2020x FOR, 8, 296 PEER REVIEW 3 of 10 3 of 10

75Hz, a space resolution of 0.18mm, a working range of 350mm and a reproducibility of ±0.15%. The free surface elevation was measured using four UltraLab ULS 80D acoustic wave gauges Video camerasplaced along were the used ﬂume in before the study the ramp section (Figure for1). recording These gauges and have photographing a maximum repetition the breaking rate of waves. The75 values Hz, a spaceof HI resolutionand Tz used of 0.18 in the mm, results a working were range the ofr.m.s. 350 mm wave and height a reproducibility and the mean of 0.15%. wave period ± at the toeVideo of the cameras ramp. were Those used invalues the study were section obtained for recording from andthe photographingstatistical analys the breakingis of the waves. recorded free surface elevationThe values time of seriesHI and byTz waveused in gauges the results 1, were2 and the 3. r.m.s.In the wave analysis, height andthe thezero-upcrossing mean wave period technique of the timeat the series toe of was the ramp.applied Those to obtain values were the indivi obtaineddual from wave the statistical heights analysis and periods of the recordedof the signal free [16]. surface elevation time series by wave gauges 1, 2 and 3. In the analysis, the zero-upcrossing technique Whileof the the time mean series period was applied coincided to obtain with the individualthe input wave period, heights the and incident periods wave of the signalheight [16 was]. usually lower than theWhile input the meanvalue period [14]. coincidedL is the wavelength, with the input period,calculated the incident with the wave linear height dispersion was usually equation, 𝜎 =𝑔𝑘lower 𝑡𝑎𝑛ℎ than the, (𝑘ℎ) where input valueσ is the [14 ].angularL is the wavelength,frequency ( calculated𝜎=2𝜋/𝑇 with); g theis the linear gravity dispersion acceleration; equation, k is the wavenumberσ2 = gk (k=2π/L tanh(kh), where). σ is the angular frequency (σ = 2π/T); g is the gravity acceleration; k is the wavenumber (k = 2π/L).

3. Results3. Results

3.1. Log-transformed3.1. Log-Transformed Experimental Experimental Space Space Firstly, it was necessary to analyze the limits of wave generation in the flume tests. For that purpose, Firstly, it was necessary to analyze the limits of wave generation in the flume tests. For that Figure2 shows the tests carried out on a 1:10 slope, plotted in the log-transformed experimental purpose,space Figure [14]. The2 shows logarithmic the axestests were carried used toout assist on in a the 1:10 visualization slope, plotted of the data. in The the sides log-transformed of the experimentalparallelepiped space [14]. indicated The thelogarithmic wave generation axes limitswere of used the wave to assist flume in (maximum the visualization and minimum of wavethe data. The sides of heightthe parallelepiped and period). This indicated figure also the shows wave the maximumgeneration wave limits steepness of the in wave the intermediate flume (maximum water and minimumdepth wave (constant height depth) and given period). by Miche’s This equation figure (Equationalso shows (1)) [the17]. maximum wave steepness in the intermediate water depth (constant depth) given by Miche’s equation (Equation 1) [17]. HI/L = 0.14tan h(kh) (1)

𝐻⁄𝐿 = 0.14tanh(𝑘ℎ) (1)

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

3.2. Breakers Photographs In what follows, the sequence of the type of wave breaker observed is shown with the pictures taken during the experiments. The ID of each picture indicates the number of the test in the log- transformed experimental space. Each test is represented by two pictures of the wave. The sequence of the five photographs shows the transition between five types of wave breaker observed on the plane impermeable 1:10 slope: − 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

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ID (a) (b) 15

ID (c) (d) 16

ID (e) (f) 17

ID (g) (h) 18

ID (i) (j) 19

FigureFigure 3. Types 3. Types of breakerof breaker transitions transitions at at the the CIAOCIAO fl ﬂumeume for for a a1:10 1:10 impermeable impermeable slope. slope. ID Numbers ID Numbers are usedare used in Figures in Figures2,4 and 2, 45 andto identify 5 to identify the types the types of wave of wave breaker breake inr the in experimentalthe experimental space. space. The The pairs of ﬁgurespairs of show figures the show transition the transition between: between: (a,b (a)) surgingand (b) surging and weak and weak bore; bore; (c,d ()c) weak and (d bore) weak and bore strong bore; (e,f) strong bore and strong plunging; (g,h) strong plunging and weak plunging; and (i,j) weak plunging and spilling. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 5 of 10

and strong bore; (e) and (f) strong bore and strong plunging; (g) and (h) strong plunging and weak plunging; and (i) and (j) weak plunging and spilling.

As can be observed, the difference between the weak and strong bore found by [13] (their Figures 5 and 6) are also observed in the physical test. In a weak bore, the front of the wave is unbalanced and starts breaking from the bottom or nearby it. In a strong bore, there is an attempt to plunge, but, before it can finish the plunge, the front “collapses”, thus developing a forward volume of water and bubbles, which are highly turbulent. For plunging breakers, the top of the front wave turns over. In the strong plunging, the water falls on the slope (or on a tongue of water), splashing and losing energy. In the weak plunging, the water lands on the main wave, building a roller which propagates with the wave [18].

3.3. The Experimental Space and the Types of Wave Breaker Figure 4 shows the same log-transformed experimental space with the experimental data, but in this case, the other information is the following: (1) the different types of wave breaker: (2) vertical red lines indicating constant values of the Iribarren number; and (3) slanting blue lines, showing the transition between breaking types, following the constant relationship between h/L and H/L. This relationship was found after analyzing the pictures and organizing the breaker types. Figure 4 clearly illustrates that for a constant value of Ir, different types of breaking wave can be expected. For Ir = 2.5J. Mar., surging, Sci. Eng. weak2020, 8 ,bore, 296 strong bore and strong plunging breakers could be possible. Thus, it cannot5 of 10 be assumed that there is a biunivocal relationship between the Iribarren number and the types of wave breaker.

FigureFigure 4. BreakingBreaking types types (blue (blue lines) vs. Iribarren Iribarren number number (red (red lines), plotted in the log-transformed experimentalexperimental space. space. S: S: surging, surging, WB: WB: weak weak bore, bore, SB: SB: strong strong bore, bore, SP: SP: strong strong plunging, plunging, WP: WP: weak J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 6 of 10 plunging, Sp: spilling.

3.4. Influence of the Breaker Types in the Flow Characteristics

Figure 5 shows sigmoid functions fitted to the values of the bulk dissipation (D*) and the total water excursion [(Ru+|Rd|)/HI], being Ru and Rd the run-up and run-down respectively, versus the alternate slope similarity parameter (𝜒 = 𝑙𝑜𝑔[ℎ/𝐿 𝐻/𝐿]). 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 𝜒 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 =1−𝐷. For impermeable and non-overtoppable slopes, it mimics the wave energy dissipation behavior. FigureFigure 5.5. Fitted sigmoid functions to the (a)) bulkbulk dissipationdissipation andand ((bb)) totaltotal waterwater excursionexcursion versusversus loglog((𝜒) χ). Light blueblue dotsdots are are data data from from the the IH-2VOF, IH-2VOF, to whichto which the the sigmoid sigmoid function function was ﬁtted.was fitted. Dark Dark blue * dotsblue aredots the are tests the conducted tests conducted at the CIAOat the ﬂumeCIAO and flume their and value their of valueD and of [ (RuD* and+ |Rd [(|Ru+|Rd|)/H)/HI] in the sigmoid.I] in the

Verticalsigmoid. lines Vertical show lines the transitionshow the transition between breaker between types. breaker types. 3.2. Breakers Photographs 4. Discussion In what follows, the sequence of the type of wave breaker observed is shown with the pictures taken The previously mentioned results showed that small changes in the relative depth and wave during the experiments. The ID of each picture indicates the number of the test in the log-transformed steepness can alter the type of wave breaker, and consequently change the flow characteristics on the experimental space. Each test is represented by two pictures of the wave. slope. It is important to highlight that the types of wave breaker were found to be strongly dependent The sequence of the five photographs shows the transition between five types of wave breaker on the slope angle ([14, 15]) and thus their location in the experimental space, (h/L) and (H/L). The observed on the plane impermeable 1:10 slope: results in Figure 3 are representative of the types of breaker on an impermeable 1:10 slope. TheID 15: analysis Surging—weak of the photographs bore and videos taken at the wave flume showed that the − characteristicsID 16: Weak of each bore—strong transition bore between the different breakers were the following: − 1) Surging—weakID 17: Strong bore—strong bore: the wave plunging trains oscillates (like a standing wave), generating no turbulence − inID the 18: profile. Strong The plunging—weak period of the plunging water rising and falling along the slope is considerably larger − than the wave period. ID 19: Weak plunging—spilling −2) Weak bore—strong bore: the inclined plane becomes more vertical and collapses in the middle orAs bottom can be observed,of the water the column. difference between the weak and strong bore found by [13] (their Figures5 and3) A1Strong) are bore—strong also observed plunging: in the physical there test.is no In volute. a weak There bore, theis an front inclined of the plane, wave ismixing unbalanced water and startsair breaking bubbles. from the bottom or nearby it. In a strong bore, there is an attempt to plunge, but, before it4) can Strong finish plunging—weak the plunge, the front plunging: “collapses”, the wave thus volute developing impacts a forward the slope, volume hits it of and water bounces and bubbles, back. which5) Weak are highlyplunging—spilling: turbulent. the wave volute begins, but disappears in turbulence before it impacts the slope. As reflected in the results, the wave breaking process determined the flow characteristics (run- up, run-down, stability…), as well as wave energy transformation on the slope. Three regimens were found: (i) a reflective regime caused by surging breakers; (ii) a dissipative domain caused by spilling and weak plunging breakers; (iii) a transition regime where strong and weak bores, and strong plunging are the most plausible type of wave breaker. Reference [2] proposed the value of 𝐼𝑟 = 2.3 to identify the change of wave energy transformation: for Ir >2.3, the flux of reflected wave energy was larger than the energy dissipation. Later, [19] showed that for Ir ≈ 2.3, the period of the up-rush and down-rush on the slope and the period of the incident wave were approximately equal. In the experiments in this study, these "quasi- resonant" conditions occurred during the transition between strong plunging and strong bore. The variability of the observed flow characteristics was significant, depending on the type of wave breaker [15]. The use of the experimental space could help to develop the experimental design. It made it possible to forecast the types of breaker, as well as the variability of the flow characteristics, wave energy transformation, and structure stability. The types of wave breaker identified previously in the numerical computation [15] were verified with the physical breakers observed in the CIAO flume. For that purpose, the application of the alternative slope parameter (𝜒) was relevant. Thus, with a

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For plunging breakers, the top of the front wave turns over. In the strong plunging, the water falls on the slope (or on a tongue of water), splashing and losing energy. In the weak plunging, the water lands on the main wave, building a roller which propagates with the wave [18].

3.3. The Experimental Space and the Types of Wave Breaker Figure4 shows the same log-transformed experimental space with the experimental data, but in this case, the other information is the following: (1) the diﬀerent types of wave breaker: (2) vertical red lines indicating constant values of the Iribarren number; and (3) slanting blue lines, showing the transition between breaking types, following the constant relationship between h/L and H/L. This relationship was found after analyzing the pictures and organizing the breaker types. Figure4 clearly illustrates that for a constant value of Ir, diﬀerent types of breaking wave can be expected. For Ir = 2.5, surging, weak bore, strong bore and strong plunging breakers could be possible. Thus, it cannot be assumed that there is a biunivocal relationship between the Iribarren number and the types of wave breaker.

3.4. Influence of the Breaker Types in the Flow Characteristics Figure5 shows sigmoid functions fitted to the values of the bulk dissipation ( D*) and the total water excursion [(Ru + |Rd|)/HI], being Ru and Rd the run-up and run-down respectively, versus the alternate slope similarity parameter (χ = log[h/LH/L]). 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 AppendixB. The tests are fully described in [ 14,15]). A sigmoid function was fitted to the numerical data and then, with the χ 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 K2 = 1 D . R − ∗ For impermeable and non-overtoppable slopes, it mimics the wave energy dissipation behavior.

4. Discussion The previously mentioned results showed that small changes in the relative depth and wave steepness can alter the type of wave breaker, and consequently change the flow characteristics on the slope. It is important to highlight that the types of wave breaker were found to be strongly dependent on the slope angle ([14,15]) and thus their location in the experimental space, (h/L) and (H/L). The results in Figure3 are representative of the types of breaker on an impermeable 1:10 slope. The analysis of the photographs and videos taken at the wave flume showed that the characteristics of each transition between the different breakers were the following:

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.

As reflected in the results, the wave breaking process determined the flow characteristics (run-up, run-down, stability ... ), as well as wave energy transformation on the slope. Three regimens were found: (i) a reflective regime caused by surging breakers; (ii) a dissipative domain caused by spilling J. Mar. Sci. Eng. 2020, 8, 296 7 of 10 and weak plunging breakers; (iii) a transition regime where strong and weak bores, and strong plunging are the most plausible type of wave breaker. Reference [2] proposed the value of Ir = 2.3 to identify the change of wave energy transformation: for Ir >2.3, the flux of reflected wave energy was larger than the energy dissipation. Later, [19] showed that for Ir 2.3, the period of the up-rush and down-rush on the slope and the period of the ≈ incident wave were approximately equal. In the experiments in this study, these “quasi-resonant” conditions occurred during the transition between strong plunging and strong bore. The variability of the observed flow characteristics was significant, depending on the type of wave breaker [15]. The use of the experimental space could help to develop the experimental design. It made it possible to forecast the types of breaker, as well as the variability of the flow characteristics, wave energy transformation, and structure stability. The types of wave breaker identified previously in the numerical computation [15] were verified with the physical breakers observed in the CIAO flume. For that purpose, the application of the alternative slope parameter (χ) was relevant. Thus, with a smaller number of tests, a wide range of results were obtained. The time of the physical experiments was also decreased; and even more importantly, costs were lowered.

5. Conclusions The objective of this research was to identify the types of wave breaker on a non-overtoppable, smooth, and impermeable 1:10 slope under regular waves. Experimental tests were carried out in the CIAO ﬂume of the IISTA. From this study, the following conclusions can be drawn:

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) The alternate slope similarity parameter (χ) [14,15] enabled us to forecast the type of wave breaker. It depends on the slope. The results of this study (Figures3 and4) were obtained on a 1:10 impermeable slope. 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: All authors conceptualized the study. M.V.M. did the physical tests with the help of M.C. M.V.M. did the analysis of the data with the guidance of M.Á.L. All authors contributed to the preparation of the manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by the research group TEP-209 (Junta de Andalucía) and by two projects: (1) “Protection of coastal urban fronts against global warming–PROTOCOL” (917PTE0538), (2) “Integrated verification of the hydrodynamic and structural behavior of a breakwater and its implications on the investment project–VIVALDI” (BIA2015-65598-P) and (3) “Laboratory testing and knowledge transfer for the development of sustainable strategies for marine energy harvesting (SUSME)” (PCI2019-103565). Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Appendix A. Atmosphere-Ocean Interaction Flume The Atmosphere-Ocean Interaction Flume (CIAO) is part of the Environmental Fluid Dynamics Laboratory and focuses on the study of the coupling processes between the sea and the atmosphere. The marine atmospheric boundary layer (ABL) and the oceanic boundary layer (OBL) are full of small and large scale ﬂow processes. The vertical dimensions of the ABL (on the order of 500 m), the OBL J. Mar. Sci. Eng. 2020, 8, 296 8 of 10

(on the order of 50 m) and the swell (on the order of 5 m) are small compared to the general height of the atmosphere and ocean. In contrast, boundary layer turbulence and waves play a major role on a large scale, as they regulate the functioning of the earth’s climate and weather systems. The coupling of the atmosphere and the ocean through these processes is particularly important and affects many scientific disciplines: climate prediction, wave breaking, bubble and spray generation, etc. This is why the CIAO flume covers a large part of the processes involved in the coupling between the ABL and the OBL, and therefore has the capacity to simulate them:

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

Thus, the new facility will provide the ability to study:

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 The CIAO ﬂume has three main components:

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.

The three components are reversible and independent, so that all phenomena can be simulated in equal or opposite directions of propagation, giving the equipment great versatility. In addition, the equipment has a series of auxiliary systems that make it unique worldwide:

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. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 8 of 10

Thus, the new facility will provide the ability to study: 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 The CIAO flume has three main components: 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 seconds 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. The three components are reversible and independent, so that all phenomena can be simulated in equal or opposite directions of propagation, giving the equipment great versatility. In addition, the equipment has a series of auxiliary systems that make it unique worldwide: 1) Rain generation system, from 75 to 300 mm/h, with water temperature variation between 10 and J. Mar. Sci. Eng.30ºC.2020 , 8, 296 9 of 10 2) Sediment collector for transport tests.

(b)

(a)

FigureFigure A1. Atmosphere-Ocean6. Atmosphere-Ocean Interaction Flume Flume (CIAO) (CIAO) pictures. pictures. (a) Inside (a) Insideof the flume of the with ﬂume the ramp with the rampinstalled installed without without water; water; (b) (Schemeb) Scheme of the of flume the ﬂume provided provided by the bymanufacturer the manufacturer (VTI S.L.). (VTI S.L.).

AppendixAppendix B. Numerical B: Numerical Model Model IH-2VOF IH-2VOF TheThe IH-2VOF IH-2VOF numerical numerical model [5] [5 is] based is based on the on volume-averaged/Reynolds the volume-averaged /averagedReynolds Navier– averaged Stokes equations (VARANS) in a two-dimensional domain. These equations are obtained when the Navier–Stokes equations (VARANS) in a two-dimensional domain. These equations are obtained RANS equations are integrated in a control volume. The volume of fluid (VOF) method is followed when the RANS equations are integrated in a control volume. The volume of fluid (VOF) method is to compute free surface. Wave conditions are introduced in the model, imposing a velocity field and followeda free to surface compute time free evolution surface. on Wave one side conditions of the numerical are introduced domain. in The the IH-2VOF model, imposingmodel has abeen velocity field andwidely a free valida surfaceted [20–25]. time evolution on one side of the numerical domain. The IH-2VOF model has been widelyThe validated current-wave [20– flume25]. of the IISTA laboratory was reproduced in the numerical model. The Thenumerical current-wave set-up was flume calibrated of theby [24] IISTA and laboratoryit is formed by was a uniform reproduced grid on in the the y-axis, numerical with a grid model. The numerical set-up was calibrated by [24] and it is formed by a uniform grid on the y-axis, J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 9 of 10 with a grid cell size of 0.5 cm, and horizontally (on the x-axis) grid with three regions: (i) a center region,cell size 5 mof long,0.5 cm, containing and horizontally the breakwater (on the x-axis) section grid with with the three finest regions: resolution (i) a center and a region, cell size 5 m of 1 cm; twolong, regions containing (ii) at the the breakwater beginning sect andion (iii) with at the the end finest of resolution the numerical and a wave cell size flow, of 1 with cm; atwo cell regions size of 2 cm. The(ii) total at the number beginning of cellsand (iii) in theat the numerical end of the domain numerical was wave 1304 flow,162. with Active a cell wavesize of absorption 2 cm. The total was used × atnumber the generation of cells in boundary. the numerical domain was 1304 × 162. Active wave absorption was used at the generationA non-overtoppable, boundary. smooth and impermeable 1:10 slope was tested under regular waves (FigureA A2 non-overtoppable,). Tests were performed, smooth and setting impermeable the value 1:10 of Tslopeand was increasing tested underH to coverregular the waves maximum (Figure 7). Tests were performed, setting the value of T and increasing H to cover the maximum number of Iribarren numbers (always Ir > 1.5). Water depth was kept constant at h = 0.35 m. Tests number of Iribarren numbers (always Ir>1.5). Water depth was kept constant at h=0.35m. Tests conditions are summarized in Table A1. conditions are summarized in Table 2.

FigureFigure A2. 7.Diagram Diagram of the the wave wave flume ﬂume and and position position of wave of wave gauges gauges (dimensions (dimensions in meters) in meters)in the in the numerical tests IH-2VOF. numerical tests IH-2VOF. Table A1. Summarized test conditions for the numerical model. Table 2. Summarized test conditions for the numerical model. tan(α) H(m) T(s) T (s) h/LH /L Ir tan(α) H(m) T(s) Tz(s) z h/L HI/LI Ir 1:10 1:100.002-0.14 0.002–0.14 1-2.2 1–2.2 0.8-2.190.8–2.19 0.09-0.36 0.09–0.36 0.0008-0.060.0008–0.06 0.45–4.0070.45-4.007

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