floating breakwaters under regular and irregular...

Journal of Hydraulic Research Vol. 43, No. 2 (2005), pp. 174–188

© 2005 International Association of Hydraulic Engineering and Research

Floating breakwaters under regular and irregular wave forcing: reflectionand transmission characteristics

Brise-lames flottants soumis à une houle régulière et irrégulière forcée:caractéristiques de réflexion et de transmissionE. KOUTANDOS, Hydraulics Laboratory, Department of Civil Engineering, Aristotle University of Thessaloniki,54124 Thessaloniki, Greece. Fax: 2310995672; e-mail: [email protected] (author for correspondence)

P. PRINOS, Hydraulics Laboratory, Department of Civil Engineering, Aristotle University of Thessaloniki,54124 Thessaloniki, Greece. E-mail: [email protected]

X. GIRONELLA, Laboratori d’ Enginyeria Maritima, Catalonia University of Technology, LIM-UPC, D1 ETSECCPB,c/Gran Capitan s/n, 08034, Barcelona, Spain. E-mail: [email protected]

ABSTRACTIn the present study the hydrodynamic interaction of regular and irregular waves with floating breakwaters (FBs) in shallow and intermediate watersis examined experimentally in a large-scale facility. The experiments were conducted in the CIEM flume of the Catalonia University of Technology,Barcelona. The influence of incident wave characteristics and certain geometric characteristics, such as the width and the draught of the structure,on its efficiency is examined. Four different FBs configurations are examined: (a) single fixed FB, (b) heave motion FB, (c) single fixed FB withattached front plate (impermeable and permeable) and (d) double fixed FB. Results related to transmission, reflection, and energy dissipation of theincident (regular and irregular) waves on the structure are presented. For the single fixed FB, the efficiency of the structure is proportional to thewidth/wavelength and draught/water depth ratios. The single fixed FB operates in a highly reflective manner. On the other hand, the heave motion FBoperates in a dissipative manner with much lower reflection. The attached plate in the front part of the FB significantly enhances the efficiency of thestructure. No significant differences are observed between the impermeable and the permeable plate cases. Generally, the most efficient configurationhas been the double fixed FB. However, with regard to cost-effectiveness, the configuration of the FB with the attached plate should be considered themost efficient for design purposes.

RÉSUMÉDans la présente étude l’interaction hydrodynamique des vagues régulières et irrégulières avec des brise-lames flottants (FBs) en eaux peu profondeset intermédiaires est examinée expérimentalement dans une installation à grande échelle. Les expériences ont été menées dans le canal de CIEM del’université de technologie de Catalogne, Barcelone. Leur efficacité est examinée en fonction des caractéristiques des vagues incidentes et de certainescaractéristiques géométriques, telles que la largeur et le tirant d’eau de la structure. Quatre configurations différentes de FBs sont examinées: (a) FBsimple fixe, (b) FB en pilonnement, (c) FB simple fixe avec une plaque attachée sur l’avant (imperméable et perméable) et (d) FB double et fixe. Onprésente les résultats liés à la transmission, à la réflexion, et à la dissipation d’énergie de des vagues incidentes (régulières et irrégulières) par la structure.Pour le FB simple fixe, l’efficacité de la structure est proportionnelle aux rapports de largeur/longueur d’onde et tirant d’eau/profondeur d’eau. Le FBfixe simple est fortement réfléchissant. D’autre part, le FB avec mouvement de pilonnement est dissipatif avec un réflexion bien inférieure. La plaqueattachée dans la partie avant du FB augmente de manière significative l’efficacité de la structure. On n’observe pas de différences significatives entreles plaques imperméables et perméables. Généralement, la configuration la plus efficace a été FB double et fixe. Cependant, en ce qui concerne larentabilité, la configuration du FB avec la plaque avant devrait être considéré comme le plus efficace pour les projets.

Keywords: Floating breakwater, transmission, reflection, energy dissipation.

1 Indroduction

In the last decade, environmentally friendly coastal structureshave become of great interest. Floating breakwaters (FBs) belongto this specific category for wave protection and restoration ofsemi-protected coastal regions.

Revision received October 14, 2004 / Open for discussion until November 30, 2005.

174

The main function of an FB is to attenuate wave action. Sucha structure cannot stop all the wave action. The incident wave ispartially transmitted, partially reflected, and partially dissipated.Energy is dissipated due to damping, friction and the generationof eddies at the edges of the breakwater. The breakwater generatesa radiated wave which is propagated in offshore and onshore

FBs under regular and irregular waves 175

directions. The movement of the breakwater is specified in termsof the anchoring, which defines the degrees of freedom of thebreakwater.

The hydrodynamic problem of FBs is extremely complexespecially in the case of a moving structure. There are sev-eral studies dealing with the hydrodynamic problem of FBs indeep and intermediate water depth. Linear models and analyt-ical solutions, which describe the full hydrodynamic problem,have been developed by Hwang and Tang (1986), Williams andMcDougal (1991), Drimer et al. (1992), Bhatta and Rahman(1993), Isaacson and Bhat (1998), Williams et al. (2000) andKriezi et al. (2001). A coupled solution for diffraction and bodymovement is proposed to eliminate the error introduced by thelinear approach of the problem (Isaacson, 1982a; Gottlieb andYim, 1995). A limited number of studies have dealt with theinteraction of the floating body with oblique waves (Isaacsonand Bhat, 1998; Sannasiraj et al., 1998). The current behind thefloating structure has also been studied (Isaacson and Cheung,1993), while overtopping has been studied by Isaacson (1982b).Different models have been studied which calculate the forces onthe mooring system of an FB (Niwinski et al., 1982; Yamamoto,1982; Yamamoto et al., 1982; Nossen et al., 1991; Yeung et al.,1992; Isaacson and Bhat, 1994; Yoon et al., 1994).

However, the experimental studies are rather limited, per-formed in small-scale facilities, and only for regular wave forcing.Sutko and Haden (1974) presented a series of small-scale exper-iments. Fugazza and Natale (1988) studied the phenomenonnumerically and experimentally. They investigated the influenceof the stiffness of the horizontal part of the mooring system.An experimental study of the phenomenon for a breakwater in afloating mode was presented by Williams (1988), in which theefficiency and the response of the structure was studied. Tolba

5720 cm

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Figure 1 Layout of the CIEM flume with the single fixed FB and the instrumentation.

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Figure 2 Layout of the CIEM flume with the double fixed FB and the instrumentation.

(1998) and Isaacson and Bhat (1998) studied experimentallypile-restrained FBs and, in particular, the influence of the heavemotion on the efficiency of the structure. Christian (2000) stud-ied a 1 : 15 scale, prefabricated form of FBs, and investigated theefficiency of the structure and the horizontal forces acting on itin a laboratory model.

In this study the hydrodynamic interaction of regular andirregular waves with FBs in shallow and intermediate waters isexamined experimentally in a large-scale facility. The influenceof the incident wave characteristics and certain geometric char-acteristics, such as the width and the draught of the structure, onits efficiency is examined for four different FBs configurations:(a) single fixed FB, (b) heave motion FB, (c) single fixed FB withattached front (permeable and impermeable) plate and (d) doublefixed FB.

2 Experimental facility and procedure

The experiments were conducted in the CIEM flume of theCatalonia University of Technology, Barcelona. The dimensionsof the flume are 100 m length, 5 m depth and 3 m width. TheFB was placed in the horizontal part of the flume in 2 m waterdepth. The length B of the breakwater was 2 m, the height 1.5 mand the transverse length 2.8 m. An HR Wallingford wedge-type, wave maker was used, while the experimental equipmentconsisted of a number of Wallingford wave gauges, Huba Con-trol pressure transducers, and two-component Delft Hydraulicscurrent meters. In Fig. 1, the layout of the flume and the instru-mentation are shown for the single breakwater test, while thedouble breakwater case is presented in Fig. 2. During the exper-iments, a moving carriage was used for the wave gauges for

176 Koutandos et al.

calculating reflection to maintain the appropriate distances pro-posed by Mansard and Funke (1980) between the three wavegauges and a distance greater than at least a half wavelengthbetween the carriage and the structure. Wave gauges in the lee ofthe structure, used for the estimation of transmission, were alsoplaced at different locations during the experiments to maintainat least half a wavelength from the structure and half wavelengthbetween them. The sampling frequency during the experimentswas 20 Hz.

The experiments were organized into four different sets,according to the configuration of the FB. Four different FB con-figurations were examined: (a) single fixed FB, (b) heave motionFB, (c) single fixed FB with attached front (permeable and imper-meable) plate and (d) double fixed FB. In every set, regular andirregular waves were generated covering a range of shallow andintermediate waters (0.04 < d/L < 0.35, d = waterdepth, L =wavelength). The four configurations are presented in Figs 3–6,respectively.

For the single, fixed FB three different draughts (dr) were used0.4 m, 0.5 m and 0.65 m (dr/d = 1/5, 1/4 and 1/3, respectively).For the regular waves case two different wave heights were used,

Figure 3 The single fixed FB under wave forcing.

Figure 4 The heave motion FB under wave forcing.

0.2 and 0.3 m. The shortest wave period was 2.04 s (B/L = 0.32)for the 0.2 m height and 2.34 s for the 0.3 m height. For the 0.3 mwave height shorter periods were avoided because violent wavebreaking on the structure occurred. In both cases, the longestwave period was 9.17 s (B/L = 0.0445). The irregular waveswere generated according to JONSWAP spectrum, with a shapeparameter γ equal to 3.3. The significant wave height was 0.3 m.Three peak wave periods were used for every draught 2.67 s(B/L = 0.19), 3.16 s (B/L = 0.15) and 5.04 s (B/L = 0.08). Itshould be noted that B/L is equal to d/L (B = d in the experi-ments). Approximately 1200 waves were generated to obtain theappropriate statistical information for the reconstruction of theenergy spectrum.

In the second set of experiments, a heave motion FB wastested. The initial draught of the FB was 0.4 m (dr/d = 1/5). Ironrails were attached to the walls of the flume to restrain horizontaland rotational motion of the structure, while greased pneumaticwheels were attached on the structure to allow unrestrained ver-tical motion with minimum friction (Fig. 4). The weight of thestructure was 2240 kg while the centre of mass was 0.2 m belowthe free surface due to the extra uniform weight put inside the

Figure 5 The fixed FB with the attached porous plate.

Figure 6 The double fixed FB under wave forcing.


breakwater. A position sensor was placed on the structure torecord the vertical motion of the floating breakwater. The testedwave conditions were the same as in the single fixed FB case.

In the third set of experiments, a single fixed FB with anattached metal plate at the front part was tested. Christian (2000)and Tolba (1998) experimentally tested FB with an attached metalplate at the middle of the submerged structure bottom. They con-cluded that the plate improves the efficiency of the structure, butnot as much as in the case of FB with overall draught equal tothat of the metal plate. The observed vortex generation in thefront submerged part for the single fixed breakwater case (Fig. 7)lead to the idea to test the FB with the plate at the front part toreveal the impact of the position of the plate on the FB efficiency.The draught of the FB was 0.2 m (dr/d = 1/10). The height ofthe iron plate was 0.2 m, leading to a local draught of 0.4 m at thefront face of the FB. The tested wave conditions were the sameas in the single fixed FB case.

Also, a single fixed FB with an attached permeable plate (witha porosity of 0.62) at the front part was tested for improving thedissipative characteristics of the plate. The geometric character-istics were the same as the impermeable plate case. Fifty holeswere drilled onto the plate. Each hole had a radius of 4.3 cm,while they were equally spaced in two rows in the plate, result-ing in a porosity of 0.62 (Fig. 5). The tested wave conditions werethe same as in the single fixed FB case.

In the fourth set of experiments, a double fixed FB was tested.The geometric characteristics of the two breakwaters were thesame. In Fig. 2, the layout of the flume with the double break-water is presented. The distance between the two breakwaterswas 9.5 m and their draught was 0.5 m. In Fig. 6, a photographfrom the specific set of experiments is presented. The tested waveconditions were the same as the single fixed FB case.

Wave reflection and transmission were estimated for everycase. The wave reflection analysis is based on the method

Figure 7 Vortex generation in the upstream bottom part of the fixed FB.

proposed by Mansard and Funke (1980). The method is employedusing the signals from wave gauges 3, 4 and 5. Energy dissipa-tion in the region of the breakwaters is also studied using thefollowing equation:

C2t + C2

r + C2d = 1 (1)

where Ct is the transmission coefficient (Ht/Hi), Cr the reflectioncoefficient (Hr/Hi), Cd the energy dissipation coefficient, Ht theheight of the transmitted wave, Hr the height of the reflectedwave, and Hi the height of the incident wave.

3 Dimensional analysis

The efficiency of the FB is expressed through the above-mentioned transmission coefficient Ct . Christian (2000) pre-sented the following equation as a result of dimensional analysisof the phenomenon for an elastically moored FB:

Ct = f(Hi/L, B/L, dr/d, d/Hi, M/γbBdr, I/MB2,

DG/dr, kB/Mg) (2)

where γb = specific weight of the breakwater, g = sea waterspecific weight, M = mass of the breakwater, I = secondmoment of inertia, DG = centre of gravity of the breakwaterfrom underside and k = stiffness of the mooring system.

The ratios of B/L and dr/d for both regular and irregular wavesin the case of the single fixed FB have been shown to be the mostimportant parameters. For the heave motion FB, the influence ofthe motion on the efficiency is examined (Fig. 8). The influenceof a plate and porous plate, offering an increased local draught,is examined in the next two sets of experiments. In the last set,a double FB configuration is tested, to reveal the structural effi-ciency and impact of any resonance phenomena concerning thewater mass between the two structures.

Figure 8 Vortex generation in the upstream bottom part of the heavemotion FB.


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Figure 9 Variation of Cr , Ct , and Cd with B/L for the single fixed FB, regular waves.

4 Analysis of the results

4.1 Single fixed FB

The results for this case are presented in Fig. 9 for regular waves.The influence of B/L (or d/L since B = d in the experiments)

on the performance of the FB is shown. For B/L greaterthan 0.25 the performance of the structure can be consid-ered satisfactory for all dr/d considered since Ct is less than0.5. The FB performs more efficiently under the forcing ofwaves with short periods for intermediate and deep waters(d/L > 0.25).


The effect of dr/d is also shown in this figure. Between thefirst two draughts (dr/d = 1/5 and dr/d = 1/4) there is nonoticeable difference. In the first case (Hi = 0.2 m) the trans-mission coefficient reaches the value of 0.39, while in the second0.35. The difference in transmission is obvious in the third case(dr/d = 1/3) where it reaches a value of 0.25.

The variation of Cd with B/L is also shown in Fig. 9. Inthe first case (dr/d = 1/5), the energy dissipation coefficientincreases with a decrease of wave period indicating an increaseof energy dissipation for short period waves. This phenomenonis mainly observed due to the increasing intensity of oscillatingair–water vortices observed in the front submerged part of thebreakwater, with decreasing wave length (Fig. 7). This indicatesthat numerical models should correctly account for the strongvortices occurring in the front part of structure rather than thosebehind the structure (Kriezi et al., 2001). The latter vortices werenot observed in the experiments indicating their very limitedstrength. For the longest period and Hi = 0.3 m, Cd reachesa value of 0.2 while for the shortest period a value of 0.4. Inthe second case (dr/d = 1/4), the coefficient tends to becomeconstant with an increasing trend from 0.3 to 0.4. Finally, forthe third draught (dr/d = 1/3), the energy dissipation coefficientis almost constant around a mean value of 0.45. This is due tothe steadiness of the vortices in the region of the FB and the factthat an FB with deeper draught performs more efficiently in areflective manner. The reflection coefficient in all cases is highwith values of 0.4 for the longest wave period and up to 0.9 forthe shortest wave period. This indicates that a fixed FB performsin a rather reflective manner, especially with deeper draught.

For irregular waves, Fig. 10 shows that the trend in the trans-mission and reflection coefficients is similar with that of theregular wave experiments for the corresponding values of B/L

and dr/d. However, there is a remarkable difference in the energydissipation coefficient. The coefficient presents an increasingtrend reaching a value of 0.65, while in the corresponding casefor regular waves, the value is less than 0.5. This phenomenonreveals the influence of chaotic processes occurring during thepropagation, reflection, and transmission of irregular waves.

4.2 Heave motion FB

For this configuration the results for regular waves are presentedin Fig. 11 together with the ones for the single fixed FB casefor comparison purposes. In Fig. 11 the effect of B/L (d/L)on the performance of the FB is presented. For B/L greater than0.275, the performance of the heave motion FB can be consideredsatisfactory since Ct is less than 0.5. The heave motion FB alsoperforms efficiently under the forcing of short period waves inintermediate and deep waters (d/L > 0.275). The transmissioncoefficient reaches the values of 0.41 and 0.46 for the 0.2 and0.3 m wave height, respectively.

The energy dissipation coefficient increases with decreasingwave period, revealing the increase of energy dissipation in shortperiod waves. Again this is due to the increasing vortex inten-sity, observed in the front submerged part of the breakwater,with decreasing wavelength (Fig. 8). The Cd reaches values

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Figure 10 Variation of Cr , Ct and Cd with B/L for the single fixed FB,irregular waves.

of 0.45–0.5 and 0.85–0.90 for the longest and shortest period,respectively. This is mainly due to the fact that for shorter periodwaves, the FB moves vertically out of phase with the standingwave formed in front of the structure, while in longer period


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Figure 11 Effect of heave on Cr , Ct , and Cd for regular waves.

waves the structure moves in phase with the standing wave. Theout of phase vertical motion of the structure creates stronger vor-tices and therefore more energy dissipation. This difference inthe phase angle between the vertical motion of the FB and the

standing wave formed in front of the structure was observed byTolba (1998) using video analysis. The reflection coefficient inall cases is less than 0.3 mainly due to the high energy dis-sipation. The high energy dissipation and low reflection for


the heave motion FB indicates that it performs in a dissipativemanner.

The comparison of the fixed and the heave motion FB reveals avery basic difference in the structure hydrodynamics. The heavemotion FB performs in a dissipative manner, contrary to the fixedbreakwater which performs in a reflective manner. Althoughthe transmission coefficient is almost the same for both con-figurations, with the fixed breakwater showing a slightly betterperformance, the reflection and dissipation coefficients presenttotally different trends due to the high energy dissipation in thecase of the heave motion FB.

Similar conclusions can be derived from Fig. 12 for irregularwaves. The trend in the transmission coefficient is the same. Thereis a remarkable difference though in reflection and energy dissi-pation. The increased energy dissipation in the case of the heavemotion FB leads to decreased reflection. Comparing values of Cd

for regular and irregular waves in the case of the heave motionFB (Figs 11 and 12), energy dissipation is higher for irregularwaves and B/L less than 0.1 with a value of the correspondingcoefficient approximately equal to 0.7.

4.3 Fixed FB with attached (permeable or impermeable)front plate

The experimental results for fixed FB with attached front platefor both regular and irregular waves are presented in Figs 13–15.In Fig. 13, experimental results of Ct , Cr and Cd for the FB withthe attached impermeable plate are compared with the ones forthe corresponding single fixed FB with the same overall draught(dr/d = 1/4). The FB with the attached front plate performs asefficiently as the single fixed FB with the same overall draught.Similar conclusions can be derived for irregular waves (Fig. 15,left column). This configuration, the FB with the attached frontplate, achieves more efficient hydrodynamic performance thanthat examined by Tolba (1998) and Christian (2000) with anattached plate in the middle part of the structure keel. This isdue to the fact that generation of energy and turbulent eddiesoccur in the front part of the structure, and hence a mechanism,like an attached plate for dissipating energy in this region, ismore effective than a similar mechanism in another part of thestructure (middle or end region). Furthermore, the proposed con-figuration provides more dissipation since reflection is lower anddissipation higher. This is mainly due to the increased local turbu-lence developed behind the plate as confirmed by video analysisperformed by the authors.

The results of an attempt to increase energy dissipation bymaking the plate permeable are presented in Fig. 14. The com-parison of the results for the impermeable and permeable plates,reveals that the efficiency of the structure is not enhanced and thelocal turbulence is not intensified by the porosity. On the contrary,although the transmission is almost the same, energy dissipationis lower in the case of the porous plate revealing that the rather bigvoids in the attached plate and its small thickness contribute posi-tively to the transmission of wave energy. However, it is believedthat the structure will operate more efficiently in the case of a per-meable plate if the porosity is reduced and the length is increased.

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Figure 12 Effect of heave on Cr , Ct , and Cd for irregular waves.

The last two parameters contribute significantly in the dissipationof energy and will be considered systematically in a subsequentstudy.

For irregular waves, however (Fig. 15), the energy dissipa-tion for the porous plate case is shown to be higher than that


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Figure 13 Effect of attached impermeable plate on Cr , Ct , and Cd for regular waves.


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0.9

1

Cr

Hi=0.2 m

porous plateplate

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35B/L

0

0.1

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0.3

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Ct

Hi=0.2 m

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35B/L

0

0.1

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Cd

Hi=0.2 m

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35B/L

0

0.1

0.2

0.3

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1

Cr

Hi=0.3 m

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35B/L

0

0.1

0.2

0.3

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0.5

0.6

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0.8

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1

Ct

Hi=0.3 m

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35B/L

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cd

Hi=0.3 m

porous plateplate

Figure 14 Effect of plate porosity on Cr , Ct , and Cd for regular waves

of the impermeable plate. This confirms again the existence ofchaotic processes in the irregular waves case. On the contrary,transmission and reflection present the same trends for the twoconfigurations. For stability purposes, a second plate should also

be attached at the back face of the structure. For design pur-poses, it is also essential that the FB should have a significantoverall draught and the height of the plate should not exceed, atmaximum, half the overall draught.


0 0.05 0.1 0.15 0.2 0.25B/L

0

0.1

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0.3

0.4

0.5

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0.9

1

Cr

0 0.05 0.1 0.15 0.2 0.25B/L

0

0.1

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1

Ct

0 0.05 0.1 0.15 0.2 0.25B/L

0

0.1

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0.8

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1

Cd

Irregular waves platefixed FB dr/d=1/4

0 0.05 0.1 0.15 0.2 0.25

B/L

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

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1

Cr

0 0.05 0.1 0.15 0.2 0.25B/L

0

0.1

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Ct

0 0.05 0.1 0.15 0.2 0.25B/L

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cd

porous plateplateIrregular waves

Figure 15 Effect of plate and its porosity on Cr , Ct , and Cd for irregular waves.

4.4 Double fixed FB

In Figs 16 and 17 the experimental results of Ct , Cr and Cd

for the double fixed FB are presented. The influence of S/L

(S = the spacing between the two FBs) on the performance of

the double FB is shown. The transmission coefficient decreaseswith an increase of S/L from 0.2 to 1.4, where a resonance pointis observed after which the transmission coefficient increases forboth wave heights. The resonance of the water masses between


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6S/L

0

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1

Cr

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6S/L

0

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1

Ct

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6S/L

0

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0.2

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1

Cd

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6S/L

0

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1

Cr

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6S/L

0

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1

Ct

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6S/L

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cd

Hi=0.2 m

Hi=0.2 m

Hi=0.2 m

Hi=0.3 m

Hi=0.3 m

Hi=0.3 m

Figure 16 Variation of Cr , Ct , and Cd with S/L for double FB, regular waves.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35B/L

0

0.1

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0.3

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Cr

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35B/L

0

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Ct

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35B/L

0

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Cd

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35B/L

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Cr

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35B/L

0

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1C

t

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35B/L

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Cd

Hi=0.2 m

Hi=0.2 m

Hi=0.2 m

Hi=0.3 m

Hi=0.3 m

Hi=0.3 m

Double breakwaterSingle breakwater

Figure 17 Effect of configuration on Cr , Ct , and Cd for regular waves.


the two breakwaters seems to be an important parameter in theefficiency of the specific configuration and a wider range, interms of wave period, of experimental tests would reveal moreresonance points.

In Fig. 17 the comparison of the single and double FB indicatesthat the latter configuration is generally much more efficient.The double FB configuration presents the lowest transmissioncoefficient, Ct = 0.12, for B/L equal to approximately 0.3.Reflection and dissipation are generally higher for the double FBcase.

The energy dissipation in this specific configuration can beattributed to three mechanisms according to the region that thedissipation occurs: (a) in the region of the first FB, (b) in the regionbetween the two FBs and (c) in the region of the second FB.Videoanalysis reveals that in regions (a) and (c) energy dissipationis mainly due to the existence of vortices formed in the frontsubmerged part of the structures, while in region (b) it is due towave breaking resulting from the interaction of various wavespropagating in opposite directions. However, from a practicalviewpoint, the basic disadvantage of the double FB configurationis its increased cost.

5 Conclusions

In the present study, the hydrodynamic interaction of regularand irregular waves with FBs in shallow and intermediate watershas been examined experimentally in a large-scale facility. Theinfluence of the incident wave characteristics and certain geo-metric characteristics of the structure on its efficiency have beenexamined. Four different FBs configurations are examined: (a)single fixed FB, (b) heave motion FB, (c) single fixed FB withattached front plate (impermeable and permeable) and (d) dou-ble fixed FB. Results related to transmission, reflection, andenergy dissipation of the incident (regular and irregular) waveson the structure are presented. The following conclusions can bederived:

1. For the single fixed FB the efficiency of the structure can beconsidered satisfactory for B/L greater than 0.25 and dr/dranging between 1/5 to 1/3.

2. The single fixed FB operates in a highly reflective mannerwith values of the reflection coefficient ranging between 0.4(longest wave period) and 0.9 (shortest wave period).

3. Energy dissipation is due to strong oscillating, air–water vor-tices occurring in the front (upstream) part of the structure.Higher energy dissipation is observed in the case of irregularwaves.

4. The heave motion FB operates in a dissipative manner, withmuch lower reflection than that of the single fixed FB. TheCd coefficient ranges between 0.45 and 0.9 for long and shortperiod waves, respectively.

5. The attached plate at the front part of the FB considerablyenhances the efficiency of the structure.

6. No significant differences are observed between the imper-meable and the permeable (with porosity 0.62 and smallthickness) plate cases.

7. The most efficient configuration is found to be the double FB,with transmission coefficient values as low as 0.12 and B/L

equal to 0.3.8. In terms of cost-effectiveness, the configuration of the FB with

the attached front plate should be considered the most efficientfor design.

Acknowledgments

The authors acknowledge the financial support of EU throughthe program “Improving the Human Research Potential-LargeScale Infrastructure”, provided to the first two authors for con-ducting experiments at LIM/UPC. Also, the authors would liketo thank the technical personnel of LIM/UPC for the assistanceand hospitality during the period of the experiments.

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