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Experimental study of the working principal and efficiency of a superposed inclined planes wave absorber
Ocean Engineering 29 (2002) 1427–1440 www.elsevier.com/locate/oceaneng
Technical Note
Experimental study of the working principal and efficiency of a superposed inclined planes wave absorber M. Lebey *, E. Rivoalen Laboratoire de Me´canique, Universite´ du Havre, BP 540, 76058 Le Havre Cedex, France Received 7 March 2001; accepted 20 June 2001
Abstract The swell reflection leads to problems in full scale conditions, shipping near seawalls and inside harbors, and for experiments in basins or channels, as well. Consequently, many studies were carried out to define wave absorbers with best efficiency. In this paper, the three main working principals of the wave absorbers, breaking waves, viscous dissipation resonating mechanism, are detailed to see how it is possible to enhance the efficiency. Through this analysis, a wave absorber made up of several superposed inclined planes in front of a wall is defined and its working principal is explained. Through experiments, it is shown that in spite of its short size its efficiency is one of the best compared to the more classical wave absorbers. Moreover, this superposed inclined planes wave absorber presents two main advantages: its short size and the possibility to be adjusted to the swell caracteristics, which make it interesting to be used in real scale and in laboratory environment, as well. 2002 Published by Elsevier Science Ltd. Keywords: Wave absorber; Wave breaking; Swell dissipation; Wave reflection; Seawall; Harbor; Shipping; Bank protection
1. Introduction The problems due to the swell reflection on sea wall remain important especially inside harbors and coast shipping. The wave reflection problem leads to the same * Corresponding author. Tel.: +33-2-32-74-43-72; fax: +33-2-32-74-43-14. E-mail address: [email protected] (M. Lebey). 0029-8018/02/$ - see front matter 2002 Published by Elsevier Science Ltd. PII: S 0 0 2 9 - 8 0 1 8 ( 0 1 ) 0 0 0 8 9 - 0
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difficulties in experimental channels or basins. The incident swell or wave produced by a model must be completely dissipated in experimental channels or basins because of the necessary quality of the tests. Many wave absorber types exist and some of them can be used in full scale conditions or in test basins, as well. The wave absorbers can be divided into two categories: i) wave absorbing beaches and ii) caissons. Wave absorbing beaches have the advantage of simple design and being very efficient for a large scale of swells. But important sizes make them impossible to use in harbors, and using them in laboratory sets requires large space especially in test basins. Consequently, they can only be used easily in wave flumes under the condition of a large increase in length. To overcome this problem of too important sizes, two main solutions are used: 1. Transform the simple wave absorbing beach design into constructions increasing the wave breaking phenomenon or the viscous dissipation process of the swell energy. 2. Use more recent constructions which are caisson type solutions designed to create an important dissipation of the swell energy under the effect of viscous phenomena and of mechanism of resonance. Although these constructions involve strong structures, they have the advantage of requiring shorter sizes. The main working principle of the wave absorbing beaches is the effect of breaking waves on a plane of weak slope and of important length, which induces the complete dissipation of the swell energy, and makes the wave reflection impossible. As shown in the Ouellet and Datta (1987) review, many solutions have been designed to decrease the size of the wave absorbing beaches. Beaches made of several successive planes of different slopes have been used. San et al. (1982) have shown that the efficiency is better when the absorbing beaches are made of parabolic profile surfaces, the concavity of which is turned upwards, than when they are made of simple planes. Constructions associating the slope of absorbing beaches and porous walls, such as the one used by Tremblay (1970), increase the efficiency and also reduce the size. More complex constructions, associating a porous wall with inclined planes and recirculation chambers, such as the device proposed by Hedar (1956), are also of good efficiency. Perfecting wave absorbing constructions have shown that the association of several swell absorbing energy effects leads to an important reduction of the construction sizes. More recent wave absorber designs, such as caissons, give the same efficiency. The main advantage of these solutions is their very short length compared with the wave absorbing beach length. It nevertheless involves a stronger and consequently more expensive construction. Two types of wave absorbing caissons are especially worthy of mention: the arc model and the Jarlan model, the efficiency of which was studied by Lebey and Rivoalen (1989). The arc model consists of rectangular and vertical apertures which represent a third or a quarter of the sea wall front surface. Each aperture communicates with an internal vertical chamber, the width of which is equal to the distance between two successive apertures. The distance between the
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front wall and the back wall is about the fifth of the wave length. The efficiency of this kind of construction is about 90%. Although it is interesting to use these constructions in real situations, they cannot be used easily in laboratory flumes because their optimum efficiency is included in a short range of wave frequencies. The second type of wave absorbers is the Jarlan caisson type, the construction of which has been getting more and more simple for several years. Originally, they comprised a dissipation energy chamber behind a front wall in which there were several cylindrical holes regularly spaced. The distance between the front and back walls was about an eighth of the wave length. The dissipation energy chamber was divided in several parts separated by vertical walls in which there were also several cylindrical holes regularly spaced. Through analysis it was shown that the internal vertical walls did not increase the efficiency. Therefore, these walls are not used any more and this type of caisson is now only made of one dissipation energy chamber behind a front wall with cylindrical holes regularly spaced. The researches carried on to increase the efficicency of wave absorbers lead to the analysis of the absorbing energy phenomena of the swell which makes the swell reflection impossible. In the wave absorbing beaches, the transformation of the wave energy into turbulence is produced by the breaking wave on a long size plane of weak slope, the turbulence is finally dissipated under the effect of viscosity. In the wave absorbers designed in modifying the wave absorbing beaches, the transformation of swell energy into turbulence is produced through porous planes whose slope is greater than the slope of the simple wave absorbing beaches. In this kind of wave absorber, devices are used to return back the residual wave motion by a fluid flow on bottom towards the incident swell. In the wave absorbing caissons, the transformation of the swell energy into turbulence has also an important part in the swell dissipation phenomena. This transformation is produced through holes in a front wall in the Jarlan caisson, or by the narrowness of the front apertures in the arc caisson. In the wave absorbing caissons, especialy in the Jarlan caisson, another phenomenon has an important part in the swell dissipation energy mechanism, this is the mechanism of resonance. The studies which aim to improve wave absorbing structures with simultaneously lower sizes and greater efficiency seem to require the combination of at least three of the phenomena which contribute to the wave dissipation in the wave absorbers: i) wave breaking, ii) turbulence, iii) mechanism of resonance. The aim of this study is to present a method of wave absorption which requires lower sizes while the efficiency level remains very high. The corresponding system combines the three wave absorbing mechanism. This proposed structure, named Superposed Inclined Planes Wave Absorber (SIPWA), is described in the next section. The experimental set-up and the measurement methods, the experiental results and the working analysis of this device are detailed in Sections 2 and 3. The final results and a comparison with other wave absorbers are presented in Section 4. The concluding remarks are given in Section 5.
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2. The superposed inclined planes wave absorber and experimental details As shown on Fig. 1 the proposed system is made of three main parts: 1) several superposed parallel and inclined planes, 2) a vertical back-wall and 3) a confining chamber between planes and back-wall. The superposed inclined planes are of the same sizes, thickness Th and the same length L, with a space S between two planes. These planes are inclined towards the confining chamber so that their incident angle a with respect to the incident swell direction is positive. The planes are lined up on the same vertical line. The number of planes depends on the S space, on the thickness Th and on the space H0 between the bottom and the lower plane. This number of planes is chosen so that the total system height is always upper than the maximum water height. In the studied system, the vertical back-wall is smooth. There is not any device in this confining chamber. The main parameter of this system is its global size Gs given by the following relation: Gs ⫽ L cos a ⫹ D Its height is given by the relation: H ⫽ H0 ⫹ n Th sin a ⫹ (n⫺1) S sin a The varying parameters in this experiment are: a, the slope angle between the planes and the horizontal, which is also the incidence of the planes with respect to the swell direction; S, the space between two planes; L, the plane length; D, the space between the planes and the wall. The experiments were carried on in a wave flume of 30 cm×30 cm section and 3 m long. The water height is 14.5 cm. The incident swell was monochromatic. A
Fig. 1. Setting-up and details of the superposed inclined planes wave absorber. D, space between the confining chamber and the back-wall; Gs, global size; e, space between two planes; L, plane length; a, incidence angle of the plane against the incident swell direction.
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frequency variator was used to adjust the frequency swell for every test. The experiments are analyzed in two ways: visualizations and reflection coefficient measures. The working principle has been detailed through visualizations and the efficiency of each kind of configuration was given by the reflection coefficient measures. Two kinds of visualization were used: the first one with rilsan particles, of density 1.06 and size 0.05 mm, in water. The second visualization was the injection of dye through holes located on each end of a profile. The flow motions in every part of this wave absorber are seen by the observation of the rilsan particle motions. The creation, evolution and destruction phenomena are seen by the dye injection, which shows the viscous dissipating process of a part of the swell energy. Each configuration was recorded on a video tape during 20 s. The swell reflection coefficient is computed using a Doppler method created by Brossard and Hemon (1995).
3. Experimental results Tests were carried on to establish the optimum configuration of this superposed and inclined planes wave absorber (SIPWA) and to determine the effects of its main parameters—the angle a, and the distance D between the planes and the back-wall. The angle a corresponding to the optimum configuration gives the lower reflection coefficient value with the smallest size, i.e. with the smallest distance D. The tests were grouped in series which are characterized by a constant value of the angle a, so that in each series the reflection coefficient R (%) was determined as a function of the distance D, i.e. as a function of the wave absorber size Gs. This optimum configuration in these test conditions is given by the analysis of all of these functions. The first step of this analyis concerns the effect of the plane incidence, and particularly the comparison between the wave absorber efficiency in the case of positive incidence angles and in the case of negative incidence angles. Fig. 2 shows results corresponding to a values of ⫺30°, ⫺10°, 0°, +20°, +30°, and +40°. On this figure we can see that the curves are divided into two groups. The first group for which the reflection coefficient value is greater than 30% corresponds to negative values of a. The second group represents the case with positive a angle values. For each curve, the reflection coefficient varies between 4% and 40%. As can be seen, the lowest reflection coefficient values are always reached with positive values of the incident angle a of the planes with respect to the incident swell direction. The best efficiency, 4%, is obtained with an a value of 20°. As is shown in the next section, this result is mainly due to the fact that in the case of negative incidence of the planes, i.e. a⬍0, there is not any eddy creation and there is not any resonating effect. The planes have then no effect on the swell which is consequently completely reflected on the back-wall. In the next section this wave absorber working principle is detailed, and it is explained why the efficiency is clearly greater when the plane incidence is positive. The effect of the space size S between the planes is shown on Figs. 3a–d. As in the previous analysis, the curves show the reflection coefficient R as a function of
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Fig. 2. Comparison of the efficiency for positive and negative incidence of the planes for the SIPWA. The lower the reflection coefficient the better the efficiency. We can see that the efficiency is better when the incidence of the planes is positive.
Fig. 3. The reflection coefficient R (%) vs. the incidence angle a and vs. the distance D between the back-wall and the planes. The space sizes S between planes are: (a) 15 mm, (b) 25 mm, (c) 35 mm and (d) 45 mm.
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the distance D between the back-wall and the planes. Each figure corresponds to a specific space size S between the planes (15 mm, 25 mm, 35 mm, and 45 mm). The variation of the reflection coefficient is studied for each space size as a function of the incidence angle a. We can see that the best efficiency, which is 3.5%, is obtained with an incidence a angle of 35°, with a space size of 25 mm between the planes and with a distance D of 33 mm between the back-wall and all the planes, i.e. a global size Gs of 80 mm. A nearly equivalent efficiency, Rc ⫽ 5%, is obtained with the following conditions: a space size S between planes of 35 mm, a lower distance D between planes and back-wall of 29 mm, and a higher incidence angle of 35°, such that the global size, Gs, is smaller, only 70 mm. For a space size S between planes of 45 mm, the reflection coefficient increases with the distance D between the planes and the back-wall and the smallest values are superior to 15%. For a smaller value of the space size S between planes, 15 mm, the minima of the reflection coefficient values are also greater, superior to 12%. In general, it can be seen that the curves are closer to each other for space sizes S between planes which give the smallest reflection coefficient values, i.e. 25 and 35 mm. All these tests were carried out with a plane length of 50 mm. Other tests were carried out in the same conditions but with two other plane lengths, a lower one of 30 mm and an upper one of 70 mm. These tests have shown that the best efficiencies with the lowest sizes are clearly obtained with a plane length of 50 mm which was consequently chosen in all this study. The main conclusions of this analysis show that firstly the optimal space size between planes is 25 mm in the present test conditions, and secondly that in the aim to obtain the best efficiencies with the smallest global length there is a relation between: 1) the space size S between planes, 2) the incidence angle a of the planes, 3) the distance D between the back-wall and the planes, and 4) the plane length L. The existence of this relation points out the capability of this wave absorber to be adjusted according to the conditions of utilization. The comparison between the efficiency of SIPWA and the efficiency of the Jarlan caisson is shown on Fig. 4. The comparison tests were carried out in the same conditions as the previous tests and the results are analyzed through the same method.
Fig. 4.
Comparison of the reflection coeficient of Jarlan caisson and of the SIPWA.
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On this figure, the curves show the reflection coefficient R as a function of the global size Gs of each wave absorber. For the Jarlan caisson, only the curve which represents the best efficiency with the smallest global size is shown, i.e. 4.6% with Gs ⫽ 100 mm. For the SIPWA two curves are shown on this figure: i) one shows the best efficiency conditions with a global size smaller than the best Jarlan one, i.e. R ⫽ 3.5% with Gs ⫽ 80 mm compared to R ⫽ 4.6% with Gs ⫽ 100 mm for the Jarlan caisson, ii) the other one shows an efficency of the SIPWA just a little higher than the best Jarlan one, 5.1% compared to 4.6%, but with a more smaller global size Gs of only 70 mm. It is clearly shown on Fig. 4 that the best efficiency, 4.6%, of the Jarlan caisson is obtained with a global size of 100 mm when the best efficiency of the presented wave absorber, 3.5%, is obtained with a global size Gs of only 80 mm which is a lower value of 20%. This comparison shows that the SIPWA involves a lower global size to give a similar efficiency.
4. Working principle of the superposed planes wave absorber To explain the working principle of the SIPWA, it should be interesting to analyze separately the reflection phenomena of each part which constitutes this system. These two main parts are: 1) the back-wall and 2) all the superposed planes. It is obvious that the reflection coefficient of the back-wall is equal to 100% whatever the swell is because this back-wall is a plane positioned in a perpendicular direction with respect to the incidence direction of the swell. The phenomena acting on the superposed planes are completely different. Fig. 5 shows the variation of the reflection cefficient of all the superposed inclined planes without the back-wall. In this case the space size S between the planes is 25 mm. The incidence angle varies between
Fig. 5. Reflection coefficient versus negative and positive incidence angles a of the superposed planes without back-wall. The reflection coefficient is higher than in the case of the entirely SIPWA, i.e. the efficiency is clearly lower for the negative angle.
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⫺40° and +30°. This figure shows that the minimum values of the reflection coefficient correspond to the positive values of the incidence angle a, and increase when these values become negative. As was shown in a previous section, in the case of the SIPWA, these results are opposite, the best efficiency is obtained with positive values of the incidence angle a of the planes. This analysis shows that the working explanation of the SIPWA is impossible through the only analysis of each part, separately, on one side the back-wall and on the other side all the superposed planes. The analysis of the whole construction is necessary to explain the SIPWA working. As will be shown in this section, the working principle of this wave absorber is based on three phenomena: 1) the viscous dissipation of the swell energy, 2) the wave breaking, and 3) the mechanism of resonance. These three main phenomena will be shown and detailed through visualizations: 1) a fluid motion between two planes and a fluid motion around all the planes, 2) the formation and breaking up of eddies, and 3) a difference of water level between outside and the confining chamber. As shown through vizualisations, there is a fluid motion around all the planes whatever the slope of the planes. Nevertheless, this fluid motion is more important when the efficiency of the SIPWA is the highest. As shown on Fig. 6, this fluid motion is created when the wave crest arrives towards the SIPWA and when the local velocity of the fluid to the SIPWA is the highest. In this case, a downward fluid motion is furthered by the slope of the planes in the confining chamber, and so an upward flow is created on the front part of the SIPWA. A fluid motion is consequently created around all the planes by this internal downward fluid motion and this external upward flow. This flow around all the planes has an alternate component due to the effect of the swell, and so its intensity is higher when the wave crest arrives on the SIPWA. The intensity of this flow has a highest value for a specific slope of the planes which is always positive. When the slope of the planes decreases the intensity becomes low and is close to zero when the slope of the planes is highly negative. In this case there is only an alternate velocity component of the fluid motion along each plane, so that there is neither breaking wave effect nor viscosity dissipation. The eddies formation is produced under the effect of the swell on each plane. This effect is similar to the effect created on the leading edge of a plane located
Fig. 6.
Fluid motion around all the planes.
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with an important incidence angle in a steady state flow (Fig. 7a). There are two cases in the SIPWA due to the cyclical velocity in the waves: i) the wave crest action, ii) the trough wave action. As shown on Fig. 7b, in the wave crest action the direction of the local fluid flow and the direction of the incident swell are the same, that is towards the SIPWA, so that the leading edge of the planes is on the external side of the SIPWA. In that conditions, the eddies are formed on the external end of each plane and are immediately dragged in the space between the plane on which they are formed and the upper plane. When the local flow is inverted due to the wave trough arrival, the eddies are dragged out into the external side of the SIPWA where they are broken up. As shown on Fig. 7c, in the wave trough action this is a similar mechanism but with a difference because in that case the local fluid flow is in the opposite direction of the incident swell, that is bakwards from the SIPWA, so that the leading edge of the planes are on the internal side of the confining chamber. In that condition, the eddies are formed on the internal end of the planes and are immediately dragged in the space between the plane where they were formed and the lower plane. And when
Fig. 7. Eddy formation on the the leading edge of a hydrofoil under a large incidence angle in a uniform flow. (b) Eddy formation on the leading edge of the planes when the wave crest arrives on the SIPWA. (c) Eddy formation on the trailing edge of the planes when the wave trough arrives on the SIPWA.
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the local flow is inverted due to the crest arrival, the eddies are dragged out into the confining chamber where they are broken up and so transformed into turbulence. These two mechanisms created by the crest and the trough of each wave transformed a part of the swell energy into turbulence because just after being dragged out of the space between planes, the eddies are broken by the flow around all the planes. This is the phenomenon through which the viscous dissipation of the swell energy is produced by the SIPWA. As shown in the previous section, the magnitude of this phenomenon has a maximum value for a specific incidence angle of the planes. In the exemple used in this study the optimum value, corresponding to the best efficiency of the SIPWA, is about 27°. For other values, the magnitude of this dissipation energy phenomenon decreases and consequently the efficiency of the SIPWA simultaneously decreases. This clearly shows the significance of the dissipation energy phenomenon through formation and breaking up of eddies in that kind of wave absorber. The free surface motion inside the confining chamber revels another mechanism: the mechanism of resonance, the consequence of which is the annihilation of a part of the swell when the incidence angle a is positive. As is shown on Fig. 8a, when the wave crest arrives on the SIPWA, the level inside the confining chamber increases with a delay due to the planes’ positive incidence, and then when the wave trough arrives on the SIPWA, this planes’ positive incidence creates a downward fluid motion inside the confining chamber. As is shown above, this downward flow produces a fluid motion around all the planes, especially an upward fluid motion on the external side of the SIPWA, the effect of which is the compensation of the decreasing water level due to the wave trough arrival. The SIPWA works as an energy accumulator when the wave crest arrives: the wave energy is retained in the confining
Fig. 8. Water level in the confining chamber as a function of the incidence: (a) positive incidence, there is a phase difference between the water level inside and outside; (b) negative incidence, the phase difference of the water level is weak.
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chamber as potential energy under the effect of the level increasing of the free surface. When the wave trough arrives on the SIPWA, this potential energy is restored into fluid motion around all the planes. The effect of the downward motion inside the confining chamber is in this way the compensation of the decreasing level when the wave trough arrives on the external side. The effect of these phenomena is to break up the swell structure, so that no reflective wave can be produced. Consequently the reflection coefficient is weak and the efficiency becomes great. Whole of this effect is similar to the mechanism of resonance in which the frequency remains the same, the swell frequency, but in which the phase-shift is controlled by the effect of the level difference between the internal and external sides of all the planes. On the other hand, as shown on Fig. 8b in the case of planes’ negative incidence, the motion of the free surface is the same inside the confining chamber and in the external side of the SIPWA. When the wave crest arrives on the external side, the water level inside the confining chamber increases simultaneously. There is no phase difference between the water level inside and outside. In the same way, when the wave trough arrives on the external side the level inside the confining chamber decreases in the same time. The planes have no effect on the swell. The reflection coefficient values are great, the SIPWA has no efficiency and its effect is nearly the same as a vertical wall. The SIPWA efficiency depends on the planes’ incidence, and we have shown there is a specific value for which the efficiency is maximal. When its efficiency is at its maximum, the effect of the swell kinetic energy is nullified under the effect of three main mechanisms: 1) viscous dissipation and 2) breaking of the waves which are two complementary mechanisms created by the formation and breaking of eddies. The third mechanism is the mechanism of resonance due to the water level difference created by the superposed planes between outside and the confining chamber, these two levels canceling each other out.
5. Discussion and concluding remarks The main physical phenomena which produce the absorption of swell, were analyzed in this paper in the aim to show that their complementary effect leads to design constructions of best efficiency with shorter size. These phenomena, turbulence and reasonance mechanisms, lead to complete wave breaking when they are optimized simultaneously. Using a superposition of several identical planes, the incidence angle of which is positive with the swell direction and located in front of a vertical wall, allows the creation of three mechanisms which produce the swell energy dissipation: i) viscous dissipation, ii) breaking wave and iii) the resonating mechanism. The viscous dissipation is always a mechanism acting in the wave absorbers as in beaches of constant slope, in wire mesh or aluminum screen sheet absorber presented by Keulegan (1973), and also in the structure created by Le Me´ haute´ (1972) which is made of chicken wire cells. In the case of the SIPWA, this mechanism is associated with the
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eddies breaking since the eddies formed by the action of the waves on the inclined planes are immediately broken and transformed into turbulence which produced viscous dissipation. The resonance mechanism is the third effect produced by the inclined planes. This mechanism is not quite different from the process acting in Kamphuis (1984) structure which is made of a superposition of horizontal planes, or in Jarlan structure which is made of only a vertical wall with holes regularly spaced and located in front of a vertical wall. This mechanism also contributes to the viscous dissipation since it creates a flow around all the planes, the effect of which is to enhance the eddies breaking and consequentely the viscous dissipation. The water flow around all the planes is similar to the one created in the Hedar system. But in this case the fluid motion is controlled by a gate located in the lower part. This gate allows fluid motion from the internal to the external part but prevents it in the opposite direction. This structure also includes inclined planes regularly spaced but in a horizontal direction. The incidence of these planes is highly negative. This device involves much more important sizes. The effect on the efficiency of the roughness of planes and of the back-wall was not studied. However, because of the system configuration and of the working principle it could be thought that the roughness would be a weak effect. Ouellet and Datta (1987) came to the same conclusion when they remarked that the increase in efficiency is only about 2% in the case of sets in which the roughness is much more important. One of the main characteristics of the SIPWA is the function of the planes which allowed us to produce simultaneously three mechanisms which lead to the nearly complete dissipation of the swell energy with the shortest sizes. With this specific caracteristic, the SIPWA is mainly different to other caisson wave absorbers, such as Jarlan caisson or arc caisson because its size does not depend on incident swell characteristics to obtained the best efficiency, but it depends i) on the planes’ length, ii) on the confining chamber size, and iii) on the planes’ incidence which is easily adjustable. This characteristic makes the SIPWA easy to use in an experimental setup, such as basins, wave flumes, etc. It is not dificult to built such a set in which the planes’ incidence is adjustable to the swell characteristics of the experiments. One of the main advantages of this system is the possibility of changing easily the planes’ incidence and consequently to adjust its characteristics to the incident swell in order to get the best efficiency. Then it becomes very interesting to use it especially in experimental basins or channels. In full scale conditions, the SIPWA gives a solution to two different problems: i) the swell absorption on a sea wall, ii) absorption of the stem waves in harbors and canals to protect banks. In the first case, the structure height must be equal to the seawall height. In that condition, the flow around the planes produces a great undermining at the bottom of the seawall which makes necessary the protection of the bottom. In the second case, when used to protect internal sides in harbors and banks in canals, the SIPWA height will be equal to the maximum stem waves height in order to restrain them.
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References Brossard, J., Hemon, A., 1995. Analyse spectrale par effet Doppler de la propagation de la houle. C.R. Acad. Sci., Paris, Se´ r. IIb 230, 171–176. Hedar, P.A., 1956. Essais effectue´ s sur un amortisseur de houle en mode`le re´ duit. La Houille Blanche 2, 748–752. Kamphuis, J.W., 1984. Evaluation of tapered slab wave absorber (phase II). Queen’s University Kingston, Ontario, Canada, 37 pp. Keulegan, G.H., 1973. Reflection on screen wave absorber. U.S. Army Engineering Water-ways Experiments Station, Research Report H-73-3, 56 pp. Lebey, M.M., Rivoalen, E., 1989. Etude sur maquette des caracte´ ristiques du caisson Jarlan. Internal report, Unpublished report, Laboratoire de Me´ canique, Universite´ du Havre, 40 pp. Le Me´ haute´ , B., 1972. Progressive wave absorber. Journal of Hydraulic Research 10 (2), 153–169. Ouellet, Y., Datta, I., 1987. A survey of wave absorbers. Journal of Hydraulic Research 24 (4), 265–280. San, S.E., Donslund, B., Hansen, K.H., Mathiesen, N., 1982. Optimization of absorbers for DHI’s offshore basin by means of 3-gauge reflection procedure. Internal Report. Unpublished report of the Danish Hydraulic Institute, 29 pp. Tremblay, A.R., 1970. Etude sur les amortisseurs a` houle. Unpublished report. De´ partement de Ge´ nie civil, Universite´ de Laval, 38 pp.
Technical Note
Experimental study of the working principal and efficiency of a superposed inclined planes wave absorber M. Lebey *, E. Rivoalen Laboratoire de Me´canique, Universite´ du Havre, BP 540, 76058 Le Havre Cedex, France Received 7 March 2001; accepted 20 June 2001
Abstract The swell reflection leads to problems in full scale conditions, shipping near seawalls and inside harbors, and for experiments in basins or channels, as well. Consequently, many studies were carried out to define wave absorbers with best efficiency. In this paper, the three main working principals of the wave absorbers, breaking waves, viscous dissipation resonating mechanism, are detailed to see how it is possible to enhance the efficiency. Through this analysis, a wave absorber made up of several superposed inclined planes in front of a wall is defined and its working principal is explained. Through experiments, it is shown that in spite of its short size its efficiency is one of the best compared to the more classical wave absorbers. Moreover, this superposed inclined planes wave absorber presents two main advantages: its short size and the possibility to be adjusted to the swell caracteristics, which make it interesting to be used in real scale and in laboratory environment, as well. 2002 Published by Elsevier Science Ltd. Keywords: Wave absorber; Wave breaking; Swell dissipation; Wave reflection; Seawall; Harbor; Shipping; Bank protection
1. Introduction The problems due to the swell reflection on sea wall remain important especially inside harbors and coast shipping. The wave reflection problem leads to the same * Corresponding author. Tel.: +33-2-32-74-43-72; fax: +33-2-32-74-43-14. E-mail address: [email protected] (M. Lebey). 0029-8018/02/$ - see front matter 2002 Published by Elsevier Science Ltd. PII: S 0 0 2 9 - 8 0 1 8 ( 0 1 ) 0 0 0 8 9 - 0
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difficulties in experimental channels or basins. The incident swell or wave produced by a model must be completely dissipated in experimental channels or basins because of the necessary quality of the tests. Many wave absorber types exist and some of them can be used in full scale conditions or in test basins, as well. The wave absorbers can be divided into two categories: i) wave absorbing beaches and ii) caissons. Wave absorbing beaches have the advantage of simple design and being very efficient for a large scale of swells. But important sizes make them impossible to use in harbors, and using them in laboratory sets requires large space especially in test basins. Consequently, they can only be used easily in wave flumes under the condition of a large increase in length. To overcome this problem of too important sizes, two main solutions are used: 1. Transform the simple wave absorbing beach design into constructions increasing the wave breaking phenomenon or the viscous dissipation process of the swell energy. 2. Use more recent constructions which are caisson type solutions designed to create an important dissipation of the swell energy under the effect of viscous phenomena and of mechanism of resonance. Although these constructions involve strong structures, they have the advantage of requiring shorter sizes. The main working principle of the wave absorbing beaches is the effect of breaking waves on a plane of weak slope and of important length, which induces the complete dissipation of the swell energy, and makes the wave reflection impossible. As shown in the Ouellet and Datta (1987) review, many solutions have been designed to decrease the size of the wave absorbing beaches. Beaches made of several successive planes of different slopes have been used. San et al. (1982) have shown that the efficiency is better when the absorbing beaches are made of parabolic profile surfaces, the concavity of which is turned upwards, than when they are made of simple planes. Constructions associating the slope of absorbing beaches and porous walls, such as the one used by Tremblay (1970), increase the efficiency and also reduce the size. More complex constructions, associating a porous wall with inclined planes and recirculation chambers, such as the device proposed by Hedar (1956), are also of good efficiency. Perfecting wave absorbing constructions have shown that the association of several swell absorbing energy effects leads to an important reduction of the construction sizes. More recent wave absorber designs, such as caissons, give the same efficiency. The main advantage of these solutions is their very short length compared with the wave absorbing beach length. It nevertheless involves a stronger and consequently more expensive construction. Two types of wave absorbing caissons are especially worthy of mention: the arc model and the Jarlan model, the efficiency of which was studied by Lebey and Rivoalen (1989). The arc model consists of rectangular and vertical apertures which represent a third or a quarter of the sea wall front surface. Each aperture communicates with an internal vertical chamber, the width of which is equal to the distance between two successive apertures. The distance between the
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front wall and the back wall is about the fifth of the wave length. The efficiency of this kind of construction is about 90%. Although it is interesting to use these constructions in real situations, they cannot be used easily in laboratory flumes because their optimum efficiency is included in a short range of wave frequencies. The second type of wave absorbers is the Jarlan caisson type, the construction of which has been getting more and more simple for several years. Originally, they comprised a dissipation energy chamber behind a front wall in which there were several cylindrical holes regularly spaced. The distance between the front and back walls was about an eighth of the wave length. The dissipation energy chamber was divided in several parts separated by vertical walls in which there were also several cylindrical holes regularly spaced. Through analysis it was shown that the internal vertical walls did not increase the efficiency. Therefore, these walls are not used any more and this type of caisson is now only made of one dissipation energy chamber behind a front wall with cylindrical holes regularly spaced. The researches carried on to increase the efficicency of wave absorbers lead to the analysis of the absorbing energy phenomena of the swell which makes the swell reflection impossible. In the wave absorbing beaches, the transformation of the wave energy into turbulence is produced by the breaking wave on a long size plane of weak slope, the turbulence is finally dissipated under the effect of viscosity. In the wave absorbers designed in modifying the wave absorbing beaches, the transformation of swell energy into turbulence is produced through porous planes whose slope is greater than the slope of the simple wave absorbing beaches. In this kind of wave absorber, devices are used to return back the residual wave motion by a fluid flow on bottom towards the incident swell. In the wave absorbing caissons, the transformation of the swell energy into turbulence has also an important part in the swell dissipation phenomena. This transformation is produced through holes in a front wall in the Jarlan caisson, or by the narrowness of the front apertures in the arc caisson. In the wave absorbing caissons, especialy in the Jarlan caisson, another phenomenon has an important part in the swell dissipation energy mechanism, this is the mechanism of resonance. The studies which aim to improve wave absorbing structures with simultaneously lower sizes and greater efficiency seem to require the combination of at least three of the phenomena which contribute to the wave dissipation in the wave absorbers: i) wave breaking, ii) turbulence, iii) mechanism of resonance. The aim of this study is to present a method of wave absorption which requires lower sizes while the efficiency level remains very high. The corresponding system combines the three wave absorbing mechanism. This proposed structure, named Superposed Inclined Planes Wave Absorber (SIPWA), is described in the next section. The experimental set-up and the measurement methods, the experiental results and the working analysis of this device are detailed in Sections 2 and 3. The final results and a comparison with other wave absorbers are presented in Section 4. The concluding remarks are given in Section 5.
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2. The superposed inclined planes wave absorber and experimental details As shown on Fig. 1 the proposed system is made of three main parts: 1) several superposed parallel and inclined planes, 2) a vertical back-wall and 3) a confining chamber between planes and back-wall. The superposed inclined planes are of the same sizes, thickness Th and the same length L, with a space S between two planes. These planes are inclined towards the confining chamber so that their incident angle a with respect to the incident swell direction is positive. The planes are lined up on the same vertical line. The number of planes depends on the S space, on the thickness Th and on the space H0 between the bottom and the lower plane. This number of planes is chosen so that the total system height is always upper than the maximum water height. In the studied system, the vertical back-wall is smooth. There is not any device in this confining chamber. The main parameter of this system is its global size Gs given by the following relation: Gs ⫽ L cos a ⫹ D Its height is given by the relation: H ⫽ H0 ⫹ n Th sin a ⫹ (n⫺1) S sin a The varying parameters in this experiment are: a, the slope angle between the planes and the horizontal, which is also the incidence of the planes with respect to the swell direction; S, the space between two planes; L, the plane length; D, the space between the planes and the wall. The experiments were carried on in a wave flume of 30 cm×30 cm section and 3 m long. The water height is 14.5 cm. The incident swell was monochromatic. A
Fig. 1. Setting-up and details of the superposed inclined planes wave absorber. D, space between the confining chamber and the back-wall; Gs, global size; e, space between two planes; L, plane length; a, incidence angle of the plane against the incident swell direction.
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frequency variator was used to adjust the frequency swell for every test. The experiments are analyzed in two ways: visualizations and reflection coefficient measures. The working principle has been detailed through visualizations and the efficiency of each kind of configuration was given by the reflection coefficient measures. Two kinds of visualization were used: the first one with rilsan particles, of density 1.06 and size 0.05 mm, in water. The second visualization was the injection of dye through holes located on each end of a profile. The flow motions in every part of this wave absorber are seen by the observation of the rilsan particle motions. The creation, evolution and destruction phenomena are seen by the dye injection, which shows the viscous dissipating process of a part of the swell energy. Each configuration was recorded on a video tape during 20 s. The swell reflection coefficient is computed using a Doppler method created by Brossard and Hemon (1995).
3. Experimental results Tests were carried on to establish the optimum configuration of this superposed and inclined planes wave absorber (SIPWA) and to determine the effects of its main parameters—the angle a, and the distance D between the planes and the back-wall. The angle a corresponding to the optimum configuration gives the lower reflection coefficient value with the smallest size, i.e. with the smallest distance D. The tests were grouped in series which are characterized by a constant value of the angle a, so that in each series the reflection coefficient R (%) was determined as a function of the distance D, i.e. as a function of the wave absorber size Gs. This optimum configuration in these test conditions is given by the analysis of all of these functions. The first step of this analyis concerns the effect of the plane incidence, and particularly the comparison between the wave absorber efficiency in the case of positive incidence angles and in the case of negative incidence angles. Fig. 2 shows results corresponding to a values of ⫺30°, ⫺10°, 0°, +20°, +30°, and +40°. On this figure we can see that the curves are divided into two groups. The first group for which the reflection coefficient value is greater than 30% corresponds to negative values of a. The second group represents the case with positive a angle values. For each curve, the reflection coefficient varies between 4% and 40%. As can be seen, the lowest reflection coefficient values are always reached with positive values of the incident angle a of the planes with respect to the incident swell direction. The best efficiency, 4%, is obtained with an a value of 20°. As is shown in the next section, this result is mainly due to the fact that in the case of negative incidence of the planes, i.e. a⬍0, there is not any eddy creation and there is not any resonating effect. The planes have then no effect on the swell which is consequently completely reflected on the back-wall. In the next section this wave absorber working principle is detailed, and it is explained why the efficiency is clearly greater when the plane incidence is positive. The effect of the space size S between the planes is shown on Figs. 3a–d. As in the previous analysis, the curves show the reflection coefficient R as a function of
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Fig. 2. Comparison of the efficiency for positive and negative incidence of the planes for the SIPWA. The lower the reflection coefficient the better the efficiency. We can see that the efficiency is better when the incidence of the planes is positive.
Fig. 3. The reflection coefficient R (%) vs. the incidence angle a and vs. the distance D between the back-wall and the planes. The space sizes S between planes are: (a) 15 mm, (b) 25 mm, (c) 35 mm and (d) 45 mm.
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the distance D between the back-wall and the planes. Each figure corresponds to a specific space size S between the planes (15 mm, 25 mm, 35 mm, and 45 mm). The variation of the reflection coefficient is studied for each space size as a function of the incidence angle a. We can see that the best efficiency, which is 3.5%, is obtained with an incidence a angle of 35°, with a space size of 25 mm between the planes and with a distance D of 33 mm between the back-wall and all the planes, i.e. a global size Gs of 80 mm. A nearly equivalent efficiency, Rc ⫽ 5%, is obtained with the following conditions: a space size S between planes of 35 mm, a lower distance D between planes and back-wall of 29 mm, and a higher incidence angle of 35°, such that the global size, Gs, is smaller, only 70 mm. For a space size S between planes of 45 mm, the reflection coefficient increases with the distance D between the planes and the back-wall and the smallest values are superior to 15%. For a smaller value of the space size S between planes, 15 mm, the minima of the reflection coefficient values are also greater, superior to 12%. In general, it can be seen that the curves are closer to each other for space sizes S between planes which give the smallest reflection coefficient values, i.e. 25 and 35 mm. All these tests were carried out with a plane length of 50 mm. Other tests were carried out in the same conditions but with two other plane lengths, a lower one of 30 mm and an upper one of 70 mm. These tests have shown that the best efficiencies with the lowest sizes are clearly obtained with a plane length of 50 mm which was consequently chosen in all this study. The main conclusions of this analysis show that firstly the optimal space size between planes is 25 mm in the present test conditions, and secondly that in the aim to obtain the best efficiencies with the smallest global length there is a relation between: 1) the space size S between planes, 2) the incidence angle a of the planes, 3) the distance D between the back-wall and the planes, and 4) the plane length L. The existence of this relation points out the capability of this wave absorber to be adjusted according to the conditions of utilization. The comparison between the efficiency of SIPWA and the efficiency of the Jarlan caisson is shown on Fig. 4. The comparison tests were carried out in the same conditions as the previous tests and the results are analyzed through the same method.
Fig. 4.
Comparison of the reflection coeficient of Jarlan caisson and of the SIPWA.
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On this figure, the curves show the reflection coefficient R as a function of the global size Gs of each wave absorber. For the Jarlan caisson, only the curve which represents the best efficiency with the smallest global size is shown, i.e. 4.6% with Gs ⫽ 100 mm. For the SIPWA two curves are shown on this figure: i) one shows the best efficiency conditions with a global size smaller than the best Jarlan one, i.e. R ⫽ 3.5% with Gs ⫽ 80 mm compared to R ⫽ 4.6% with Gs ⫽ 100 mm for the Jarlan caisson, ii) the other one shows an efficency of the SIPWA just a little higher than the best Jarlan one, 5.1% compared to 4.6%, but with a more smaller global size Gs of only 70 mm. It is clearly shown on Fig. 4 that the best efficiency, 4.6%, of the Jarlan caisson is obtained with a global size of 100 mm when the best efficiency of the presented wave absorber, 3.5%, is obtained with a global size Gs of only 80 mm which is a lower value of 20%. This comparison shows that the SIPWA involves a lower global size to give a similar efficiency.
4. Working principle of the superposed planes wave absorber To explain the working principle of the SIPWA, it should be interesting to analyze separately the reflection phenomena of each part which constitutes this system. These two main parts are: 1) the back-wall and 2) all the superposed planes. It is obvious that the reflection coefficient of the back-wall is equal to 100% whatever the swell is because this back-wall is a plane positioned in a perpendicular direction with respect to the incidence direction of the swell. The phenomena acting on the superposed planes are completely different. Fig. 5 shows the variation of the reflection cefficient of all the superposed inclined planes without the back-wall. In this case the space size S between the planes is 25 mm. The incidence angle varies between
Fig. 5. Reflection coefficient versus negative and positive incidence angles a of the superposed planes without back-wall. The reflection coefficient is higher than in the case of the entirely SIPWA, i.e. the efficiency is clearly lower for the negative angle.
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⫺40° and +30°. This figure shows that the minimum values of the reflection coefficient correspond to the positive values of the incidence angle a, and increase when these values become negative. As was shown in a previous section, in the case of the SIPWA, these results are opposite, the best efficiency is obtained with positive values of the incidence angle a of the planes. This analysis shows that the working explanation of the SIPWA is impossible through the only analysis of each part, separately, on one side the back-wall and on the other side all the superposed planes. The analysis of the whole construction is necessary to explain the SIPWA working. As will be shown in this section, the working principle of this wave absorber is based on three phenomena: 1) the viscous dissipation of the swell energy, 2) the wave breaking, and 3) the mechanism of resonance. These three main phenomena will be shown and detailed through visualizations: 1) a fluid motion between two planes and a fluid motion around all the planes, 2) the formation and breaking up of eddies, and 3) a difference of water level between outside and the confining chamber. As shown through vizualisations, there is a fluid motion around all the planes whatever the slope of the planes. Nevertheless, this fluid motion is more important when the efficiency of the SIPWA is the highest. As shown on Fig. 6, this fluid motion is created when the wave crest arrives towards the SIPWA and when the local velocity of the fluid to the SIPWA is the highest. In this case, a downward fluid motion is furthered by the slope of the planes in the confining chamber, and so an upward flow is created on the front part of the SIPWA. A fluid motion is consequently created around all the planes by this internal downward fluid motion and this external upward flow. This flow around all the planes has an alternate component due to the effect of the swell, and so its intensity is higher when the wave crest arrives on the SIPWA. The intensity of this flow has a highest value for a specific slope of the planes which is always positive. When the slope of the planes decreases the intensity becomes low and is close to zero when the slope of the planes is highly negative. In this case there is only an alternate velocity component of the fluid motion along each plane, so that there is neither breaking wave effect nor viscosity dissipation. The eddies formation is produced under the effect of the swell on each plane. This effect is similar to the effect created on the leading edge of a plane located
Fig. 6.
Fluid motion around all the planes.
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with an important incidence angle in a steady state flow (Fig. 7a). There are two cases in the SIPWA due to the cyclical velocity in the waves: i) the wave crest action, ii) the trough wave action. As shown on Fig. 7b, in the wave crest action the direction of the local fluid flow and the direction of the incident swell are the same, that is towards the SIPWA, so that the leading edge of the planes is on the external side of the SIPWA. In that conditions, the eddies are formed on the external end of each plane and are immediately dragged in the space between the plane on which they are formed and the upper plane. When the local flow is inverted due to the wave trough arrival, the eddies are dragged out into the external side of the SIPWA where they are broken up. As shown on Fig. 7c, in the wave trough action this is a similar mechanism but with a difference because in that case the local fluid flow is in the opposite direction of the incident swell, that is bakwards from the SIPWA, so that the leading edge of the planes are on the internal side of the confining chamber. In that condition, the eddies are formed on the internal end of the planes and are immediately dragged in the space between the plane where they were formed and the lower plane. And when
Fig. 7. Eddy formation on the the leading edge of a hydrofoil under a large incidence angle in a uniform flow. (b) Eddy formation on the leading edge of the planes when the wave crest arrives on the SIPWA. (c) Eddy formation on the trailing edge of the planes when the wave trough arrives on the SIPWA.
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the local flow is inverted due to the crest arrival, the eddies are dragged out into the confining chamber where they are broken up and so transformed into turbulence. These two mechanisms created by the crest and the trough of each wave transformed a part of the swell energy into turbulence because just after being dragged out of the space between planes, the eddies are broken by the flow around all the planes. This is the phenomenon through which the viscous dissipation of the swell energy is produced by the SIPWA. As shown in the previous section, the magnitude of this phenomenon has a maximum value for a specific incidence angle of the planes. In the exemple used in this study the optimum value, corresponding to the best efficiency of the SIPWA, is about 27°. For other values, the magnitude of this dissipation energy phenomenon decreases and consequently the efficiency of the SIPWA simultaneously decreases. This clearly shows the significance of the dissipation energy phenomenon through formation and breaking up of eddies in that kind of wave absorber. The free surface motion inside the confining chamber revels another mechanism: the mechanism of resonance, the consequence of which is the annihilation of a part of the swell when the incidence angle a is positive. As is shown on Fig. 8a, when the wave crest arrives on the SIPWA, the level inside the confining chamber increases with a delay due to the planes’ positive incidence, and then when the wave trough arrives on the SIPWA, this planes’ positive incidence creates a downward fluid motion inside the confining chamber. As is shown above, this downward flow produces a fluid motion around all the planes, especially an upward fluid motion on the external side of the SIPWA, the effect of which is the compensation of the decreasing water level due to the wave trough arrival. The SIPWA works as an energy accumulator when the wave crest arrives: the wave energy is retained in the confining
Fig. 8. Water level in the confining chamber as a function of the incidence: (a) positive incidence, there is a phase difference between the water level inside and outside; (b) negative incidence, the phase difference of the water level is weak.
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chamber as potential energy under the effect of the level increasing of the free surface. When the wave trough arrives on the SIPWA, this potential energy is restored into fluid motion around all the planes. The effect of the downward motion inside the confining chamber is in this way the compensation of the decreasing level when the wave trough arrives on the external side. The effect of these phenomena is to break up the swell structure, so that no reflective wave can be produced. Consequently the reflection coefficient is weak and the efficiency becomes great. Whole of this effect is similar to the mechanism of resonance in which the frequency remains the same, the swell frequency, but in which the phase-shift is controlled by the effect of the level difference between the internal and external sides of all the planes. On the other hand, as shown on Fig. 8b in the case of planes’ negative incidence, the motion of the free surface is the same inside the confining chamber and in the external side of the SIPWA. When the wave crest arrives on the external side, the water level inside the confining chamber increases simultaneously. There is no phase difference between the water level inside and outside. In the same way, when the wave trough arrives on the external side the level inside the confining chamber decreases in the same time. The planes have no effect on the swell. The reflection coefficient values are great, the SIPWA has no efficiency and its effect is nearly the same as a vertical wall. The SIPWA efficiency depends on the planes’ incidence, and we have shown there is a specific value for which the efficiency is maximal. When its efficiency is at its maximum, the effect of the swell kinetic energy is nullified under the effect of three main mechanisms: 1) viscous dissipation and 2) breaking of the waves which are two complementary mechanisms created by the formation and breaking of eddies. The third mechanism is the mechanism of resonance due to the water level difference created by the superposed planes between outside and the confining chamber, these two levels canceling each other out.
5. Discussion and concluding remarks The main physical phenomena which produce the absorption of swell, were analyzed in this paper in the aim to show that their complementary effect leads to design constructions of best efficiency with shorter size. These phenomena, turbulence and reasonance mechanisms, lead to complete wave breaking when they are optimized simultaneously. Using a superposition of several identical planes, the incidence angle of which is positive with the swell direction and located in front of a vertical wall, allows the creation of three mechanisms which produce the swell energy dissipation: i) viscous dissipation, ii) breaking wave and iii) the resonating mechanism. The viscous dissipation is always a mechanism acting in the wave absorbers as in beaches of constant slope, in wire mesh or aluminum screen sheet absorber presented by Keulegan (1973), and also in the structure created by Le Me´ haute´ (1972) which is made of chicken wire cells. In the case of the SIPWA, this mechanism is associated with the
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eddies breaking since the eddies formed by the action of the waves on the inclined planes are immediately broken and transformed into turbulence which produced viscous dissipation. The resonance mechanism is the third effect produced by the inclined planes. This mechanism is not quite different from the process acting in Kamphuis (1984) structure which is made of a superposition of horizontal planes, or in Jarlan structure which is made of only a vertical wall with holes regularly spaced and located in front of a vertical wall. This mechanism also contributes to the viscous dissipation since it creates a flow around all the planes, the effect of which is to enhance the eddies breaking and consequentely the viscous dissipation. The water flow around all the planes is similar to the one created in the Hedar system. But in this case the fluid motion is controlled by a gate located in the lower part. This gate allows fluid motion from the internal to the external part but prevents it in the opposite direction. This structure also includes inclined planes regularly spaced but in a horizontal direction. The incidence of these planes is highly negative. This device involves much more important sizes. The effect on the efficiency of the roughness of planes and of the back-wall was not studied. However, because of the system configuration and of the working principle it could be thought that the roughness would be a weak effect. Ouellet and Datta (1987) came to the same conclusion when they remarked that the increase in efficiency is only about 2% in the case of sets in which the roughness is much more important. One of the main characteristics of the SIPWA is the function of the planes which allowed us to produce simultaneously three mechanisms which lead to the nearly complete dissipation of the swell energy with the shortest sizes. With this specific caracteristic, the SIPWA is mainly different to other caisson wave absorbers, such as Jarlan caisson or arc caisson because its size does not depend on incident swell characteristics to obtained the best efficiency, but it depends i) on the planes’ length, ii) on the confining chamber size, and iii) on the planes’ incidence which is easily adjustable. This characteristic makes the SIPWA easy to use in an experimental setup, such as basins, wave flumes, etc. It is not dificult to built such a set in which the planes’ incidence is adjustable to the swell characteristics of the experiments. One of the main advantages of this system is the possibility of changing easily the planes’ incidence and consequently to adjust its characteristics to the incident swell in order to get the best efficiency. Then it becomes very interesting to use it especially in experimental basins or channels. In full scale conditions, the SIPWA gives a solution to two different problems: i) the swell absorption on a sea wall, ii) absorption of the stem waves in harbors and canals to protect banks. In the first case, the structure height must be equal to the seawall height. In that condition, the flow around the planes produces a great undermining at the bottom of the seawall which makes necessary the protection of the bottom. In the second case, when used to protect internal sides in harbors and banks in canals, the SIPWA height will be equal to the maximum stem waves height in order to restrain them.
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References Brossard, J., Hemon, A., 1995. Analyse spectrale par effet Doppler de la propagation de la houle. C.R. Acad. Sci., Paris, Se´ r. IIb 230, 171–176. Hedar, P.A., 1956. Essais effectue´ s sur un amortisseur de houle en mode`le re´ duit. La Houille Blanche 2, 748–752. Kamphuis, J.W., 1984. Evaluation of tapered slab wave absorber (phase II). Queen’s University Kingston, Ontario, Canada, 37 pp. Keulegan, G.H., 1973. Reflection on screen wave absorber. U.S. Army Engineering Water-ways Experiments Station, Research Report H-73-3, 56 pp. Lebey, M.M., Rivoalen, E., 1989. Etude sur maquette des caracte´ ristiques du caisson Jarlan. Internal report, Unpublished report, Laboratoire de Me´ canique, Universite´ du Havre, 40 pp. Le Me´ haute´ , B., 1972. Progressive wave absorber. Journal of Hydraulic Research 10 (2), 153–169. Ouellet, Y., Datta, I., 1987. A survey of wave absorbers. Journal of Hydraulic Research 24 (4), 265–280. San, S.E., Donslund, B., Hansen, K.H., Mathiesen, N., 1982. Optimization of absorbers for DHI’s offshore basin by means of 3-gauge reflection procedure. Internal Report. Unpublished report of the Danish Hydraulic Institute, 29 pp. Tremblay, A.R., 1970. Etude sur les amortisseurs a` houle. Unpublished report. De´ partement de Ge´ nie civil, Universite´ de Laval, 38 pp.