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Experimental study on the performance of the multiple-layer breakwater
ARTICLE IN PRESS
Ocean Engineering 33 (2006) 1829–1839 www.elsevier.com/locate/oceaneng
Technical note
Experimental study on the performance of the multiple-layer breakwater Yongxue Wang, Guoyu Wang, Guangwei Li State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, PR China Received 2 February 2005; accepted 25 October 2005 Available online 20 January 2006
Abstract Based on the idea of disturbing the water motion in the upright direction, a new kind of multiple-layer breakwater is proposed in this article, which mainly consists of several horizontal plates. The breakwater’s performance of dissipating waves has been investigated in detail in the regular wave tests. The factors identified with the characteristics of the breakwater are discussed, such as the relative width, the wave steepness and the models geometrical parameters (the width and the gap). The comparison and analysis of the transmission and reflection coefficients with respect to different factors are presented. The model test results indicate that the multiple-layer breakwater has the good characteristic of dissipating waves. Further more, only in a little extent can it reflect the waves. The multiple-layer breakwater proposed in the paper is very significative to promote the open type breakwater to be the permanent wave attenuator in the application. r 2006 Elsevier Ltd. All rights reserved. Keywords: Multiple-layer breakwater; Dissipating waves; Transmission coefficient; Tests
1. Introduction The open type breakwater is a special wave attenuator in coastal engineering. It usually consists of the upper structure and the lower pier supports. It is proposed by Corresponding author. Fax: +86 411 84708526.
E-mail addresses: [email protected] (Y. Wang), [email protected] (G. Wang). 0029-8018/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2005.10.017
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Nomenclature Cr Ct d e g H L k T W f o
reflection coefficient transmission coefficient water depth gap of two adjacent plates acceleration of gravity wave height wave length wave number wave period width of breakwater velocity potential wave frequency
the idea that the upper breakwater can reflect most of the wave energy near the water surface. Compared with the traditional wave breaker, it is very economical that the open type breakwater can save materials and reduce the cost. Furthermore, because water can be exchangeable through the lower permeable part, it can preserve the good water quality in the harbor. For the reasons above, the research about the open type breakwater has been developed recent years, and many kinds of open type breakwater has been reported during the research. McDougal et al. (1996) set up a numerical model to solve the problem of the interaction of waves and the multiple-pit breakwaters by the linearized shallow-water theory and a two-dimensional Green’s function. It was found that the appropriate selection of pit dimensions and placement could significantly dissipate waves. Yan et al. (1998) reviewed the computation methods about the ratio of wave transmission of the open type breakwater, and analyzed the mechanism of the open type breakwater with pickets and multiple-layer baffles. Based on the two-dimensional model tests, the performance of the breakwater was discussed, and it was pointed out that the two most important factors to the characteristic of the breakwater were the permeable ratio and setting manner of the baffles. Issacson et al. (2000) discussed the modification to the Jarlan-type breakwaters that involves filling the chamber with large size stone. Based on the linear wave theory and an eigenfunction expansion method, a numerical model was set up to analyze the interaction of waves and the structure theoretically. The effects of porosity, breakwater geometry, and relative wavelength were discussed. Twu and Chieu (2000) developed a breakwater composed of n layers of porous materials. By a complex eigenfunction expansion method, the coefficients of wave transmission, reflection and wave energy loss were calculated. Several experiments were conducted to draw the conclusion that both of the coefficients of transmission and reflection had low values. Williams et al. (2000) set up a numerical model to analyze the interaction of the absorbing-type caisson breakwaters with linear waves by an eigenfunction expansion technique. Energy
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dissipation in the interior fluid region inside the breakwater was modelled through a damping function, and the damping coefficients were determined by the experiments. The extension to the interaction of irregular waves with the structure was introduced by Requejo et al. (2002). Wang (2001) investigated the performance of the plate-type breakwater by numerical method and physical model tests, and concluded that the most important factors that influence the breakwater’s performance was the ratio of the wave height to the submerging depth of the plate and the ratio of the wave length to the length of the plate. In addition, Neelamani and Rajendran (2002b, a) investigated the interaction of wave with T and ‘?’ type breakwaters by physical model experiments. The comparison of the hydrodynamic performance of the two kind breakwaters showed that the former was better than the latter. In fact, there exist many problems if the open type breakwater used as the permanent wave attenuator in coastal engineering. Large amount of wave energy can creep into the harbor through the permeable parts of the breakwater, and influence the anchor condition of the port. Especially, when acted by the long period waves, the open type breakwater cannot protect the harbor effectively. Additionally, strong wave force will act on the upper part of the breakwater, and the security and the stability will be much threatened under the execrable wave condition. At present, the open type breakwater can only be applied in the area with small wave height and short wave period. They can dissipate waves either by reflecting waves from some breakwaters or promoting waves to break up from some special configuration. In this article, a new kind of multiple-layer breakwater is proposed, which consists of several multiple horizontal plates. The main goal of this paper is to investigate the performance and the influencing factor of the new kind breakwater by physical model tests, then demonstrate the validity of designing the breakwater, thus to develop the open type breakwater to be applied widely in coastal engineering.
2. The configuration of the multiple-layer breakwater The multiple-layer breakwater proposed in this article consists of a certain number of thin horizontal plates which are connected by the poles in the corner. The gap of the two layers is nearly equal to the short diameter of the fluid particles trajectory in a certain depth. When the wave comes, the breakwater can disturb the motion of the particles, and some waves will break up, then the wave energy can be dissipated. Additionally, the total area of the structure towards the incident waves is very small, so the wave force in the horizontal direction is very weak. Just for this reason, the breakwater can be anchored very easily. Based on the linear wave theory, the velocity potential f can be expressed by the following equation (Qiu, 1984): Hg cosh kðz þ dÞ sinðkx otÞ, (1) 2o cosh kd where H is the wave height, d is the water depth, o is the wave frequency, k is the wave number, and g is the gravity acceleration. f¼
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The velocity of the fluid particles is u
¼
v
¼
9 qf Hgk cosh kðz þ dÞ > ¼ cosðkx otÞ; > = qx 2o cosh kd qf Hgk sinh kðz þ dÞ > ¼ sinðkx otÞ > ; qz 2o cosh kd
(2)
and the trajectory of the fluid particle ðx0 ; z0 Þ can be described by ðx x0 Þ2 ðz z0 Þ2 þ ¼ 1, a2 b2 where the long and short diameter (a and b) of the ellipse are 9 H cosh kðz0 þ dÞ > a ¼ ;> = 2 sinh kd H sinh kðz0 þ dÞ > :> b ¼ ; 2 sinh kd
(3)
(4)
Considering that the water depth is 12.0, 1.2 m can be selected as the gap of the two plates from Eq. (4).
3. Model tests design The physical model tests are conducted in the small flume with 22.00 m in length, 0.60 m in depth, and 0.45 m in width of the state key laboratory of coastal and offshore engineering, Dalian university of technology. The model scale is 1:30, and the water depth is 0.4 m in the tests. Fig. 1 is the tests sketch. There is a wave maker on the left side of the flume to generate regular waves in the tests, and on the right side, there is an absorber with a slope. Before the model, there are two wave gauges to record the wave surface evaluation, and by the Goda’s two point method (Yu, 2000), the incident and reflected wave height can be separated. The same method is applied after the model, thus the reflection influence of the absorber can be eliminated, and the transmission coefficient can be obtained exactly.
Fig. 1. The sketch of the physical model tests.
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Fig. 2. The cross-section of the model (unit: m).
Table 1 Wave parameters in the tests H (m)
T (s)
0.040 0.080 0.118 0.160
1.10, 1.10, 0.73, 1.10,
1.28, 1.28, 0.91, 1.28,
1.46 1.46 1.10, 1.28, 1.46 1.46
The configuration of the multiple-layer breakwater is described in detail in Fig. 2. The height of the model is 0.50 m, and from 0.10 m above the bed, there is a plate with 0.002 m in thickness every 0.04 m. So there are 11 layers. The model is higher than the still level about 0.10 m. In the tests, the model width W is selected as 0.20, 0.40 and 0.60 m, respectively. The wave parameters in the tests are listed in Table 1. Additionally, another model test is added to explore the influence of the gap to the performance of dissipating waves, which is conducted in another flume (56.0 m in length, 0.7 m in width, and 1.0 m in depth) of the lab with the same scale and water depth as before. And the wave parameters of 0.040 and 0.118 m wave height with the whole periods was selected. It should be noticed that the gaps of the two plates are 0.04, 0.10 and 0.20 m in this test, and that the width of the model is 0.40 m only.
4. Data analysis The relations of the transmission and reflection coefficients with respect to the parameters of the relative width ðW =LÞ, the relative gap ðe=HÞ and the wave steepness are discussed during the data analysis. The method used to calculate the coefficients is the Goda’s two points method, as mentioned above.
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4.1. The relative width Gathering all the data of the different models with different wave parameters, the transmission and reflection coefficients with respect to the relative width can be obtained, shown in Figs. 3 and 4, together with the fit curves. It is evident that there exists a close relationship between the transmission coefficient and the relative width in Fig. 3. The transmission coefficient decreases with the increasing of the relative width. In the tests, the transmission coefficient can drop below 0.5 when the relative width is greater than 0.25. It indicates that the multiple-layer breakwater proposed in this article can dissipate waves significantly. Similarly, the relative width influences the reflection coefficient much as shown in Fig. 4. When the relative width is less than 0.2, the reflection coefficient increases along with the increasing of the relative width. But, when the relative width is greater than 0.2, the reflection coefficient will not increase evidently, and it almost maintains below 0.5.
Fig. 3. The fit curve of C t with respect to W =L.
Fig. 4. The fit curve of C r with respect to W =L.
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4.2. The wave steepness To show the relation between the performance and the wave steepness, the data of the transmission and reflection coefficients with the different models are displayed in Figs. 5 and 6, respectively, when the incident wave height is 0.118 m. From Fig. 5, it is easy to see that the width influences the transmission coefficient very much. With the increasing of the model width, the transmission coefficient decreases clearly. When the width is 0.20 m, the transmission coefficient is greater than 0.6. When the width is 0.40 m and the steepness is greater than 0.07 (period is greater than 1.10 s), the transmission coefficient can be dropped down 0.5. When the width is 0.60 m, the transmission coefficient decreases much. In the tests, it is less than 0.5 on the whole. Additionally, it is easy to see that the transmission coefficient decreases with the increasing of the wave steepness. Under a certain height wave action, with the decreasing of the period, the wave length increasing, and the same of the wave steepness. Thus the surface wave is easy to break up, so the transmission coefficient decreases.
Fig. 5. The relation between C t and H=L ðH ¼ 0:118 mÞ.
Fig. 6. The relation between C r and H=L ðH ¼ 0:118 mÞ.
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From the data and the curves in Fig. 6, it is safe to say that the width of the model can influence the reflection coefficient in a certain extent. With the increasing of the width, the reflection coefficient increase a little. But compared with that of the transmission coefficient, the change is small. This is because that the reflection coefficient is mainly depended on the area of the structure that towards the incident waves. In the test, the model consists of some layers of thin plates, so the total area towards the incident waves is very small. Just for this, the multiple-layer breakwater cannot reflect waves strongly. Otherwise, the wave steepness can influence the reflection coefficient a little. With the increasing of the wave steepness, the reflection coefficient decreases in a little extent. 4.3. The relative gap 4.3.1. Constant gap To investigate the influence of the gap of the two plates on wave attenuation, and to test whether the gap selected is right or not, the data are analyzed and compared with the same gap of 0.04 m by the same wave period with different wave heights. When the wave period is 1.10 s, the results about the transmission and reflection coefficients of the three models are shown in Figs. 7 and 8, respectively. Here, the relative gap is defined as the ratio of the gap and the incident wave height, that is e=H. The curves in Fig. 7 indicate that the relative gap influence the transmission coefficient a little. There is a trend that the transmission coefficient decreases with the increasing of the relative gap. It should be noticed that the gap is a constant above. The gap results of different will be discussed latter. The similar result on reflection can be drawn from Fig. 8, except that the reflection coefficient increases a little with the increasing of the relative gap. 4.3.2. Variation gap To explore the influence of the gap in detail, the added test was conducted as mentioned in Section 3.
Fig. 7. The result of C t with respect of e=H ðperiod ¼ 1:10 sÞ.
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Fig. 8. The result of C r with respect of e=H ðperiod ¼ 1:10 sÞ.
Fig. 9. The result of C t with respect of W =L ðH ¼ 0:118 mÞ.
Figs. 9 and 10 display the transmission and reflection coefficients with respect to the relative width of the models with different gaps, when the incident wave height is 11.8 m. From Fig. 9, it is easy to see that the transmission coefficients of the models with different gaps are very close when the relative width is close to 0.2. But along with the increasing of the relative width, there is a trend that the smaller of the gap, the lower of the transmission coefficient. However, it is different about the reflection coefficient. As shown in Fig. 10, it seems that the reflection coefficient keeps a constant about 0.3. That is to say that the reflection coefficient will not change much, even the gap has changed a lot from 0.04 to 0.20 m. It indicates that the multiple-layer breakwater cannot reflect waves strongly. 5. Conclusions In this article, a new idea that dissipating waves by the method of using multiplelayer plates to disturb the fluid particles motion in the upright direction is explored.
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Fig. 10. The result of C r with respect of W =L ðH ¼ 0:118 mÞ.
Compared with the traditional idea of designing the open type breakwater, it is a fire-new technique entirely. From the model tests, the following conclusions can be obtained. The relative width directly influences the performance of the multiple-layer breakwater. The new kind open type breakwater proposed in this article can significantly reduce 50% waves when the relative width is about 0.25; and the reflection coefficient will not increase very much when the relative width is greater than 0.2, it maintains near 0.4. The performance of the multiple-layer breakwater will not change much along with the change of the relative gap, even the transmission coefficient decreases with the reducing of the gap in a certain extent. Yet the influence of the gap to the reflection coefficient is negligible. The small gap is suggested to dissipate much more wave energy. The influence of the wave steepness to the transmission coefficient is much more than that of the reflection coefficient. The transmission coefficient decreases clearly with the increasing of the wave steepness, while the reflection coefficient increases a little. The wave force acted on the multiple-layer breakwater in horizontal direction is weak, which is safe for the structure. But to every layer plate, the wave force in the upright direction is relatively strong. As to the application, under the long time action of the wave force, it needs a great deal of model tests and some applied cases to demonstrate whether the multiple-layer breakwater will be destroyed for the fatigue or not. References Issacson, M., Baldwin, J., Allyn, N., Cowdell, S., 2000. Wave interactions with perforated breakwater. Journal of Waterway Port Coastal and Ocean Engineering 126 (5), 229–235.
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McDougal, W.G., Williams, A.N., Furukawa, K., 1996. Multiple-pit breakwaters. Journal of Waterway Port Coastal and Ocean Engineering 122 (1), 27–33. Neelamani, S., Rajendran, R., 2002a. Wave interaction with ?-type breakwaters. Ocean Engineering 29, 561–589. Neelamani, S., Rajendran, R., 2002b. Wave interaction with T-type breakwaters. Ocean Engineering 29, 151–175. Qiu, D.H., 1984. Wave Theory and Application in Engineering (in Chinese). Requejo, S., Vidal, C., Losada, I.J., 2002. Modelling of wave loads and hydraulic performance of vertical permeable structures. Coastal Engineering 46, 249–276. Twu, S.W., Chieu, C.C., 2000. A highly wave dissipation offshore breakwater. Ocean Engineering 27, 315–330. Wang, K., 2001. Study on submerged horizontal plate-type breakwater. Ph.D. thesis, Dalian University of Technology (in Chinese). Williams, A.N., Mansour, A.-E.M., Lee, H.S., 2000. Simplified analytical solutions for wave interaction with absorbing-type caisson breakwaters. Ocean Engineering 27, 1231–1248. Yan, Y.X., Zheng, J.H., Zeng, X.C., Xie, H.D., 1998. Characteristics of wave dissipation for pilefoundation tier-retainer breakwaters. The ocean engineering 16 (1), 67–74 (in Chinese). Yu, Y.X., 2000. Random Waves and its Application in Engineering (in Chinese).
Ocean Engineering 33 (2006) 1829–1839 www.elsevier.com/locate/oceaneng
Technical note
Experimental study on the performance of the multiple-layer breakwater Yongxue Wang, Guoyu Wang, Guangwei Li State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, PR China Received 2 February 2005; accepted 25 October 2005 Available online 20 January 2006
Abstract Based on the idea of disturbing the water motion in the upright direction, a new kind of multiple-layer breakwater is proposed in this article, which mainly consists of several horizontal plates. The breakwater’s performance of dissipating waves has been investigated in detail in the regular wave tests. The factors identified with the characteristics of the breakwater are discussed, such as the relative width, the wave steepness and the models geometrical parameters (the width and the gap). The comparison and analysis of the transmission and reflection coefficients with respect to different factors are presented. The model test results indicate that the multiple-layer breakwater has the good characteristic of dissipating waves. Further more, only in a little extent can it reflect the waves. The multiple-layer breakwater proposed in the paper is very significative to promote the open type breakwater to be the permanent wave attenuator in the application. r 2006 Elsevier Ltd. All rights reserved. Keywords: Multiple-layer breakwater; Dissipating waves; Transmission coefficient; Tests
1. Introduction The open type breakwater is a special wave attenuator in coastal engineering. It usually consists of the upper structure and the lower pier supports. It is proposed by Corresponding author. Fax: +86 411 84708526.
E-mail addresses: [email protected] (Y. Wang), [email protected] (G. Wang). 0029-8018/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2005.10.017
ARTICLE IN PRESS Y. Wang et al. / Ocean Engineering 33 (2006) 1829–1839
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Nomenclature Cr Ct d e g H L k T W f o
reflection coefficient transmission coefficient water depth gap of two adjacent plates acceleration of gravity wave height wave length wave number wave period width of breakwater velocity potential wave frequency
the idea that the upper breakwater can reflect most of the wave energy near the water surface. Compared with the traditional wave breaker, it is very economical that the open type breakwater can save materials and reduce the cost. Furthermore, because water can be exchangeable through the lower permeable part, it can preserve the good water quality in the harbor. For the reasons above, the research about the open type breakwater has been developed recent years, and many kinds of open type breakwater has been reported during the research. McDougal et al. (1996) set up a numerical model to solve the problem of the interaction of waves and the multiple-pit breakwaters by the linearized shallow-water theory and a two-dimensional Green’s function. It was found that the appropriate selection of pit dimensions and placement could significantly dissipate waves. Yan et al. (1998) reviewed the computation methods about the ratio of wave transmission of the open type breakwater, and analyzed the mechanism of the open type breakwater with pickets and multiple-layer baffles. Based on the two-dimensional model tests, the performance of the breakwater was discussed, and it was pointed out that the two most important factors to the characteristic of the breakwater were the permeable ratio and setting manner of the baffles. Issacson et al. (2000) discussed the modification to the Jarlan-type breakwaters that involves filling the chamber with large size stone. Based on the linear wave theory and an eigenfunction expansion method, a numerical model was set up to analyze the interaction of waves and the structure theoretically. The effects of porosity, breakwater geometry, and relative wavelength were discussed. Twu and Chieu (2000) developed a breakwater composed of n layers of porous materials. By a complex eigenfunction expansion method, the coefficients of wave transmission, reflection and wave energy loss were calculated. Several experiments were conducted to draw the conclusion that both of the coefficients of transmission and reflection had low values. Williams et al. (2000) set up a numerical model to analyze the interaction of the absorbing-type caisson breakwaters with linear waves by an eigenfunction expansion technique. Energy
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dissipation in the interior fluid region inside the breakwater was modelled through a damping function, and the damping coefficients were determined by the experiments. The extension to the interaction of irregular waves with the structure was introduced by Requejo et al. (2002). Wang (2001) investigated the performance of the plate-type breakwater by numerical method and physical model tests, and concluded that the most important factors that influence the breakwater’s performance was the ratio of the wave height to the submerging depth of the plate and the ratio of the wave length to the length of the plate. In addition, Neelamani and Rajendran (2002b, a) investigated the interaction of wave with T and ‘?’ type breakwaters by physical model experiments. The comparison of the hydrodynamic performance of the two kind breakwaters showed that the former was better than the latter. In fact, there exist many problems if the open type breakwater used as the permanent wave attenuator in coastal engineering. Large amount of wave energy can creep into the harbor through the permeable parts of the breakwater, and influence the anchor condition of the port. Especially, when acted by the long period waves, the open type breakwater cannot protect the harbor effectively. Additionally, strong wave force will act on the upper part of the breakwater, and the security and the stability will be much threatened under the execrable wave condition. At present, the open type breakwater can only be applied in the area with small wave height and short wave period. They can dissipate waves either by reflecting waves from some breakwaters or promoting waves to break up from some special configuration. In this article, a new kind of multiple-layer breakwater is proposed, which consists of several multiple horizontal plates. The main goal of this paper is to investigate the performance and the influencing factor of the new kind breakwater by physical model tests, then demonstrate the validity of designing the breakwater, thus to develop the open type breakwater to be applied widely in coastal engineering.
2. The configuration of the multiple-layer breakwater The multiple-layer breakwater proposed in this article consists of a certain number of thin horizontal plates which are connected by the poles in the corner. The gap of the two layers is nearly equal to the short diameter of the fluid particles trajectory in a certain depth. When the wave comes, the breakwater can disturb the motion of the particles, and some waves will break up, then the wave energy can be dissipated. Additionally, the total area of the structure towards the incident waves is very small, so the wave force in the horizontal direction is very weak. Just for this reason, the breakwater can be anchored very easily. Based on the linear wave theory, the velocity potential f can be expressed by the following equation (Qiu, 1984): Hg cosh kðz þ dÞ sinðkx otÞ, (1) 2o cosh kd where H is the wave height, d is the water depth, o is the wave frequency, k is the wave number, and g is the gravity acceleration. f¼
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The velocity of the fluid particles is u
¼
v
¼
9 qf Hgk cosh kðz þ dÞ > ¼ cosðkx otÞ; > = qx 2o cosh kd qf Hgk sinh kðz þ dÞ > ¼ sinðkx otÞ > ; qz 2o cosh kd
(2)
and the trajectory of the fluid particle ðx0 ; z0 Þ can be described by ðx x0 Þ2 ðz z0 Þ2 þ ¼ 1, a2 b2 where the long and short diameter (a and b) of the ellipse are 9 H cosh kðz0 þ dÞ > a ¼ ;> = 2 sinh kd H sinh kðz0 þ dÞ > :> b ¼ ; 2 sinh kd
(3)
(4)
Considering that the water depth is 12.0, 1.2 m can be selected as the gap of the two plates from Eq. (4).
3. Model tests design The physical model tests are conducted in the small flume with 22.00 m in length, 0.60 m in depth, and 0.45 m in width of the state key laboratory of coastal and offshore engineering, Dalian university of technology. The model scale is 1:30, and the water depth is 0.4 m in the tests. Fig. 1 is the tests sketch. There is a wave maker on the left side of the flume to generate regular waves in the tests, and on the right side, there is an absorber with a slope. Before the model, there are two wave gauges to record the wave surface evaluation, and by the Goda’s two point method (Yu, 2000), the incident and reflected wave height can be separated. The same method is applied after the model, thus the reflection influence of the absorber can be eliminated, and the transmission coefficient can be obtained exactly.
Fig. 1. The sketch of the physical model tests.
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Fig. 2. The cross-section of the model (unit: m).
Table 1 Wave parameters in the tests H (m)
T (s)
0.040 0.080 0.118 0.160
1.10, 1.10, 0.73, 1.10,
1.28, 1.28, 0.91, 1.28,
1.46 1.46 1.10, 1.28, 1.46 1.46
The configuration of the multiple-layer breakwater is described in detail in Fig. 2. The height of the model is 0.50 m, and from 0.10 m above the bed, there is a plate with 0.002 m in thickness every 0.04 m. So there are 11 layers. The model is higher than the still level about 0.10 m. In the tests, the model width W is selected as 0.20, 0.40 and 0.60 m, respectively. The wave parameters in the tests are listed in Table 1. Additionally, another model test is added to explore the influence of the gap to the performance of dissipating waves, which is conducted in another flume (56.0 m in length, 0.7 m in width, and 1.0 m in depth) of the lab with the same scale and water depth as before. And the wave parameters of 0.040 and 0.118 m wave height with the whole periods was selected. It should be noticed that the gaps of the two plates are 0.04, 0.10 and 0.20 m in this test, and that the width of the model is 0.40 m only.
4. Data analysis The relations of the transmission and reflection coefficients with respect to the parameters of the relative width ðW =LÞ, the relative gap ðe=HÞ and the wave steepness are discussed during the data analysis. The method used to calculate the coefficients is the Goda’s two points method, as mentioned above.
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4.1. The relative width Gathering all the data of the different models with different wave parameters, the transmission and reflection coefficients with respect to the relative width can be obtained, shown in Figs. 3 and 4, together with the fit curves. It is evident that there exists a close relationship between the transmission coefficient and the relative width in Fig. 3. The transmission coefficient decreases with the increasing of the relative width. In the tests, the transmission coefficient can drop below 0.5 when the relative width is greater than 0.25. It indicates that the multiple-layer breakwater proposed in this article can dissipate waves significantly. Similarly, the relative width influences the reflection coefficient much as shown in Fig. 4. When the relative width is less than 0.2, the reflection coefficient increases along with the increasing of the relative width. But, when the relative width is greater than 0.2, the reflection coefficient will not increase evidently, and it almost maintains below 0.5.
Fig. 3. The fit curve of C t with respect to W =L.
Fig. 4. The fit curve of C r with respect to W =L.
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4.2. The wave steepness To show the relation between the performance and the wave steepness, the data of the transmission and reflection coefficients with the different models are displayed in Figs. 5 and 6, respectively, when the incident wave height is 0.118 m. From Fig. 5, it is easy to see that the width influences the transmission coefficient very much. With the increasing of the model width, the transmission coefficient decreases clearly. When the width is 0.20 m, the transmission coefficient is greater than 0.6. When the width is 0.40 m and the steepness is greater than 0.07 (period is greater than 1.10 s), the transmission coefficient can be dropped down 0.5. When the width is 0.60 m, the transmission coefficient decreases much. In the tests, it is less than 0.5 on the whole. Additionally, it is easy to see that the transmission coefficient decreases with the increasing of the wave steepness. Under a certain height wave action, with the decreasing of the period, the wave length increasing, and the same of the wave steepness. Thus the surface wave is easy to break up, so the transmission coefficient decreases.
Fig. 5. The relation between C t and H=L ðH ¼ 0:118 mÞ.
Fig. 6. The relation between C r and H=L ðH ¼ 0:118 mÞ.
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From the data and the curves in Fig. 6, it is safe to say that the width of the model can influence the reflection coefficient in a certain extent. With the increasing of the width, the reflection coefficient increase a little. But compared with that of the transmission coefficient, the change is small. This is because that the reflection coefficient is mainly depended on the area of the structure that towards the incident waves. In the test, the model consists of some layers of thin plates, so the total area towards the incident waves is very small. Just for this, the multiple-layer breakwater cannot reflect waves strongly. Otherwise, the wave steepness can influence the reflection coefficient a little. With the increasing of the wave steepness, the reflection coefficient decreases in a little extent. 4.3. The relative gap 4.3.1. Constant gap To investigate the influence of the gap of the two plates on wave attenuation, and to test whether the gap selected is right or not, the data are analyzed and compared with the same gap of 0.04 m by the same wave period with different wave heights. When the wave period is 1.10 s, the results about the transmission and reflection coefficients of the three models are shown in Figs. 7 and 8, respectively. Here, the relative gap is defined as the ratio of the gap and the incident wave height, that is e=H. The curves in Fig. 7 indicate that the relative gap influence the transmission coefficient a little. There is a trend that the transmission coefficient decreases with the increasing of the relative gap. It should be noticed that the gap is a constant above. The gap results of different will be discussed latter. The similar result on reflection can be drawn from Fig. 8, except that the reflection coefficient increases a little with the increasing of the relative gap. 4.3.2. Variation gap To explore the influence of the gap in detail, the added test was conducted as mentioned in Section 3.
Fig. 7. The result of C t with respect of e=H ðperiod ¼ 1:10 sÞ.
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Fig. 8. The result of C r with respect of e=H ðperiod ¼ 1:10 sÞ.
Fig. 9. The result of C t with respect of W =L ðH ¼ 0:118 mÞ.
Figs. 9 and 10 display the transmission and reflection coefficients with respect to the relative width of the models with different gaps, when the incident wave height is 11.8 m. From Fig. 9, it is easy to see that the transmission coefficients of the models with different gaps are very close when the relative width is close to 0.2. But along with the increasing of the relative width, there is a trend that the smaller of the gap, the lower of the transmission coefficient. However, it is different about the reflection coefficient. As shown in Fig. 10, it seems that the reflection coefficient keeps a constant about 0.3. That is to say that the reflection coefficient will not change much, even the gap has changed a lot from 0.04 to 0.20 m. It indicates that the multiple-layer breakwater cannot reflect waves strongly. 5. Conclusions In this article, a new idea that dissipating waves by the method of using multiplelayer plates to disturb the fluid particles motion in the upright direction is explored.
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Fig. 10. The result of C r with respect of W =L ðH ¼ 0:118 mÞ.
Compared with the traditional idea of designing the open type breakwater, it is a fire-new technique entirely. From the model tests, the following conclusions can be obtained. The relative width directly influences the performance of the multiple-layer breakwater. The new kind open type breakwater proposed in this article can significantly reduce 50% waves when the relative width is about 0.25; and the reflection coefficient will not increase very much when the relative width is greater than 0.2, it maintains near 0.4. The performance of the multiple-layer breakwater will not change much along with the change of the relative gap, even the transmission coefficient decreases with the reducing of the gap in a certain extent. Yet the influence of the gap to the reflection coefficient is negligible. The small gap is suggested to dissipate much more wave energy. The influence of the wave steepness to the transmission coefficient is much more than that of the reflection coefficient. The transmission coefficient decreases clearly with the increasing of the wave steepness, while the reflection coefficient increases a little. The wave force acted on the multiple-layer breakwater in horizontal direction is weak, which is safe for the structure. But to every layer plate, the wave force in the upright direction is relatively strong. As to the application, under the long time action of the wave force, it needs a great deal of model tests and some applied cases to demonstrate whether the multiple-layer breakwater will be destroyed for the fatigue or not. References Issacson, M., Baldwin, J., Allyn, N., Cowdell, S., 2000. Wave interactions with perforated breakwater. Journal of Waterway Port Coastal and Ocean Engineering 126 (5), 229–235.
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