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A floating breakwater produces less environmental impact, but is easily destroyed by large waves. In this paper, the spar buoy floating breakwater is introduced with a study on the wave reflection and transmission characteristics and mooring line tension induced by the waves. Mei (The Applied Dynamics ofOcean Surface Waves, Wiley, New York (1983) 740 p) proposed a theoretical solution for the reflection and transmission coefficients as the wave propagates through a onelayer slotted barrier. For a multiplelayer fence system, the analytical solution is proposed linearly. The results show that the theoretical computations agree well with the experimental trends. For a multiplelayer fence system, the transmission coefficients become maximal as the layer spacing to wavelength ratio moves to 12. Conversely, the coefficients become minimal, as the ratio moves to 0.3. To estimate the maximum tension ofthe mooring line, both numerical calculations and laboratory experiments were executed. The numerical calculation results were similar to the exp
Ocean Engineering 31 (2004) 43–60 www.elsevier.com/locate/oceaneng A study of spar buoy floating breakwater Nai-Kuang Liang Ã, Jen-Sheng Huang, Chih-Fei Li Institute of Oceanography, National Taiwan University, Taipei, P.O Box No 23-13, Taipei 106, Taiwan, ROC Received 26 February 2002; accepted 23 May 2003 Abstract A floating breakwater produces less environmental impact, but is easily destroyed by large waves In this paper, the spar buoy floating breakwater is introduced with a study on the wave reflection and transmission characteristics and mooring line tension induced by the waves Mei (The Applied Dynamics of Ocean Surface Waves, Wiley, New York (1983) 740 p) proposed a theoretical solution for the reflection and transmission coefficients as the wave propagates through a one-layer slotted barrier For a multiple-layer fence system, the analytical solution is proposed linearly The results show that the theoretical computations agree well with the experimental trends For a multiple-layer fence system, the transmission coefficients become maximal as the layer spacing to wavelength ratio moves to 1/2 Conversely, the coefficients become minimal, as the ratio moves to 0.3 To estimate the maximum tension of the mooring line, both numerical calculations and laboratory experiments were executed The numerical calculation results were similar to the experimental results # 2003 Elsevier Ltd All rights reserved Keywords: Floating breakwater; Spar buoy; Semi-closed pipe; Vena-contracta; Wave transmission; Slant wire tension Introduction Breakwaters are used in near shore sea areas to produce wave amplitude reduction in areas such as harbors, fishing ports, marinas, power plant in and outtakes and offshore cage aquaculture support bases The traditional breakwater is composed of caissons, rubble mounts or a hybrid This breakwater type could change the original near shore current system and destroy littoral sand balance and à Corresponding author Tel.: +886-2-236-92-034; fax: +886-2-239-25-294 E-mail address: liangnk@ccms.ntu.edu.tw (N.-K Liang) 0029-8018/$ - see front matter # 2003 Elsevier Ltd All rights reserved doi:10.1016/S0029-8018(03)00107-0 44 N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 Fig Schematic diagram of single spar buoy ecological system The breakwater construction is expensive and time-consuming Breakwaters are also difficult to remove The traditional breakwater is required for highly stable harbor A floating breakwater can be employed for shore facilities that require a lower level of stability Many studies have been produced on floating breakwaters (Twu and Lee, 1983; Guo et al., 1996; Murali and Mani, 1997; etc.) The floating breakwater has low sheltering efficiency and maintenance difficulties The floating breakwater has therefore been seldom used The first author proposed a spar buoy floating breakwater design, i.e the Semiclosed Pipe Floating Breakwater (SPFB), registered as a new type patent in Taiwan, ROC (Liang, 2000) A pipe made of polyethylene is closed at one end Holes are drilled for anchoring at the other end The semi-closed pipe is aerated from the open end This pipe becomes a tautly moored spar buoy if the water is deep enough To suppress spar buoy pitching, two slant wires are anchored at the top of the buoy (Fig 1) There is pretension in the slant wire Successive spar buoys are installed on a line like a slotted vertical column fence (Fig 2) More fences can be added to increase the sheltering effect A rod is used to pierce the lower end of the pipe with used tires piled on it to enlarge the cross section and protect the pipe (Fig 3) Several application possibilities are suggested in Section of this work There are two questions that should be answered, i.e the wave sheltering effect (or wave transmission) and the maximum tension of the slant wire during huge waves Theoretical and experimental studies are presented in Sections and (Huang, 2002; Li, 2002) Fig Schematic diagram of spar buoy fences N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 45 Fig Schematic diagram of practical spar buoy Practical design concept and possible applications For a small island with tourism value, such as the Tung-Sa corral reef island in the northern South China Sea, a multiple-layered semi-closed pipe fence system could be used to build a breakwater and established a simple harbor (Fig 4) The environmental impact of such a breakwater is minimal, the cost is the lowest and the breakwater fence can be easily removed There are many islands in the South Pacific where the sea is rather calm year round A floating breakwater is to provide effective shelter in these areas A beach for swimming is an important recreation area across the world However, many beaches are open only part of the year due to high waves An offshore floating breakwater could increase the beach utilization rate Traditional breakwaters are commonly old and dangerous in large waves Often the harbor basin or entrance is not stable enough due to poor breakwater design A spar buoy floating breakwater can be installed outside of the weak part of the old breakwater in the former case In the latter case, such a breakwater could be installed at a proper location that the entrance becomes calm and ships can easily Fig Schematic diagram of a simple harbor with floating breakwater 46 N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 come into and out of the harbor Ships will be unharmed even if they collide with the floating breakwater Theoretical approach As regards to the wave sheltering of the spar buoy floating breakwater, an assumption is made for simplicity that fixed vertical pipes are assumed to simulate the aerated semi-closed pipes in studying the wave reflection and transmission characteristics There is much published literatures on vertical slotted barrier wave shelters Wiegel (1960, 1961) proposed the power transmission theory which states that if the energy dissipation and reflection of waves transmitted through the porous portion of the barrier is neglected, the wave transmission coefficient is pffiffiffiffiffiffiffiffiffi pffiffiffiffi Ht =Hi ¼ b=B ¼ P P is the porosity and is equal to b/B, where B is equal to D ỵ b (Fig 5) Hi is the incident wave height, and Ht is the transmitted wave height Hayashi et al (Hayashi et al., 1966; Hayashi et al., 1968) proposed a transmission coefficient Kt and a reflection coefficient Kr for a closely spaced pile breakwater The long wave assumption considers that only the horizontal water particle current exists A jet flow in the slot and a vena-contracta could take place (Fig 5) Mei (Mei et al., 1974, Mei, 1983) proposed a solution for the transmission coefficient under the long wave assumption (shallow water wave) Their study pointed out that the velocity variation in the jet flow could result in energy losses and the wave steepness, porosity and relative depth are the main factors Referring to Mei’s theory (1983), Kriebel (1992) integrated the momentum equation in the water depth direction and obtained a transmission coefficient solution for any water depth The solution can approach Mei’s result for a shallow water wave Several researchers (Williams et al., 2000; Suh et al., 2001; Zhu and Chwang, 2001) executed serial studies on the reflection of an absorbing-type caisson breakwater This type of breakwater is a caisson with permeable thin structures that are installed at equal spacing As the S=L ẳ 2n ỵ 1ị=4, in which n ẳ 0,1,2,3, and L is the Fig Schematic diagram of vena-contracta through slotted pile barriers N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 47 wavelength, the reflection wave height is minimal Conversely, as S=L ¼ n=2, the reflection becomes maximal There is little literature on the slant wire tension 3.1 Wave sheltering The reflection coefficient is K r ¼ H r =H i and the transmission coefficient is K t ¼ H t =H i where Hr is the wave height of the reflected wave The energy loss coefficient is ELOSS ¼ À Kr2 À Kt2 : For a single-layer structure or fence, Mei (1983) proposed the theoretical result as: p ỵ ỵ 24=3ịf =khịHi =Lị 1ị Kt ẳ 4=3ịf =khịHi =Lị Kr ẳ Kt 2ị where f is the dissipation coefficient and is equal to ðð1=CPÞ À 1Þ and C is the vena-contracta coefficient For multiple-layer fences, it is assumed that the successive incident, transmitted and reflected waves are linearly superimposed (Huang, 2002) A two-layer fence case is used as an example (Fig 6) As the incident wave g0 passes the 1st fence, the 1st reflected wave gr1 and the 1st transmitted wave gt1 are generated As the 1st transmitted wave passes the 2nd fence, the 2nd reflected wave gr2 and the 2nd transmitted wave gt2 take place As the 2nd reflected wave propagates to the 1st fence, Fig Schematic diagram of the linear superimposition of wave components in two-layer fence system 48 N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 the 3rd reflected wave gr3 and the 3rd transmitted wave gt3 come out, and so on There will be theoretically infinite number of reflected and transmitted waves They are: gr1 ẳ H1r coskx ỵ rtị H1r ẳ H0 RH0 ị H1t coskx rtị H1t ẳ H0 TH0 ị Hr gr2 ẳ cosk2S xị ỵ rtị H2r ẳ H1t RH1t ị gt1 ẳ H2t coskx rtị H2t ẳ H1t TH1t ị Hr gr3 ẳ coskx ỵ 2Sị rtị H3r ẳ H2r RH2r ị gt2 ẳ H3t coskx ỵ 2Sị ỵ rtị Hr gr4 ẳ cosk4S xị ỵ rtị gt3 ẳ gt4 ẳ H4t coskx ỵ 2Sị rtị 3ị 4ị 5ị 6ị 7ị H3t ẳ H2r TH2r ị 8ị H4r ẳ H3r RH3r Þ ð9Þ H4t ¼ H3r Á TðH3r Þ ð10Þ where THi ị ẳ ỵ p ỵ 24=3ịf =khịHi =Lị 4=3ịf =khịHi =Lị RHi ị ẳ TðHi Þ ð11Þ ð12Þ The total number of reflected and transmitted waves are determined as follows: grTotal ẳ gr1 ỵ X gt2iỵ1 ; 13ị x ! 2S 14ị x iẳ1 gtTotal ẳ gt2 ỵ X gt2i ; i¼2 This principle can be applied to any layered fence system 3.2 Tension of slant wire A two-dimensional rectangular coordinate system is assumed (Li, 2002) As shown in Fig 7, x is the horizontal axis and z the vertical axis The origin is at point a, which is the anchor point of the slant wire For simplicity, the assumptions are as follows: N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 49 Fig Sketch definition for wave propagation on an anchored spar buoy The wire elongation and buoy deformation are very small and can be neglected The diameter of the wire is small The drag, inertial, buoyancy and gravity forces are all neglected Only waves are considered and there is no current The entire system is in a static state The entire buoy is submersed in the water The environmental forces acting at the buoy or pipe are as shown in Fig They are gravity, buoyancy, tension and wave forces Because the wire cannot sustain compressive force, the right slant wire is idle, as the wave force directs to the right, and vice versa The force balance equations for the positive wave force are as Fig Sketch definition for environmental forces on a spar buoy 50 N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 follows: For the x direction X Fxi ẳ 15ị iẳ1 For the z direction X Fzi ẳ 16ị iẳ1 For the moment X Mi ẳ 17ị iẳ1 where Fxi is the force in the x direction, Fzi the force in the z direction and Mi the moment referring to the lower end of the buoy The sub-index i indicates the various environmental forces, introduced as follows: Gravity (i ¼ 1): Fx1 ẳ 18ị ~g Fz1 ẳ W 19ị M1 ẳ 20ị is the mass of the buoy and g the gravitational acceleration in which W Buoyancy force (i ẳ 2): Fx2 ẳ 21ị Fz2 ẳ qVg 22ị M2 ẳ 23ị where q is the water density and V the volume of the buoy Drag force (i ¼ 3): according to the Morison equation, we have r2 qCDX DUịjUjdz Fx3 ẳ r1 qCDZ AðW ÞjW j ð r2 Wẳ W dz L0 r1 r2 qCDX DUịjUjz r1 ịdz M3 ẳ r1 Fz3 ẳ 24ị ð25Þ ð26Þ ð27Þ where r1 is the z-coordinate of the buoy lower end, r2 the z-coordinate of the buoy upper end, D the spar buoy diameter, A is the cross-sectional area, CDX is the horizontal drag coefficient, CDZ is the vertical drag coefficient, U is the horizontal velo the average vertical velocity of the water particles city of the water particles, W and L0 the spar buoy length N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 51 Inertial force (i ¼ 4): according to the Morison equation, the inertial forces are as follows: ð r2 Fx4 ¼ qCMX AU_ dz 28ị r1 _ Fz4 ẳ qCMZ V W ð r2 _ ¼ _ dz W W L0 r1 ð r2 M4 ¼ qCMX AU_ ðz À r1 ịdz 29ị 30ị 31ị r1 CMX ẳ ỵ kMX 32ị CMZ ẳ ỵ kMZ 33ị _ is the average vertical acceleration of the water particles, K where W MX the horizontal added mass coefficient and KMZ the vertical added mass coefficient Left slant wire tension (i ¼ 5): the slant tension TE is decomposed into x and z components: FX5 ẳ TE cosh 34ị FZ5 ẳ TE sinh 35ị M5 ẳ TEL0 cosh 36ị Buoy bottom wire tension (i ¼ 6): this tension is divided into x and z components: FX6 ẳ T2X 37ị FZ6 ẳ T2Z 38ị M6 ẳ 39ị After rearrangement, we have the following equations: the force balance equation in the x direction: ÀTE cosh T2X ẳ WFX 40ị The force balance equation in the z direction: ÀTE sinh À T2Z ¼ ÀWFZ þ Wg À qVg ð41Þ The moment balance equation: ÀTEL0 cosh ẳ WFM 42ị 52 N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 where WFX ¼ ð r2 r1 qCDX DUịjUjdz ỵ r2 qCMX AU_ dz 43ị r1 _ qCDZ AW ịjW j ỵ qCMZ V W ð r2 ð r2 qCDX DUịjUjz r1 ịdz ỵ qCMX AU_ z r1 Þdz ¼ r1 r1 WFZ ¼ ð44Þ WFM ð45Þ Eqs (40), (41) and (42) are the governing equations for numerically calculating the slant wire tension TE Laboratory experiments and comparison with theories These experiments were carried out at the wave flume at the Institute of Oceanography, National Taiwan University This flume has the following dimensions: 17 m in length, 0.8 m in height and 0.6 m in width The wave maker is piston type with a 1:6 slope at the end of the flume to eliminate the reflection waves Capacitance wave meters and tension meters were used to measure the wave and tension The data acquisition was accomplished using a personal computer 4.1 Wave sheltering The layout of the wave sheltering experiment is shown in Fig The fixed vertical cylinders used to simulate the spar buoy floating breakwater were made of PVC pipe, 3.5 cm in diameter The pipes were fixed in a steel framework mounted on the flume The pipe spacing was 0.5 cm The porosity P was equal to 0.125 (0.5/4) In this experiment, the water depth h was a constant, i.e 45 cm The model wave Fig Schematic diagram of wave sheltering experiment setup N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 53 period was between 0.8 and 1.2 s, of which the corresponding wavelength was between 0.99 and m The wave height ranged from to 15 cm The Goda and Suzuki (1976) method was employed to separate the incident and reflected wave components in front of the wave barrier (Huang, 2002) As mentioned in Section 3.1, the vena-contracta coefficient C was an empirical constant From the literature, the C constant is a function of the slot shape and varied between 0.5 and 1.0 Mei (1983) suggested that for a sharp-edge orice C ẳ 0:6 ỵ 0:4P2 Hayashi et al (1966) compared the experimental result with the theoretical calculation by substituting C ¼ 0:9 or 1:0 According to Fig 10, C ¼ 1:0 is a better choice From Fig 10, as the wave steepness Hi/L increases, Kr increases, Kt decreases and ELOSS increases However, Kr, Kt and ELOSS gradually approach constant, as the wave steepness Hi/L increases As shown in Fig 11, the comparisons for the two-layer fence reveal that Kr, Kt and ELOSS oscillate with the relative spacing S/L in a sinusoidal wave As S=L ¼ 1=4, the Kr and Kt values are minimal but ELOSS becomes maximal Conversely, as S=L ¼ 1=2, the Kr and Kt values become maximal but ELOSS becomes minimal However, for the experimental Kt value, the minimum is at S=L ¼ 0:3 instead of 0.25 The results are shown in Fig 12 for the threelayer fence system Both for theory and experiment Kr, Kt and ELOSS also oscillate with the relative spacing As S=L ¼ 1=2, the Kr and Kt values become maximal but ELOSS becomes minimal This is the same as the two-layer fence system However, as S=L ¼ 1=4, the Kr, Kt and ELOSS become a little different from that in the twolayer fence system The Kr and Kt minimums appear at the two sides of the point S=L ¼ 1=4 for the theoretical calculations This phenomenon is not clear for the Fig 10 Comparisons of theory (solid curve for C ¼ 1:0 and dotted curve for C ¼ 0:6) and experiment (symbols) in the one-layer fence system 54 N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 Fig 11 Comparisons of theory (solid curve) and experiment (symbols) in the two-layer fence system Fig 12 Comparisons of theory (solid curve) and experiment (symbols) in the three-layer fence system N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 55 Fig 13 Schematic diagram of slant wire tension experiment setup experiment data The minimum of the Kt experimental value which is smaller than that for the calculated value also appears at about S=L ¼ 0:3 4.2 Maximum tension of slant wire This experiment was carried out in the same wave flume (Fig 13) There are three kinds of models The 1st model is composed of a spar buoy (40 cm long, 3.5 cm in diameter and 110 g weight) with three nylon wires, of which two are 54 cm length and the other 4.3 cm (Fig 14) The 2nd model adds a soft pipe to the spar buoy in the 1st model to simulate used car tires in Fig (Fig 15) The dimensions of the soft pipe are 30 cm in length, 6.3 cm in outer diameter and cm in inner diameter The 3rd model adds a fixed pipe fence used in the previous wave sheltering experiment, of which one pipe is substituted by the 1st model buoy (Fig 16) The water depth in the experiment was 47.6 cm There are four wave periods, i.e 0.8, 1.0, 1.2, and 1.5 s, and five wave heights, i.e 3.0, 4.0, 5.0, 6.0, and 7.0 cm, in the experiment (Li, 2002) The slant wire tension variation for the 1st model is shown in Fig 17 The corresponding theoretical result is shown in Fig 18 Because only the positive half cycle of the particle velocity is considered for the left slant wire, only the half cycle wire tension is calculated We were interested in the maximum tension TEmax Fig 14 The 1st slant wire tension model 56 N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 Fig 15 The 2nd slant wire tension model with a soft pipe A non-dimensional comparison between the experimental and numerical data is shown in Fig 19, where B0 ¼ qVg À Wg They coincide with one another well The experimental data for the 2nd model are shown in Fig 20 The maximum tension is larger than that in the 1st model This is obvious due to the enlarged diameter In the 3rd model, the maximum tension is a little larger than that in the 1st model (Fig 21) The gap between adjacent pipes is 0.5 cm Discussions and conclusions The reflected waves in the two-layer fence system are calculated as follows: grTotal ¼ gr1 ỵ gt3 ỵ gt5 ỵ gt7 ỵ Á for x As S=L ¼ 1=4, the phase lag between gr1 and gt3 is p and the super-position reduces the wave Although gt5 has a phase lag of 2p with gr1 and strengthens the superposition, it does not have an influence because gt5 is much smaller than gt3 due to its two more reflections As regards to the total transmission wave, the superposed wave is mainly composed of gt2 and gt4 As the phase lag is p, i.e S=L ¼ 1=4, the superposed wave is the minimum However, gt4 is much smaller than gt2 Hence, the oscillation amplitude of Kt is smaller than that for Kr (Fig 11) Another reason to explain that Kr and Kt are minimal as S=L ¼ 1=4 is that two adjacent fences are both the reflection wall and node point for one another At the node point, the horizontal velocity of the water particles in a partial standing wave is the greatest This results in larger energy loss at the slotted barrier Fig 16 The 3rd slant wire tension model N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 Fig 17 Experimental results of 1st slant wire tension model Fig 18 Theoretical results of 1st slant wire tension model 57 58 N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 Fig 19 Comparison between non-dimensional experimental and numerical data for the 1st model The theoretical calculation for the maximal slant wire tension was verified by the laboratory experiment Using the numerical calculation, the maximal slant wire tension is influenced mainly by the pipe diameter and is almost not Fig 20 Theoretical results of the 2nd slant wire tension model N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 59 Fig 21 Experimental results of the 3rd model slant wire tension affected by the net buoyancy for the same wave condition A prototype estimation is as follows: water depth ¼ 10 m, wave height ¼ 7:8 m, wave period ¼ 12 s, wave length ¼ 113 m, pipe diameter ¼ 0:5 m, pipe length ¼ m, middle anchor wire length ¼ m, slant wire length ¼ 12:5 m, distance between the slant wire anchor and the middle anchor ¼ 7:5 m, pipe and tire weight ¼ 200 kg, tire diameter ¼ 0:6 m, tire column length ¼ m The maximum slant wire tension is estimated to be 3.3 tons In practical use, the slant wires should be pre-tensioned so that the buoy will be more stable and the wire connection will grind less To lower the demand of derricks, geotubes or geobags made of geotextile and sand can be used for the anchorage The following conclusions were made: The proposed ‘Semi-closed Pipe Floating Breakwater’ is feasible for simple harbors for fishing, cage farming, yachts, or as a supplementary breakwater for a traditional breakwater or a beach for swimming This breakwater is economical and environmentally benign The transmission coefficient Kt is a function of the porosity P, the relative spacing S/L and the number of layers For a three-layer breakwater Kt can be kept under 0.3, as P is equal to 0.125 and S=L ¼ 0:3 The maximum slant wire tension is influenced mainly by the pipe diameter and the wave, not the net buoyancy of the spar buoy For an m height wave with a 12 s period and 0.6 m pipe diameter and 10 m water depth, the maximum tension is about tons In the practical use, the wire should be pre-tensioned so that the wire connection parts grind less To lower the demand of derricks, geotubes or geobags made of geotextile and sand can be used for the anchorage References Goda, Y., Suzuki, Y., 1976 Estimation of incident and reflected waves in random wave experiments In: Proc 15th Coastal Eng Conf., ASCE, pp 828–845 60 N.-K Liang et al / Ocean Engineering 31 (2004) 43–60 Guo, I.Y., et al., 1996 Wave reduced effect and mooring force of the floating tire breakwater Journal of Harbour Technology 11 (1), 89–111, ((in Chinese)) Hayashi, T., Hattori, M., Shirai, M., 1968 Closely spaced pile breakwater as a protection structure against beach erosion Coastal engineering in Japan 11, 149–160 Hayashi, T., Kano, T., Shirai, M., 1966 Hydraulic research on the closely spaced piled breakwater In: Proc 10th Coastal Eng Conf., ASCE, pp 873–884 Huang, J.S., 2002 A study of wave sheltering through multi-layer vertical cylinder fences Master Thesis, Institute of Oceanography, National Taiwan University, Taiwan, Rep of China, 63 p (in Chinese) Kriebel, D.L., 1992 Vertical wave barriers: wave transmission and wave forces In: Proc 23rd Coastal Eng Conf., ASCE, pp 1313–1326 Li, C.F., 2002 A study on the mooring line tension of a three wire tautly moored spar buoy Master Thesis, Institute of Oceanography, National Taiwan University, Taiwan, Rep of China, 73 p (in Chinese) Liang, N.K., 2000 A new floating breakwater concept design Acta Oceanographica Taiwanica 38, 79– 89, ((in Chinese)) Mei, C.C., 1983 The Applied Dynamics of Ocean Surface Waves Wiley, New York, pp 740 Mei, C.C., Liu, P.L.-F., Ippen, A.T., 1974 Quadratic loss and scattering of long waves Journal Waterway, Port, Coastal and Ocean Division, ASCE 100, 217–239 Murali, K., Mani, J.S., 1997 Performance of cage floating breakwater Journal of Waterway, Port, Coastal and Ocean Engineering 123 (4), 172–179 Suh, K.D., Choi, J.C., Kim, B.H., Park, W.S., Lee, K.S., 2001 Reflection of irregular waves from perforated-wall caisson breakwaters Coastal Engineering 44, 141–151 Twu, S.W., Lee, J.S., 1983 Wave transmission in shallow water through the arrangements of net-tubes and buoyant balls Proceedings, The Seventh Conference on Ocean Engineering, Taipei, Taiwan, Rep of China, Vol II, pp 26-1–26-21 (in Chinese) Wiegel, R.L., 1960 Transmission of waves past a rigid vertical thin barrier Journal of the Waterways and Harbors Division, ASCE WW1, 1–12 Wiegel, R.L., 1961 Closely spaced piles as a breakwater Dock and Harbor Authority 42 (491), 150 Williams, A.N., Mansour, A.M., Lee, H.S., 2000 Simplified analytical solution for wave interaction with absorbing-type caisson breakwaters Ocean Engineering 27, 1231–1248 Zhu, S., Chwang, A.T., 2001 Investigations on the reflection behaviour of a slotted seawall Coastal Engineering 43, 93–104 ... the beach utilization rate Traditional breakwaters are commonly old and dangerous in large waves Often the harbor basin or entrance is not stable enough due to poor breakwater design A spar buoy. .. buoy floating breakwater can be installed outside of the weak part of the old breakwater in the former case In the latter case, such a breakwater could be installed at a proper location that the... were made: The proposed ‘Semi-closed Pipe Floating Breakwater is feasible for simple harbors for fishing, cage farming, yachts, or as a supplementary breakwater for a traditional breakwater or a