Difference between revisions of "Floating breakwaters"
Dronkers J (talk | contribs) |
|||
| (39 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
| − | |||
| − | == | + | ==Use of floating breakwaters== |
| − | Floating breakwaters | + | |
| + | [[Image:FBimage006.JPG|350px|thumb|right|Fig. 1. Example of floating box-breakwater (Fezzano,SP-Italy; courtesy of INGEMAR srl)]] | ||
| + | |||
| + | Floating breakwaters work by dissipating and reflecting part of the wave energy. No surplus water is brought into the sheltered area by wave overtopping. Floating breakwaters are normally used as [[piers and trestles|piers]] in marinas, but they are also used as protective structures for marinas in semi-protected areas. They are especially suited for areas where the tidal range is high, as they follow the water-level. Floating breakwaters are seldom used as shoreline protection structures because they are not suitable for installation in the open sea. | ||
| + | |||
| + | Floating breakwaters provide a relatively cheap solution to protect an area from wave attack, compared to conventional fixed breakwaters. They can be effective in coastal areas with mild wave environment conditions (significant wave height not much greater than 1 m and wave periods of 4 s or less<ref name=H81>Hales, L.Z. 1981. Floating Breakwaters: State-of-the-Art Literature Review. US Army Corps of Engineers Technical Report 81-1</ref>). Some of the conditions that favour floating breakwaters are<ref name=MC>McCartney, B. 1985. Floating breakwater design, J. of Waterway, Port, Coastal and Ocean Engineering 111: 304-318</ref>: | ||
#'' Poor foundation:'' Floating breakwaters might be a proper solution where poor foundations possibilities prohibit the application of bottom supported breakwaters. | #'' Poor foundation:'' Floating breakwaters might be a proper solution where poor foundations possibilities prohibit the application of bottom supported breakwaters. | ||
| Line 11: | Line 15: | ||
#'' Breakwater layout:'' Floating breakwaters can usually be rearranged into a new layout with minimum effort. | #'' Breakwater layout:'' Floating breakwaters can usually be rearranged into a new layout with minimum effort. | ||
| − | |||
| − | |||
| − | + | ==Types of floating breakwaters== | |
| − | |||
| − | + | Floating breakwaters are commonly divided into four general categories<ref name=MC/>: | |
| − | Floating breakwaters are commonly divided into four general categories: | ||
# Box | # Box | ||
# Pontoon | # Pontoon | ||
| Line 24: | Line 24: | ||
# Tethered float. | # Tethered float. | ||
| − | For each category, some types of floating breakwaters are shown in | + | For each category, some types of floating breakwaters are shown in figures 2 - 5. The first three types have been more widely investigated by means of physical models and prototype experience than the last one. |
| + | |||
| + | Floating breakwaters often consist of several interconnected modules. Connections are either flexible, allowing preferably only the roll along the breakwater axis, or pre- or post-tensioned, to make them act as a single unit. In the latter case the efficiency is higher, but the forces between modules are higher. The modular assemblage and the mooring system (including position of connections) are primary points of concern for this kind of structures. The wave-induced forces on the connections increase with peak wave period and obliquity; intermediate connections withstand much higher forces than terminal connections<ref>Cebada-Relea, A.J., Lopez, M., Claus, R. and Aenlle, M. 2023. Short-term analysis of extreme wave-induced forces on the connections of a floating breakwater. Ocean Engineering 280, 114579</ref>. | ||
| + | |||
| + | The performance of a floating breakwater depends on the strongly non-linear interaction of the incident wave (that may partially overtop the module and is in general short-crested and oblique) with the structure dynamics. The forces induced by the mooring system and the connections between the modules complicate the interactions. Accurate design is necessarily based on the combination of numerical and physical models<ref>Martinelli, L. and Ruol, P. 2006. 2D Model of Floating Breakwater Dynamics under Linear and Nonlinear Waves, 2nd Comsol User Conference, 14 Nov., Milano</ref>. | ||
| + | |||
| + | Large breakwaters are frequently built with used barges, ballasted to the desired draft with sand or rock. | ||
| + | |||
| + | Floating breakwaters are most effective for wave damping when their width <math>w</math> is of order of half the [[wavelength]] <math>L</math> or larger. The net forces on the mooring and anchoring system are also substantially less for such large widths, because different parts of the structure are subjected to opposite wave forces<ref name=H81/>. | ||
| + | |||
| + | The natural period of oscillation of a floating breakwater is of the order of <math>\; T \sim 2 \, \pi \, \sqrt{\large\frac{M}{\rho g A}\normalsize} \;</math>, where <math>\rho</math> is the seawater density, <math>g</math> the gravitational acceleration, <math>A</math> the horizontal section of the breakwater, and <math>M</math> the mass. This period should be much longer than the wave period to avoid resonance. These requirements imply that floating breakwaters are not suited in areas with long-period high waves. | ||
| + | |||
| + | |||
| + | ==Effectiveness== | ||
===Box breakwaters=== | ===Box breakwaters=== | ||
| − | + | Box type breakwaters are used most frequently (see figures 1 and 2). Most box-type breakwaters have been constructed of reinforced concrete modules. Reinforced concrete modules are either empty inside or, more frequently, have a [[core]] of light material (e.g. polystyrene). In the former case the risk of sinking of the structure is not negligible. The width and depth (draft) are usually limited to a few meters. | |
| − | Box type breakwaters are used most frequently (see | + | [[Image:FBimage002.JPG|450px|thumb|center|Fig. 2. Box breakwaters<ref name=MC/>.]] |
| − | |||
| − | |||
| − | + | ===Pontoon breakwaters=== | |
| + | Pontoon type breakwaters (figure 3) are effective since the overall width can be of the order of half the [[wavelength]]. In this case the expected attenuation of the wave height is significant. | ||
| + | [[Image:PontoonBreakwaters.jpg|450px|thumb|centre|Fig. 3. Different types of pontoon breakwaters<ref name=MC/><ref>Li, C., Zhang, H., Zhang, H., Sun, B. and Yang, S. 2022. Wave-attenuation and hydrodynamic properties of twin pontoon floating breakwater with kelp. Applied Ocean Research 124 (2022) 103213</ref>]] | ||
| + | ===Mat breakwaters=== | ||
| + | Within the mat category, the most used are made with tires. They have a low cost, they can be removed more easily, they can be constructed with unskilled labour and minimal equipment, they are subjected to lower anchor loads, they reflect less and they dissipate relatively more wave energy. However, they are less robust and suitable only in mild wave climates (significant wave height less than 0.5 m). | ||
| + | [[Image:FBimage004.JPG|450px|thumb|centre|Fig. 4. Mat breakwaters<ref name=MC/>]] | ||
| + | Other types of mat breakwaters are made of horizontal flexible porous membranes. The porosity of membranes contributes to viscous wave energy dissipation. Wave attenuation is increased by adding more mat layers<ref>Guo, Y.C., Mohapatra, S.C. and Guedes Soares, C. 2023. Experimental performance of multi-layered membrane breakwaters. Ocean Engineering 281, 114716</ref>. A wave transmission coefficient (ratio of transmitted to incident wave height) below 0.8 can be achieved only if the membrane width is greater than a half wavelength. | ||
| + | |||
| + | ===Tethered float breakwaters=== | ||
| + | Tethered float types are not much used. Two schemes are shown in figure 5. | ||
| + | [[Image:FBimage005.JPG|450px|thumb|centre|Fig. 5. Tethered float breakwaters<ref name=MC/>]] | ||
| + | |||
| + | ==Wave transmission== | ||
| + | [[Image:transmission rationame.jpg|right|400px|thumb|Fig. 6. Rough relation the between the transmission coefficient <math>H_t / H_i</math> and the ratio <math>L/w</math> between the wavelength <math>L</math> and the width of the floating structure <math>w</math>.]] | ||
| + | Many laboratory experiments have been performed to establish empirical formulas for the wave transmission of floating breakwaters, especially for the box-type breakwaters<ref>Koutandos, E. and Prinos, P. 2005. Design formulae for wave transmission behind floating breakwaters. XXXI IAHR congress, paper 4081</ref><ref>Alizadeh, M.J., Kolahdoozan, M., Tahershamsi, A. and Abdolali, A. 2014. Experimental Study of the Performance of Floating Breakwaters with Heave Motion. Civil Engineering Infrastructures Journal 47(1): 59 – 70</ref><ref>Moghim, N. and Botshekan, M. 2017. Analysis of the performance of pontoon-type floating breakwaters. Hong Kong Institution of Engineers Transactions 24: 9–16</ref><ref>Elsheikh, A.K., Mostafa, Y.E. and Mohamed, M.M. 2022. A comparative study between some different types of permeable breakwaters according to wave energy dissipation. Ain Shams Engineering Journal 13, 101646</ref>. The parameters considered in these experiments are the width <math>w</math> (along the wave propagation direction), the draft | ||
| + | <math>D</math>, the incident wave height <math>H_i</math> (most experiments considered regular waves), the wavelength <math>L</math> and the depth <math>h</math>. The dependence of the wave transmission coefficient <math>C_t=H_t/H_i</math> (where <math>H_t</math> is the transmitted wave height) on these various parameters shows a fairly large spread between the different experiments. However, in a qualitative sense, the dependency is similar: the transmission coefficient decreases for increasing values of <math>w</math>, <math>D</math> and <math>H_i</math> and increases for increasing values of <math>L</math> and <math>h</math>. The transmission coefficient is most sensitive to the ratio <math>L/w</math>. | ||
| + | As a rule-of-thumb the transmission varies between <math>H_t / H_i = 0.3</math> for <math>L/w = 3</math> and <math>H_t / H_i = 0.9 – 1.0</math> for <math>L/w = 8</math>, see figure 6. | ||
| + | |||
| + | Consider the example of a pontoon width of <math>w =</math> 3 m in 2 m deep water, and a requirement of a wave transmission of <math>H_t / H_i < 0.5</math>. In this case the wavelength should be smaller than <math>L < 4.3 w \approx 13</math> m, which corresponds to an approximate wave period of <math>T \approx 3 </math> s. Floating breakwaters can only be used in waters of very limited [[fetch]]. | ||
| + | Floating breakwaters thus cannot be used as shoreline management structures at moderately exposed and exposed locations. | ||
| − | |||
| − | |||
| − | |||
| + | ==Appendix== | ||
| + | [[File:BuoyantBody.jpg|thumb|right|350px|Fig. A1. Balance of vertical forces on a buoyant body in a wave field .]] | ||
| + | The vertical motion <math>\zeta(t)</math> of a buoyant body at <math>x=0</math> in a regular wave field <math>\eta(x,t)=a \cos(kx-\omega t)</math> is described by the heave equation (Archimedes' law, see figure A1): | ||
| + | <math>M \, \Large\frac{\partial^2 \zeta}{\partial t^2}\normalsize = - \rho g \, A \, D + A \, p(z,t) - dissipation - fluid \; inertia, \quad z = -D + \zeta(t) . \qquad (A1)</math> | ||
| + | Meaning of the symbols: <math>M=</math> body mass, <math>A=</math> horizontal body section area, <math>D=</math> body draft, <math>p=</math> pressure, <math>h=</math> water depth, <math>a=</math> wave amplitude, <math>\omega=</math> radial wave frequency, <math>k=</math> wave number, <math>\rho=</math> seawater density, <math>g=</math> gravitational acceleration. The moving body generates waves and accelerates the surrounding fluid. The dissipation term corresponds mainly to momentum dissipation through outward radiation of the waves generated by the moving body. It is parameterized as a force opposing the vertical velocity of the body relative to the fluid surface | ||
| + | <math>\; dissipation = \Large\frac{4}{3 \pi}\normalsize C_d \, A \, \rho \, a \, \omega \, \frac{\partial (\zeta - \eta)}{\partial t}\normalsize , </math> | ||
| + | where <math>C_d</math> is a dimensionless friction coefficient of order 1<ref>Quartier, N., Ropero-Giralda, P., Domínguez, J.M., Stratigaki, V. and Troch, P. 2021. Influence of the Drag Force on the Average Absorbed Power of Heaving Wave Energy Converters Using Smoothed Particle Hydrodynamics. Water 13, 384</ref>. Other body motions (e.g. pitch, roll, sway) are ignored. | ||
| − | + | According to linear wave theory (see [[Shallow-water wave theory]]), the pression is given by | |
| − | |||
| − | [[ | ||
| + | <math>p(-D+\zeta,t) = \rho g \, D - \rho g \, \zeta + \rho g \, K_p(-D+\zeta) \, \eta(t) , \qquad (A2)</math> | ||
| + | where <math>K_p(-D+\zeta) \approx K_p(-D) = \Large\frac{\cosh(k(h-D))}{\cosh(kh)}\normalsize . </math> | ||
| + | Energy dissipation dampens the free oscillations of the buoyant body and causes a phase shift <math>\phi</math> with respect to the wave motion. Assuming waves of small amplitude, small dissipation and neglecting the influence of inertia of the surrounding fluid, the vertical motion of the body will have the form | ||
| + | <math>\zeta(t) \approx \zeta_0 \, K_p(-D) \, \cos(\omega t - \phi). \qquad (A3)</math> | ||
| + | Substitution in Eqs. (A1) and (A2) gives | ||
| − | === | + | <math>\zeta_0 \approx a \, \sqrt{\Large\frac{1+b^2}{(1-m)^2+b^2}\normalsize} , \quad b = \Large\frac{4 a \omega^2}{3 \pi g}\normalsize C_d , \quad m = \Large\frac{M \omega^2}{\rho g A}\normalsize = \Large\frac{\rho_{fbw} D \omega^2}{\rho g}\normalsize , \qquad (A4)</math> |
| − | |||
| − | |||
| + | where <math>\rho_{fbw}</math> is the average density of the floating breakwater. The phase shift <math>\phi</math> is given by | ||
| + | <math>\tan \phi = \Large\frac{bm}{1-m+b^2}\normalsize. \qquad (A5)</math> | ||
| + | The draft <math>D</math> should be chosen such that resonance <math>m=1</math> under energetic wave conditions is avoided. | ||
| + | ==Related articles== | ||
| + | :[[Detached breakwaters]] | ||
| + | :[[Detached shore parallel breakwaters]] | ||
| + | :[[Port breakwaters and coastal erosion]] | ||
| + | :[[Applicability of detached breakwaters]] | ||
| − | |||
| − | |||
| − | |||
==References== | ==References== | ||
| + | <references/> | ||
| + | |||
| + | |||
| + | ==Other sources== | ||
| + | *Allyn N., E. Watchorn, W. Jamieson and Y. Gang, 2001. Port of Brownsville Floating Breakwater, Proc. Ports Conference. | ||
| + | *Briggs M, Y. Ye, Z. Demirbilek and J. Zhang, Field and numerical comparisons of the RIBS floating breakwater, J. of Hydraulic Research, 40(3), 289-301. | ||
| + | *Gesrah M.R. 2006. Analysis of 5 shaped floating breakwater in oblique waves: I. Impervious rigid wave boards. Applied Ocean Research, 28(5) 327–338. | ||
| + | *Isaacson M and O.U. Nwogu, 1987. Wave loads and motions of long structures in directional seas, J Offshore Mech Arct Eng 109, 126–132. | ||
| + | *Isaacson M. (1993): Wave effects of floating breakwaters, Proc. of the 1993 Canadian Coastal Conference, May 4-7, Vancouver, British Columbia, 53-66. | ||
| + | *Isaacson M. and S. Sinha, 1986. Directional wave effects on large offshore structures, J. of Waterway, Port, Coastal and Ocean Engineering, 112(4), 482-497. | ||
| + | *Martinelli L., Zanuttigh B., Ruol P., 2007. Effect of layout on floating breakwater performance: results of wave basin experiments . Proc. Coastal Structures '07, Venice. | ||
| + | *PIANC. Floating breakwaters - a practical guide for design and construction PTC2 report of WG 13 – 1994 | ||
| + | *Richey E.P. (1982): Floating Breakwater Field experience, West Coast. Report MR 82-5, U.S. Army, Corps of Engineers, Coastal Engineering Research Center; Springfield, Va, 64 pp. | ||
| + | *Ruol P. and Martinelli L., 2007. Wave flume investigation on different mooring systems for floating breakwaters. Proc. Coastal Structure '07, Venice. | ||
| + | *Sannasiraj S.A., V. Sundar and R. Sundaravadivelu, 1998. Mooring forces and motion responses of pontoon-type floating breakwaters, Ocean Eng., 25 (1), 27-48. | ||
| + | *Silander, J. 1999 Floating Breakwater and Environment. | ||
| + | *Tsinker G., 1994. Marine structure engineering: specialized application, Chapman & Hall, International Thomson Publishing Inc. | ||
| + | *Van der Meer J.W., R. Briganti, B. Zanuttigh and B. Wang, 2005. Wave transmission and reflection at low-crested structures: Design formulae, oblique wave attack and spectral change, Coastal Eng., 52(10-11), 915-929. | ||
| + | *Yamamoto T., 1981. Moored floating breakwater response to regular and irregular waves. Applied Ocean Research 3, 27–36. | ||
| + | |||
| + | |||
| + | {{3Authors | ||
| + | |AuthorID1=13321 | ||
| + | |AuthorFullName1= Piero Ruol | ||
| + | |AuthorName1= Piero.ruol | ||
| + | |AuthorID2=120 | ||
| + | |AuthorFullName2=Job Dronkers | ||
| + | |AuthorName2=Dronkers J | ||
| + | |AuthorID3=13331 | ||
| + | |AuthorFullName3=Mangor, Karsten | ||
| + | |AuthorName3=Karsten | ||
| + | }} | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | + | [[Category:Coastal protection]] | |
| − | + | [[Category:Hard structures]] | |
| − | + | [[Category:Soft coastal interventions]] | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | [[Category:Coastal | ||
| − | [[Category: | ||
| − | [[Category: | ||
Latest revision as of 14:28, 30 March 2024
Contents
Use of floating breakwaters
Floating breakwaters work by dissipating and reflecting part of the wave energy. No surplus water is brought into the sheltered area by wave overtopping. Floating breakwaters are normally used as piers in marinas, but they are also used as protective structures for marinas in semi-protected areas. They are especially suited for areas where the tidal range is high, as they follow the water-level. Floating breakwaters are seldom used as shoreline protection structures because they are not suitable for installation in the open sea.
Floating breakwaters provide a relatively cheap solution to protect an area from wave attack, compared to conventional fixed breakwaters. They can be effective in coastal areas with mild wave environment conditions (significant wave height not much greater than 1 m and wave periods of 4 s or less[1]). Some of the conditions that favour floating breakwaters are[2]:
- Poor foundation: Floating breakwaters might be a proper solution where poor foundations possibilities prohibit the application of bottom supported breakwaters.
- Deep water: In water depths in excess of 6 m, bottom connected breakwaters are often more expensive than floating breakwaters.
- Water quality: Floating breakwaters present a minimum interference with water circulation and fish migration.
- Ice problems: Floating breakwaters can be removed and towed to protected areas if ice formation is a problem. They may be suitable for areas where summer anchorage or moorage is required.
- Visual impact: Floating breakwaters have a low profile and present a minimum intrusion on the horizon, particularly for areas with high tide ranges.
- Breakwater layout: Floating breakwaters can usually be rearranged into a new layout with minimum effort.
Types of floating breakwaters
Floating breakwaters are commonly divided into four general categories[2]:
- Box
- Pontoon
- Mat
- Tethered float.
For each category, some types of floating breakwaters are shown in figures 2 - 5. The first three types have been more widely investigated by means of physical models and prototype experience than the last one.
Floating breakwaters often consist of several interconnected modules. Connections are either flexible, allowing preferably only the roll along the breakwater axis, or pre- or post-tensioned, to make them act as a single unit. In the latter case the efficiency is higher, but the forces between modules are higher. The modular assemblage and the mooring system (including position of connections) are primary points of concern for this kind of structures. The wave-induced forces on the connections increase with peak wave period and obliquity; intermediate connections withstand much higher forces than terminal connections[3].
The performance of a floating breakwater depends on the strongly non-linear interaction of the incident wave (that may partially overtop the module and is in general short-crested and oblique) with the structure dynamics. The forces induced by the mooring system and the connections between the modules complicate the interactions. Accurate design is necessarily based on the combination of numerical and physical models[4].
Large breakwaters are frequently built with used barges, ballasted to the desired draft with sand or rock.
Floating breakwaters are most effective for wave damping when their width [math]w[/math] is of order of half the wavelength [math]L[/math] or larger. The net forces on the mooring and anchoring system are also substantially less for such large widths, because different parts of the structure are subjected to opposite wave forces[1].
The natural period of oscillation of a floating breakwater is of the order of [math]\; T \sim 2 \, \pi \, \sqrt{\large\frac{M}{\rho g A}\normalsize} \;[/math], where [math]\rho[/math] is the seawater density, [math]g[/math] the gravitational acceleration, [math]A[/math] the horizontal section of the breakwater, and [math]M[/math] the mass. This period should be much longer than the wave period to avoid resonance. These requirements imply that floating breakwaters are not suited in areas with long-period high waves.
Effectiveness
Box breakwaters
Box type breakwaters are used most frequently (see figures 1 and 2). Most box-type breakwaters have been constructed of reinforced concrete modules. Reinforced concrete modules are either empty inside or, more frequently, have a core of light material (e.g. polystyrene). In the former case the risk of sinking of the structure is not negligible. The width and depth (draft) are usually limited to a few meters.
Pontoon breakwaters
Pontoon type breakwaters (figure 3) are effective since the overall width can be of the order of half the wavelength. In this case the expected attenuation of the wave height is significant.
Mat breakwaters
Within the mat category, the most used are made with tires. They have a low cost, they can be removed more easily, they can be constructed with unskilled labour and minimal equipment, they are subjected to lower anchor loads, they reflect less and they dissipate relatively more wave energy. However, they are less robust and suitable only in mild wave climates (significant wave height less than 0.5 m).
Other types of mat breakwaters are made of horizontal flexible porous membranes. The porosity of membranes contributes to viscous wave energy dissipation. Wave attenuation is increased by adding more mat layers[6]. A wave transmission coefficient (ratio of transmitted to incident wave height) below 0.8 can be achieved only if the membrane width is greater than a half wavelength.
Tethered float breakwaters
Tethered float types are not much used. Two schemes are shown in figure 5.
Wave transmission
Many laboratory experiments have been performed to establish empirical formulas for the wave transmission of floating breakwaters, especially for the box-type breakwaters[7][8][9][10]. The parameters considered in these experiments are the width [math]w[/math] (along the wave propagation direction), the draft [math]D[/math], the incident wave height [math]H_i[/math] (most experiments considered regular waves), the wavelength [math]L[/math] and the depth [math]h[/math]. The dependence of the wave transmission coefficient [math]C_t=H_t/H_i[/math] (where [math]H_t[/math] is the transmitted wave height) on these various parameters shows a fairly large spread between the different experiments. However, in a qualitative sense, the dependency is similar: the transmission coefficient decreases for increasing values of [math]w[/math], [math]D[/math] and [math]H_i[/math] and increases for increasing values of [math]L[/math] and [math]h[/math]. The transmission coefficient is most sensitive to the ratio [math]L/w[/math].
As a rule-of-thumb the transmission varies between [math]H_t / H_i = 0.3[/math] for [math]L/w = 3[/math] and [math]H_t / H_i = 0.9 – 1.0[/math] for [math]L/w = 8[/math], see figure 6.
Consider the example of a pontoon width of [math]w =[/math] 3 m in 2 m deep water, and a requirement of a wave transmission of [math]H_t / H_i \lt 0.5[/math]. In this case the wavelength should be smaller than [math]L \lt 4.3 w \approx 13[/math] m, which corresponds to an approximate wave period of [math]T \approx 3 [/math] s. Floating breakwaters can only be used in waters of very limited fetch. Floating breakwaters thus cannot be used as shoreline management structures at moderately exposed and exposed locations.
Appendix
The vertical motion [math]\zeta(t)[/math] of a buoyant body at [math]x=0[/math] in a regular wave field [math]\eta(x,t)=a \cos(kx-\omega t)[/math] is described by the heave equation (Archimedes' law, see figure A1):
[math]M \, \Large\frac{\partial^2 \zeta}{\partial t^2}\normalsize = - \rho g \, A \, D + A \, p(z,t) - dissipation - fluid \; inertia, \quad z = -D + \zeta(t) . \qquad (A1)[/math]
Meaning of the symbols: [math]M=[/math] body mass, [math]A=[/math] horizontal body section area, [math]D=[/math] body draft, [math]p=[/math] pressure, [math]h=[/math] water depth, [math]a=[/math] wave amplitude, [math]\omega=[/math] radial wave frequency, [math]k=[/math] wave number, [math]\rho=[/math] seawater density, [math]g=[/math] gravitational acceleration. The moving body generates waves and accelerates the surrounding fluid. The dissipation term corresponds mainly to momentum dissipation through outward radiation of the waves generated by the moving body. It is parameterized as a force opposing the vertical velocity of the body relative to the fluid surface
[math]\; dissipation = \Large\frac{4}{3 \pi}\normalsize C_d \, A \, \rho \, a \, \omega \, \frac{\partial (\zeta - \eta)}{\partial t}\normalsize , [/math]
where [math]C_d[/math] is a dimensionless friction coefficient of order 1[11]. Other body motions (e.g. pitch, roll, sway) are ignored.
According to linear wave theory (see Shallow-water wave theory), the pression is given by
[math]p(-D+\zeta,t) = \rho g \, D - \rho g \, \zeta + \rho g \, K_p(-D+\zeta) \, \eta(t) , \qquad (A2)[/math]
where [math]K_p(-D+\zeta) \approx K_p(-D) = \Large\frac{\cosh(k(h-D))}{\cosh(kh)}\normalsize . [/math]
Energy dissipation dampens the free oscillations of the buoyant body and causes a phase shift [math]\phi[/math] with respect to the wave motion. Assuming waves of small amplitude, small dissipation and neglecting the influence of inertia of the surrounding fluid, the vertical motion of the body will have the form
[math]\zeta(t) \approx \zeta_0 \, K_p(-D) \, \cos(\omega t - \phi). \qquad (A3)[/math]
Substitution in Eqs. (A1) and (A2) gives
[math]\zeta_0 \approx a \, \sqrt{\Large\frac{1+b^2}{(1-m)^2+b^2}\normalsize} , \quad b = \Large\frac{4 a \omega^2}{3 \pi g}\normalsize C_d , \quad m = \Large\frac{M \omega^2}{\rho g A}\normalsize = \Large\frac{\rho_{fbw} D \omega^2}{\rho g}\normalsize , \qquad (A4)[/math]
where [math]\rho_{fbw}[/math] is the average density of the floating breakwater. The phase shift [math]\phi[/math] is given by
[math]\tan \phi = \Large\frac{bm}{1-m+b^2}\normalsize. \qquad (A5)[/math]
The draft [math]D[/math] should be chosen such that resonance [math]m=1[/math] under energetic wave conditions is avoided.
Related articles
- Detached breakwaters
- Detached shore parallel breakwaters
- Port breakwaters and coastal erosion
- Applicability of detached breakwaters
References
- ↑ 1.0 1.1 Hales, L.Z. 1981. Floating Breakwaters: State-of-the-Art Literature Review. US Army Corps of Engineers Technical Report 81-1
- ↑ 2.0 2.1 2.2 2.3 2.4 2.5 McCartney, B. 1985. Floating breakwater design, J. of Waterway, Port, Coastal and Ocean Engineering 111: 304-318
- ↑ Cebada-Relea, A.J., Lopez, M., Claus, R. and Aenlle, M. 2023. Short-term analysis of extreme wave-induced forces on the connections of a floating breakwater. Ocean Engineering 280, 114579
- ↑ Martinelli, L. and Ruol, P. 2006. 2D Model of Floating Breakwater Dynamics under Linear and Nonlinear Waves, 2nd Comsol User Conference, 14 Nov., Milano
- ↑ Li, C., Zhang, H., Zhang, H., Sun, B. and Yang, S. 2022. Wave-attenuation and hydrodynamic properties of twin pontoon floating breakwater with kelp. Applied Ocean Research 124 (2022) 103213
- ↑ Guo, Y.C., Mohapatra, S.C. and Guedes Soares, C. 2023. Experimental performance of multi-layered membrane breakwaters. Ocean Engineering 281, 114716
- ↑ Koutandos, E. and Prinos, P. 2005. Design formulae for wave transmission behind floating breakwaters. XXXI IAHR congress, paper 4081
- ↑ Alizadeh, M.J., Kolahdoozan, M., Tahershamsi, A. and Abdolali, A. 2014. Experimental Study of the Performance of Floating Breakwaters with Heave Motion. Civil Engineering Infrastructures Journal 47(1): 59 – 70
- ↑ Moghim, N. and Botshekan, M. 2017. Analysis of the performance of pontoon-type floating breakwaters. Hong Kong Institution of Engineers Transactions 24: 9–16
- ↑ Elsheikh, A.K., Mostafa, Y.E. and Mohamed, M.M. 2022. A comparative study between some different types of permeable breakwaters according to wave energy dissipation. Ain Shams Engineering Journal 13, 101646
- ↑ Quartier, N., Ropero-Giralda, P., Domínguez, J.M., Stratigaki, V. and Troch, P. 2021. Influence of the Drag Force on the Average Absorbed Power of Heaving Wave Energy Converters Using Smoothed Particle Hydrodynamics. Water 13, 384
Other sources
- Allyn N., E. Watchorn, W. Jamieson and Y. Gang, 2001. Port of Brownsville Floating Breakwater, Proc. Ports Conference.
- Briggs M, Y. Ye, Z. Demirbilek and J. Zhang, Field and numerical comparisons of the RIBS floating breakwater, J. of Hydraulic Research, 40(3), 289-301.
- Gesrah M.R. 2006. Analysis of 5 shaped floating breakwater in oblique waves: I. Impervious rigid wave boards. Applied Ocean Research, 28(5) 327–338.
- Isaacson M and O.U. Nwogu, 1987. Wave loads and motions of long structures in directional seas, J Offshore Mech Arct Eng 109, 126–132.
- Isaacson M. (1993): Wave effects of floating breakwaters, Proc. of the 1993 Canadian Coastal Conference, May 4-7, Vancouver, British Columbia, 53-66.
- Isaacson M. and S. Sinha, 1986. Directional wave effects on large offshore structures, J. of Waterway, Port, Coastal and Ocean Engineering, 112(4), 482-497.
- Martinelli L., Zanuttigh B., Ruol P., 2007. Effect of layout on floating breakwater performance: results of wave basin experiments . Proc. Coastal Structures '07, Venice.
- PIANC. Floating breakwaters - a practical guide for design and construction PTC2 report of WG 13 – 1994
- Richey E.P. (1982): Floating Breakwater Field experience, West Coast. Report MR 82-5, U.S. Army, Corps of Engineers, Coastal Engineering Research Center; Springfield, Va, 64 pp.
- Ruol P. and Martinelli L., 2007. Wave flume investigation on different mooring systems for floating breakwaters. Proc. Coastal Structure '07, Venice.
- Sannasiraj S.A., V. Sundar and R. Sundaravadivelu, 1998. Mooring forces and motion responses of pontoon-type floating breakwaters, Ocean Eng., 25 (1), 27-48.
- Silander, J. 1999 Floating Breakwater and Environment.
- Tsinker G., 1994. Marine structure engineering: specialized application, Chapman & Hall, International Thomson Publishing Inc.
- Van der Meer J.W., R. Briganti, B. Zanuttigh and B. Wang, 2005. Wave transmission and reflection at low-crested structures: Design formulae, oblique wave attack and spectral change, Coastal Eng., 52(10-11), 915-929.
- Yamamoto T., 1981. Moored floating breakwater response to regular and irregular waves. Applied Ocean Research 3, 27–36.
Please note that others may also have edited the contents of this article.
|
