Floating breakwaters
Contents
Use of floating breakwaters
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]}). Therefore, they are used for protecting small craft harbours or marinas or, less frequently, the shoreline, aiming at erosion control. 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 1  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 posttensioned, 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 waveinduced 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 nonlinear interaction of the incident wave (that may partially overtop the module and is in general shortcrested 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 longperiod high waves.
Effectiveness
Box breakwaters
Box type breakwaters are used most frequently (see figures 1 and 2). Most boxtype 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 (Fig. 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^{[5]}. 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 boxtype breakwaters^{[6]}^{[7]}^{[8]}^{[9]}. 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]W/L[/math].
Application
Floating breakwaters can provide suitable protection measures for small boat harbor at some locations. However, they must be properly designed for the site conditions with an understanding of their limitations^{[2]}.
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 Fig. 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 = \rho \, C_d \, A \,\Large\frac{4 a \omega}{3 \pi}\frac{\partial (\zeta  \eta)}{\partial t}\normalsize , [/math]
where [math]C_d[/math] is a dimensionless friction coefficient of order 1^{[10]}. Other body motions (e.g. pitch, roll, sway) are ignored.
According to linear wave theory (see Shallowwater 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(hD))}{\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}{(1m)^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}{1m+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.
See also
Articles about breakwaters in general:
Articles about detached breakwaters:
Articles about shore or coastal protection:
References
 ↑ ^{1.0} ^{1.1} Hales, L.Z. 1981. Floating Breakwaters: StateoftheArt Literature Review. US Army Corps of Engineers Technical Report 811
 ↑ ^{2.0} ^{2.1} ^{2.2} ^{2.3} ^{2.4} ^{2.5} ^{2.6} McCartney, B. 1985. Floating breakwater design, J. of Waterway, Port, Coastal and Ocean Engineering 111: 304318
 ↑ CebadaRelea, A.J., Lopez, M., Claus, R. and Aenlle, M. 2023. Shortterm analysis of extreme waveinduced 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
 ↑ Guo, Y.C., Mohapatra, S.C. and Guedes Soares, C. 2023. Experimental performance of multilayered 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 pontoontype 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., RoperoGiralda, 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
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