Wave set-up and wave transmission by low-crested breakwaters

Definition of Low-crested breakwaters: Low-crested breakwaters are artificial wave damping structures in nearshore waters with crest level just above or just below the still water level (SWL). The latter category, also known as submerged breakwater, has a negative freeboard [math]R_c[/math]. This is the common definition for Low-crested breakwaters, other definitions can be discussed in the article

Definition of Transmitted wave: The transmitted wave is the wave propagating landward of an artificial or natural obstacle after transformation by reflection, dissipation and transmission over or through the obstacle. The wave transmission coefficient [math]K_t[/math] is the ratio of the wave heights of the transmitted and incoming waves. This is the common definition for Transmitted wave, other definitions can be discussed in the article

Fig. 1. Wave transmission over a submerged breakwater at Mandara beach, Alexandria (Egypt). The yellow arrows indicate the location of rip currents.

Arguments for low-crested/submerged breakwaters

Submerged and low-crested breakwaters are specifically designed to mitigate the attack of incoming waves on the coast and thereby aim to protect beaches against erosion. While these structures only partially reduce incoming waves, they offer several advantages over high-crested breakwaters. They do not obstruct the view of the sea and allow water circulation and flushing between the structure and the beach. These types of breakwaters are commonly utilized to protect tourist beaches (see Fig. 1). Low-crested or submerged breakwaters are sometimes termed 'artificial reefs'. This is usually the case when the breakwater fulfills an important function as habitat for ecological enhancement or ecological restoration (see Ecological enhancement of coastal protection structures). However, low-crested breakwaters also produce undesirable side effects, as explained in the following paragraphs.

Wave set-up by low-crested breakwaters

Fig.2. Schematic of net wave-induced onshore water transport over a submerged breakwater.

When waves pass over a low-crested or submerged breakwater, breaking, overtopping and transmission produce a net shoreward flux of water and a shoreward decrease in wave momentum flux. The resulting water-level set-up in the lee of the structure drives compensating return currents, often concentrated as rip currents through gaps or around the breakwater heads.

When passing a low-crested breakwater, breaking waves raise the sea level at the shore by two mechanisms:

• Shoreward mass transport, resulting from the greater landward water flux under wave crests compared to the seaward flux under wave troughs (Fig. 2);
• Radiation stress resulting from the landward decrease in wave height (see explanation in the article wave set-up).

The elevated sea levels at the shore drive seaward directed currents (so-called rip currents) through the gaps between breakwaters (Fig. 3). These currents are dangerous for bathers and small craft and they produce important scour at the extremities (roundheads) of the breakwaters. The eroded sediment is deposited at the seaward flank of the low-crested breakwater. See also Detached breakwaters.

In periods of high incident waves, rip currents cannot rapidly evacuate the water piled up against the shore, unless the gaps between low-crested breakwaters are very large. Under storm conditions, this wave-induced set-up adds to the water level set-up by winds and low air pressure. Low-crested breakwaters therefore increase flooding risks of homes and infrastructure on the coast.

Fig. 3. Schematic of beach response and rip cell circulation induced by a submerged breakwater situated seaward of the surf zone.

Low-crested breakwaters also have an impact on the position of the shoreline. Depending on the relative width of the gaps between breakwater segments (ratio of gap width to segment length) and depending on the relative distance from the shoreline (ratio of distance to surf zone width), the shoreline behind the breakwater may advance or retreat. Accretion generally prevails for small relative gap width and large (order of 1) relative distance from the shoreline. For an explanation and more details, see Detached breakwaters#Submerged or low-crested breakwaters. In some configurations, especially where strong rip currents export sediment offshore, the net sand balance landward of the submerged breakwater can be negative because offshore transport by rip currents is not fully compensated by onshore transport over the breakwater.

Fig. 4. Wave transmission over a low-crested breakwater and mathematical symbols. The freeboard [math]R_c[/math] is negative when the breakwater crest is below the still water level [math]SWL[/math].

Wave transmission by low-crested breakwaters

Wave attenuation by a low-crested breakwater results from the partition of incoming wave energy into reflected, dissipated and transmitted components. Dissipation occurs mainly through breaking on or above the crest, turbulence in the armor or reef pores, and bottom/frictional losses. Transmission can occur over the crest, through a permeable structure and by re-formation of waves in the lee. The transmission coefficient [math]K_t[/math] therefore summarizes a complex transformation and should be applied only within the range of geometry, porosity, wave conditions and water levels for which the chosen formula was calibrated.

The wave transmission coefficient [math]K_t = H_t / H_i[/math] (ratio of transmitted to incident wave height) expresses the wave attenuation performance of a low-crested breakwater. The transmission coefficient depends primarily on (see Fig. 4):

• the freeboard [math]R_c[/math], the distance between the breakwater crest level and the still-water level (negative for a submerged breakwater)
• the width [math]G_c[/math] of the breakwater crest
• the spectral wave height [math]H_i[/math] of the incoming wave at the toe of the structure (approximately equal to the significant wave height, see Statistical description of wave parameters)
• The wave conditions, represented by the surf similarity parameter [math]\xi = \Large\frac{\tan \alpha}{\sqrt{H_i / L}}[/math].

Meaning of the symbols:

• [math]H_t[/math] the spectral height of the transmitted wave
• [math]L = g T_p^2 / (2 \pi)[/math] the equivalent deep-water wavelength based on the peak period [math]T_p[/math]
• [math]T_p[/math] the peak spectral wave period
• [math]\tan\alpha[/math] the slope of the structure
• [math]g[/math] the gravitational acceleration

Several empirical expressions for the wave transmission coefficient have been derived from laboratory experiments and tested in field situations. The formulas are mainly intended for cross-shore transmission over idealized structure sections. For segmented breakwaters, oblique waves, directional spreading, diffraction through gaps and rip-current circulation can strongly modify the wave field in the lee; the formulas should therefore be used cautiously for three-dimensional field situations. Because [math]R_c[/math] is measured relative to the still-water level, the performance of low-crested and submerged breakwaters can change strongly with tide, storm surge and sea-level rise.

A frequently used formula was established by D’Angremond et al. (1997) for unbroken waves and for the range [math]0.075 \lt K_t \lt 0.8[/math],

[math]K_t \equiv \Large\frac{H_t}{H_i}\normalsize = c_1 \Large\frac{R_c}{H_i}\normalsize + c_2 \Big( \Large\frac{G_c}{H_i} \Big)^{c_3} \normalsize [1 - \exp(c_4 \xi)] , \qquad (1) [/math]

where [math]c_1=-0.4, \; c_2=0.8, \; c_3=-0.31, \; c_4=-0.5[/math]. For permeable breakwaters (e.g. rubble-mound breakwaters with porosity of about 0.5) the coefficient [math]c_2=0.8[/math] should be replaced by [math]c_2=0.64[/math].

Application of this formula to over 4000 available laboratory and field data showed that 62% of data falls within a confidence level of 20% and 87% of data falls within a confidence level of 50%.

Since it was observed that this formula overestimates the wave transmission of wide-crested breakwaters ([math]G_c / H_i \gt 10[/math]), an adjusted set of parameters for this case was proposed by Briganti et al. (2004) with coefficients [math]c_1=-0.35, \; c_2=0.51, \; c_3=-0.65, \; c_4=-0.41[/math].

Wave attenuation can also be obtained with biogenic reefs instead of rubble-mound or other artificial submerged structures. Wave attenuation by oyster reefs is dealt with in the article Oyster reef shore protection.

Fig. 5. Graphical estimate of the wave transmission coefficient as a function of the relative freeboard, based on laboratory data. The red glow of the curve indicates the level of accuracy.

Noticing the weak dependence of the transmission coefficient on the wave steepness and the slope of the structure, Van Gent et al. (2023) derived from a series of flume experiments the alternative formula,

[math]K_t = c_5 + c_1 \tanh \Bigg(c_4 - \Large\frac{R_c}{H_i}\normalsize - c_2 \bigg( \Large\frac{G_c}{L} \bigg)^{c_3} \normalsize \Bigg) , \qquad (2)[/math]

where [math]c_1=0.47, \; c_2=3.1, \; c_3=0.75, \; c_4=0, \; c_5=0.5 [/math] for impermeable smooth structures. For permeable structures (e.g. rubble-mound, with porosity of about 0.5) the values of the coefficients [math]c_1, c_4[/math] should be replaced by [math]c_1=0.43, \; c_4=0.25[/math]. The formula (2) was established for a series of experiments with [math]\; -2.5\lt R_c/H_i \lt 2.5, \; 0.017 \lt G_c / L \lt 0.27, \; 0.015 \lt H_i / L \lt 0.033[/math] and trapezoidal structures with slope 1:2.

Fig. 5 gives a rough graphical estimate of the transmission coefficient from laboratory data as a function of the relative freeboard.

Huang et al. (2024) conducted flume experiments of wave transmission over artificial reefs with a substantially higher porosity [math]n = 0.68[/math]. From these experiments it appeared that the structure of the porosity plays a role in the wave dissipation, which hampers direct comparison of their results with the experiments of Van Gent.

Wave dissipation and transmission depended for high porosity primarily on the extended water depth [math]h_{ce} = - R_c + n h_r[/math], which takes into account the height [math]n h_r[/math] of pore water in the reef. Here [math]h_r[/math] is the reef height measured from the toe. Since [math]R_c \lt 0[/math] for submerged structures, the crest submergence is [math]-R_c[/math]. The upper-bound transmission coefficient for non-breaking conditions is [math]K_{tu}[/math]. The crest width was larger than in the experiments of Van Gent et al., but only a small dependence of wave transmission on the relative crest width [math]G_c/L[/math] was found. The following formula was proposed for wave transmission over the highly porous reef (for [math]K_t \lt 1[/math]):

[math]K_t \approx 0.13+ 0.4 (K_{tu} - 0.13) \dfrac{h_{ce}}{H_i} \, , \; H_i \lt 0.4 h_r \, ; \quad K_t \approx K_{tu} \, , \; H_i \gt 0.4 h_r \; ; \quad K_{tu} = - 0.5 \Large\frac{R_c}{h_r}\normalsize +0.4 \, . \qquad (3)[/math]

This simplified expression corresponds to the porous artificial reef tested by Huang et al. with porosity [math]n=0.68[/math]; Huang et al. also proposed a weak additional correction for relative crest width.

Related articles

Detached breakwaters

Wave set-up

Wave overtopping

Stability of rubble mound breakwaters and shore revetments

Modelling coastal hydrodynamics

Artificial reefs

References

The main author of this article is Job Dronkers Please note that others may also have edited the contents of this article. Citation: Job Dronkers (2026): Wave set-up and wave transmission by low-crested breakwaters. Available from http://www.coastalwiki.org/wiki/Wave_set-up_and_wave_transmission_by_low-crested_breakwaters [accessed on 6-07-2026] For other articles by this author see Category:Articles by Job Dronkers For an overview of contributions by this author see Special:Contributions/Dronkers J