Wave transmission by low-crested breakwaters

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

Notes

Submerged and low-crested breakwaters are specifically designed to mitigate the attack of incoming waves and thereby 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). One drawback is the presence of rip currents along the extremities of the breakwater, which counterbalance the overall onshore water flow across the submerged breakwater^[1][2].

Fig. 2. 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].

The wave transmission performance of a low-crested breakwater is expressed through the wave transmission coefficient [math]K_t = H_t / H_i[/math]. The transmission coefficient depends primarily on (see Fig. 2):

• Freeboard [math]R_c[/math], the distance between the breakwater crest level and the still water level (positive for emergent crest and negative for submerged crest)
• Width [math]G_c[/math] of the breakwater crest
• The wave conditions, represented by the surf similarity parameter [math]\xi = T_p \, \tan \alpha \, \sqrt{ \Large\frac{g}{2 \pi H_i}\normalsize}[/math].

Meaning of the symbols:

• [math]H_i[/math] the spectral wave height of the incoming wave at the toe of the structure (approximately equal to the significant wave height, see Statistical description of wave parameters)
• [math]H_t[/math] the spectral height of the transmitted wave
• [math]T_p[/math] the peak spectral wave period
• [math]\tan\alpha[/math] the slope of the structure
• [math]g[/math] the gravitational acceleration

Fig. 3. Graphical estimate of the wave transmission coefficient as a function of the relative freeboard, based on laboratory data^[3]. The hatched area indicates the level of accuracy.

Several empirical expressions for the wave transmission coefficient have been derived from laboratory experiments and tested in field situations. A frequently used formula was established by D’Angremond et al. (1997^[4]) for unbroken waves,

[math]K_t \equiv \Large\frac{H_t}{H_i}\normalsize = - 0.4 \Large\frac{R_c}{H_i}\normalsize + C \Big( \Large\frac{G_c}{H_i}\normalsize \Big)^{-0.31} , \qquad (1) [/math]

where [math]C[/math] is a coefficient with value 0.8 for impermeable breakwaters and 0.64 for permeable breakwaters.

Application of this formula to over 4000 available laboratory and field data shows that 62% of data falls within a confidence level of 20% and 87% of data falls within a confidence level of 50%^[5].

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 version for this case was proposed by Briganti et al. (2004^[6]),

[math]K_t = - 0.35 \Large\frac{R_c}{H_i}\normalsize + 0.51 \Big( \Large\frac{G_c}{H_i}\normalsize \Big)^{-0.65} [1 - \exp(-0.41 \xi)] . \qquad (2) [/math]

Fig. 3 gives a rough visual estimate of the transmission coefficient from laboratory data as a function of the relative freeboard.

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References