Wave overtopping

Definition of Wave overtopping: Wave overtopping is the average amount of water that is discharged per linear meter by waves over a protection structure (e.g. breakwater, dike) whose crest is higher than the still water level (SWL). This is the common definition for Wave overtopping, other definitions can be discussed in the article

Fig. 1a. Wave-overtopping of a breakwater in a flume test.	Fig. 1b. Wave-overtopping of a breakwater in nature.

Notes

Pictures of wave overtopping in the laboratory and in the field are shown in Fig. 1; a schematic representation with definitions is displayed in Fig. 2. During overtopping, two important processes take place: wave run-up on the structure and partial transmission of waves. There is no permanent discharge over the crest of a structure during overtopping. The process of wave overtopping is very random in time, space and volume. The highest waves will wash a large volume of water over the crest in a short period of time (less than a wave period), whereas lower waves may not produce any overtopping.

An empirical formula of wave overtopping of coastal structures is given in the EurOtop manual. As observational overtopping rates of more than a factor 10 higher were observed in several experiments, a revised formula was developed by Eldrup et al. 2022. The general form of the formula for the average water discharge [math]q[/math] per linear meter by waves over a protection structure is

[math]q=a \, \sqrt{gH_{m0}^3} \, \exp\Big[ \big(-b \large\frac{R_c}{H_{m0}}\normalsize \big)^c \Big], [/math]

Fig. 2. Waves overtopping a breakwater; definition of symbols.

where the coefficients [math]a, b, c[/math] depend on (see Fig. 2):

• The spectral wave height [math]H_{m0}[/math] (approximately equal to the significant wave height [math]H_s[/math], see Statistical description of wave parameters)
• The mean wave energy period [math]T_{m-1,0}[/math]
• The water depth [math]h[/math] at the toe of the structure
• The breakwater wave run-up [math]R_2[/math] exceeded by only 2 % of the waves; [math]R_2/ H_{m0}[/math] depends on the roughness (and permeability) reduction factor [math]\gamma_f[/math], the surf similarity parameter [math]\xi[/math] and the wave obliqueness
• The freeboard [math]R_c[/math] (the structure crest level relative to the still water level (SWL); overtopping occurs if [math]\; R_c \lt R_2 \;[/math])
• The seabed slope [math]m[/math]
• The front slope of the structure [math]\tan \alpha[/math]
• The crest width of the structure [math]G_c[/math]
• The surf similarity parameter (Iribarren number) [math]\xi[/math]
• The roughness (and permeability) reduction factor [math]\gamma_f[/math] that accounts for the roughness and percolation of structures’ slope. The reduction factor [math]\gamma_f[/math] may further depend on the surf similarity parameter and the overtopping flow rate. Usual values are in the range [math]\gamma_f \sim 0.38 – 0.6[/math].

A simpler formula for overtopping of rubble mound breakwaters by surging waves was empirically derived by Etemad-Shahidi et al. 2022:

[math]q = (1.22 \pm 0.13) 10^{-4} \, \sqrt{gH_{m0}^3} \, \exp \big[ (3.5 \pm 0.13) \large\frac{R_2 -R_c}{H_{m0}}\normalsize – (0.64 \pm 0.07) \large\frac{G_c}{H_{m0}}\normalsize \big] . [/math]

The standard deviation of observational data with respect to this formula is about a factor 2-3.

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