Formulating Wave Overtopping at Vertical and Sloping Structures with Shallow Foreshores Using Deep-Water Wave Characteristics

Acknowledgments

Notation

C_ηη

wave-variance density (m²/Hz);

g

gravitational constant of acceleration (m²/s);

H_1/3

significant wave height based on zero-crossing analysis (m);

H_m0

significant wave height, based on spectral moments = $4\sqrt{{\int }_0^{\mathrm{\infty }}{C}_{\eta \eta }df}$ (m);

H_m0,deep

significant wave height offshore in deep water (m);

H_m0,toe

significant wave height at the structure toe (m);

h_toe

initial water depth at the structure toe (m);

L_m−1,0

wave length in deep water based on the spectral wave period (m);

m

foreshore slope angle (°);

q

mean wave overtopping discharge (m³/s/m);

R²

coefficient of determination (—);

R_c

crest freeboard (m);

R_u2%

2% exceedance wave run-up (m) with respect to the number of incident waves;

s_om−1,0

deep-water wave steepness based on the spectral wave period (—);

s_op

deep-water wave steepness based on the peak wave period (—);

T_1/3

significant wave period (s) ≈ T_p/1.04;

T_m−1,0,deep

spectral wave period in deep-water (s) ≈ T_p/1.1;

T_m−1,0,toe

spectral wave period at the structure toe (s);

T_p

peak wave period in deep water (s);

${\overline{x}}_G$

geometric mean (—);

α

structure slope angle (°);

δ

equivalent slope, following Altomare et al. (2016) (—);

$\overline{\eta }$

wave-induced setup (m);

ξ_m−1,0

breaker index (Iribarren number) based on the spectral wave period and significant wave height at the structure toe (—); and

$\sigma ({\overline{x}}_G)$

geometric standard deviation (—).

References