The passage of ships in confined waterways creates a stern wave that can overflow bank protection structures such as groins. This overflow, due to the long-period primary ship-induced waves, can be high in velocity, especially at the lee-side slope of groins, potentially causing significant damage to the structure. This study derives an equation to express overflow velocities, intended as a design tool for groins exposed to these types of waves. A detailed experimental investigation was performed on four physical models of groins with different slopes and stone sizes in the armor layer under the influence of different hydraulic heads. Particle image velocimetry (PIV) was used to measure the flow velocities at the crest and lee sides of the structure. All PIV measurements were performed thrice under free-flow conditions with no initial water level at the lee side of the structure. The depth- and time-averaged flow velocities (Uavg) were extracted from four positions along the lee-side slope and accelerated from 0.7 to 2.2 m/s. A dimensionless equation of the overflow velocities was obtained as a function of the hydraulic head (h), slope (θ), freeboard (Rc), and nominal rock diameter (dn50).

This study treats a detached homogenous low-crested structure (HLCS) made of Cubipod concrete elements placed seaward of a vertical wall (forming a basin in between) to reduce overtopping. Assessing the complex hydrodynamics and effects of changing the geometry of such a system in relation to overtopping reduction is challenging. The numerical model OpenFOAM was applied to this end. Forchheimer coefficients for wave transmission and the flow through the HLCS were calibrated and validated using existing physical modeling data (α = 500 and β = 1.0, with varying porosity based on the Cubipod shape), while the effect of the basin and vertical seawall was determined fully numerically. The crest freeboard (R_c), crest width (B), and basin length (L_B) were the main geometrical parameters that influenced the performance of the HLCS in reducing overtopping. An exponential decay was observed in the overtopping discharge when the values of these geometrical parameters increased. As L_B increased, this decay was primarily due to the dissipation of the broken-wave bores. The largest gradient in the predicted overtopping discharge was noted at R_c/H_s,i ≈ 0, B/H_s,i ≈ 4.5, and L_B/L_p ≈ 1.2, where H_s,i is the incident significant wave height and L_p is the peak wavelength in the basin.