Spatial distribution of wave-by-wave overtopping behind coastal structures: a critical review of the literature and a novel semi-analytical model

Understanding the spatial distribution of wave overtopping behind coastal protection structures is critical for an accurate safety assessment of the protected regions. This paper presents a systematic review of the current state of research in this field, summarizing the key mechanisms and predictive methodologies. While physical modeling has traditionally been the primary method for investigating spatial overtopping, its outcomes are often simplified into empirical formulas. However, their predictive accuracy of these formulas is compromised when applied to diverse structural geometries, a limitation stemming from their calibration against a narrow range of configurations. To address this limitation, this study proposes a novel semi-analytical model that, by refining the calculation of overtopping velocity at the structure’s crest, achieves a more accurate prediction of the spatial distribution of overtopping on coastal structures with diverse slopes. The model results show good agreement with numerical simulations and multiple sets of experimental data. Additionally, researchers still face challenges in addressing uncertainties from scale effects, quantifying wind effects in laboratory settings and translating them into practical guidance, predicting overtopping distribution under extreme climatic conditions, and assessing the effects of oblique waves and 3D effects on the spatial distribution of overtopping.