Transformation of significant wave height and set-up due to entrained air bubbles effect in breaking waves

Abstract

The transformation of wave height is of paramount significance in coastal engineering and the design of coastal structures. Considering the influence of air bubbles, this study devised an optimal dissipation model for accurately calculating changes in significant wave height (H_m0) and wave set-up for irregular waves undergoing breaking. Existing regular wave breaking models, which consider the effects of air bubbles, were adapted for direct application to irregular waves by deriving novel formulations. The proposed models leverage the probability of the fraction of broken waves. H_m0 was computed using the energy balance equation, while the wave set-up was calculated based on the momentum balance equation. A wide range of test scenarios, incorporating diverse scales (small and large) and experimental field data, was considered for validation. One of the proposed models, namely model-I (M-I), particularly demonstrated superior performance, manifesting lower error indices (P20), root-mean-square relative error (RMSRE), and Brier skill score (BSS) values in computing both H_m0 and wave set-up. Therefore, utilising M-I is strongly recommended for the precise estimation of H_m0 and set-up transformation.