Wave height distribution for plunging breakers induced by air bubbles

Abstract

This study highlights the wave height distributions based on plunging breaking waves and air bubble effects in the surf zone. Wave height distributions predicted previously by different models have been reformulated in terms of air bubble effects. Some of the most commonly applied wave height distributions are judged using laboratory observations in a custom-built wave flume. Results have revealed a notable deviation from the Rayleigh distribution, with the proposed model demonstrating a closer match to experimental data, particularly for larger wave heights. Probability densities of larger wave heights are reduced significantly by entrained air bubbles, leading to measured wave heights below Rayleigh distribution predictions. In addition, the different wave height parameters derived from the proposed model exhibited good agreement with laboratory data compared to the Rayleigh distribution. Furthermore, theoretical analysis shows the scale parameter's dependence on the decay coefficient, aligning well with measurements and simplifying the proposed distribution to a one-parameter model. Again, based on the error analysis, the proposed model's results show good performance compared to others.