Wave breaking is a complex physical process about which open questions remain. For some applications, it is critical to include breaking effects in phase-resolved envelope-based wave models such as the non-linear Schrödinger. A promising approach is to use machine learning to capture breaking effects. In the present paper we develop the machine learning architecture to model breaking developed by Eeltink et al. (2022) further, potentially enabling more detailed breaking physics to be captured. We show that this model can be trained on focused wave groups but can also capture breaking in random waves and modulated plane waves. Analysis of the model suggests that the machine learning has broken the problem into two—one part which detects whether the wave is breaking and another which captures the subsequent behaviour, consistent with the way human scientists routinely understand the breaking problem.

Wave breaking is a multifaceted physical phenomenon that is not fully understood and remains challenging to model. An effective method for investigating wave breaking involves utilising the two-phase Reynolds-averaged Navier–Stokes (RANS) equations to directly simulate breaking waves. In this study, we apply a RANS model with an adaptively refined mesh to simulate breaking waves in deep water using the stabilised RANS model proposed by Larsen and Fuhrman. This approach enables a more efficient simulation of the physics of breaking waves compared to Direct Numerical Simulations, as it places less stringent demands on grid resolution. Our findings demonstrate that the RANS model compares well with deep water wave breaking experiments in terms of surface elevation. We also give estimates of the breaking strength parameter of our RANS simulations and compared them with the literature.

Wave breaking is the main mechanism that dissipates energy from ocean waves by wind. Its effects on the frequency spectrum cause a downshift of the spectral peak and dissipation of the total energy of the spectrum. Various reduced-form wave breaking models have been developed to capture wave breaking in envelope-based wave evolution equations for perturbed plane-wave systems, but their applicability to waves with a continuous spectrum has not been examined. In this paper we perform modified nonlinear Schrödinger equation simulations to study four existing wave breaking models and compare the results with new experimental data for breaking unidirectional wave groups. We first compare the different wave breaking models for perturbed plane-wave simulations and then examine their potential extension to waves with a continuous spectrum. We find that most existing models are able to model breaking in perturbed plane waves, but none produce the correct spectral dissipation for focused wave groups. We propose a modification to the breaking model by Kato and Oikawa [J. Phys. Soc. Jpn. 64, 4660 (1995)0031-901510.1143/JPSJ.64.4660] in order to model breaking in focused wave groups. The modified model incorporates both a breaking criterion, which activates and deactivates the dissipation term proposed by Kato and Oikawa, and a heuristic spectral weighting function that is obtained by fitting to experimental data. The modified model also predicts breaking in perturbed plane waves well.