A machine learning architecture for including wave breaking in envelope-type wave models

Aug 3, 2026

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Wave breaking is a complex physical process with open research questions, and many applications require breaking effects in phase-resolved envelope-based wave models such as the nonlinear Schrödinger. This paper extends the machine-learning architecture proposed by Eeltink et al. (2022) to model breaking effects in a more detailed way. The model is trained on focused wave groups, yet it also represents breaking in random waves and modulated plane waves. Analysis indicates the learning separates breaking detection from subsequent evolution, matching common scientific understanding of the problem.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages17

Reading Time43 min

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Introduction

Wave breaking physics and significance

Multi-scale modeling challenges in ocean waves

Breaking criteria and breaking inception

Post-breaking evolution and modeling approaches

Ocean Engineering 305 (2024) 118009 | A machine learning architecture for including wave breaking in envelope-type wave models
Yuxuan Liu a,∗, Debbie Eeltinka,b,c, Ton S. van den Bremer a,d, Thomas A.A. Adcock aa Department of Engineering Science, University of Oxford, Oxford, OX1 3PJ, United Kingdom
b Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, 02139 -4307, MA, USAc Laboratory of Theoretical Physics of Nanosystems, EPFL, Lausanne, Ch-1015, Switzerland
d Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, 2628 CD, The Netherlands | | | | --- | --- | --- | | A R T I C L E I N F O
Keywords:
Wave breaking
Nonlinear process
Phase-resolved envelope-based wave models Machine learning | A B S T R A C T | | | | 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. | | 1. Introduction Surface gravity wave breaking is a familiar phenomenon to those observing the ocean (Babanin, 2011), yet a good understanding capturing the fundamental physics of wave breaking has proved difficult for scientists and engineers. Understanding breaking is important for multiple reasons, including for understanding the energy balance in the ocean (Hasselmann, 1974), ocean mixing (Melville et al., 1998), airsea interaction (Melville, 1996; Deike, 2022), short-term wave statistics (Toffoli et al., 2010), and loading on maritime structures (Peregrine, 2003). The problem of wave-breaking in the ocean is multi-scale. Wave breaking must be represented in phase-average sea-state models which typically have the scale of 􀁏(10–100 km) but ultimately these are trying to capture energy dissipation processes which occur at 􀁏(1 μm- 10 m) (Deike, 2022). Understanding the problem of wave breaking on a wave-by-wave basis (as opposed to a phased-averaged sea-state analysis) is frequently broken down into understanding when waves break and then understanding the subsequent evolution. Both parts of the problem are active areas of research. Wave breaking criteria typically use the wave steepness, wave speed and water depth to provide a threshold above which waves would break. Various formulations for breaking criteria exist. Recent developments on this is the concept of breaking inception introduced ∗ Corresponding author. E-mail address: [yuxuan.liu@eng.ox.ac.uk](yuxuan.liu@eng.ox.ac.uk) (Y. Liu). in Derakhti et al. (2020), which describes the initiation of an irreversible process within the crest that leads to breaking and occurs prior to the stage of breaking onset. The breaking inception indicator proposed by Derakhti et al. (2020) is based on the diagnostic parameter 􀁂 thresh used in the kinematic breaking criterion (Barthelemy et al., 2018). In Barthelemy et al. (2018), a threshold value 􀁂 thresh ≈ 0.855 is suggested, and this experimental threshold value is verified in laboratory experiments and numerical studies for a variety of wave packet types. The post-breaking behaviour is a complex multi-scale process. The breaking process generates turbulence, which is chaotic and complex. In simplified potential flow-bas

FAQs

Why must wave breaking be included in phase-resolved envelope-based wave models?

Many applications require capturing breaking effects within phase-resolved envelope-based models, such as nonlinear Schrödinger-type equations, to improve physical realism.

How is the proposed machine learning model trained and what wave types can it handle?

The architecture is trained on focused wave groups and can also capture breaking in random waves and modulated plane waves.

What does the analysis suggest about how the machine learning model works?

The learning process splits the task into two components: one that detects whether the wave is breaking and another that models the subsequent behavior.

Aug 3, 2026

Upload by Eliana