arXiv subjects

Adrian H. Callaghan

Publications and source records attributed to Adrian H. Callaghan.

5 recordsLinked to original sources

arXiv2026

Breaking-induced energy dissipation of surface gravity waves at varying scales and co-flowing wind stresses

Breaking-induced energy dissipation is studied for individual unsteady breaking waves using laboratory measurements of unidirectional surface gravity wave groups across a range of wave scales and wind stresses. A refined framework to estimate breaking-induced dissipation $\Delta E_{br}$ is proposed that accounts for background dissipation from non-breaking processes. Using this framework, we show that variations in wave scale primarily influence breaking energetics, such as fractional dissipation $\Delta E_{br}/E_0$ and dissipation rate $\epsilon_b$, by modifying the breaking onset threshold. Also, co-flowing wind systematically reduces both $\Delta E_{br}/E_0$ and $\epsilon_b$ relative to unforced conditions, as wind-forced waves break earlier with reduced crest forward-leaning. Exploiting the crest-front steepness at incipient breaking $\mathcal{S}_{\text{front}}(t_b)$ to characterise breaking onset and local crest geometry, we formulate a scaling for $\epsilon_b$ based on this local measure. This then yields $\Delta E_{br}/E_0 \propto \beta^{*}\,\mathcal{S}_b\,(\tau_b/T_b)$, where $\beta^{*}$ is crest forward leaning, $\mathcal{S}_b$ local steepness, and $\tau_b/T_b$ non-dimensional breaking duration. This scaling highlights the important roles of crest asymmetry and breaking duration in setting the breaking energy dissipation. Finally, we consider the breaking strength parameter $b$ by assessing existing steepness-based scaling laws, and relate $b$ to $\mathcal{S}_{\text{front}}(t_b)$, yielding an approximately linear dependence once the breaking-onset threshold is considered.

physics.flu-dyn↗

arXiv2026

On the limiting geometry of unsteady breaking waves subject to co-flowing wind: spectrally-informed versus locally-measured steepness

Wave steepness is a key geometric variable for describing breaking occurrence and its consequences, including energy dissipation and air entrainment. Using three laboratory campaigns under varying spectral conditions and co-flowing wind forcing, we contrast two types of steepness commonly used for unsteady breaking waves: spectrally-informed wave-group steepness (prognostic), obtained from fixed-point surface-elevation records, and locally-measured crest steepness (diagnostic), obtained from spatial surface profiles extracted using the SDBW-I image-processing method developed herein. For the former, the long-adopted $\mathcal{S}_n$ (linear sum of Fourier-component steepness) increases appreciably within about two dominant wavelengths upstream of breaking because of its sensitivity to evolving high-frequency content. When measured sufficiently far upstream, however, wave-group steepness remains approximately linearly related to the local zero-crossing steepness $\mathcal{S}_b$ across bulk unforced conditions. Notwithstanding this, we argue that the crest-front steepness, $\mathcal{S}_{\mathrm{front}}(t_b)$, which delineates the front-face slope at incipient breaking, is the most physically meaningful metric examined here. It exhibits a consistent breaking-onset lower-bound threshold of $\mathcal{S}_{\mathrm{front}}(t_b)\approx0.2$, while values above this threshold decrease with wind speed as crests become less forward leaning. This may be attributed to wind-modified dispersion, enhanced high-frequency spectral content and aerodynamic sheltering, suggesting that wind--wave and wave--wave interactions act as competing mechanisms in triggering breaking through kinematic and energetic processes beyond what geometry alone can explain. Even so, $\mathcal{S}_{\mathrm{front}}(t_b)$ has strong potential as a controlling variable for future studies of breaking energetics and crest-scale dynamics.

physics.flu-dyn↗

arXiv2025

Generative Discovery of Partial Differential Equations by Learning from Math Handbooks

Data driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data driven techniques face the dilemma of balancing search space with optimization efficiency. This study introduces a knowledge guided approach that incorporates existing PDEs documented in a mathematical handbook to facilitate the discovery process. These PDEs are encoded as sentence like structures composed of operators and basic terms, and used to train a generative model, called EqGPT, which enables the generation of free form PDEs. A loop of generation evaluation optimization is constructed to autonomously identify the most suitable PDE. Experimental results demonstrate that this framework can recover a variety of PDE forms with high accuracy and computational efficiency, particularly in cases involving complex temporal derivatives or intricate spatial terms, which are often beyond the reach of conventional methods. The approach also exhibits generalizability to irregular spatial domains and higher dimensional settings. Notably, it succeeds in discovering a previously unreported PDE governing strongly nonlinear surface gravity waves propagating toward breaking, based on real world experimental data, highlighting its applicability to practical scenarios and its potential to support scientific discovery.

cs.LG↗

arXiv2025

Physics-informed neural networks for phase-resolved data assimilation and prediction of nonlinear ocean waves

The assimilation and prediction of phase-resolved surface gravity waves are critical challenges in ocean science and engineering. Potential flow theory (PFT) has been widely employed to develop wave models and numerical techniques for wave prediction. However, traditional wave prediction methods are often limited. For example, most simplified wave models have a limited ability to capture strong wave nonlinearity, while fully nonlinear PFT solvers often fail to meet the speed requirements of engineering applications. This computational inefficiency also hinders the development of effective data assimilation techniques, which are required to reconstruct spatial wave information from sparse measurements to initialize the wave prediction. To address these challenges, we propose a novel solver method that leverages physics-informed neural networks (PINNs) that parameterize PFT solutions as neural networks. This provides a computationally inexpensive way to assimilate and predict wave data. The proposed PINN framework is validated through comparisons with analytical linear PFT solutions and experimental data collected in a laboratory wave flume. The results demonstrate that our approach accurately captures and predicts irregular, nonlinear, and dispersive wave surface dynamics. Moreover, the PINN can infer the fully nonlinear velocity potential throughout the entire fluid volume solely from surface elevation measurements, enabling the calculation of fluid velocities that are difficult to measure experimentally.

cs.LG↗

arXiv2024

Discovering Boundary Equations for Wave Breaking using Machine Learning

Many supervised machine learning methods have revolutionised the empirical modelling of complex systems. These empirical models, however, are usually "black boxes" and provide only limited physical explanations about the underlying systems. Instead, so-called "knowledge discovery" methods can be used to explore the governing equations that describe observed phenomena. This paper focuses on how we can use such methods to explore underlying physics and also model a commonly observed yet not fully understood phenomenon - the breaking of ocean waves. In our work, we use symbolic regression to explore the equation that describes wave-breaking evolution from a dataset of in silico waves generated using expensive numerical methods. Our work discovers a new boundary equation that provides a reduced-order description of how the surface elevation (i.e., the water-air interface) evolves forward in time, including the instances when the wave breaks - a problem that has defied traditional approaches. Compared to the existing empirical models, the unique equation-based nature of our model allows further mathematical interpretation, which provides an opportunity to explore the fundamentals of breaking waves. Further expert-AI collaborative research reveals the physical meaning of each term of the discovered equation, which suggests a new characteristic of breaking waves in deep water - a decoupling between the water-air interface and the fluid velocities. This novel reduced-order model also hints at computationally efficient ways to simulate breaking waves for engineering applications.

physics.flu-dyn↗