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.

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Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, pp. 364–391) and Pizzo et al. (J. Phys. Oceanogr., vol. 49, no. 4, 2019, pp. 983–992) have indicated transport by deep-water breaking waves is enhanced compared with non-breaking waves. To model particle transport in irregular waves, some of which break, we develop a stochastic differential equation describing both mean particle transport and its uncertainty. The equation combines a Brownian motion, which captures non-breaking drift-diffusion effects, and a compound Poisson process, which captures jumps in particle positions due to breaking. From the corresponding Fokker–Planck equation for the evolution of the probability density function for particle position, we obtain closed-form expressions for its first three moments. We corroborate these predictions with new experiments, in which we track large numbers of particles in irregular breaking waves. For breaking and non-breaking wave fields, our experiments confirm that the variance of the particle position grows linearly with time, in accordance with Taylor's single-particle dispersion theory. For wave fields that include breaking, the compound Poisson process increases the linear growth rate of the mean and variance and introduces a finite skewness of the particle position distribution.@en

Wave breaking is the main mechanism that dissipates energy input into ocean waves by wind and transferred across the spectrum by nonlinearity. It determines the properties of a sea state and plays a crucial role in ocean-atmosphere interaction, ocean pollution, and rogue waves. Owing to its turbulent nature, wave breaking remains too computationally demanding to solve using direct numerical simulations except in simple, short-duration circumstances. To overcome this challenge, we present a blended machine learning framework in which a physics-based nonlinear evolution model for deep-water, non-breaking waves and a recurrent neural network are combined to predict the evolution of breaking waves. We use wave tank measurements rather than simulations to provide training data and use a long short-term memory neural network to apply a finite-domain correction to the evolution model. Our blended machine learning framework gives excellent predictions of breaking and its effects on wave evolution, including for external data.

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One of the promising platforms for creating Majorana bound states is a hybrid nanostructureconsisting of a semiconducting nanowire covered by a superconductor. We analyze the previouslydisregarded role of electrostatic interaction in these devices. Our main result is that Coulombinteraction causes the chemical potential to respond to an applied magneticfield, while spin–orbitinteraction and screening by the superconducting lead suppress this response. Consequently, theelectrostatic environment influences two properties of Majorana devices: the shape of the topologicalphase boundary and the oscillations of the Majorana splitting energy. We demonstrate that bothproperties show a non-universal behavior, and depend on the details of the electrostatic environment.We show that when the wire only contains a single electron mode, the experimentally accessibleinverse self-capacitance of this mode fully captures the interplay between electrostatics and Zeemanfield. This offers a way to compare theoretical predictions with experiments@en