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We examine the implementation of a wave-breaking mechanism into a nonlinear potential flow solver. The success of the mechanism will be studied by implementing it into the numerical model HOS-NWT, which is a computationally efficient, open source code that solves for the free surface in a numerical wave tank using the high-order spectral (HOS) method. Once the breaking mechanism is validated, it can be implemented into other nonlinear potential flow models. To solve for wave-breaking, first a wave-breaking onset parameter is identified, and then a method for computing wave-breaking associated energy loss is determined. Wave-breaking onset is calculated using a breaking criteria introduced by Barthelemy et al. (J Fluid Mech https://arxiv.org/pdf/1508.06002.pdf, submitted) and validated with the experiments of Saket et al. (J Fluid Mech 811:642–658, 2017). Wave-breaking energy dissipation is calculated by adding a viscous diffusion term computed using an eddy viscosity parameter introduced by Tian et al. (Phys Fluids 20(6): 066,604, 2008, Phys Fluids 24(3), 2012), which is estimated based on the pre-breaking wave geometry. A set of two-dimensional experiments is conducted to validate the implemented wave breaking mechanism at a large scale. Breaking waves are generated by using traditional methods of evolution of focused waves and modulational instability, as well as irregular breaking waves with a range of primary frequencies, providing a wide range of breaking conditions to validate the solver. Furthermore, adjustments are made to the method of application and coefficient of the viscous diffusion term with negligible difference, supporting the robustness of the eddy viscosity parameter. The model is able to accurately predict surface elevation and corresponding frequency/amplitude spectrum, as well as energy dissipation when compared with the experimental measurements. This suggests the model is capable of calculating wave-breaking onset and energy dissipation successfully for a wide range of breaking conditions. The model is also able to successfully calculate the transfer of energy between frequencies due to wave focusing and wave breaking. This study is limited to unidirectional waves but provides a valuable basis for future application of the wave-breaking model to a multidirectional wave field. By including parameters for removing energy due to wave-breaking into a nonlinear potential flow solver, the risk of developing numerical instabilities due to an overturning wave is decreased, thereby increasing the application range of the model, including calculating more extreme sea states. A computationally efficient and accurate model for the generation of a nonlinear random wave field is useful for predicting the dynamic response of offshore vessels and marine renewable energy devices, predicting loads on marine structures, and in the study of open ocean wave generation and propagation in a realistic environment.

This article presents an overview of breaking waves and liquid sloshing impact acting on rigid walls and in liquid containers. The physics of breaking waves against rigid walls can be understood through the Bagnold/Mitsuyasu piston theory. The flip-through is a major feature associated with the occurrence of violent waves without any actual impact on the wall. The physics of the phase transition during liquid impacts involves two- and multi-phase flows due to the entrapped gas pockets is addressed. The liquid sloshing assessment of liquefied natural gas tanks together with the dimensionless parameters governing the design of small-scale models is discussed. The nonlinear liquid sloshing dynamics under sway and rotational excitations is described for different container geometries. This article will discuss recent developments of numerical algorithms and computer codes capable to describe breaking waves and extreme sloshing impacts. Moreover, recent advances in breaking Faraday waves are also addressed together with an assessment of breaking interfacial gravity waves, in which a multilayer or stratified medium is a stack of different thin layers.

We investigate the influence of capillary effects on wave breaking through direct numerical simulations of the Navier–Stokes equations for a two-phase air–water flow. A parametric study in terms of the Bond number, $\\mathit{Bo}$ , and the initial wave steepness, ${\\it\\epsilon}$ , is performed at a relatively high Reynolds number. The onset of wave breaking as a function of these two parameters is determined and a phase diagram in terms of $({\\it\\epsilon},\\mathit{Bo})$ is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. At high Bond number, a critical steepness ${\\it\\epsilon}_{c}$ defines the onset of wave breaking. At low Bond number, the influence of surface tension is quantified through two boundaries separating, first gravity–capillary waves and breakers, and second spilling and plunging breakers; both boundaries scaling as ${\\it\\epsilon}\\sim (1+\\mathit{Bo})^{-1/3}$ . Finally the wave energy dissipation is estimated for each wave regime and the influence of steepness and surface tension effects on the total wave dissipation is discussed. The breaking parameter $b$ is estimated and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation by parasitic capillaries is consistent with the dissipation due to breaking waves.

The role of wave breaking in microwave backscattering from the sea surface is a problem of great importance for the development of theories and methods on ocean remote sensing, in particular for oil spill remote sensing. Recently it has been shown that microwave radar return is determined by both Bragg and non-Bragg (non-polarized) scattering mechanisms and some evidence has been given that the latter is associated with wave breaking, in particular, with strong breaking such as spilling or plunging. However, our understanding of mechanisms of the action of strong wave breaking on small-scale wind waves (ripples) and thus on the radar return is still insufficient. In this paper an effect of suppression of radar backscattering after strong wave breaking has been revealed experimentally and has been attributed to the wind ripple suppression due to turbulence generated by strong wave breaking. The experiments were carried out in a wind wave tank where a frequency modulated wave train of intense meter-decimeter-scale surface waves was generated by a mechanical wave maker. The wave train was compressed according to the gravity wave dispersion relation (“dispersive focusing”) into a short-wave packet at a given distance from the wave maker. Strong wave breaking with wave crest overturning (spilling) occurred for one or two highest waves in the packet. Short decimeter-centimeter-scale wind waves were generated at gentle winds, simultaneously with the long breaking waves. A Ka-band scatterometer was used to study microwave backscattering from the surface waves in the tank. The scatterometer looking at the area of wave breaking was mounted over the tank at a height of about 1 m above the mean water level, the incidence angle of the microwave radiation was about 50 degrees. It has been obtained that the radar return in the presence of short wind waves is characterized by the radar Doppler spectrum with a peak roughly centered in the vicinity of Bragg wave frequencies. The radar return was strongly enhanced in a wide frequency range of the radar Doppler spectrum when a packet of long breaking waves arrived at the area irradiated by the radar. After the passage of breaking waves, the radar return strongly dropped and then slowly recovered to the initial level. Measurements of velocities in the upper water layer have confirmed that the attenuation of radar backscattering after wave breaking is due to suppression of short wind waves by turbulence generated in the breaking zone. A physical analysis of the effect has been presented.

Prolonged periods (e.g., several days or more) of heavy precipitation can result in sustained high-impact flooding. Herein, an investigation of long-duration heavy precipitation events (HPEs), defined as periods comprising ≥3 days with precipitation exceeding the climatological 95th percentile, is conducted for 1979–2019 for the U.S. West Coast, specifically Northern California. An objective flow-based categorization method is applied to identify principal large-scale flow patterns for the events. Four categories are identified and examined through composite analyses and case studies. Two of the categories are characterized by a strong zonal jet stream over the eastern North Pacific, while the other two are characterized by atmospheric blocking over the central North Pacific and the Bering Sea–Alaska region, respectively. The composites and case studies demonstrate that the flow patterns for the HPEs tend to remain in place for several days, maintaining strong baroclinicity and promoting occurrences of multiple cyclones in rapid succession near the West Coast. The successive cyclones result in persistent water vapor flux and forcing for ascent over Northern California, sustaining heavy precipitation. For the zonal jet patterns, cyclones affecting the West Coast tend to occur in the poleward jet exit region in association with cyclonic Rossby wave breaking. For the blocking patterns, cyclones tend to occur in association with anticyclonic Rossby wave breaking on the downstream flank of the block. For Bering Sea–Alaska blocking cases, cyclones can move into this region in conjunction with cyclonically breaking waves that extend into the eastern North Pacific from the upstream flank of the block.

This work documents how the midlatitude, eddy-driven jets respond to climate change using model output from phase 5 of the Coupled Model Intercomparison Project (CMIP5). The authors consider separately the North Atlantic, the North Pacific, and the Southern Hemisphere jets. The analysis is not limited to annual-mean changes in the latitude and speed of the jets, but also explores how the variability of each jet changes with increased greenhouse gases. All jets are found to migrate poleward with climate change: the Southern Hemisphere jet shifts poleward by 2° of latitude between the historical period and the end of the twenty-first century in the representative concentration pathway 8.5 (RCP8.5) scenario, whereas both Northern Hemisphere jets shift by only 1°. In addition, the speed of the Southern Hemisphere jet is found to increase markedly (by 1.2 m s−1between 850 and 700 hPa), while the speed remains nearly constant for both jets in the Northern Hemisphere. More importantly, it is found that the patterns of jet variability are a strong function of the jet position in all three sectors of the globe, and as the jets shift poleward the patterns of variability change. Specifically, for the Southern Hemisphere and the North Atlantic jets, the variability becomes less of a north–south wobbling and more of a pulsing (i.e., variation in jet speed). In contrast, for the North Pacific jet, the variability becomes less of a pulsing and more of a north–south wobbling. These different responses can be understood in terms of Rossby wave breaking, allowing the authors to explain most of the projected jet changes within a single dynamical framework.