Onset Of Wave Breaking Research Articles

Three-dimensional wave breaking

Although a ubiquitous natural phenomenon, the onset and subsequent process of surface wave breaking are not fully understood. Breaking affects how steep waves become and drives air–sea exchanges1. Most seminal and state-of-the-art research on breaking is underpinned by the assumption of two-dimensionality, although ocean waves are three dimensional. We present experimental results that assess how three-dimensionality affects breaking, without putting limits on the direction of travel of the waves. We show that the breaking-onset steepness of the most directionally spread case is double that of its unidirectional counterpart. We identify three breaking regimes. As directional spreading increases, horizontally overturning ‘travelling-wave breaking’ (I), which forms the basis of two-dimensional breaking, is replaced by vertically jetting ‘standing-wave breaking’ (II). In between, ‘travelling-standing-wave breaking’ (III) is characterized by the formation of vertical jets along a fast-moving crest. The mechanisms in each regime determine how breaking limits steepness and affects subsequent air–sea exchanges. Unlike in two dimensions, three-dimensional wave-breaking onset does not limit how steep waves may become, and we produce directionally spread waves 80% steeper than at breaking onset and four times steeper than equivalent two-dimensional waves at their breaking onset. Our observations challenge the validity of state-of-the-art methods used to calculate energy dissipation and to design offshore structures in highly directionally spread seas.

The influence of spectral bandwidth and shape on deep-water wave breaking onset

Deep-water surface wave breaking affects the transfer of mass, momentum, energy and heat between the air and sea. Understanding when and how the onset of wave breaking will occur remains a challenge. The mechanisms that form unforced steep waves, i.e. nonlinearity or dispersion, are thought to have a strong influence on the onset of wave breaking. In two dimensions and in deep water, spectral bandwidth is the main factor that affects the roles these mechanism play. Existing studies, in which the relationship between spectral bandwidth and wave breaking onset is investigated, present varied and sometimes conflicting results. We perform potential-flow simulations of two-dimensional focused wave groups on deep water to better understand this relationship, with the aim of reconciling existing studies. We show that the way in which steepness is defined may be the main source of confusion in the literature. Locally defined steepness at breaking onset reduces as a function of bandwidth, and globally defined (spectral) steepness increases. The relationship between global breaking onset steepness and spectral shape (using the parameters bandwidth and spectral skewness) is too complex to parameterise in a general way. However, we find that the local surface slope of maximally steep non-breaking waves, of all spectral bandwidths and shapes that we simulate, approaches a limit of$1/\tan ({\rm \pi} /3)\approx 0.5774$. This slope-based threshold is simple to measure and may be used as an alternative to existing kinematic breaking onset thresholds. There is a potential link between slope-based and kinematic breaking onset thresholds, which future work should seek to better understand.

The superharmonic instability and wave breaking in Whitham equations

The Whitham equation is a model for the evolution of surface waves on shallow water that combines the unidirectional linear dispersion relation of the Euler equations with a weakly nonlinear approximation based on the Korteweg–De Vries equation. We show that large-amplitude, periodic, traveling-wave solutions to the Whitham equation and its higher-order generalization, the cubic Whitham equation, are unstable with respect to the superharmonic instability (i.e., a perturbation with the same period as the solution). The threshold between superharmonic stability and instability occurs at the maxima of the Hamiltonian and L2-norm. We examine the onset of wave breaking in traveling-wave solutions subject to the modulational and superharmonic instabilities. We present new instability results for the Euler equations in finite depth and compare them with the Whitham results. We show that the Whitham equation more accurately approximates the wave steepness threshold for the superharmonic instability of the Euler equations than does the cubic Whitham equation. However, the cubic Whitham equation more accurately approximates the wave steepness threshold for the modulational instability of the Euler equations than does the Whitham equation.

CHANNEL CONCENTRATION AND ITS IMPACT ON NEARSHORE WAVE CONDITIONS

Channel concentration is an important wave process in coastal regions. It occurs when a shallow water wave approaches a deep channel at a shallow angle, producing a localized region of increased wave height at the edge of the channel, and the early onset of wave breaking. Channel concentration can occur at dredge channels, so is of particular significance to port entrances and surrounding infrastructure, especially for breakwater heads. It also occurs at natural features such as submarine canyons, particularly where the canyon is perpendicular to the coastline. In contrast to refraction or channel reflection, channel concentration is not well documented in the available literature. While studies show wave concentration as a significant coastal process, there is insufficient information on the process to provide general design guidance for its consideration in harbour projects. As such, there is still the need to use design tools such as physical modelling to ensure the site specific wave conditions are characterised correctly.

An Experimental Study on Measuring Breaking-Wave Bubbles with LiDAR Remote Sensing

Laboratory experiments were conducted to evaluate the feasibility of profiling and characterizing subsurface bubble plumes following a breaking wave event from an above-water Light Detection and Ranging (LiDAR) system. Measurements of LiDAR backscatter profiles of bubble plumes under mechanically generated breaking waves in a wave tank were collected and analyzed. After onset of wave breaking, the LiDAR backscatter increases rapidly by injected bubble plumes of active wave breaking. This intensification reaches a depth of one wave height within one wave period. After active wave breaking, the LiDAR backscatter from dissipated bubble plumes in the upper layer of water column decreases very slowly. The temporal variations of LiDAR backscatter are comparable to the collocated in-water measurements of optical backscatter at 850 nm wavelength and acoustic backscatter at 2000 kHz frequency. The decay rate of LiDAR backscatter of dissipated bubble plumes follows a power-law function consistent with decay rate of void fraction measurements in previous studies. This study demonstrates the viability and potential of using above-water LiDAR remote sensing to characterize subsurface bubble plumes.

Predicting the breaking onset of wave groups in finite water depths based on the Hilbert-Huang transform method

This experimental study focuses on the nonlinear characteristics and breaking onset of extreme waves. The critical value of the first-order instantaneous frequency f1 obtained by the Hilbert-Huang transform method is proposed to determine the wave breaking onset. Specifically, when the normalized instantaneous frequency f1/fp ≥ 2 (fp denotes the dominant frequency), the wave breaks; otherwise, it is less likely to break. For the wave groups considered in this study, the normalized maximum crest height shows an exponential growth as the normalized instantaneous frequency increases. Moreover, it was found that there is a close logarithmic growth relationship between the normalized instantaneous frequency and the local wave steepness. Thus, the instantaneous frequency can be an effective indicator for evaluating extreme wave nonlinearity.

The effects of smoothing length on the onset of wave breaking in smoothed particle hydrodynamics (SPH) simulations of highly directionally spread waves

Ocean wave breaking is a difficult-to-model oceanographic process, which has implications for extreme wave statistics, the dissipation of wave energy, and air–sea interaction. Numerical methods capable of reliably simulating real-world directionally spread breaking waves are useful for investigating the physics of wave breaking and for the design of offshore structures and floating bodies. Smoothed particle hydrodynamics is capable of modelling highly steep and overturning free surfaces, which makes it a promising method for simulating breaking waves. This paper investigates the effect of smoothing length on simulated wave breaking in both following and crossing seas. To do so, we reproduce numerically the experiments of highly directionally spread breaking waves in McAllister et al. (J Fluid Mech 860:767–786, 2019. https://doi.org/10.1017/jfm.2018.886) using a range of normalised smoothing lengths: \(h/d_p=1.4\), 1.7, 2.0, 2.3, with h smoothing length and \(d_p\) particle spacing. The smallest smoothing length we use appears to adversely affect the fidelity of the simulated surface elevation, so that the tallest wave crest observed in experiments is not fully reproduced (coefficient of determination \(r^2\approx 0.7\)). For smoothing lengths \(h/d_p=1.7\), 2.0, and 2.3, the experiments are well reproduced (\(r^2\ge 0.88\)); in these simulations smoothing length predominantly affects the spatial extent and duration of breaking. Qualitative and quantitative comparison of our simulations shows that values of \(h/d_p\) in the range \(1.7{-}2\) best reproduce the wave breaking phenomena observed in experiments.

Gravity–capillary wave interactions generated by moving disturbances: Euler equations framework

The aim of this work is to investigate the interaction of gravity–capillary waves resonantly excited by two moving disturbances along the free surface. The problem is formulated using the full Euler equations, and numerical computations are performed in a simplified domain through the use of a conformal mapping which flattens the free surface. We focus on nearly-critical flows with intermediate capillary effects and characterise their main features. In the supercritical regime, the wave interaction can be strongly nonlinear leading to the onset of wave breaking. In the subcritical regime, depression solitary waves are generated remaining trapped between the disturbances bouncing back and forth. In addition, we notice a dependence of the number of trapped waves on the distance of the disturbances. Furthermore, differently from when only one disturbance is considered, we find that the critical regime captures features from the subcritical and supercritical regime simultaneously.

A new spectral parameter to predict dominant wave breaking based on the JONSWAP spectrum

Finding a robust and universal diagnostic parameter that determines the onset of deep-water breaking and its strength has been challenging in wave breaking research. In this paper, a new diagnostic parameter (wave-breaking spectral parameter, WSP) is defined based on the significant steepness of the spectral peak ϵp that was initially proposed by Banner et al. (2000) and Babanin et al. (2001). In addition, the WSP formula contains the spectral peakedness parameter Qp and spectral width ν for taking into account the effect of spectral shape on the value of breaking threshold. To derive the WSP formula and verify the prediction ability of this diagnostic parameter, multiple wave types including nonbreaking waves, critical waves, and single and multiple breaking wave trains were generated in our experiments. The wave trains were generated using a linear focusing theory with components following the JONSWAP distribution. Results show that the threshold value of the new WSP, which distinguishes single and multiple breaking events from non-breaking waves, is found to be 0.042. Furthermore, WSP is used in isolated deep-water spilling breaking packets, and its prediction accuracy is compared with that of the kinematic criterion parameter Bx. The results show that WSP has advantages in predicting the onset of wave breaking, especially for non-sharp wave conditions. Finally, the spatial variation of the total loss rate of the wave energy flux ΔFbrE¯¯ΔFbE¯¯ in deep-water unsteady breaking waves was investigated. It was found that the new WSP has a strong linear correlation with the total loss rate of the wave energy flux. Considering that WSP can be mathematically expressed directly using the spectrum, WSP will be parameterized into the dissipation term of the spectral wind-wave model in our future work. It is expected that the calculation accuracy of the dissipation term will be improved, and the wave model's prediction accuracy of wave parameters will be enhanced because WSP provides a reliable wave-breaking threshold value and has a strong linear relationship with the dissipation rate.

Harmonic-induced wave breaking due to abrupt depth transitions: An experimental and numerical study

Abrupt depth transitions (ADTs) have been shown to induce the release of bound waves into free waves, which results in spatially inhomogeneous wave fields atop ADTs. Herein, we examine the role of free-wave release in the generation and spatial distribution of higher-harmonic wave components and in the onset of wave breaking for very steep periodic waves upon interaction with an ADT. We utilise a Smoothed Particle Hydrodynamics (SPH) model, making use of its ability to automatically capture breaking and overturning surfaces. We validate the model against experiments. The SPH model is found to accurately reproduce the phase-resolved harmonic components up to the sixth harmonic, particularly in the vicinity of the ADT. For the cases studied, we conclude that second-order free waves released at the ADT, and their interaction with the linear and second-order bound waves (beating), drive higher-order bound-wave components, which show spatial variation in amplitude as a result. For wave amplitudes smaller than the breaking threshold, this second-order beating phenomenon can be used to predict the locations where peak values of surface elevation are located, whilst also predicting the breaking location for wave amplitudes at the breaking threshold. Beyond this threshold, the contributions of the second-order and higher harmonics (second-harmonic amplitudes are up to 60% and sixth-harmonic up to 10% of the incident amplitude) cause breaking to occur nearer to the ADT, and hence the wave breaking onset location is confined to the region between the ADT and the first anti-node location of the second-order components. Counter-intuitively, we find that, at the point of breaking, steeper incident waves are found to display reduced non-linearity as a result of breaking nearer to the ADT.

On the Wave State Dependence of the Sea Surface Roughness at Moderate Wind Speeds under Mixed Wave Conditions

AbstractWind stress depends on the sea surface roughness, which can be significantly changed by surface wind waves. Based on observations from a fixed platform, we examined the dependences of the sea surface roughness length on dominant wave characteristic parameters (wave age, wave steepness) at moderate wind speeds and under mixed-wave conditions. No obvious trend was found in the wave steepness dependence of sea surface roughness, but a wave steepness threshold behavior was readily identified in the wave age dependence of sea surface roughness. The influence of dominant wind waves on the surface roughness was illustrated using a wind–wave coupling model. The wave steepness threshold behavior is assumed to be related to the onset of dominant wave breaking. The important role of the interaction between swell and wind wave was highlighted, as swell can absorb energy from locally generated wind wave, which subsequently reduces the wave steepness and the probability of dominant wave breaking.

Predicting deep water wave breaking with a non-hydrostatic shock-capturing model

A non-hydrostatic shock-capturing model is developed to address deep water wave evolution including wave breaking. The present model is based on the Euler equations, with a hybrid finite volume/finite difference (FV/FD) method and the high-resolution Godunov-type numerical scheme. Using these numerical schemes, wave breaking can be captured as a shock or a hydraulic jump without adopting additional wave breaking parameters or terms, such as breaking-onset criteria. The parallel method of the Message Passing Interface (MPI) is used to accelerate the simulation. This model was applied to simulate deep-water wave propagation including breaking as a consequence of dispersive focusing or due to the modulational instability. By comparison with existing experiments, the ability of the present model to predict breaking onset and breaking energy dissipation is evaluated. Additionally, a dynamic criterion is applied to provide additional information on wave breaking onset, and the wavelet transform is applied to predict the energy as a function of frequency and time.

A Unified Breaking Onset Criterion for Surface Gravity Water Waves in Arbitrary Depth

AbstractWe investigate the validity and robustness of the Barthelemy et al. (2018, https://doi.org/10.1017/jfm.2018.93) wave‐breaking onset prediction framework for surface gravity water waves in arbitrary water depth, including shallow water breaking over varying bathymetry. We show that the Barthelemy et al. (2018) breaking onset criterion, which they validated for deep and intermediate water depths, also segregates breaking crests from nonbreaking crests in shallow water, with subsequent breaking always following the exceedance of their proposed generic breaking threshold. We consider a number of representative wave types, including regular, irregular, solitary, and focused waves, shoaling over idealized bed topographies including an idealized bar geometry and a mildly to steeply sloping planar beach. Our results show that the new breaking onset criterion is capable of detecting single and multiple breaking events in time and space in arbitrary water depth. Further, we show that the new generic criterion provides improved skill for signaling imminent breaking onset, relative to the available kinematic or geometric breaking onset criteria in the literature. In particular, the new criterion is suitable for use in wave‐resolving models that cannot intrinsically detect the onset of wave breaking.

A New Approach for Modeling Dissipation due to Breaking in Wind Wave Spectra

AbstractA robust spectral dissipation term for wind waves has long been a goal of detailed-balance spectral modeling and is represented by many different approximations in spectral models of random wave fields. A Monte Carlo approach is employed here to create a random-phase sea surface that is used to simulate the distribution of horizontal surface velocities at the sea surface and to relate these velocities to deep-water wind wave breaking. Results are consistent with many recent studies that show a kinematic-based breaking criterion can provide a consistent depiction of the onset of wave breaking. This criterion is combined with the calculated nonlinear flux rates to estimate a transition point within a spectrum at which a spectrum changes from an f−4 equilibrium-range form to an f−5 region dominated by dissipation, potentially an important factor within several air–sea interaction mechanisms, turbulence at the sea surface, and remote sensing applications. It also has the potential to improve operational modeling capabilities.

Comparing methods of modeling depth-induced breaking of irregular waves with a fully nonlinear potential flow approach

The modeling of wave breaking dissipation in coastal areas is investigated with a fully nonlinear and dispersive wave model. The wave propagation model is based on potential flow theory, which initially assumes non-overturning waves. Including the impacts of wave breaking dissipation is however possible by implementing a wave breaking initiation criterion and dissipation mechanism. Three criteria from the literature, including a geometric, kinematic, and dynamic-type criterion, are tested to determine the optimal criterion predicting the onset of wave breaking. Three wave breaking energy dissipation methods are also tested: the first two are based on the analogy of a breaking wave with a hydraulic jump, and the third one applies an eddy viscosity dissipative term. Numerical simulations are performed using combinations of the three breaking onset criteria and three dissipation methods. The simulation results are compared to observations from four laboratory experiments of regular and irregular waves breaking over a submerged bar, irregular waves breaking on a beach, and irregular waves breaking over a submerged slope. The different breaking approaches provide similar results after proper calibration. The wave transformation observed in the experiments is reproduced well, with better results for the case of regular waves than irregular waves. Moreover, the wave statistics and wave spectra are predicted well in general, and in particular for regular waves. Some differences are observed for irregular wave cases, in particular in the low-frequency range. This is attributed to incomplete absorption of the long waves in the numerical model. Otherwise, the wave spectra in the range $[0.5f_p,\: 5f_p]$ are reproduced well, before, inside, and after the breaking zone for the three irregular wave experiments.

Extreme wave crest distribution by direct numerical simulations of long-crested nonlinear wave fields

The wave crest height qualification checks are required during the wave calibration before the model test in wave basin. However, the reliable criteria of nonlinear wave crest probability distribution in 3-h duration (full-scale) has not been well established yet. We investigate wave crest-height statistics of long-crested nonlinear wave fields using high-order spectral (HOS) method, which can take the effects of both second-order bound waves and third-order free waves into account. The energy dissipation effects due to wave breaking were included by employing an eddy viscosity model. Sensitivity analyses to the wave breaking onset criterion have been performed. Validation is provided by comparing the obtained numerical results with the available calibration test data. Based on extensive and direct numerical simulations, semi-empirical single realization distributions for wave calibration have been developed through 3-parameter Weibull fitting and systematic regression analyses. Particular attention has been paid to the tail of upper bound of wave crest distributions. The effects of wave steepness and water depth on the maximum wave crest height in 3-h duration have been examined. It is found that with the increase of wave steepness, the extreme wave crest height increases until it reaches a critical value. In addition, for the scale water depth kph < 1.36, the maximum crest height decreases as the water depth increases, while in the opposite case the maximum crest height increases as the water depth increases. Moreover, it is confirmed that that the fourth-order nonlinearity does not have significant effects on the distribution of the wave crest height.

PREDICTING THE BREAKING STRENGTH OF GRAVITY WATER WAVES FROM DEEP TO SHALLOW WATER

We revisit the classical but as yet unresolved problem of predicting the breaking strength of 2-D and 3-D gravity water waves.Our goal is to find a robust and local parameterization to predict the breaking strength of 2-D and 3-D gravity water waves. We use a LES/VOF model described by Derakhti &amp; Kirby (2014) to simulate nonlinear wave evolution, breaking onset and post-breaking behavior for representative cases of focused wave packets or modulated wave trains. Using these numerical results, we investigate the relationship between the breaking strength parameter b and the breaking onset parameter B proposed by Barthelemy et al. (2018). While the results are potentially applicable more generally, in this paper we concentrate on breaking events due to focusing or modulational instability in wave packets over flat bottom topography and for conditions ranging from deep to intermediate depth, with depth to wavelength ratios ranging from 0.68 to 0.13.

Laboratory recreation of the Draupner wave and the role of breaking in crossing seas

Freak or rogue waves are so called because of their unexpectedly large size relative to the population of smaller waves in which they occur. The 25.6 m high Draupner wave, observed in a sea state with a significant wave height of 12 m, was one of the first confirmed field measurements of a freak wave. The physical mechanisms that give rise to freak waves such as the Draupner wave are still contentious. Through physical experiments carried out in a circular wave tank, we attempt to recreate the freak wave measured at the Draupner platform and gain an understanding of the directional conditions capable of supporting such a large and steep wave. Herein, we recreate the full scaled crest amplitude and profile of the Draupner wave, including bound set-up. We find that the onset and type of wave breaking play a significant role and differ significantly for crossing and non-crossing waves. Crucially, breaking becomes less crest-amplitude limiting for sufficiently large crossing angles and involves the formation of near-vertical jets. In our experiments, we were only able to reproduce the scaled crest and total wave height of the wave measured at the Draupner platform for conditions where two wave systems cross at a large angle.

Experimental investigation of airflow above waves in a horizontal pipe

We investigate the effect of waves on the airflow in horizontal two-phase pipe flow. Velocity fields in the gaseous phase were acquired by particle image velocimetry (PIV), while interfacial elevation was measured with conductance wave probes. The velocity fields were sampled on a wave-following coordinate system which allows for a decomposition of the velocity field into a mean, wave-coherent and fluctuating component by means of a three-component Reynolds decomposition. Additionally, coherent vortical structures were identified by the swirling strength criterion, and their distribution along the waves is investigated.Results suggest that the interaction between turbulent airflow and propagating waves in a pipe has a number of features reminiscent of wind-wave interaction in open systems. Above waves generated by sufficiently high gas flow rates, there is a distinct region of sheltered airflow, and a lifting of the critical layer on the leeward side of the crest. Streamlines of the phase-averaged flow field show a cat’s eye structure located close to the crest in this region. Above waves of moderate steepness, we observe a shear layer that remains adjacent to the wave surface. Above steeper waves and higher gas flow rate, this layer detaches from the surface just downstream of the crest. Shear layer separation above waves is traditionally linked to the onset of wave breaking, and it is interesting to note that the case where we observe a separated shear layer in the phase-averaged vorticity field is in a regime of amplitude saturation.The swirling strength criterion reveals that vortical structures are shed from the interface and populate the detached shear layer above the trough. Below the detached shear layer, there is a region populated by counter-rotating vortices. The critical height coincides with the border between these two regions.

Chaos in breaking waves

This study investigates the chaotic behavior of breaking waves by laboratory experiments and numerical modeling. Repeated laboratory runs with different initial velocity perturbations show that the wave profile before the wave breaks can be accurately reproduced, but the subsequent breaking process varies among runs, indicating the lack of repeatability of breaking waves in reality. Numerical simulations based on the Smoothed Particle Hydrodynamics method are further carried out to examine the repeatability of wave breaking process. Consistent with the laboratory observation, multiple numerical simulations with variations in initial conditions present highly repeatable velocity field and free surface profile in the potential flow region but considerable variation at the breaking and post-breaking processes. Comparison also shows that 3D vortex structures induced by breaking waves are different among cases. Analysis of particle trajectory reveals that there is a similar trajectory thus a minor trajectory divergence among particles that are initially located at the pre-breaking region and the flume bottom, which are not directly impacted by the breaking process. However, a much more significant particle trajectory divergence is observed among particles that are initially located at the wave-splash region and the bore propagation region. The rate of divergence of particle trajectory under breaking waves is further examined by computing the Lyapunov exponent, a widely used indicator of chaos. This study reveals that different initial velocity perturbations lead to variations of near-surface velocity at the onset of wave breaking, which eventually cause the development of drastically different breaking wave jets and splashes. Therefore, the process of wave breaking, like many other dynamic processes in nature, exhibits a chaotic behavior.