Wave Breaking Dissipation Research Articles

Unified depth-limited wave breaking detection and dissipation in fully nonlinear potential flow models

Unified depth-limited wave breaking detection and dissipation in fully nonlinear potential flow models

Derivation of governing equation for short-term shoreline response due to episodic storm wave incidence: comparative verification in terms of longshore sediment transport

The shoreline temporarily recedes significantly as incoming storm waves reach the beach and cause wave breaking and energy dissipation. However, since the existing shoreline change model simulates shoreline change based on the longshore sediment transport rate (LSTR) empirical formulae, which are derived using the correlation between energy flux and littoral drift, it is difficult to simulate this phenomenon, which is drafted with transverse drift. Therefore, in this study, by applying the concept of the horizontal behavior of suspended sediments, a set of governing equations were derived that can simulate short-term shoreline changes in which the shoreline temporarily recedes, and then recovers. Among the three variables of the governing equation, the two main physical variables related to transverse drift—the beach response factor and the beach recovery factor—can be obtained from the median grain size. However, in the present study, the third variable, the actual transport speed of littoral drift, was estimated by comparison with the CERC formula and discussed from the point of view of alongshore energy flux and wave duration. This was established by introducing the delay factor of longshore sediment transport (DFLST), which indicates how slowly suspended sediments move relative to the longshore current speed. It was found that the littoral sediment speed is inversely proportional to the square root of the beach scale factor. The LSTR formula derived in this study was compared with the observed LSTR values collected from 25 beaches in the United States and with the results of four existing empirical formulae. The proposed governing equation is expected to be widely used as a means of predicting short-term shoreline changes, unlike existing shoreline change models, because it can consider the temporal shoreline retreat and recovery due to storm wave incidence.

Experimental Investigation of Infragravity Wave Propagation on a Porous Reef

A laboratory experiment is carried out to study the generation mechanism and the evolution process of an infragravity wave (IG wave) on a typical permeable fringing reef. Fifteen capacitance wave gauges are installed along the reef model to record the water surface elevation under irregular wave action. Based on the experimental data, both IG wave generation and strong IG wave interaction are systematically analyzed. The experimental results indicate that the IG waves are generated by the time-varying breakpoint mechanism at the reef edge, and the tidal modulations on the IG wave height are mainly influenced by wave breaking and wave dissipation. Around the reef edge, the tidal modulation is controlled by wave breaking and the IG wave height monotonously decreases with the increase of the tide level. At the shoreline, the tidal modulation is controlled by wave dissipation at the low tide level and wave breaking at the high tide level. Therefore, the IG wave height first increases and then decreases with the increase of the tide level, and the maximum IG wave height occurs at the middle tide level.

Tide-modulated wave characteristics and breaking regimes in the intertidal zone of a dissipative beach

Waves propagating on sandy beaches are naturally affected by tides. A better understanding of tide-modulated wave characteristics and breaking regimes in the intertidal zone is important for beach protection and disaster mitigations. Here, field measurements are conducted in the intertidal zone on a dissipative beach. Wave characteristics are found to be highly modulated by changing tidal levels. Waves in the intertidal zone is depth-controlled within water depths of 3 m. Measured wave data are used to verify and evaluate parametric wave breaking dissipation models. The model accounting for the ratio of wave height to depth which is neglected previously provides the best predictions. The breaking regimes change during a tidal cycle. The breaking dissipation is more rapid at low to medium tidal levels and the wave breaking is more saturated at medium to high tidal levels. This is because the region for breaking dissipation is highly modulated by tidal levels. Finally, it is found that the breaking dissipation should be large enough in relatively deep water to maintain a constant wave height to depth ratio in the intertidal zone, implying the previous definition of depth-limited breaking seems too strict for the present case.

Passive Acoustic Determination of Spectral Wave Breaking Dissipation

Abstract When a wave breaks, it produces bubbles whose sizes depend on the breaking severity. This paper attempts to estimate wave breaking dissipation through a passive acoustic method. Initially, regular waves were forced to break in a flume. The breaking energy loss (severity) and the underwater acoustic noise were recorded. Two kinds of thresholds, in terms of sound wave amplitude and the ratio of sound wave height to period, respectively, were used together to identify the sound waves generated by newly formed bubbles. The frequencies of these sound waves are connected with the bubble sizes. Thus, a relationship between the mean bubble radius and the breaking severity was established and found to be linear. This laboratory relationship was then applied to Lake George data to study the breaking dissipation rate across the spectrum. An average acoustic spectral density threshold was proposed to identify breaking events from acoustic records in the field. The sound waves associated with bubble formation were selected by means of the same two kinds of threshold as used in the laboratory. Thus, the mean bubble radius of each breaking event was obtained and translated into the breaking severity. The values of experimental dissipation were compared with previous relevant results obtained through different methods as well as the wave breaking dissipation source terms ST6 (WAVEWATCH-III model) and are in good agreement with both of them.

Incorporating wave-breaking data in the calibration of a Boussinesq-type wave model

Wave breaking is one of the main forcing mechanisms in coastal hydrodynamics, driving mean water levels and currents. Its accurate representation and modeling is therefore essential to develop a thorough understanding and predictive capabilities. In this work, the performance of a 1D Boussinesq Type Model is assessed by expanding the traditional approach of calibrating the models against profiles and time series of wave quantities data, with remotely sensed observations of the spatio-temporal occurrence of breaking events, on a laboratory setting considering one regular and one irregular wave condition over a fixed barred beach. A re-analysis of calibrated parameters from a wave breaking model based on the turbulent roller analogy is performed using observed wave-by-wave breaking events. The calibration process aims at matching the initiation/cessation of individual breaking events, and the histograms of breaking occurrence at each location. Results confirm that it is possible to find a physically sound parameter space that yields minimal differences in profiles of phase averaged quantities such as the root-mean-square wave height, wave setup, skewness, and asymmetry; nevertheless, not all of these parameter combinations succeed in representing the spatio-temporal occurrence of breaking events. These results suggest that models can reproduce the overall behavior of wave breaking dissipation, although this does not necessarily mean that the process itself is appropriately modeled. This could in turn influence the modeling capability of other quantities derived from these models, such as mean currents. It is thus considered that incorporating spatio-temporal wave breaking data is essential in assessing model performances.

Wave Dissipation and Sediment Transport Patterns during Shoreface Nourishment towards Equilibrium

Implementing shoreface nourishment is an effective method to protect sandy beaches. A better understanding of the equilibrium mechanism of shoreface nourishments is necessary for coastal engineering designs and constructions. Two experiments on the beach profile equilibrium of the shoreface nourishment are carried out under mild wave conditions on the reflective and intermediate beach. It is observed that the shoreface nourishment increases local wave height and strengthens wave nonlinearity by its shallow water depth. The most intense wave breaking dissipation has been found on the crest of the shoreface nourishment, and the distribution of wave energy dissipation rate is more uniform on the quasi-equilibrium profile than that on the initial profile. A process-based numerical model is used to reproduce bed profile evolution successfully. On that basis, it is found that onshore bedload transport is the primary cause for the onshore migration of the shoreface nourishment. The magnitude of bedload transport decreases during the evolution of the shoreface nourishment towards equilibrium. The most intense sediment transport rate occurs over the shoreface nourishment or in front of the shoreline, depending on the ’lee effect’ of the nourishment. Furthermore, the effects of incident wave height, wave period, and sea-level rise on the equilibrium profile of the shoreface nourishment under mild wave conditions are analyzed.

2D Parametric Model for Surface Wave Development Under Varying Wind Field in Space and Time

AbstractA fully consistent 2D parametric model of wave development under spatially and/or time varying winds is developed. Derived coupled equations are written in their characteristic form to provide practical means to rapidly assess how the energy, frequency and direction of dominant surface waves are developing and distributed under varying wind forcing conditions. For young waves, nonlinear interactions drive the peak frequency downshift, and the wind energy input and wave breaking dissipation are governing the wave energy evolution. With a prescribed wind wave growth rate, proportional to (u*/c) squared, wave breaking dissipation must follow a power‐function of the dominant wave slope. For uniform wind conditions, this choice for the growth rate imposes solutions to follow fetch laws, with exponents q = −1/4, p = 3/4 correspondingly. This set of exponents recovers the Toba's laws, and imposes the wave breaking exponent equal to 3. A varying wind direction can then drive spectral peak direction changes, leading to the occurrence of focusing/defocusing wave groups over localized areas where wave‐rays merge and cross. Significant (but finite) local variations of the energy are then expected under varying wind forcing. Propagating away from a stormy area, wave rays generally diverge, leading to dispersive swell systems. Examples of practical applications of this model are provided in (Kudryavtsev et al., 2021, companion paper).

Laser-like wave amplification in straits

We present the research of ocean surface wind waves excitation in non-homogeneous situations, on the example of deep water strait in presence of the constant wind, blowing perpendicular to the coastal line. The used statistical wave model is based on Hasselmann equation with high-wavenumbers wave-breaking dissipation, exact nonlinear four-waves interaction and ZRP wind input term. At the first stage, the waves propagate in the wind direction in a step-like moving front manner, which is the combination of self-similar fetch-limited and duration-limited solutions of Hasselmann equation. The second stage begins further, when sufficient amount of wave energy is concentrated at the incoming waves shore line. Beginning with that time, the nonlinear wave interactions start formation of the wave groups, propagating across and against the wind. Despite the absence of long-wave dissipation, the system asymptotically evolves into complicated quasi-stationary state, comprising of the self-similar ``wind sea'' in the wind direction, and quasi-monochromatic waves, radiated close to orthogonally with respect to the wind, while slightly tilting counter the wind direction with the angle increasing toward the wave turbulence origination shore line, and reaching $15^{\circ}$ close to it. The total wave energy in the asymptotic state surpasses the wave sea energy propagating along the wind by two times due to the presence of quasi-orthogonal and counter the wind wave fields. The very similar turbulence structure was previously observed experimentally, this paper presents theoretical explanation of these results. It is suggested to name this laser-like radiation phenomenon by Nonlinear Ocean Waves Amplifier, simplified to the abbreviation NOWA.

BATHYMETRY INVERSION IN THE SURF ZONE VIA ASSIMILATION OF REMOTELY SENSED WAVE BREAKING ENERGY DISSIPATION

In this work, a data assimilation approach treating bathymetry as an uncertain model parameter, is introduced where direct dissipation estimates from remote sensing data are the unique data source. Two dimensional wave breaking dissipation fields are retrieved on a wave-by-wave basis with the algorithms of Daz et al. (2018), who were able to reliably estimate breaking dissipation by removing spurious signals affecting electro-optical and microwave data. After a six hour application, the system was able to retrieve improved bathymetric estimates, without any in situ depth measurement. A prominent feature of this approach is its ability to reliably capture the amplitude and position of nearshore sandbars.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/Y7mgiSvmRYc

Surface and Interfacial Waves in a Strongly Stratified Upper Ocean

AbstractIn an idealized two-layer fluid, surface waves can generate waves at the internal interface through class-3 resonant triads in which all waves are propagating in the same direction. The triads are restricted to wavenumbers above a critical value kcrit that depends on the density ratio R between the two layers and their depths. We perform numerical simulations to analyze the evolution of a surface wave field, initially specified by a Pierson–Moskowitz-type spectrum, for R = 0.97 (representing a realistic lower a bound for oceanic stratification). At high initial steepness and peak wavenumber kp ≪ kcrit, the energy increases in the spectral tail; as a parameterization of resulting wave breaking, at each time step individual waves with a steepness greater than the limiting Stokes steepness are removed. The energy change of the surface wave field is a combination of energy transfer to the interfacial waves, spectral downshift, and wave breaking dissipation. At wavenumbers there is a net loss of energy, with the greatest dissipation at ≈1.3kp. The maximum gain occurs at ≈0.5kp. The onset of the spectral change shows a strong threshold behavior with respect to the initial wave steepness. For steep initial waves the integrated energy dissipation can reach >30% of the initial energy, and only ≈1% of the initial surface wave energy is transferred to the interfacial wave field. The spectral change could be expressed as an additional dissipation source term, and coupled ocean–wave models should include additional mixing associated with the interfacial waves and enhanced wave breaking turbulence.

From local-to global-scale control factors of wave attenuation in mangrove environments and the role of indirect mangrove wave attenuation

Wave dissipation by drag forces is considered the dominant wave transformation process in fringe mangroves even though other process may be present. Furthermore, mangrove loss generates vertical erosion and changes in the nearshore profile that can affect wave breaking, whereas changes in vegetation density owing to species composition or disturbances may affect drag dissipation. The aim of this study is to identify local and global geographical control factors of wave attenuation in mangrove environments and to assess the effect of nearshore profile modifications by mangrove loss on wave breaking dissipation. Bottom wave attenuation from breaking and shoaling, the total wave energy attenuation rate, and wave reflection were estimated using modeling, pressure sensors, and reflection coefficients, respectively, at sites with contrasting wave power, bathymetric slope changes, vegetation density, and logging disturbance. Wave breaking changes by mangrove loss were estimated using wave evolution modeling under three successive slope increments by 0.7% in two background mangrove nearshore profiles. The wave energy attenuation rate at the study sites was affected by incident wave height (28–76%), epiphytic oyster presence, vegetation density, tidal inundation (41–55%), and wave reflection from cliffs. The last two variables explained the wave attenuation rate variability at a cliffed study site (61–70%), whereas the last three variables explained the wave attenuation rate variability on a global scale (92%). Wave attenuation rates by vegetation and bottom friction were underestimated (2–59% from global scale data) when wave shoaling was not considered. The wave energy increased or moved further inland in unvegetated scenarios in comparison with vegetated shores. In addition to drag forces, mangroves can promote wave attenuation by inducing friction, wave breaking, and wave reflection from prop-roots epiphytic organisms, shallow nearshore profiles, and cliffed edges, respectively.

A numerical model for simulation of near-shore waves and wave induced currents using the depth-averaged non-hydrostatic shallow water equations with an improvement of wave energy dissipation

This study proposes a numerical model based on the depth-integrated non-hydrostatic shallow water equations with an improvement of wave breaking dissipation. Firstly, studies of parameter sensitivity were carried out using the proposed numerical model for simulation of wave breaking to understand the effects of the parameters of the breaking model on wave height distribution. The simulated results of wave height near the breaking point were very sensitive to the time duration parameter of wave breaking. The best value of the onset breaking parameter is around 0.3 for the non-hydrostatic shallow water model in the simulation of wave breaking. The numerical results agreed well with the published experimental data, which confirmed the applicability of the present model to the simulation of waves in near-shore areas.

Sparse Sampling of Intermittent Turbulence Generated by Breaking Surface Waves

AbstractWe examine how Eulerian statistics of wave breaking and associated turbulence dissipation rates in a field of intermittent events compare with those obtained from sparse Lagrangian sampling by surface following drifters. We use a polydisperse two-fluid model with large-eddy simulation (LES) resolution and volume-of-fluid surface reconstruction (VOF) to simulate the generation and evolution of turbulence and bubbles beneath short-crested wave breaking events in deep water. Bubble contributions to dissipation and momentum transfer between the water and air phases are considered. Eulerian statistics are obtained from the numerical results, which are available on a fixed grid. Next, we sample the LES/VOF model results with a large number of virtual surface-following drifters that are initially distributed in the numerical domain, regularly or irregularly, before each breaking event. Time-averaged Lagrangian statistics are obtained using the time series sampled by the virtual drifters. We show that convergence of statistics occurs for signals that have minimum length of approximately 1000–3000 wave periods with randomly spaced observations in time and space relative to three-dimensional breaking events. We further show important effects of (i) extent of measurements over depth and (ii) obscuration of velocity measurements due to entrained bubbles, which are the two typical challenges in most of the available in situ observations of upper ocean wave breaking turbulence. An empirical correction factor is developed and applied to the previous observations of Thomson et al. Applying the new correction factor to the observations noticeably improves the inferred energy balance of wind input rates and turbulence dissipation rates. Finally, both our simulation results and the corrected observations suggested that the total wave breaking dissipation rates have a nearly linear relation with active whitecap coverage.

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.

Distribution of Surface Wave Breaking Fronts

AbstractThis study describes a model of Phillips' Λ(c) distribution, which is the expected length of breaking fronts (per unit surface area) moving with velocity c to c+dc, providing a framework for coupled atmosphere‐wave‐ocean models to explicitly account for wave breaking related air‐sea fluxes. The model of Λ depends on the spectral saturation, based on Gaussian statistics of the lengths of crest exceeding wave slope criteria, and long wave‐short wave modulation. A wave breaking dissipation function based on Λ was implemented in the model WaveWatchIII. The wave solutions are consistent with the observations, including several metrics of the spectrum and Λ(c) distributions. The whitecap coverage derived from Λ reproduces recent parameterizations saturating at high winds. The wave breaking variability due to wave‐current interaction is significant at submesoscales (order 1 km or smaller). The wave breaking model can be further developed to model gas transfer coefficients and aerosol production.

Observation-Based Source Terms in the Third-Generation Wave Model WAVEWATCH III: Updates and Verification

AbstractThe observation-based source terms available in the third-generation wave model WAVEWATCH III (i.e., the ST6 package for parameterizations of wind input, wave breaking, and swell dissipation terms) are recalibrated and verified against a series of academic and realistic simulations, including the fetch/duration-limited test, a Lake Michigan hindcast, and a 1-yr global hindcast. The updated ST6 not only performs well in predicting commonly used bulk wave parameters (e.g., significant wave height and wave period) but also yields a clearly improved estimation of high-frequency energy level (in terms of saturation spectrum and mean square slope). In the duration-limited test, we investigate the modeled wave spectrum in a detailed way by introducing spectral metrics for the tail and the peak of the omnidirectional wave spectrum and for the directionality of the two-dimensional frequency–direction spectrum. The omnidirectional frequency spectrum E(f) from the recalibrated ST6 shows a clear transition behavior from a power law of approximately f−4 to a power law of about f−5, comparable to previous field studies. Different solvers for nonlinear wave interactions are applied with ST6, including the Discrete Interaction Approximation (DIA), the more expensive Generalized Multiple DIA (GMD), and the very expensive exact solutions [using the Webb–Resio–Tracy method (WRT)]. The GMD-simulated E(f) is in excellent agreement with that from WRT. Nonetheless, we find the peak of E(f) modeled by the GMD and WRT appears too narrow. It is also shown that in the 1-yr global hindcast, the DIA-based model overestimates the low-frequency wave energy (wave period T > 16 s) by 90%. Such model errors are reduced significantly by the GMD to ~20%.

A model chain approach for coastal inundation: Application to the bay of Alghero

Coastal inundation is an important threat for many nearshore regions worldwide, and has significantly increased in the last years also due to sea-level rise and augmented impact of extreme events, like sea storms. Many countries and regions have recently invested to overcome such problems, which commonly lead to structure damages, beach erosion and many other consequences. Numerical modeling is an important tool for coastal inundation prediction, being a valuable support for management issues to mitigate the inundation risk or suggest resilient solutions. The present work illustrates a novel approach, based on a numerical model chain that exploits a tide-surge-wave operational modeling system (Kassandra), a phase-averaged model (ROMS-SWAN) for the wave propagation towards the shore, and a phase-resolving solver (NSWE) for the prediction of runup and coastal inundation. Such a chain is applied to the bay of Alghero (Sardinia, Italy), where the results of the mentioned chain are compared to those obtained using, in place of the phase-averaged model, an analytical model for the wave propagation. Results confirm that both chain approaches provide comparable inundations, though the use of the analytical, more approximate (e.g., less accurate and reliable description of wave breaking dissipation), model suggests more severe conditions and larger flooded areas. Our contribution provides a methodological approach for an accurate and reliable estimate of coastal flooding.

The Competing Effects of Breaking Waves on Surfzone Heat Fluxes: Albedo Versus Wave Heating

AbstractDepth‐limited wave breaking modifies the heat flux in the surfzone relative to the inner‐shelf (where waves are not breaking). Surfzone wave breaking generates heat through viscous dissipation (wave heating), but also increases surface foam coverage and albedo, thereby reducing solar heating, that is, cooling relative to the inner‐shelf. These two competing breaking wave effects are quantified with a yearlong experiment at the Scripps Institution of Oceanography Pier. Cross‐shore averaged surfzone albedo estimates were more than three times higher than inner‐shelf albedo, reducing the yearly averaged surfzone water‐entering shortwave radiation by 41 W/m2 relative to the inner‐shelf. Surfzone breaking wave dissipation added an additional yearly averaged 28 W/m2 relative to the inner‐shelf. The albedo‐induced solar heating reduction in spring, summer, and fall was usually greater than the wave heating. However, in winter, large waves and relatively weak shortwave solar radiation (due to both lower top of the atmosphere solar radiation and clouds) resulted in a nearly equal number of days of breaking wave‐induced heating or cooling. These two heat flux terms are coupled via wave breaking dissipation. Averaged over the surfzone, the albedo‐induced solar radiation reduction is linearly related to the downwelling solar radiation and is independent of wave height. Consequently, the albedo‐induced cooling to wave heating ratio is a function of breaking wave height to the −3/2 power, allowing evaluation of the relative importance of these terms in other geographic regions.

The Permanent Downshifting at Later Stages of Benjamin–Feir Instability of Waves

Some of the prominent features in later stages of the Benjamin–Feir (BF) instability development are still not well clarified: What are the conditions for a permanent downshifting in the wave energy spectrum, is this process inevitable accompanied by wave breaking dissipation? What is the mechanism of multiple downshifting and discrete energy spreading to higher frequencies, how does it depend on the initial steepness and frequency space of waves? We conducted experimental and theoretical studies on this issue and revealed a number of new features of the development of instability in the late stages of wave’s evolution. We employ the reduced (truncated) version of Zakharov equations, the multi-wave near-neighbor resonance model (NN model), which takes into account the most effective quasi-resonances with minimum detuning from the exact resonance conditions. We show that the near-neighbor model of wave interactions can adequately describe the number of new characteristic features of BF instability. NN model is much simpler than Zakharov equation for computation and analysis. The dissipation version of Zakharov equations based on the Tulin’s semi-empirical model is employed for the description of breaking wave’s propagation. We verify the new characteristic features of BFI for various initial wave conditions by experiments conducted in Tainan Hydraulics Laboratory and confirm the theoretical predictions of NN model. A strong permanent downshifting of the spectral maximum for gentle waves without wave breaking is revealed for initially two-time narrower spectral width in comparison with the most unstable case. For steep waves, a multiple downshifting regime is detected, accompanied by a wave breaking. The discrete energy flow to higher spectral components takes place in the breaking and no-breaking regimes. Results of numerical simulations of Zakharov and NN models reasonably correspond to each other and to our experimental and field observations on wave modulation.