Depth-induced Wave Breaking Research Articles

Spectral analysis of near-breaking wave data observed in macro-tidal environment by zero up-crossing transform method

In this study, frequency spectra were obtained by applying the Zero-Up Crossing Transform (ZUCT) and the fast Fourier transform (FFT) methods from the waveform data observed at one point of a macro-tidal beach. Their frequency spectrum conversion characteristics according to changes in water depth can be investigated and compared with the TMA spectrum applicable to shallow water. The ZUCT method is based on the reproducibility of the actual wave height and period and applies a technique that guarantees energy conservation. In particular, when the tidal level is low, the spectrum by the ZUCT method seems to show a similar shape to the TMA spectrum over the entire tidal range even if the spectrum is deformed due to partial depth-induced wave breaking. This study derived the reduction rate of the frequency spectrum by wave breaking, assuming that the wave height distribution for each frequency followed the Rayleigh distribution. Based on this, we proposed the TMA-SOON (Spectrum Operated On Nearshore), a frequency spectrum equation applicable to the nearshore zone where wave breaking occurs. Therefore, by using this formula, it is possible to estimate the incoming wave energy as well as the incoming frequency spectrum from the observation data in the wave breaking region.

A modified breaker index formula for depth-induced wave breaking in spectral wave models

The breaker index, defined as the ratio of wave height to local water depth for incipient breaking, is a key parameter in contemporary spectral wave models. In the present study, we modified the breaker index of Goda's formula using the SWAN model (Simulating WAves Nearshore). We suggested that the breaker index is a function of the deep-water wave steepness, bottom slope and relative water depth. The formula is evaluated against observational data, and the evaluation indicates that the modeled wave heights using the formula are significantly improved, especially for cases over mild and flat slopes. The formula is further evaluated through comparisons with published formulas and the improved formula overall shows better performance.

Nonhydrostatic Numerical Modeling of Fixed and Mobile Barred Beaches: Limitations of Depth-Averaged Wave Resolving Models around Sandbars

Along sandy coastlines, submerged, shore-parallel sandbars play an essential role in shoreline morphology by dissipating wave energy through depth-induced wave breaking. While wave breaking and sediment transport around sandbars are complex three-dimensional (3D) processes, shoreline morphology is typically simulated with depth-averaged models that feature lower computational demand than do 3D models. In this context, this study examines the implications of depth-averaging the flow field and approximating the breaking process in nonhydrostatic models (e.g., XBeach nonhydrostatic) for the hydro- and morphodynamic processes around sandbars. The implications are drawn based on reproducing large-scale experiments of a barred beach profile using the single-layer (XBNH) and the reduced two-layer (XBNH+) modes of XBeach. While hydrodynamic processes were predicted with high accuracy on the sandbar’s seaward side, wave heights were overpredicted on the bar’s landward side. The overestimation was due to the simplified reproduction of the complex breaking process near the sandbar’s peak, particularly in terms of the generated turbulence in the water column. Moreover, the velocity profile with a strong undertow could only be represented in a simplified way even using the two-layer mode XBNH+, thus resulting in inaccurate predictions of sediment loads around the sandbar. A parametric study is performed, and it revealed which model parameters control the simulation of the wave-breaking process. Thus, wave height predictions could be improved by tuning the energy-dissipation parameters. However, flow velocities and morphodynamic predictions could not be improved accordingly. Thus, this study identifies possible hydrodynamic model improvements, such as incorporating a roller dissipation model. Moreover, it improves understanding of key drivers and processes that should be included in nonhydrostatic depth-averaged models to simulate morphological changes around sandbars more efficiently.

Concerted nonlinear mild-slope wave models for enhanced simulation of coastal processes

• One-way coupling of parabolic and hyperbolic models. • Introducing exact nonlinear wave effects in parabolic models. • Handling efficiently the principal wave propagation direction in parabolic models. • Models verification against demanding experiments. The present paper aims to incorporate nonlinear amplitude dispersion effects in parabolic and hyperbolic approximation models. First, an explicit and analytical method for considering nonlinearities in parabolic approximation models is investigated. This method follows the concept of calculating spatially and temporally varying wave phase celerities within the simulation. The nonlinear dispersion relation to be applied is dependent on the local Ursell number and wave steepness, in relation to valid regions of analytical wave theories. Furthermore, nonlinearities are introduced in a hyperbolic approximation model by proposing a novel method which combines a parabolic and a hyperbolic model without a significant loss in accuracy, leading to a substantial reduction in the required simulation time. This is achieved by inputting initial boundary conditions into the hyperbolic model based on the output of the parabolic model, which is used for an initial calculation of the spatial distribution of nonlinear dispersion effects over the entire numerical domain. Numerical results were compared with measurements obtained via demanding experimental setups and illustrated satisfactory performance of the models. These concerted nonlinear models offer ease in implementation, short simulation times, and accurate results while incorporating the majority of wave transformation processes including shoaling, refraction, diffraction, reflection, bottom friction and depth-induced wave breaking.

Wave packet focusing in shallow water

ABSTRACT In coastal engineering, as shoaling waves break in shallow water, most wave-breaking research has been focused on depth-induced wave breaking. However, violent wave breaking under storm conditions may be caused by superposition of many shoaling wave components. In order for simulating extreme waves in open ocean, theories to focus wave-packets, assuming that wave speed of each wave component is unchanged during propagation (i.e. deep water or shallower water without bathymetry changes), have been derived, while shoaling effects of the focusing process in shallower waters have not been considered in the previous studies. The extension to shoaling coastal wave-packets may aid in simulating extreme coastal wave breaking under violent storm conditions via laboratory experiments. Here, we derive the general wave-packet focusing conditions for arbitrary water depth. The proposed conditions were used to simulate shoaling wave-packet focusing on flat and sloped bottoms in shallow water experiments for validation purposes. The effects of depth-induced wave breaking in the focusing wave groups are discussed in this paper. The current focusing technique can fully control the focus location and time in wave experiments with an arbitrary bottom structure, which may be useful for further extreme wave research in coastal engineering.

Analysis of the spatial and temporal sensitivities of key parameters in the SWAN model: An example using Chan-hom typhoon waves

In this work, the spatial and temporal sensitivities of the significant wave height (SWH) to ten key parameters in the SWAN model under typhoon conditions are assessed through comprehensive observations at four buoy stations along the eastern coast of China. Experiments were conducted using wind forcing based on Typhoon Chan-hom, which made landfall at Zhujiajian island in 2015. Assessments included wind input and whitecapping, bottom friction, depth-induced wave breaking, and nonlinear quadruplet wave interactions parameterizations. The results show that in shallow water whose depth is less than the threshold depth, depth-induced wave breaking dominates the SWH, and the SWH is most sensitive to the parameter gamma (the ratio of maximum individual wave height to depth) of depth-induced wave breaking. However, beyond a certain threshold depth, the sensitivity of the SWH to depth-induced wave breaking begins to reduce. This threshold depth depends on sea states and ranges from 5 m to 30 m. In deep water, where the water depth is more than the threshold depth, SWH is primarily influenced by wind input and whitecapping. In general, the sensitivity is greater in coastal areas than in the open ocean. With regard to sea state, the higher the sea state, the deeper the threshold depth. The four different numerical procedures of four-wave interactions (so-called quadruplets) mainly affect the distribution of wave energy, not the SWH. In addition, the SWH is most sensitive to the drag coefficient, and bigger wave implies greater sensitivity. The study of spatial and temporal sensitivities of key parameters is of great significance for further application of the SWAN model and wave simulations, especially typhoon wave simulations.

Modelling of depth-induced wave breaking in a fully nonlinear free-surface potential flow model

Two methods to treat wave breaking in the framework of the Hamiltonian formulation of free-surface potential flow are presented, tested, and validated. The first is an extension of Kennedy et al. (2000)’s eddy-viscosity approach originally developed for Boussinesq-type wave models. In this approach, an extra term, constructed to conserve the horizontal momentum for waves propagating over a flat bottom, is added in the dynamic free-surface condition. In the second method, a pressure distribution is introduced at the free surface that dissipates wave energy by analogy to a hydraulic jump (Guignard and Grilli, 2001). The modified Hamiltonian systems are implemented using the Hamiltonian Coupled-Mode Theory, in which the velocity potential is represented by a rapidly convergent vertical series expansion. Wave energy dissipation and conservation of horizontal momentum are verified numerically. Comparisons with experimental measurements are presented for the propagation of a breaking dispersive shock wave following a dam break, and then incident regular waves breaking on a mildly sloping beach and over a submerged bar.

DEPENDENCIES OF BREAKING TYPE, BREAKING CRITERIA AND ENERGY DISSIPATION ON AMPLITUDE-PHASE FREQUENCY STRUCTURE OF WAVES

Type of wave breaking - plunging or spilling - depends on symmetry of waves. The spilling waves are asymmetric against horizontal axis and are practically symmetric against vertical axis so the phase shift between first and second nonlinear harmonics (or biphase) is close to zero. The plunging breaking waves have larger asymmetry against vertical axis, (biphase is close to -pi/2), and near symmetric on horizontal axis (close to saw-toothed form). Non-linear wave transformation influences on depth-induced wave breaking. Breaking index depends on relation of wave energy in frequency range of second nonlinear harmonics to wave energy in frequency range of main harmonic and on biphase. The dissipation rate of spilling breaking waves energy quadratically depends on frequency, while in plunging breaking, this dependency is practically linear for all frequencies.

Nearshore wave processes numerical study for a better prediction of hydrodynamic loads on coastal structures

Taking into account the sensible approach in the coastal zones, in these types of areas were found different ways of understanding and description of the phenomena occurring during the water wave propagation. The waves hit the zone with a force that can affect the shoreline. Coastal protection measures were implemented, which include the hydrodynamic structures. The hydrodynamic process plays an important role in coastal area which involves the need for knowledge on the prediction of hydrodynamic loading required up to a very detailed level, such as maximum or minimum pressures. In this paper, we will present a study of wave fields that propagates in a simplified, constant-slope coastal model and relations between waves and hydrodynamics structures. The processes of wave fields include dissipative mechanisms such as depth-induced wave breaking, bottom friction and the interaction between wave field and coastal dike. The numerical models were constructed using ANSYS-Fluent program for modelling fluid flow and to solve the unsteady, two dimensional Navier-Stokes equations of incompressible fluid. Water waves are generated in two-phase fluid domain, where Volume of Fluid Model is used for generation of the two-phase flow model - the water-air interaction.

Spectral Wave Modeling in Very Shallow Water at Southern Coast of Caspian Sea

This study evaluates the capability of the Simulating WAves Nearshore (SWAN) wave model (version 41.01) in predicting significant wave height and spectral peak energy content for swell waves in very shallow water of surf zone during depth-induced wave breaking and dissipation. The model results were compared with field measurements at five nearshore stations. The results demonstrated that some breaker index formulations were successful for significant wave height prediction in surf zones. However, an incorrect shape of the energy spectrum and overestimated near spectral peak energy content at shallow water stations were obtained using all of the embedded depth-induced wave breaking formulations in SWAN. The dependent breaker index on relative depth (Kpd) formulation, which was successful in predicting near spectral peak energy content, resulted in an average error of 30%. Finally, this formulation was modified to enhance the model performance in reproducing the spectral peak energy content.

Assessing the performance of wave breaking parameterizations in shallow waters in spectral wave models

Depth-induced wave breaking is the primary dissipation mechanism for ocean surface waves in shallow waters. Different parametrizations were developed for parameterizing depth-induced wave breaking process in ocean surface wave models. The performance of six commonly-used parameterizations in simulating significant wave heights (SWHs) is assessed in this study. The main differences between these six parameterizations are representations of the breaker index and the fraction of breaking waves. Laboratory and field observations consisting of 882 cases from 14 sources of published observational data are used in the assessment. We demonstrate that the six parameterizations have reasonable performance in parameterizing depth-induced wave breaking in shallow waters, but with their own limitations and drawbacks. The widely-used parameterization suggested by Battjes and Janssen (1978, BJ78) has a drawback of underpredicting the SWHs in the locally-generated wave conditions and overpredicting in the remotely-generated wave conditions over flat bottoms. The drawback of BJ78 was addressed by a parameterization suggested by Salmon et al. (2015, SA15). But SA15 had relatively larger errors in SWHs over sloping bottoms than BJ78. We follow SA15 and propose a new parameterization with a dependence of the breaker index on the normalized water depth in deep waters similar to SA15. In shallow waters, the breaker index of the new parameterization has a nonlinear dependence on the local bottom slope rather than the linear dependence used in SA15. Overall, this new parameterization has the best performance with an average scatter index of ∼8.2% in comparison with the three best performing existing parameterizations with the average scatter index between 9.2% and 13.6%.

On the distribution of wave height in shallow water

The statistical distribution of the height of sea waves in deep water has been modelled using the Rayleigh (Longuet-Higgins, 1952) and Weibull distributions (Forristall, 1978). Depth-induced wave breaking leading to restriction on the ratio of wave height to water depth requires new parameterisations of these or other distributional forms for shallow water. Glukhovskiy (1966) proposed a Weibull parameterisation accommodating depth-limited breaking, modified by van Vledder (1991). Battjes and Groenendijk (2000) suggested a two-part Weibull–Weibull distribution. Here we propose a two-part Weibull-generalised Pareto model for wave height in shallow water, parameterised empirically in terms of sea state parameters (significant wave height, HS, local wave-number, kL, and water depth, d), using data from both laboratory and field measurements from 4 offshore locations. We are particularly concerned that the model can be applied usefully in a straightforward manner; given three pre-specified universal parameters, the model further requires values for sea state significant wave height and wave number, and water depth so that it can be applied. The model has continuous probability density, smooth cumulative distribution function, incorporates the Miche upper limit for wave heights (Miche, 1944) and adopts HS as the transition wave height from Weibull body to generalised Pareto tail forms. Accordingly, the model is effectively a new form for the breaking wave height distribution. The estimated model provides good predictive performance on laboratory and field data.

Nature-based flood protection: using vegetated foreshores for reducing coastal risk

Vegetated foreshores such as salt marshes, mangrove forests and reed fields can reduce wave loads on coastal dikes due to depth-induced wave breaking and wave attenuation by vegetation. Here we present field measurements of wave propagation over salt marshes during severe storm conditions, a modelling approach to describe the effect of vegetated foreshores on wave loads on the dike, and a probabilistic model to quantify the effect of vegetated foreshores on failure probabilities of the dike due to wave overtopping.

Modeling depth-induced wave breaking over complex coastal bathymetries

The correct representation of depth-induced wave breaking is important for understanding coastal morphology and for design and management in the coastal zone. Although numerous studies have demonstrated the applicability of a constant scaling of the Battjes and Janssen (1978) dissipation model for depth-induced breaking, recent studies have shown its inability to sufficiently reproduce wave dissipation over complex field cases. In the present study, we contrast the application of such a constant scaling to two alternative wave breaking parameterizations with a variable scaling based on either the wave nonlinearity (the φ parameterization) or on both bottom slope and normalized wavelength supplemented with wave directionality (the β−kd parameterization). We consider three field data sets characteristic of a simple beach-bar profile, a bay partially protected by a shoal and a complex intertidal region. We demonstrate that in these cases the β−kd parameterization provides a better alternative to the use of a constant scaling or the φ parameterization. To illustrate the operational consequences, we up-scale the conditions over the case of the intertidal region to correspond to design conditions for the Dutch coast (storm conditions with a 4000year return period). Under these extreme conditions, for locally generated waves both the β−kd and φ parameterizations predict qualitatively similar increased significant wave heights but the β−kd parameterization increased the waves twice as much as the φ parameterization. Under other conditions, when non-locally generated waves (swell) dissipates over a gently sloping bottom, the β−kd parameterization predicts lower significant wave heights compared to either the constant scaling or φ parameterization.

Stochastic modeling of inhomogeneous ocean waves

Refraction of swell waves in coastal waters can result in fast-scale variations of wave statistics due to wave interference. These variations cannot be resolved by wave models based on the radiative transport equation. More advanced models based on quasi-coherent theory, a generalization of the radiative transfer equation, can be coupled or nested into larger-scale models to resolve such local inhomogeneous effects. However, source terms for quasi-coherent models to account for non-conservative and nonlinear effects are not available, which hampers their operational use. In the present work we revisit the derivation of quasi-coherent theory to consistently include a source term for dissipation associated with depth-induced wave breaking. We demonstrate how general source terms can be incorporated in this class of models and compare model simulations with the new dissipation term to laboratory observations of focusing and breaking waves over a submerged shoal. The results show that a consistent derivation of source terms is essential to accurately capture coherent effects in coastal areas. Specifically, our results show that if coherent effects are ignored in the dissipation term, interference effects are strongly exaggerated. With the development of source terms for quasi-coherent models they can be effectively nested inside or otherwise coupled to larger-scale wave models to efficiently improve operational predictive capability of wave models near the coast.

Scaling depth-induced wave-breaking in two-dimensional spectral wave models

Wave breaking in shallow water is still poorly understood and needs to be better parameterized in 2D spectral wave models. Significant wave heights over horizontal bathymetries are typically under-predicted in locally generated wave conditions and over-predicted in non-locally generated conditions. A joint scaling dependent on both local bottom slope and normalized wave number is presented and is shown to resolve these issues. Compared to the 12 wave breaking parameterizations considered in this study, this joint scaling demonstrates significant improvements, up to ∼50% error reduction, over 1D horizontal bathymetries for both locally and non-locally generated waves. In order to account for the inherent differences between uni-directional (1D) and directionally spread (2D) wave conditions, an extension of the wave breaking dissipation models is presented. By including the effects of wave directionality, rms-errors for the significant wave height are reduced for the best performing parameterizations in conditions with strong directional spreading. With this extension, our joint scaling improves modeling skill for significant wave heights over a verification data set of 11 different 1D laboratory bathymetries, 3 shallow lakes and 4 coastal sites. The corresponding averaged normalized rms-error for significant wave height in the 2D cases varied between 8% and 27%. In comparison, using the default setting with a constant scaling, as used in most presently operating 2D spectral wave models, gave equivalent errors between 15% and 38%.

Storm Surge and Storm Waves Modelling Due to Typhoon Haiyan in November 2013 with Improved Dynamic Meteorological Conditions

In November 2013, Typhoon Haiyan caused devastating coastal disasters in the central Philippines triggered by large storm surges which occurred during its passage. It is the strongest typhoon that have ever attacked Philippines in its history. In this study, numerical simulations are performed for the storm surge and storm waves, together with dynamic meteorological fields such as wind and pressure induced by Typhoon Haiyan, using an integrated atmosphere-waves-ocean modelling system. The wave-induced dissipation stress from breaking waves, whitecapping and depth-induced wave breaking, is parameterized and implemented in the wave-current interaction process, in addition to its influence on the storm surge level in shallow water along the coast of central Philippines. The simulated track of the typhoon captures the best track well. The effects of wave-induced dissipation stress in the wave-current interaction resulted in increased surge heights in the relatively shallow areas such as Leyte Gulf and Visayan Sea in the central region, where the bottom slope of the bathymetry ranges from mild to moderate. The results also show that wave-breaking has to be considered for accurate storm surge prediction along the east coast of Samar Island over the narrow surf zone with much finer meshes of the order of several meters.

Wave modelling in archipelagos

The Archipelago Sea, located in the Baltic Sea between the Gulf of Bothnia and the Baltic Proper, comprises thousands of small islands and shoals. The sheltering effects, depth-induced wave breaking and refraction make the modelling of waves challenging in this area. Ten different high-resolution grids were generated based on coastal nautical charts with horizontal resolutions of 0.1nmi and 0.5nmi using two different methods to compile land–sea mask and additional grid obstructions. The wave model WAM was used to model the wave field in the Archipelago Sea. The modelled wave field was compared against measurements made during a research cruise of R/V Aranda in September 2010. The 0.1nmi grids had the highest accuracy in modelling the local wave field. However, they overestimated the attenuation of the open sea waves propagating into the Archipelago Sea. The 0.5nmi grids overestimated the energy of the local wind waves and underestimated the attenuation of the open sea waves. When grid obstructions were used in the 0.5nmi grids, the attenuation of wave energy was modelled with good accuracy, but the energy of the local wind waves was still slightly overestimated. The accuracy of the forcing wind field had significant effect on the accuracy of the locally generated wave field inside the archipelago. The depth-induced wave breaking and wave refraction were shown to have a prominent effect on the modelled wave field at the southern edge of the Archipelago Sea. The 0.5nmi grids were unable to describe these features in as much detail as the 0.1nmi grids.

Wave-tide-surge coupled simulation for typhoon Maemi

The main task of this study focuses on studying the effect of wave-current interaction on currents, storm surge and wind wave as well as effects of current induced wave refraction and current on waves by using numerical models which consider the bottom boundary layer and sea surface roughness parameter for shallow and smooth bed area around Korean Peninsula. The coupled system (unstructured-mesh SWAN wave and ADCIRC) run on the same unstructured mesh. This identical and homogeneous mesh allows the physics of wave-circulation interactions to be correctly resolved in both models. The unstructured mesh can be applied to a large domain allowing all energy from deep to shallow waters to be seamlessly followed. There is no nesting or overlapping of structured wave meshes, and no interpolation is required. In response to typhoon Maemi (2003), all model components were validated independently, and shown to provide a faithful representation of the system’s response to this storm. The waves and storm surge were allowed to develop on the continental shelf and interact with the complex nearshore environment. The resulting modeling system can be used extensively for prediction of the typhoon surge. The result show that it is important to incorporate the wave-current interaction effect into coastal area in the wave-tide-surge coupled model. At the same time, it should consider effects of depth-induced wave breaking, wind field, currents and sea surface elevation in prediction of waves. Specially, we found that: (1) wave radiation stress enhanced the current and surge elevation otherwise wave enhanced nonlinear bottom boundary layer decreased that, (2) wind wave was significantly controlled by sea surface roughness thus we cautiously took the experimental expression. The resulting modeling system can be used for hindcasting (prediction) the wave-tide-surge coupled environments at complex coastline, shallow water and fine sediment area like areas around Korean Peninsula.

Depth-induced wave breaking in a non-hydrostatic, near-shore wave model

The energy dissipation in the surf-zone due to wave breaking is inherently accounted for in shock-capturing non-hydrostatic wave models, but this requires high vertical resolutions. To allow coarse vertical resolutions a hydrostatic front approximation is suggested. It assumes a hydrostatic pressure distribution at the front of a breaking wave which ensures that the wave front develops a vertical face. Based on the analogy between a hydraulic jump and a turbulent bore, energy dissipation is accounted for by ensuring conservation of mass and momentum. Results are compared with observations of random, uni-directional waves in wave flumes, and to observations of short-crested waves in a wave basin. These demonstrate that the resulting model can resolve the relevant near-shore wave processes in a short-crested wave-field, including wave breaking and wave-driven horizontal circulations.