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Barred macrotidal beaches are affected by continuous horizontal displacements of different hydrodynamic zones associated with wave transformation (shoaling, breaker and surf zones) due to significant tide-induced water level changes. A series of wave and current meters, complemented by a video imagery system, were deployed on a barred beach of northern France during a 6-day experiment in order to characterize the spatial and temporal variability of wave-induced processes across the beach. Wave and current spectral analyses and analyses of cross-shore current direction and asymmetry resulted in the identification of distinct hydrodynamic processes, including the development of infragravity waves and offshore-directed flows in the breaker and surf zones. Our results revealed a high spatial variability in the hydrodynamic processes across the beach, related to the bar-trough topography, as well as significant variations in the directions and intensity of cross-shore currents at fixed locations due to the horizontal translation of the different hydrodynamic zones resulting from continuous changes in water level due to tides.

A series of wave-flume tests were performed to study the characteristics of regular waves breaking on coral reefs, including the breaker type, breaker height, breaker position and surf-zone width. The tests were performed on the composite slope section of a reef rim at the specified conditions combined with serial wave heights and wave periods for two water levels. The test studied the criteria for differentiating the breaker types, assessed the applicability of the four breaker indexes on coral reefs with a composite slope, and provided an experience formula describing the breaker position and surf-zone width. Thus the following conclusions were drawn:the breaker types could be differentiated by the ratio of reef-edge water depth to the deep-water wave height;in the relational expressions of four breaker indexes, the correlation between the ratio of breaker height to deep-water wave height and the deep-water wave steepness was the best;the deep-water wave height and reef-edge water depth had great influence on breaker position and surf-zone width;with the increase in the ratio of deep-water wave height to reef-edge water depth, the dimensionless breaker position(the ratio of distance between the breaker point and the reef edge to the reef-edge shallow-water wave length) decreased and the dimensionless surf-zone width(the ratio of surf-zone width to reef-edge shallow-water wave length) increased. [ABSTRACT FROM AUTHOR]

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%. [ABSTRACT FROM AUTHOR]

The forces and loading resulting from shallow water breaking waves are one of the most important drivers in coastal engineering design and morphological change. The importance of accurately and precisely predicting breaking wave conditions cannot be overstated. Using a novel dataset of laboratory and field scale breaking wave conditions, this study assesses the performance of widely applied empirical relationships for breaking waves and uses newly available artificial neural networks and gene expression programming (GEP) numerical methods to develop an accurate and easily applied predictor of breaking conditions for coastal engineers and planners. A novel GEP model is developed and shown to: provide excellent predictive ability at all scales, greatly improve prediction compared with previous works at laboratory scale and clearly identify the relevant importance of seafloor slope and the water depth to wavelength ratio. [ABSTRACT FROM AUTHOR]

Filipot, J.-F., 2016. Investigation of the bottom-slope dependence of the nonlinear wave evolution toward breaking using SWASH. Numerical simulations of irregular waves propagating over planar beaches with slopes varying from 1 to 10% are performed with the Simulating WAves till SHore (SWASH) model. As reported in observational studies, waves shoaling over steep (mild) slopes break in shallower (deeper) water. The bottom slope is found to influence the cumulative contribution of the triad wave interactions to the wave spectrum. The triad contribution affects wave skewness and wave asymmetry at breaking point. This consolidates findings reported in previous field studies and has significant implications for coastal applications. [ABSTRACT FROM AUTHOR]

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. • A new breaker index formula used in spectral wave model is presented by modification of Goda (2010). • It solves the uncertainty of the empirical coefficient of Goda's formula through considering the deep-water wave steepness. • The updated breaker index can be used in a very large range of beach slopes for SWAN model simulation. • Experimental wave height data over 1:100 to 1:300 beach slopes are provided. [ABSTRACT FROM AUTHOR]

Surfzone wave characteristics, measured using a wave and tide gauge (WTG) during a flood tide, were studied at three different beaches having different nearshore slopes. The spectral wave characteristics viz., wave-height and mean wave period were estimated considering different sample sizes. Inter-comparisons of wave climate between each of three beaches for a similar tide level are presented. The wave-height and mean wave period values obtained from the wave analysis for each of the record using waves by wave method show that surfzone wave-height increased with time during a flood tide and the mean wave period decreased with time up to mid tide and then increased during the rest of the measurement period at Keri and Miramar beaches. At Candolim, the reversing trend of mean wave period increase is observed to occur much before reaching the mid tide level. The surfzone waves during a flood tide indicated that the wave-heights increased with time while the mean wave period showed a decreasing trend in general. The variation of breaker index showed a decreasing trend from low tide to high tide ranging between 0.45 and 0.23. The surf similarity parameter estimated corroborates with the visual observations. [ABSTRACT FROM AUTHOR]

Robertson, B.; Hall, K.; Nistor, I.; Zytner, R., and Storlazzi, C., 2015. Remote sensing of irregular breaking wave parameters in field conditions. The analysis of wave breaking in shallow water has been ongoing for almost 150 years. Numerous research papers have been published that approximate both the local conditions and geometric characteristics of breaking waves. However, much of this knowledge is based on laboratory results or limited field investigations because traditional methods of extracting breaking wave measurements from the surfzone are expensive, dangerous, and feature low-resolution data. Unfortunately, laboratory studies are prone to scaling and friction effects that introduce unwanted variability in the data. This study presents a novel, safe, and low-cost method of extracting relevant breaking-wave properties from irregular waves in the surfzone, using optical and in situ measurement systems. Published, contradictory breaking-water depth definitions are compared, and the water depth at the wave-trough depth, corrected for optical offsets using a still-water correction of one-third of the wave height, is found to exhibit the least variability. A new, effective seafloor-slope definition, based on individual, breaking wavelength-to-depth ratios, was found to increase predictive ability over previously variable seafloor slope extraction methods. Collected field data are compared against established breaking-wave height formulas with the general exponential form consistently finding the best correlation. Finally, an optimized breaking-wave height-prediction method finds a root mean square relative error of just 1.672% within the ranges of the measured data set. Irregular waves investigated on an individual wave basis are shown to follow regular wave-breaker height and depth prediction methods. [ABSTRACT FROM AUTHOR]

A fringing reef is a reef that is directly attached to a shore. Since fringing reefs resemble plane beaches in some aspects, it is important to understand the similarities and discrepancies between the wave breaking over fringing reefs and the wave breaking over plane beaches. With an idealized fringing reef (a plane sloping fore reef and a submerged horizontal reef flat), a series of laboratory experiments were conducted in a wave flume to understand how the reef-flat submergence and the fore-reef slope may affect the characteristics of wave breaking over fringing reefs. The results show that the relative reef-flat submergence (the ratio of the reef-flat submergence to the wave height) is an important factor to characterize most wave-breaking features (the breaker type and location, the surf-zone width, and the incipient breaker depth index). The influence of the fore-reef slope appears to be insignificant in our experimental conditions. The findings in this study can be used to calibrate or improve some existing analytical or numerical models developed for cross-shore wave transformation, wave-induced setup and wave-driven flow over fringing reefs. [ABSTRACT FROM AUTHOR]

Abstract: This paper provides a joint distribution of wave height and surf parameter, as well as a joint distribution of wave height and breaker index; both joint distributions are for individual waves within a sea state. This is relevant for characterizing surf zone processes and can be used to make assessments of e.g. wave run-up on beaches and coastal structures, as well as of breaking waves on slopes. An example of results corresponding to typical field conditions is also provided. [Copyright &y& Elsevier]

A bivariate Fréchet distribution which is obtained by transforming a bivariate Rayleigh distribution is presented. The emphasis is on its application to the statistics of two successive surf parameters. The results are illustrated by estimating the probability of two successive spilling breakers and two successive plunging breakers on different slopes by using wave parameters corresponding to typical field conditions. [ABSTRACT FROM AUTHOR]

Statistics of breaking waves across the surf zone are reanalyzed on the basis of various sets of field and laboratory data so as to provide coastal engineers with reliable information on breaking waves. The breaker index or the ratio of wave height to water depth is to be expressed as a function of the two parameters of beach slope and relative depth, and Goda's breaker index formula is revised slightly to reduce the slope effect. The breaker index for regular waves has inherent variability as expressed with the coefficient of variability, which increases from 6% to 14% as the beach slope becomes steep up to 1/10. The incipient breaking height of the significant wave is about 30% lower than that of regular waves, but the ratio of significant wave height to water depth gradually increases within the surf zone toward the shoreline. The wave height distribution is the narrowest in the middle of the surf zone, but it returns to the Rayleigh distribution near the shoreline owing to wave regeneration after breaking. The nonlinearity of random waves is strongest at the outer edge of the surf zone, but it is destroyed by the wave breaking process inside the surf zone. The ratios of statistical wave heights H1/10, H1/3 and Hrms to the spectral significant wave height Hm0 are shown to increase as the wave nonlinearity parameter increases up to the outer edge of the surf zone. [ABSTRACT FROM AUTHOR]

The purpose of these comments and discussion has been to point out that wave statistics can be incorporated in future applications of the nearshore wave breaker index formula proposed by Zhang et al. (2021). This is demonstrated by using a joint distribution of significant wave height and spectral peak period provided by Li et al. (2015). • Extension of suggested nearshore wave breaker index formula to random waves. • Random waves given by joint statistics of significant wave height and spectral peak period. • Examples of results given in terms of expected values and coefficients of variation. [ABSTRACT FROM AUTHOR]

Random wave transformations with breaking in shallow water of 2-D bathymetry are computed with the parabolic equation. A new system of gradational breaker index, the value of which gradually decreases as the level of wave height within a wave group is lowered, is introduced to simulate gradual shape variations of wave height distribution in the surf zone. Wave attenuation in the trough area of a barred beach is treated with a secondary gradational breaker index, which is applied for locations in water of constant or increasing depth. Its empirical coefficients are assigned values different from those in water of decreasing depth. The wave attenuation factor due to bottom friction is formulated by evaluating the rate of energy dissipation by shear stress along the sea bottom. Computation is made for directional spectral components with multiple levels of wave heights under the Rayleigh distribution, and the results are synthesized for the calculation of wave height distributions. The new computational scheme succeeds in reproducing the random wave breaking diagrams by Goda (1975), and shows good agreements with several experimental results on wave transformations over horizontal shelves, barred beaches, and an elliptical shoal. The scheme also yields wave height predictions in good agreement with several field measurements across the surf zone. [ABSTRACT FROM AUTHOR]

The performances of phase-averaged parametric nearshore wave transformation models depend significantly on a reliable estimate of the wave breaker index γ (the breaker height-to-depth ratio), a free model parameter that essentially controls the amount of breaking energy dissipation. While the previous studies have suggested separate relationships between γ and the offshore wave steepness (s 0) or the normalized local water depth (kh), the parameterization of γ still requires further investigation considering a wider variety of conditions and a sounder physical basis. In this study, we use the field datasets of wave height and the inverse modelling approach to reveal a composite dependence of γ on both s 0 and kh. Specifically, the results show a positive dependence of γ on kh for larger s 0 , and a negative dependence of γ on kh for smaller s 0. Based on such composite relationships, a new γ formula is proposed, and its performance is verified against the available datasets of wave height in three coasts and 14 laboratory tests. Implementation of this new formula in a parametric wave model leads to the error reduction of wave height prediction by 10–24% (mean = 19%) relative to seven widely used models in literatures. In particular, a remarkably higher model accuracy is obtained under wave conditions with small offshore wave steepness, which is important for studying onshore sediment transport and beach recovery. Two counteractive physical mechanisms for wave nonlinearity effects, namely the breaking intensification mechanism and the breaking resistance mechanism, are suggested to explain the opposite γ - kh relationships within different ranges of s 0. • The composite dependence of wave breaker index on both the offshore wave steepness and the normalized local water depth. • A new formula for wave breaker index used for parametric wave transformation modelling leads to improved wave height prediction especially under wave conditions with small offshore wave steepness. • Two counteractive physical mechanisms to explain the composite relationships. [ABSTRACT FROM AUTHOR]

Barred macrotidal beaches are affected by continuous horizontal displacements of different hydrodynamic zones associated with wave transformation (shoaling, breaker and surf zones) due to significant tide-induced water level changes. A series of wave and current meters, complemented by a video imagery system, were deployed on a barred beach of northern France during a 6-day experiment in order to characterize the spatial and temporal variability of wave-induced processes across the beach. Wave and current spectral analyses and analyses of cross-shore current direction and asymmetry resulted in the identification of distinct hydrodynamic processes, including the development of infragravity waves and offshore-directed flows in the breaker and surf zones. Our results revealed a high spatial variability in the hydrodynamic processes across the beach, related to the bar-trough topography, as well as significant variations in the directions and intensity of cross-shore currents at fixed locations due to the horizontal translation of the different hydrodynamic zones resulting from continuous changes in water level due to tides. [ABSTRACT FROM AUTHOR]

This paper presents detailed laboratory experiments investigating the effect onshore and offshore wind conditions have on nearshore wave dynamics, including extreme winds. The experiments were performed using monochromatic waves and a linearly sloping bed. The results show that offshore wind conditions delay wave breaking and promote steep breakers, while onshore wind conditions extend the surf zone and flatten the waves. Firstly, linear and cnoïdal wave models were used in standard formulations to predict the cross-shore wave evolution under no-wind conditions. Secondly, wind effect was added to account for wind-induced modifications of breaker height and energy balance. Despite experimental limitations, the overall satisfactory agreement between theory and observations suggests that such an approach can be used to describe the wind effect in wave nearshore models. • First laboratory experiments showing the effect of on/offshore wind conditions on nearshore wave dynamics. • Strong effects are observed in both the shoaling and surf zone. • On/offshore winds tend to extend/reduce the surf zone and modify the wave skewness, asymmetry and energy dissipation. • Strong wind-induced variations are observed for the wave height-to-depth breaker index ranging from 0.4 to 1.3. • New parameterizations are proposed to represent the wind effect in the surf zone. [ABSTRACT FROM AUTHOR]

Most studies of wave breaking on slopes to date have investigated regular waves or normal incident unidirectional waves. In this study, wave breakings of normal and oblique incident irregular waves and multidirectional irregular waves on a 1:15 slope were investigated. The breaking criteria of irregular waves based on significant wave height and individual wave height were determined. Firstly, breaker indexes calculated using significant wave heights at incipient breaking were analyzed; they were substantially lower than the breaker indexes of regular waves. The breaker index formulae of irregular waves are presented based on the referred formula of regular waves. Furthermore, the breaker indexes of oblique incident waves were larger than the breaker indexes of normal incident waves. However, wave directionality had little effect on breaker indexes under the present experimental conditions. Secondly, the breaker index (the ratio of significant wave height to water depth) in surf zone was analyzed. It increased with a decrease in relative water depth. Thirdly, information of individual waves in irregular wave trains was tracked by the wave-by-wave method. The breaker indexes derived by individual wave heights were larger than the incipient breaker indexes derived from significant wave heights. Based on previous empirical formulae, some relatively simple expressions are proposed to calculate individual breaking wave heights for unidirectional irregular waves. • Experiments on a 1:15 slope for normal and oblique incident irregular waves and multidirectional waves are performed. • The breaker indexes calculated by significant wave height at incipient wave breaking and in the surf zone are analyzed. • The breaker indexes calculated by individual wave height for normal incident irregular waves are proposed. • These results can provide reference values for other slope terrain and for verifying the corresponding numerical models. [ABSTRACT FROM AUTHOR]