A probability distribution for depth-limited extreme wave heights in a sea state

A model for the depth-limited distribution of the highest wave in a sea state is presented. The distribution for the extreme wave height is based on a probability density function (pdf) for depth-limited wave height distribution for individual waves [Méndez, F.J., Losada, I.J., Medina, R. 2004. Transformation model of wave height distribution. Coastal Eng, Vol. 50, 97:115.] and considers the correlation between consecutive waves. The model is validated using field data showing a good representation of the extreme wave heights in the surf zone. Some important statistical wave heights are parameterized obtaining useful expressions that can be used in further calculations.     

Wave groupiness and spectral bandwidth as relevant parameters for the performance assessment of wave energy converters

To date the estimation of long-term wave energy production at a given deployment site has commonly been limited to a consideration of the significant wave height H_s and mean energy period T_e. This paper addresses the sensitivity of power production from wave energy converters to the wave groupiness and spectral bandwidth of sea states. Linear and non-linear systems are implemented to simulate the response of converters equipped with realistic power take-off devices in real sea states. It is shown in particular that, when the converters are not much sensitive to wave directionality, the bandwidth characteristic is appropriate to complete the set of overall wave parameters describing the sea state for the purpose of estimating wave energy production.     

Stability of rubble-mound breakwater using H50 wave height parameter

The prediction of rubble mound breakwaters' stability is one of the most important issues in coastal and maritime engineering. The stability of breakwaters strongly depends on the wave height. Therefore, selection of an appropriate wave height parameter is very vital in the prediction of stability number. In this study, H₅₀, the average of the 50 highest waves that reach the breakwater in its useful life, was used to predict the stability of the armor layer. First, H₅₀ was used instead of the significant wave height in the most recent stability formulas. It was found that this modification yields more accurate results. Then, for further improvement of the results, two formulas were developed using model tree.To develop the new formulas, two experimental data sets of irregular waves were used. Results indicated that the proposed formulas are more accurate than the previous ones for the prediction of the stability parameter. Finally, the proposed formulas were applied to regular waves and a wide range of damage levels and it was seen that the developed formulas are applicable in these cases as well.     

Effects of high-order nonlinear interactions on unidirectional wave trains

Numerical simulations of gravity waves with high-order nonlinearities in two-dimensional domain are performed by using the pseudo spectral method. High-order nonlinearities more than third order excite apparently chaotic evolutions of the Fourier energy in deep water random waves. The high-order nonlinearities increase kurtosis, wave height distribution and H_max/H_1/3 in deep water and decrease these wave statistics in shallow water. Moreover, they can generate a single extreme high wave with an outstanding crest height in deep water. High-order nonlinearities (more than third order) can be regarded as one cause of freak waves in deep water.     

Scour below marine pipelines in shoaling conditions for random waves

This paper provides an approach by which the scour depth below pipelines in shoaling conditions beneath non-breaking and breaking random waves can be derived. Here the scour depth formula in shoaling conditions for regular non-breaking and breaking waves with normal incidence to the pipeline presented by Cevik and Yüksel [Cevik, E. and Yüksel, Y., (1999). Scour under submarine pipelines in waves in shoaling conditions. ASCE J. Waterw., Port, Coast. Ocean Eng., 125 (1), 9–19.] combined with the wave height distribution including shoaling and breaking waves presented by Mendez et al. [Mendez, F.J., Losada, I.J. and Medina, R., (2004). Transformation model of wave height distribution on planar beaches. Coast. Eng. 50 (3), 97–115.] are used. Moreover, the approach is based on describing the wave motion as a stationary Gaussian narrow-band random process. An example of calculation is also presented.     

General longshore transport model

In the present paper a general longshore transport (LT) model is proposed after a re-calibration of the model originally introduced by Lamberti and Tomasicchio (1997) based on a modified stability number, N_s^⁎⁎, for stone mobility at reshaping or berm breakwaters. N_s^⁎⁎ resembles the traditional stability number (Ahrens, 1987; van der Meer, 1988) taking into account the effects of a non-Rayleighian wave height distribution at shallow water (Klopman and Stive, 1989), wave steepness, wave obliquity, and nominal diameter of the units. Nine high-quality data sets from field and laboratory experiments have been considered to extend the validity of the original model for a wider mobility range of the units: from stones to sands. The predictive capability of the proposed model has been verified against the most popular formulae in literature for the LT estimation of not cohesive units at a coastal body. The comparison showed that the model gives a better agreement with the physical data with respect to the other investigated formulae.The proposed transport model presents a main advantage with respect to other formulae: it can represent an engineering tool suitable for a large range of conditions, from sandy beaches till reshaping breakwaters.     

Analysis of temporal and spatial characteristics of waves in the Indian Ocean based on ERA-40 wave reanalysis

Based on the 45-year (09/1957-08/2008) European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA-40) wave reanalysis dataset, this study analyzes interannual and interdecadal variabilities and intraseasonal oscillations of sea surface wind speed (WS), wind sea wave height (H^w), swell wave height (H^s) and significant wave height (H_s) in the Roaring Forties and tropical waters of the Indian Ocean, to determine swell propagation characteristics. The results show: (1) monthly variabilities of H^s in the Roaring Forties are in good agreement with those in tropical waters of the Indian Ocean; swell plays a dominant role in mixed waves throughout most of the Indian Ocean; and WS, H^w, H^s, and H_s exhibit a significant increasing trend over the 45-year study period. (2) H^s in the Roaring Forties and tropical waters of the Indian Ocean share a common period of 9.8–10.4 years on an interdecadal scale; and WS and H^s in the Roaring Forties and H^s in the tropical waters of the Indian Ocean share a common period of approximately 8 days (weekly oscillation) on an intraseasonal scale. (3) Swell of the Roaring Forties needs approximately 30 h to fully respond to the wind in this region. Approximately 84 h are required for H^s to propagate from the Roaring Forties to the tropical waters of the south Indian Ocean, while it takes approximately 132–138 h for H^s to propagate from the Roaring Forties to the tropical waters of the north Indian Ocean.     

随机波浪中畸形波在三维岛礁地形上的试验研究

在试验水池中，开展了波浪在岛礁地形上演化问题的研究。首先在实验水池中建立了西太平洋某岛礁地形的模型，然后采用改进的JONSWAP谱，由造波机产生不同周期、波高的随机波浪。试验中观察到了不同类型畸形波生成的过程及不同波面形态的畸形波。对偏度、峰度及水深与畸形波要素H_m/H_s（H_m表示波列中的最大波高， H_s为有效波高）的关系进行了详细的分析，同时，对畸形波波高H_fr与偏度的关也进行了分析。通过对试验结果分析，发现峰度与畸形波要素i>H_m/H_s呈正相关， H_fr增大时相应的偏度也会呈现增大的趋势。此外，水深的变化剧烈时（如斜坡、海山位置）有助于畸形波的发生。     

Profiles of fully developed (Airy) waves in different water depths

Airy waves have a sinusoidal profile in deep water that can be modeled by a time series at any point x and time t, given by η(x,t) = (H_o/2) cos[2πx/L_o − 2πt/T_w], where H_o is the deepwater height, L_o is the deepwater wavelength, and T_w is the wave period. However, as these waves approach the shore they change in form and dimension so that this equation becomes invalid. A method is presented to reconstruct the wave profile showing the correct wavelength, wave height, wave shape, and displacement of the water surface with respect to the still water level for any water depth.     

Improvement of sand activation depth prediction under conditions of oblique wave breaking

This study presents sand activation depth (SAD) measurements recently obtained on two contrasting beaches located along the Atlantic coast of France: the gently sloping, high-energy St Trojan beach where wave incidence is usually weak, and the steep, low-energy Arçay Sandspit beach where waves break at highly oblique angles. Comparisons between field measurements and predictions from existing formulae show good agreement for St Trojan beach but underestimate the SAD on the Arçay Sandspit beach by 40–60%. Such differences suggest a strong influence of wave obliquity on SAD. To verify this hypothesis, the relative influence of wave parameters was investigated by means of numerical modelling. A quasi-linear increase of SAD with wave height was confirmed for shore-normal and slightly oblique wave conditions, and a quasi-linear increase in SAD with wave obliquity was also revealed. Combining the numerical results with previously published relations, both a new semi-empirical and an empirical formula for the prediction of SAD were developed which showed good SAD predictions under conditions of oblique wave breaking. The new empirical formula for the prediction of SAD (Z ₀) takes into account the significant wave height (H _s), the beach face slope (β) and the wave angle at breaking (α), and is of the form $ Z_{0} = 1.6\tan {\left( \beta \right)}H^{{0.5}}_{{\text{s}}} {\sqrt {1 + \sin {\left( {2\alpha } \right)}} } This study presents sand activation depth (SAD) measurements recently obtained on two contrasting beaches located along the Atlantic coast of France: the gently sloping, high-energy St Trojan beach where wave incidence is usually weak, and the steep, low-energy Ar?ay Sandspit beach where waves break at highly oblique angles. Comparisons between field measurements and predictions from existing formulae show good agreement for St Trojan beach but underestimate the SAD on the Ar?ay Sandspit beach by 40–60%. Such differences suggest a strong influence of wave obliquity on SAD. To verify this hypothesis, the relative influence of wave parameters was investigated by means of numerical modelling. A quasi-linear increase of SAD with wave height was confirmed for shore-normal and slightly oblique wave conditions, and a quasi-linear increase in SAD with wave obliquity was also revealed. Combining the numerical results with previously published relations, both a new semi-empirical and an empirical formula for the prediction of SAD were developed which showed good SAD predictions under conditions of oblique wave breaking. The new empirical formula for the prediction of SAD (Z ₀) takes into account the significant wave height (H _s), the beach face slope (β) and the wave angle at breaking (α), and is of the form . The use of a dataset from the literature demonstrates the predictive skill of these new formulae for a wide range of wave heights, wave incidence and beach gradients.     

Wave modelling in the vicinity of submerged breakwaters

This paper describes a simple method for modelling wave breaking over submerged structures, with the view of using such modelling approach in a coastal area morphodynamic modelling system.A dominant mechanism for dissipating wave energy over a submerged breakwater is depth-limited wave breaking. Available models for energy dissipation due to wave breaking are developed for beaches (gentle slopes) and require further modifications to model wave breaking over submerged breakwaters.In this paper, wave breaking is split into two parts, namely: 1) depth-limited breaking modelled using Battjes and Janssen's (1978) theory [Battjes, J.A. and Jannsen, J.P.F.M. (1978). Energy loss and setup due to breaking of random waves. Proceedings of the 16th Int. Conf. Coast. Eng., Hamburg, Germany, pp. 569-587.] and 2) steepness limited breaking modelled using an integrated form of the Hasselmann's whitecapping dissipation term, commonly used in fully spectral wind–wave models. The parameter γ₂, governing the maximum wave height at incipient breaking (H_max = γ₂d) is used as calibration factor to tune numerical model results to selected laboratory measurements. It is found that γ₂ varies mainly with the relative submergence depth (ratio of submergence depth at breakwater crest to significant wave height), and a simple relationship is proposed. It is shown that the transmission coefficients obtained using this approach compare favourably with those calculated using published empirical expressions.     

Design weight of armour stone considering the effect of extreme waves

In this study, waves with the heights higher than H_1/3 in an irregular wave train are called as extreme waves and defined with the help of extreme wave parameter, α_extreme. In order to see the effect of extreme waves on the design weight of armour stone, stability analysis is carried out based on the hydraulic model test results. The test results of high α_extreme cases (HE) and low α_extreme cases (LE) are compared with currently used van der Meer's formulae with permeability factor P=0.4 and 0.45 and Hudson formula by using H_1/3 and H_1/10 in terms of the design weight of armour stone. As a result of the comparison, it is found that Hudson formula by using H_1/3 underestimates the necessary armour weight. Usage of H_1/10 instead of H_1/3 in Hudson formula doubles the weight which seems overestimated when Irribaren number is away from the transition zone in which both wave run-up and run-down forces become effective. However, it seems underestimated near the transition zone where experiment case HE gives higher armour weights. When the design weight of armour stone is calculated by van der Meer's formulae with P=0.4, it may be necessary to increase the weight up to 30% in the case of high extreme waves. On the other hand, van der Meer's formulae may overestimate the weight 14% when the extreme waves are low.     

Experimental study of unidirectional irregular wave slamming on the three-dimensional structure in the splash zone

The experimental investigation of unidirectional random wave slamming on the three-dimensional structure in the splash zone is presented. The experiment is conducted in the marine environment channel in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology. The test wave is unidirectional irregular wave. The experiments are carried out with perpendicular random waves (β=0°) and oblique random waves (β=15°, 30°, 45°), the significant wave heights H_1/3 ranging from 7.5 to 20 cm with 2.5 cm increment, the peak wave periods T_p ranging from 0.75 to 2.0 s with 0.25 s increment, and the clearance of the model with respect to the significant wave height s/H_1/3 ranging from 0.0 to 0.5 with 0.1 increment. The statistical analysis results of different test cases are presented. The statistical distribution characteristics of the perpendicular irregular wave impact pressures are compared with that of the oblique irregular wave on the underside of the structure. The effect of the wave direction β on the wave impact forces on the underside of the structure is determined. The relation between the impact forces and the parameters such as the significant wave height, the relative structure width and the relative clearance of the structure is also discussed.     

Prediction of geometrical properties of perfect breaking waves on composite breakwaters

Breaking wave loads on coastal structures depend primarily on the type of wave breaking at the instant of impact. When a wave breaks on a vertical wall with an almost vertical front face called the “perfect breaking”, the greatest impact forces are produced. The correct prediction of impact forces from perfect breaking of waves on seawalls and breakwaters is closely dependent on the accurate determination of their configurations at breaking. The present study is concerned with the determination of the geometrical properties of perfect breaking waves on composite-type breakwaters by employing artificial neural networks. Using a set of laboratory data, the breaker crest height, h_b, breaker height, H_b, and water depth in front of the wall, d_w, from perfect breaking of waves on composite breakwaters are predicted using the artificial neural network technique and the results are compared with those obtained from linear and multi-linear regression models. The comparisons of the predicted results from the present models with measured data show that the h_b, H_b and d_w values, which represent the geometry of waves breaking directly on composite breakwaters, can be predicted more accurately by artificial neural networks compared to linear and multi-linear regressions.     

Megacusps on rip channel bathymetry: Observations and modeling

The formation of beach megacusps along the shoreline of southern Monterey Bay, CA, is investigated using time-averaged video and simulated with XBeach, a recently developed coastal sediment transport model. Investigations focus on the hydrodynamic role played by the bay's ever-present rip channels. A review of four years of video and wave data from Sand City, CA, indicates that megacusps most often form shoreward of rip channels under larger waves (significant wave height (H_s) = 1.5–2.0 m). However, they also occasionally appear shoreward of shoals when waves are smaller (H_s ~ 1 m) and the mean water level is higher on the beach. After calibration to the Sand City site, XBeach is shown to hindcast measured shoreline change moderately well (skill = 0.41) but to overpredict the erosion of the swash region and beach face. Simulations with small to moderate waves (H_s = 0.5–1.2 m) suggest, similar to field data, that megacusps will form shoreward of either rip channels or shoals, depending on mean daily water level and pre-existing beach shape. A frequency-based analysis of sediment transport forcing is performed, decomposing transport processes to the mean, infragravity, and very-low-frequency (VLF) contributions for two highlighted cases. Results indicate that the mean flow plays the dominant role in both types of megacusp formation, but that VLF oscillations in sediment concentration and advective flow are also significant.