A ten-year data set for fetch- and depth-limited wave growth

This paper presents the key results from a ten-year data set for Lake IJssel and Lake Sloten in The Netherlands, containing information on wind, storm surges and waves, supplemented with SWAN 40.51 wave model results. The wind speeds U₁₀, effective fetches x and water depths d for the data set ranged from 0–24 m s^− 1, 0.8–25 km and 1.2–6 m respectively. For locations with non-sloping bottoms, the range in non-dimensional fetch x? ( = gxU₁₀^− 2) was about 25–80,000, while the range in dimensionless depth d? ( = g d U₁₀^− 2) was about 0.03–1.7. Land–water wind speed differences were much smaller than the roughness differences would suggest. Part of this seems due to thermal stability effects, which even play a role during near-gale force winds. For storm surges, a spectral response analysis showed that Lake IJssel has several resonant peaks at time scales of order 1 h. As for the waves, wave steepnesses and dimensionless wave heights H? ( = gH_m0U₁₀^− 2) agreed reasonably well with parametric growth curves, although there is no single curve to which the present data fit best for all cases. For strongly depth-limited waves, the extreme values of d? (0.03) and H_m0 / d (0.44) at the 1.7 m deep Lake Sloten were very close to the extremes found in Lake George, Australia. For the 5 m deep Lake IJssel, values of H_m0 / d were higher than the depth-limited asymptotes of parametric wave growth curves. The wave model test cases of this study demonstrated that SWAN underestimates H_m0 for depth-limited waves and that spectral details (enhanced peak, secondary humps) were not well reproduced from H_m0 / d = 0.2–0.3 on. SWAN also underestimated the quick wave response (within 0.3–1 h) to sudden wind increases. For the remaining cases, the new [Van der Westhuysen, A.J., Zijlema, M., and Battjes, J.A., 2007. Nonlinear saturation-based whitecapping dissipation in SWAN for deep and shallow water, Coast. Eng., 54, 151–170] SWAN physics yielded better results than the standard physics of Komen, G.J., Hasselmann, S., Hasselmann, K., 1984. On the existence of a fully developed wind-sea spectrum. J. Phys. Oceanogr. 14, 1271–1285, except for persistent overestimations that were found for short fetches. The present data set contains many interesting cases for detailed model validation and for further studies into the evolution of wind waves in shallow lakes.     

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.     

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.     

Modelling analysis of the sensitivity of shoreline change to a wave farm

Change of shoreline wave climate caused by the installation of a wave farm is assessed using the SWAN wave model. The 30 MW-rated wave farm is called the ‘Wave Hub’ and will be located 20 km off the north coast of Cornwall, UK. Changes in significant wave height and mean wave period due to the presence of the Wave Hub are presented. The results suggest that the shoreline wave climate will be affected, although the magnitude of effects decreases linearly as wave energy transmitted increases. At probable wave energy transmission levels, the predicted change in shoreline wave climate is small.     

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.     

Characteristics of a breaking wind-wave field in the light of the individual wind-wave concept

The relation between the intensity of breaking of individual wind-wave crests and parameters of wave size and wave form (e. g., height, period, steepness and skewness) is examined, and the process of change of these parameters is studied in a wind-wave tank (reference wind speed 15 m sec⁻¹, fetch 16 m). Distributions of the wave form parameters are different for breaking and nonbreaking waves. Fully breaking waves seem to hold the relationH ∞T ², whereH is the individual wave height andT is the period. The condition of breaking is not simply determined by the simple criterion of Stokes' limit. Wave height and steepness of a breaking wave are not always larger than those of a nonbreaking wave. This suggests the existence of an overshooting phenomenon in the breaking wave. The wave form parameters are found to change cyclically in a statistical sense during the wave propagation. The period of the cycle in the present case is estimated to be longer than four wave periods. An intermittency of wave breaking is associated with this cyclic process. Roughly speaking, two or three succeeding breaking-waves sporadically exist among a series of nonbreaking waves along the fetch.     

Wave model predictions in the Black Sea: Sensitivity to wind fields

This paper evaluates the impact of using different wind field products on the performance of the third generation wave model SWAN in the Black Sea and its capability for predicting both normal and extreme wave conditions during 1996. Wind data were obtained from NCEP CFSR, NASA MERRA, JRA-25, ECMWF Operational, ECMWF ERA40, and ECMWF ERA-Interim. Wave data were obtained in 1996 at three locations in the Black Sea within the NATO TU-WAVES project. The quality of wind fields was assessed by comparing them with satellite data. These wind data were used as forcing fields for the generation of wind waves. Time series of predicted significant wave height (H_mo), mean wave period (T_m02), and mean wave direction (DIR) were compared with observations at three offshore buoys in the Black Sea and its performance was quantified in terms of statistical parameters. In addition, wave model performance in terms of significant wave height was also assessed by comparing them against satellite data.The main scope of this work is the impact of the different available wind field products on the wave hindcast performance. In addition, the sensitivity of wave model forecasts due to variations in spatial and temporal resolutions of the wind field products was investigated. Finally, the impact of using various wind field products on predicting extreme wave events was analyzed by focussing on storm peaks and on an individual storm event in October 1996. The numerical results revealed that the CFSR winds are more suitable in comparison with the others for modelling both normal and extreme events in the Black Sea. The results also show that wave model output is critically sensitive to the choice of the wind field product, such that the quality of the wind fields is reflected in the quality of the wave predictions. A finer wind spatial resolution leads to an improvement of the wave model predictions, while a finer temporal resolution in the wind fields generally does not significantly improve agreement between observed and simulated wave data.     

Sub aerial random wave pressure and layer thickness on impermeable sea walls

Investigations on sub aerial wave pressures and layer thickness on plane impermeable and non-overtopping seawallns were carried out by using physical model studies. Seawalls with slopes of 1:3, 1:4 and 1:6 were used. JONSWAP spectrum with significant wave height, H_s from 0.08 to 0.2 m and peak periods, T_p from 1.5 to 6.0 s and a constant water depth of 0.7 m is used. Based on extensive measurements, empirical formulas for practical applications are proposed to predict the maximum, significant and mean sub aerial random wave pressure and layer thickness (thickness of water layer perpendicular to the still water level on the run-up zone) by using the surf similarity parameter, significant wave height and elevation on the sub aerial region as inputs. It is found that the maximum layer thickness is 1.11 times the significant layer thickness and maximum sub Arial wave pressure is 1.06 times the significant wave pressures. The predictive equations based on extensive measurements can be used for the design of non-overtopping seawalls.     

中国浙江和福建海域台风浪变化特征和趋势

基于非结构网格的海浪-海流耦合模式SWAN+ADCIRC(Simulating Waves Nearshore+Advanced Circulation model),模拟了1997—2016年共20年间所有影响浙江和福建海域台风过程期间的海浪过程。利用4个台风过程期间的海浪观测数据对模拟结果进行了验证,模拟结果和实测结果吻合较好。基于该长时间序列台风浪模拟结果,分别分析了浙江和福建海岸带台风浪有效波高极值以及台风浪有效波高大于1m和1.5m的持续时间。结果显示,在福建北部海岸带台风浪有效波高极值和台风浪有效波高大于1m的持续时间(tHs1)有显著增长的趋势。其中,台风浪高极值的增长趋势最大可达0.05m/a,tHs1的增长趋势位于0.54至1.72h/a之间。分析tHs1与ENSO指数的关系发现,福建省南部海域台风浪与ENSO指数有较显著的负相关,浙江省北部海域台风浪与ENSO指数有较显著的正相关,ENSO信号对这两个海域的台风浪有着较显著的影响。     

Evaluation of a high-resolution wave hindcast model SWAN for the West Mediterranean basin

This study aims to present an evaluation and implementation of a high-resolution SWAN wind wave hindcast model forced by the CFSR wind fields in the west Mediterranean basin, taking into account the recent developments in wave modelling as the new source terms package ST6. For this purpose, the SWAN model was calibrated based on one-year wave observations of Azeffoune buoy (Algerian coast) and validated against eleven wave buoys measurements through the West Mediterranean basin. For the calibration process, we focused on the whitecapping dissipation coefficient C_ds and on the exponential wind wave growth and whitecapping dissipation source terms. The statistical error analysis of the calibration results led to conclude that the SWAN model calibration corrected the underestimation of the significant wave height hindcasts in the default mode and improved its accuracy in the West Mediterranean basin. The exponential wind wave growth of Komen et al (1984) and the whitecapping dissipation source terms of Janssen (1991) with C_ds = 1.0 have been thus recommended for the western Mediterranean basin. The comparison of the simulation results obtained using this calibrated parameters against eleven measurement buoys showed a high performance of the calibrated SWAN model with an average scatter index of 30% for the significant wave heights and 19% for the mean wave period. This calibrated SWAN model will constitute a practical wave hindcast model with high spatial resolution (˜3 km) and high accuracy in the Algerian basin, which will allow us to proceed to a finer mesh size using the SWAN nested grid system in this area.     

Testing and calibrating parametric wave transformation models on natural beaches

To provide coastal engineers and scientists with a detailed inter-comparison of widely used parametric wave transformation models, several models are tested and calibrated with extensive observations from six field experiments on barred and unbarred beaches. Using previously calibrated (“default”) values of a free parameter γ, all models predict the observations reasonably well (median root-mean-square wave height errors are between 10% and 20%) at all field sites. Model errors can be reduced by roughly 50% by tuning γ for each data record. No tuned or default model provides the best predictions for all data records or at all experiments. Tuned γ differ for the different models and experiments, but in all cases γ increases as the hyperbolic tangent of the deep-water wave height, H_o. Data from two experiments are used to estimate empirical, universal curves for γ based on H_o. Using the new parameterization, all models have similar accuracy, and usually show increased skill relative to using default γ.     

Wave climate off northern Norway

The wave climate off northern Norway is considered and the investigation is based on wave measurements made at Tromsøflaket by means of a waverider buoy during the years 1977–1981. Data quality of waverider measurements is briefly commented upon; however, more emphasis is given to an evaluation of the long-term representativity of the actual measuring period and to a procedure accounting approximately for a lack of representativity. The wave climate is presented in terms of a smoothed joint probability density function of the significant wave height, H_s, and the spectral peak period, T_p. Based on this distribution a consistent design curve in the H_s, T_p space is established.     

Trade-wind waves and mud dynamics on the French Guiana coast,South America: Input from ERA-40 wave data and field investigations

The South American coast between Brazil and Venezuela is affected by longshore migrating mud banks derived from the fine-grained Amazon sediment discharge. Onshore mud migration prevails over shallow ‘bank’ areas alternating alongshore with deeper ‘inter-bank’ areas. The transport on the inner shelf, and attachment to the shoreline, of this migrating mud has been attributed mainly to wind waves. However, the lack of in situ data on waves hampers understanding of the relationship between waves and mud dynamics. A 44-yr record (1960–2004) of the ERA-40 wave dataset generated by the European Centre for Medium-Range Weather Forecasts (ECMWF) was used, in conjunction with field investigations in French Guiana, to define both event-scale and longer-term patterns of mud mobilisation induced by waves. The ratio H₀³ / T², combining wave height H and period T, and the angle of wave incidence α, were singled out as the most relevant parameters for describing wave forcing. Typical ‘bank’ and ‘inter-bank’ profiles and corresponding mud densities, and a 3-month record of changes in the thickness of the fluid mud layer in an estuarine navigation channel were monitored by echo-sounding from October 2002 to January 2003. An 80-day record of bed-level changes in the intertidal zone was obtained from August to November 2004 using a pressure transducer. The results on the wave regime of French Guiana confirm a distinctly seasonal pattern, and highlight an increase in H₀³ / T² over the 44-yr period related to an increase in trade-wind velocities determined from corresponding trends in Atlantic wind pseudo-stress off the South American coast. Wave forcing over bank areas leads to the liquefaction of a 1–3 m-thick layer of mud that is transported onshore (and alongshore by the longshore component of wave energy). The episodic nature of high wave energy events generally results in the formation of mud bar features from the shoreward mobilisation of gel-like fluid mud. The effect of waves on mud is particularly marked following long periods of low energy, and especially at the onset of the high wave energy season (October to May), when even moderate wave energy events can lead to significant mobilisation of mud.Significant phases of increased wave energy are attended by higher long-term (annual) rates of longshore mud bank migration but the correlation is rather poor between the wave forcing parameter H₀³ / T² and migration rates because stronger wave forcing is generally associated with low angles of wave incidence. This suggests a complementary role of other hydrodynamic mechanisms, such as geostrophic and tidal currents, in longshore mud bank migration.     

Adjustment of Wind Waves to Sudden Changes of Wind Speed

An experiment was conducted in a small wind-wave facility at the Ocean Engineering Laboratory, California, to address the following question: when the wind speed changes rapidly, how quickly and in what manner do the short wind waves respond? To answer this question we have produced a very rapid change in wind speed between U _low (4.6 m s^?1) and U _high (7.1 m s^?1). Water surface elevation and air turbulence were monitored up to a fetch of 5.5 m. The cycle of increasing and decreasing wind speed was repeated 20 times to assure statistical accuracy in the measurement by taking an ensemble mean. In this way, we were able to study in detail the processes by which the young laboratory wind waves adjust to wind speed perturbations. We found that the wind-wave response occurs over two time scales determined by local equilibrium adjustment and fetch adjustment, Δt ₁/T = O(10) and Δt ₂/T = O(100), respectively, in the current tank. The steady state is characterized by a constant non-dimensional wave height (H/gT ² or equivalently, the wave steepness for linear gravity waves) depending on wind speed. This equilibrium state was found in our non-steady experiments to apply at all fetches, even during the long transition to steady state, but only after a short initial relaxation Δt ₁/T of O(10) following a sudden change in wind speed. The complete transition to the new steady state takes much longer, Δt ₂/T of O(100) at the largest fetch, during which time energy propagates over the entire fetch along the rays (dx/dt = c _g) and grows under the influence of wind pumping. At the same time, frequency downshifts. Although the current study is limited in scale variations, we believe that the suggestion that the two adjustment time scales are related to local equilibrium adjustment and fetch adjustment is also applicable to the ocean.     

An experimental study on geometric characteristics of beach erosion profiles

The beach profile and sediment transport are very important factors in the design of coastal structures, and the beach profile is mainly affected by a number of parameters, such as wave height and period, beach slope, and the material properties of the bed. In this study, considering wave height (H₀=6.5, 11.5, 16, 20, 23, 26 and 30 cm), wave period (T=1.46 and 2.03 s), beach slope (m=1/10 and 1/15) and mean sediment diameter (d₅₀=0.18, 0.26, 0.33 and 0.40 mm), an experimental investigation of coastal erosion profile (storm profile) was carried out in a wave flume using regular waves, and geometric characteristics of erosion profile were determined by the resultant erosion profile. Dimensional and non-dimensional equations were obtained by using linear and non-linear regression methods through the experimental data and were compared with previously developed equations in the literature. The results have shown that the experimental data fitted well to the proposed equations with respect to the previously developed equations.     

Characteristics of developing waves as a function of atmospheric conditions,water properties,fetch and duration

For any specific wind speed, waves grow in period, height and length as a function of the wind duration and fetch until maximum values are reached, at which point the waves are considered to be fully developed. Although equations and nomograms exist to predict the parameters of developing waves for shorter fetch or duration conditions at different wind speeds, these either do not incorporate important variables such as the air and water temperature, or do not consider the combined effect of fetch and duration. Here, the wind conditions required for a fully developed sea are calculated from maximum wave heights as determined from the wind speed, together with a published growth law based on the friction velocity. This allows the parameters of developing waves to be estimated for any combination of wind velocity, fetch and duration, while also taking account of atmospheric conditions and water properties.     

Evaluation of two WAM white capping parameterizations using parallel unstructured SWAN with application to the Northern Gulf of Mexico, USA

The performance of two well accepted formulations for white capping and wind input of third generation wave models, viz., WAM-3 and WAM-4, were investigated using parallel unstructured SWAN (PunSWAN). Several alternative formulations were also considered to evaluate the effects of higher order steepness and wave number terms in white capping formulations. Distinct model configurations were calibrated and validated against available in situ measurements from the Gulf of Mexico. The results showed that some of the in situ calibrated models outperform the saturation level calibrated models in reproducing the idealized wave growth curves. The simulation results also revealed that increasing the power of the steepness term can enhance the accuracy of significant wave height (H_s), at the expense of a higher bias for large waves. It also has negative effects on mean wave period (T_a) and peak wave period (T_p). It is also demonstrated that the use of the quadratic wave number term in the WAM-3 formulation, instead of the existing linear term, ameliorates the T_a underestimation; however, it results in the model being unable to reach any saturation level. In addition, unlike H_s and T_p, it has been shown that T_a is sensitive to the use of the higher order WAM-4 formulation, and the bias is decreased over a wide range of wave periods. However, it also increases the scatter index (SI) of simulated T_a. It is concluded that the use of the WAM-4 wind input formulation in conjunction with the WAM-3 dissipation form, is the most successful case in reproducing idealized wave growth curves while avoiding T_a underestimation of WAM-3 and a potential spurious bimodal spectrum of WAM-4; consequently, this designates another perspective to improve the overall performance of third generation wave models.     

Estimation of infragravity waves at intermediate water depth

The accuracy of nearshore infragravity wave height model predictions has been investigated using a combination of the spectral short wave evolution model SWAN and a linear 1D SurfBeat model (IDSB). Data recorded by a wave rider located approximately 3.5 km from the coast at 18 m water depth have been used to construct the short wave frequency-directional spectra that are subsequently translated to approximately 8 m water depth with the third generation short wave model SWAN. Next the SWAN-computed frequency-directional spectra are used as input for IDSB to compute the infragravity response in the 0.01 Hz–0.05 Hz frequency range, generated by the transformation of the grouped short waves through the surf zone including bound long waves, leaky waves and edge waves at this depth. Comparison of the computed and measured infragravity waves in 8 m water depth shows an average skill of approximately 80%. Using data from a directional buoy located approximately 70 km offshore as input for the SWAN model results in an average infragravity prediction skill of 47%. This difference in skill is in a large part related to the under prediction of the short wave directional spreading by SWAN. Accounting for the spreading mismatch increases the skill to 70%. Directional analyses of the infragravity waves shows that outgoing infragravity wave heights at 8 m depth are generally over predicted during storm conditions suggesting that dissipation mechanisms in addition to bottom friction such as non-linear energy transfer and long wave breaking may be important. Provided that the infragravity wave reflection at the beach is close to unity and tidal water level modulations are modest, a relatively small computational effort allows for the generation of long-term infragravity data sets at intermediate water depths. These data can subsequently be analyzed to establish infragravity wave height design criteria for engineering facilities exposed to the open ocean, such as nearshore tanker offloading terminals at coastal locations.     

A model for wave growth in fetch-limited conditions

In this paper, it is held that the universal relationships of wave growth in fetch-limited conditions , i. e.,(f|~) p=A(x|~)-Band (m|~)0= C(x|~) Dshould satisfy the Toba 3/2 power law and the wave energy balance equation. In the ideal generation situation, theoretically it can be derived that the ideal fetch-limited wave growth relationship should have D=3B and D B =1, (i.e., B = 0.25, D = 0.75 ) and A3C=2. 1×l(T4C~(1/2)_d , where Cd is the drag coefficient. The 3/2 power law, the wave energy balance equation and the decrease of wave steepness with increasing fetch have became three requirements which should be satisfied by fetch-limited wave growth algorithms. A semi-empirical and semi-theoretical model for fetch-limited wave growth is presented. In the application to the slanting wind situation an un(?)ersal relationship of dimensionless wave energy vs dimensionless peak frequency is presented and the comparisons show that the model is in good agreement with observations.     

Short-term statistics of waves measured off Ratnagiri,eastern Arabian Sea

The short-term wave characteristics are required for design and operation of industrial facilities within the coastal areas. Water surface displacement measured using waverider buoy moored at 13 m water depth in the eastern Arabian Sea off the west coast of India have been analyzed to study the short-term statistics of waves covering full one year period. The study indicates that the values of the observed maximum wave height as a function of duration are not consistent with the theoretical expected value. There is significant variation (1.29–2.19) in the ratio between highest 1% wave and significant wave height compared to the theoretical value of 1.67. The data recorded at 13 m water depth indicates that the significant wave height is ∼8% lower than that predicted by the conventional Rayleigh distribution. The theoretical bivariate log-normal distribution represents the joint distributions of wave heights and periods for the study area.