Nonlinear saturation-based whitecapping dissipation in SWAN for deep and shallow water

This study investigates the effectiveness of a revised whitecapping source term in the spectral wind wave model SWAN (Simulating WAves Nearshore) that is local in frequency space, nonlinear with respect to the variance density and weakly dependent on the wave age. It is investigated whether this alternative whitecapping expression is able to correct the tendency towards underprediction of period measures that has been identified in the default SWAN model. This whitecapping expression is combined with an alternative wind input source term that is more accurate for young waves than the default expression. The shallow water source terms of bottom friction, depth-induced breaking and triad interaction are left unaltered. It is demonstrated that this alternative source term combination yields improved agreement with fetch- and depth-limited growth curves. Moreover, it is shown, by means of a field case over a shelf sea, that the investigated model corrects the erroneous overprediction of wind-sea energy displayed by the default model under combined swell-sea conditions. For a selection of field cases recorded at two shallow lakes, the investigated model generally improves the agreement with observed spectra and integral parameters. The improvement is most notable in the prediction of period measures.     

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.     

Calibration and verification of a spectral wind–wave model for Lake Okeechobee

A spectral wind wave model SWAN (Simulation WAves Nearshore) that represents the generation, propagation and dissipation of waves was applied to Lake Okeechobee. This model includes the effects of refraction, shoaling, and blocking in wave propagation. It accounts for wave dissipation by whitecapping, bottom friction, and depth-induced wave breaking. The wave–wave interaction effect also is included in this model. Measurements of wind and wave heights were made at different stations and different time periods in Lake Okeechobee. Significant wave height values were computed from the recorded data. The correlation between wind stress and significant wave height also was analyzed. A 6-day simulation using 1989 data was conducted for model calibration. Another 6-day simulation using 1996 data was conducted for model verification. The simulated significant wave heights were found to agree reasonably well with measured significant wave heights for calibration and verification periods. Agreement between observed and simulated values was based on graphical comparisons, mean, absolute and root mean square errors, and correlation coefficient. Comparisons showed that the model reproduced both general observed trends and short term fluctuations.     

A Model for Nonlinear Irregular Waves in Coastal Area

Based on the refraction-diffraction theory of irregular waves in the waters of slowly-varying cur-rents and depths,and the generation dissipation theory of wind wave,a model for nonlinear irregular wavesin coastal area is developed.In light of the specific conditions of coastal wave character and engineering ap-plication,a practical mathematical model for the nonlinear irregular waves is presented.with directional spec-trum in coastal area.Coast effect,refraction,whitecapping.bottom friction.current,wind and nonlinearaction are considered in this model.The numerical methods and schemes for wave refraction ray,energy con-servation of propagation,energy balance of the generation and dissipation of wind waves have been studied.Finally,the model is used for the directional wave spectrum computation in the Daya Bay.Compared withthe measured data with 956 wave bouys in the Daya Bay,the model results are in good agreement with themeasured results.     

Comparison Study on Wind Input and Whitecapping Dissipation Expressions in Numerical Simulation of Typhoon Generated Waves

In order to investigate the effect of wind input and whitecapping dissipation on the simulation of typhoon-waves, three experiments are conducted with the latest version of SWAN （Simulating WAves Nearshore） model. The three experiments adopt the Komen, Janssens, and Westhuysen expressions for wind input and whitecapping dissipation, respectively. Besides the above-mentioned source tems, other parameterization schemes in these experiments are the same. It shows that the experiment with the Westhuysen expression result in the least simulation errors while that with the Janssens expression has the most. The results from the experiments with Komen and Westhuysen expressions show that the differenees in significant wave height （SWH） have a good correlation with the differences in dissipation energy caused by whiteeapping. This indicates that the whitecapping dissipation source term plays an important role in the resultant differences of the simulated SWH between the two experiments.     

Local balance in the air-sea boundary processes

A new growth equation for wind waves of simple spectrum is presented upon three basic concepts. The period and the wave height of significant waves in dimensionless forms, which are considered to correspond to the peak frequency and the energy level, respectively, are used as representative quantities of wind waves. One of the three basic concepts is the concept of local balance, and the other two concern the acquisition of wave energy and the dissipation of wave energy, respectively. It is shown from some actual data that the equation, together with two universal constants concerning the acquisition and the dissipation of wave energy (B=6.2×10^?2 andK=2.16×10^?5, respectively), is applied universally to wide ranges of wind waves from those in a wind-wave tunnel to fully developed sea in the open ocean. “The three-second power law for wind waves of simple spectrum”, and a few relations as the lemmas, are derived, such that the mean surface transport due to the orbital motion of wind waves is always proportional to the friction velocity in wind, and that the steepness is inversely proportional to the root of the wave age. It is also derived that the portion of wind stress which directly enters the wind waves decreases exponentially with increasing wave age and is 7.5 % of the total wind stress for very young waves. Also, equations are presented as to the increase of momentum of drift current, and as to the supply of turbulent energy by wind waves into the upper ocean.     

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.     

Numerical simulation and preliminary analysis of typhoon waves during three typhoons in the Yellow Sea and East China Sea

In this study,typhoon waves generated during three typhoons(Damrey(1210),Fung-wong(1416),and Chan-hom(1509))in the Yellow Sea and East China Sea were simulated in a simulating waves nearshore(SWAN)model,and the wind forcing was constructed by combining reanalyzed wind data with a Holland typhoon wind model.Various parameters,such as the Holland fitting parameter(B)and the maximum wind radius?,were investigated in sensitivity experiments in the Holland model that affect the wind field construction.Six different formulations were considered and the parameters determined by comparing the simulated wind results with in-situ wind measurements.The key factors affecting wave growth and dissipation processes from deep to shallow waters were studied,including wind input,whitecapping,and bottom friction.Comparison with in-situ wave measurements suggested that the KOMEN scheme(wind input exponential growth and whitecapping energy dissipation)and the JONSWAP scheme(dissipation of bottom friction)resulted in good reproduction of the significant wave height of typhoon waves.A preliminary analysis of the wave characteristics in terms of wind-sea and swell wave revealed that swell waves dominated with the distance of R to the eye of the typhoon,while wind-sea prevailed in the outer region up to six to eight times the R values despite a clear misalignment between wind and waves.The results support the hypothesis that nonlinear wave-wave interactions may play a key role in the formation of wave characteristics.     

CHGS method for numerical forecasting of typhoon waves——Ⅰ. Spectrum of waves in growing phase

Owing to the fact that the wind speed and direction of typhoon vary rapidly with time and space in typhoon fetch; the nearer to the typhoon eye the greater the wind velocity, and the shorter the wind fetch the smaller the wind time,as a result,the more difficult for the wind wave to fully grow. Hence.in typhoon wave numerical calculation it is impossible to use the model for a fully grown wave spectrum. Lately, the author et at. presented a CHGS method for numerical forecasting of typhoon waves, where a model for the growing wave spectrum was set up (see Eq. (2) in the text). The model involves a parameter indicating the growing degree of wind wave, i. e. ,the mean wave age β. When βvalue is small, the wave energy is chiefly concentrated near the peak frequency, so that the spectral peak gets high and steep; with the increase of β the spectral shape gradually gets lower and gentler; when β=Ⅰ, the wave fully grows, the growing spectrum becomes a fully grown P-M spectrum. The model also shows a spect     

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.     

A representation for the frequency spectrum of wind-generated waves

This paper proposes the following generalized representation for a wind-wave frequency spectrum:

Full-size image (1K)

where E = ∫S(f)df is the variance of the surface displacement; f_m is the frequency of the spectral peak; and C_i's, i = 1,2,3, are dimensionless parameters that can be determined from the internal spectral parameters of a given spectrum.When applied to 234 sets of wave spectra recorded in the Great Lakes, this representation has been realistic, accurate, and capable of representing widely varied wave processes. The C_i's are clearly related to wave growth processes; they are large during early growth, decrease as waves grow, and reach approximate equilibrium when waves are fully developed.     

Comparison Study on Wind Input and Whitecapping Dissipation Expressions in Numerical Simulation of Typhoon-Generated Waves

In order to investigate the effect of wind input and whitecapping dissipation on the simulation of typhoon-waves, three experiments are conducted with the latest version of SWAN (Simulating WAves Nearshore) model.The three experiments adopt the Komen, Janssens, and Westhuysen expressions for wind input and whitecappingdissipation, respectively. Besides the above-mentioned source terms, other parameterization schemes in these experiments are the same. It shows that the experiment with the Westhuysen expression result in the least simulationerrors while that with the Janssens expression has the most. The results from the experiments with Komen and Westhuysen expressions show that the differences in significant wave height (SWH) have good correlation with thedifferences in dissipation energy caused by whitecapping. This indicates that the whitecapping dissipation sourceterm plays an important role in the resultant differences of the simulated SWH between the two experiments.     

论风浪的局域结构──Ⅱ.风浪局域小波能谱的性质及应用

引入了局域小波能谱的局域间歇性度量,分析了不同风速下的风浪资料,结果表明,局域小波能谱可依局域频率分为三部分。风浪的群性在三维局域小波能谱图像下显示得更为明显,与风浪有关的一切性质都是局域的,包括风浪的群性。讨论了局域小波谱峰值与谱峰频率的涨落,指出了前者在工程设计中的重要意义,并发现了后者与风浪破碎有关的两种非线性现象。     

Triangular Configuration Tension Leg Platform behaviour under random sea wave loads

This study investigates the dynamic response of a Triangular Configuration Tension Leg Platform (TLP) under random sea wave loads. The random wave has been generated synthetically using the Monte-Carlo simulation with the Peirson–Moskowitz (P–M) spectrum. Diffraction effects and second-order wave forces have not been considered. The evaluation of hydrodynamic forces is carried out using the modified Morison equation with water particle kinematics evaluated using Airy's linear wave theory. Wave forces are taken to be acting in the surge degree-of-freedom. The effect of coupling of various structural degrees-of-freedom (surge, sway, heave, roll, pitch and yaw) on the dynamic response of the TLP under random wave loads is studied. Parametric studies for random waves with different H_s and T_z under the presence of current have also been carried out. For the orientation of the TLP, surge, heave and pitch degrees-of-freedom responses are influenced significantly. The surge power spectral density function (PSDF) indicates that the mean square response is affected by the amplification at the natural frequency of the surge degree-of-freedom and also at the peak frequency of the wave loading. The PSDF of the heave response shows higher peak values near the surge frequency and near the peak frequency of the wave loading. Surge response, therefore, influences heave response to the maximum. Variable submergence seems to be a major source of nonlinearity and significantly enhances the responses in surge, heave and pitch degrees-of-freedom. In the presence of current, the response behaviour of the TLP is altered significantly introducing a non-zero mean response in all degrees-of-freedom.     

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.     

近岸区不规则波成长模型的研究 Ⅰ.模型的建立

以不规则波在缓变地形和缓变流场水域的折射-绕射理论以及风浪的成长、衰减理论为基础,得到近岸区不规则波成长模型。结合近岸波浪特性和海洋工程应用的实际情况,建立综合考虑海岸、折射、白浪、底摩擦、流、风和非线性作用诸因素的近岸不规则波数值计算模型。该模型具有二维波谱特性及实用性。文章力图使模式更合理地反映近岸波浪的传播、成长和衰减规律,而整个计算工作量则较小,可在微型电子计算机上得以实现。     

The energy balance in the wind-wave spectrum

The spectral energy balance in the wind-wave spectrum is studied with taking into account the energy input from turbulent wind to waves, the energy rearrangement due to conservative nonlinear wave-wave interaction and the energy dissipation due to water turbulence. Using the Ichikawa's (1978) model on the turbulent wind field over wind-waves and assuming that the energy dissipation is times greater than that due to molecular viscosity of water, the energy input and dissipation are determined so as to satisfy the condition that the nonlinear-transfers of momentum and energy conserve the total momentum and energy of waves. The nonlinear energy-transfer is estimated from the energy balance at each frequency. It is found that the energy input and dissipation satisfying the condition on the conservative nonlinear-transfer are determined by the characteristic height of wind-wave field and the friction velocity of air, and that the spectral distribution of the nonlinear energy-transfer estimated in this paper is qualitatively similar to that estimated by the non-linear wave-wave interaction theory ofHasselmann (1962).     

Generation mechanisms for capillary-gravity wind wave spectrum

We investigate the role of different physical mechanisms in the generation of the capillary-gravity wind wave spectrum. This spectrum is calculated by integrating a nonstationary kinetic equation until the solution becomes stready. The mechanisms of spectrum generation under consideration include three-wave interactions, viscous dissipation, energy influx from wind, nonlinear dissipation, and the generation of a parasitic capillary ripple. The three-wave interactions are taken into account as an integral of collisions without additional simplifications. It is shown that the three-wave interactions lead to solution instability if the kinetic equation takes into account only linear sources. To stabilize the solution, the kinetic equation should incorporate a nonlinear dissipation term, which in the range of short gravity waves corresponds to energy losses during wave breaking and microscale wave breaking. In the range of capillary waves, the account of nonlinear dissipation is also needed to ensure a realistic level of the spectrum for large wind velocities. For the steady-state spectrum, the role of three-wave interactions remains essential merely in the range of the minimum of phase velocity, where a trough on the curvature spectrum is formed. At the remaining intervals of the spectrum, the main contribution into the spectral energy balance is provided by the mechanisms of wave injection, nonlinear dissipation, and the generation of parasitic capillaries.