Phase-decoupled refraction–diffraction for spectral wave models

Conventional spectral wave models, which are used to determine wave conditions in coastal regions, can account for all relevant processes of generation, dissipation and propagation, except diffraction. To accommodate diffraction in such models, a phase-decoupled refraction–diffraction approximation is suggested. It is expressed in terms of the directional turning rate of the individual wave components in the two-dimensional wave spectrum. The approximation is based on the mild-slope equation for refraction–diffraction, omitting phase information. It does therefore not permit coherent wave fields in the computational domain (harbours with standing-wave patterns are excluded). The third-generation wave model SWAN (Simulating WAves Nearshore) was used for the numerical implementation based on a straightforward finite-difference scheme. Computational results in extreme diffraction-prone cases agree reasonably well with observations, analytical solutions and solutions of conventional refraction–diffraction models. It is shown that the agreement would improve further if singularities in the wave field (e.g., at the tips of breakwaters) could be properly accounted for. The implementation of this phase-decoupled refraction–diffraction approximation in SWAN shows that diffraction of random, short-crested waves, based on the mild-slope equation can be combined with the processes of refraction, shoaling, generation, dissipation and wave–wave interactions in spectral wave models.     

基于Boussinesq方程近岸波浪演变的数值研究

首先对目前描述近岸波浪传播变形的数学模型进行了回顾与总结;对不同数学模型的特点、适用范围和发展情况进行了阐述与对比。应用基于Boussinesq方程的Coulwave模式针对几个经典实验地形进行了数值实验,数值结果和实验实测数据吻合较好。此外,分别采用不同的近岸波浪模型模拟了某渔港附近波浪的传播变形,结果表明:当考虑波浪的折射、绕射、反射联合作用时,Coulwave模式计算结果明显较缓坡方程及SWAN模型计算结果更加合理。     

Wave prediction in a port using a fully nonlinear Boussinesq wave model

A wave forecasting system using FUNWAVE-TVD which is based on the fully nonlinear Boussinesq equations by Chen(2006) was developed to provide an accurate wave prediction in the Port of Busan, South Korea. This system is linked to the Korea Operational Oceanographic System(KOOS) developed by Park et al.(2015). The computational domain covers a region of 9.6 km×7.0 km with a grid size of 2 m in both directions, which is sufficient to resolve short waves and dominant sea states. The total number of grid points exceeds 16 millions,making the model computational expensive. To provide real-time forecasting, an interpolation method, which is based on pre-calculated results of FUNWAVE-TVD and SWAN forecasting results at the FUNWAVE-TVD offshore boundary, was used. A total of 45 cases were pre-calculated, which took 71 days on 924 computational cores of a Linux cluster system. Wind wave generation and propagation from the deep water were computed using the SWAN in KOOS. SWAN results provided a boundary condition for the FUNWAVE-TVD forecasting system. To verify the model, wave observations were conducted at three locations inside the port in a time period of more than 7 months. A model/model comparison between FUNWAVE-TVD and SWAN was also carried out. It is found that, FUNWAVE-TVD improves the forecasting results significantly compared to SWAN which underestimates wave heights in sheltered areas due to incorrect physical mechanism of wave diffraction, as well as large wave heights caused by wave reflections inside the port.     

Numerical Study of Wave Diffraction Effect Introduced in the SWAN Model

New version of SWAN model includes the wave diffraction effect which is the main improvement compared with the previous versions.Experimental data collected in the wave basin of the University of Delaware were used to test its performance.Wave heights were compared in the four cases(with different wave energies and directional spreading spectra).The results agreed well with the measurements,especially for the broad directional spectra cases.The effect of wave diffraction was analyzed by switching on/off the corresponding term.By introducing the diffraction term,the distributions of wave height and wave direction were smoothed,especially obvious for the narrow spectrum cases.Compared with the calculations without diffraction,the model with diffraction effect gave better results.     

WAVEWATCH和SWAN嵌套模拟台风浪场的结果分析

利用WAVEWATCH和SWAN嵌套模拟2007年8月墨西哥湾飓风迪安的波浪场.将QSCAT/NCEP混合风场与台风模型风场合成为背景风场.修改WAVEWATCH和SWAN嵌套接口以使WAVEWATCH和SWAN2种海浪预报模式能够有效地嵌套运行.利用WAVEWATCH和SWAN嵌套模拟飓风迪安的波浪场,采用浮标资料检验模拟结果,以验证WAVEWATCH和SWAN模拟的准确性及修改后嵌套接口的可用性.结果表明,修改嵌套接口之后模式运行平稳,2种模式的结果与浮标及高度计观测数据均基本吻合.嵌套模拟结果好于单纯使用WAVEWATCH模拟的结果,体现了利用2种模式嵌套模拟台风浪场的科学性.     

Wind-wave variability in a shallow tidal sea—Spectral modelling combined with neural network methods

In this paper the wind-wave variability in the tidal basins of the German Wadden Sea is modelled with combined numerical and neural-network (NN) methods. First, the wave propagation and transformation in the study area are modelled with the state-of-the-art third-generation spectral wave model SWAN. The ability of SWAN to accurately reproduce the phenomena of interest in nonstationary conditions governed by highly variable winds, water levels and currents is shown by comparisons of the modelled and measured mean wave parameters at four stations. The principal component analysis of the SWAN results is then used to reveal the dominating spatial patterns in the data and to reduce their dimensionality, thus enabling an efficient and relatively straightforward NN modelling of mean wave parameters in the whole study area. It is shown that the data produced with the approach developed in this work have statistical properties (discrete probability distributions of the mean wave parameters etc.) very close to the properties of the data obtained with SWAN, thus proving that this approach can be used as a reliable tool for wind wave simulation in coastal areas, complementary to (often computationally demanding) spectral wave models.     

SWAN模型对实验室小尺度浅水波浪模拟研究

基于浅水斜坡地形的物理模型试验数据,考察SWAN模型对实验室小尺度浅水波浪的模拟效果,进而检验其浅水项的模拟精度。模拟中采用直接输入初始测点的实测海浪谱进行造波,重点考察浅水中三波相互作用和变浅破碎两个源项,对不同工况下,SWAN模式在水深条件变化下的有效波高、谱平均周期、海浪谱演化的模拟能力进行研究。研究表明:模拟的有效波高较符合实测波浪的增长和衰减,但谱平均周期计算值明显偏小;海浪谱的能量转移机制同实测有较大区别,频谱模拟结果出现高频高估、低频低估现象。对两个源项进行对比分析得出三波相互作用对海浪谱的能量转换影响远大于变浅破碎耗散。想要提高近岸区谱平均周期和海浪谱的模拟精度则SWAN模型中三波非线性项的计算精确度仍需更多研究和改进。     

Wave Numerical Model for Shallow Water

The history of forecasting wind waves by wave energy conservation equation is briefly des-cribed.Several currently used wave numerical models for shallow water based on different wave theoriesare discussed.Wave energy conservation models for the simulation of shallow water waves are introduced,with emphasis placed on the SWAN model,which takes use of the most advanced wave research achieve-ments and has been applied to several theoretical and field conditions.The characteristics and applicabilityof the model,the finite difference numerical scheme of the action balance equation and its source termscomputing methods are described in detail.The model has been verified with the propagation refractionnumerical experiments for waves propagating in following and opposing currents;finally.the model is ap-plied to the Haian Gulf area to simulate the wave height and wave period field there,and the results arecompared with observed data.     

Modelling the influence of currents on wave propagation at the entrance of the Tagus estuary

A study of the wave propagation and of the consequences of the influence of currents on waves in the Tagus estuary is performed in the present work. For this purpose a high-resolution SWAN domain was coupled to a wave prediction system based on the two state of the art phase averaged wave models, WAM for wave generation and SWAN for nearshore wave transformation. The most important factors affecting the incoming waves are the local currents and the wind. These influences were evaluated by performing SWAN simulations in the target area with and respectively without considering the tide level and tide induced currents. The model results were compared with wave measurements, validating in this way the results of the wave prediction system developed herewith.     

荣喜近岸区波流耦合作用下的流场模拟

一方面将波浪对底部剪切应力、表面拖曳力系数,辐射应力以及表面混合长度的影响引入至COHERENS.另一方面又将水动力模型COHERENS和第三代波浪模型SWAN耦合,使两模型能够随时互相交换水流、水位以及波浪信息,最终获得波流耦合模型COHERENS-SWAN并将其应用于荣喜近岸区波流共同存在情况下的波流作用模拟研究.计算所得的流速、流向和水位与实测数据吻合较好.     

Hindcast of the wave conditions along the west Iberian coast

This paper describes the development of a wave prediction system for the west Iberian coast. The implemented wave prediction system is based on two state-of-the-art spectral wave models, WAM for the ocean area and SWAN for the nearshore. However, because of its extended geographical space the SWAN model will include some generation effects in the coarse SWAN simulations, complemented by wave transformation effects near the coast. The system was validated by means of extended hindcast runs in various regions belonging to the continental Portuguese coastal environment, which were compared with buoy data, focusing on the extreme energetic events and both direct comparisons and statistical results are presented.     

Implementation and evaluation of alternative wave breaking formulas in a coastal spectral wave model

This paper describes methods and results of research for incorporating four different parameterized wave breaking and dissipation formulas in a coastal wave prediction model. Two formulations assume the breaking energy dissipation to be limited by the Rayleigh distribution, whereas the other two represent the breaking wave energy by a bore model. These four formulations have been implemented in WABED, a directional spectral wave model based on the wave action balance equation with diffraction, reflection, and wave–current interaction capabilities. Four parameterized wave breaking formulations are evaluated in the present study using two high-quality laboratory data sets. The first data set is from a wave transformation experiment at an idealized inlet entrance, representing four incident irregular waves in a slack tide and two steady-state ebb current conditions. The second data set is from a laboratory study of wave propagation over a complex bathymetry with strong wave-induced currents. Numerical simulation results show that with a proper breaking formulation the wave model can reproduce laboratory data for waves propagating over idealized or complicated bathymetries with ambient currents. The extended Goda wave breaking formulation with a truncated Rayleigh distribution, and the Battjes and Janssen formulation with a bore model produced the best agreement between model and data.     

寒潮影响下江苏沿海风浪场数值模拟研究

基于第三代浅水波浪数值预报模型SWAN,建立自西北太平洋嵌套至东中国海、江苏沿海的三重嵌套模型,对2010年12月12日至15日江苏沿海寒潮大风引起的风浪过程进行了数值模拟研究。利用西北太平洋和江苏沿海实测数据对模型进行了验证,结果表明SWAN嵌套模型能较好地模拟江苏沿海寒潮风浪场的时空分布。通过响水站实测数据对江苏沿海底摩擦系数进行了率定,研究表明选取Collins拖曳理论中摩擦因数C_f=0.001时,有效波高模拟误差相对较小。寒潮风浪场的特征分析表明,有效波高分布与风场分布基本一致,寒潮风浪在江苏沿海北部影响较为显著,辐射沙洲附近由于其特殊地形影响相对较小。     

Spectral wave transformation model for simulating refraction-diffraction with strongly reflecting coastal structures

On the basis of the wave action balance equation which incorporates refraction, diffraction, reflection and wave-current interaction, a directional spectral wave transformation model WABED is developed for predicting the irregular wave refraction-diffraction with strongly reflecting structures in coastal regions. In the model, diffraction is taken into account by introducing a term formulated from a parabolic approximation wave equation, and reflection is calculated through a back-marching numerical approach at the reflecting boundary. Two experimental data sets are used to examine the performance of present model with regard to wave characteristics around reflecting coastal structures. One is from a physical experiment at idealized inlet with parallel jetties, while the other is from a laboratory study on a coastal project of the concave breakwater. Reasonably good agreements are found for both cases, revealing the applicability of the present model for predicting combined wave refraction-diffraction processes with strongly reflecting coastal structures.     

Simulation of Typhoon-Driven Waves in the Yangtze Estuary with Multiple-Nested Wave Models

Typhoon-generated waves are simulated with two numerical wave models, the SWAN model for the coastal and Yangtze Estuary domain, nested within the WAVEWATCHIII （WW3） for the basin-scale East China Sea domain. Typhoon No. 8114 is chosen because it was very strong, and generated high waves in the Estuary. WW3 was implemented for the East China Sea coarse-resolution computational domain, to simulate the waves over a large spatial scale and provide boundary conditions for SWAN model simulations, implemented on a fine-resolution nested domain for the Yangtze Estuary area. The Takahashi wind model is applied to the simulation of the East China Sea scale （3-hourly） and Yangtze Estuary scale （1-hourly） winds. Simulations of significant wave heights in the East China Sea show that the highest waves are on the right side of the storm track, and maxima tend to occur at the eastern deep-water open boundary of the Yangtze Estuary. In the Yangtze Estuary, incoming swell is dominant over locally generated waves before the typhoon approaches the Estuary. As the typhoon approaches the Estuary, wind waves and swell coexist, and the wave direction is mainly influenced by the swell direction and the complex topography.     

太湖风浪场的计算与比较

首先探讨了浅水风浪数值模型—SWAN模型应用于模拟内陆湖泊风浪生成和传播变形时的特点。该模型存在不能有效地模拟近固壁边界处风浪场的缺点,以能正确地模拟湖区的风浪场和节约计算时间为原则,确定了计算范围。对太湖进行了风场和风浪场的现场观测。分别利用规范公式和SWAN模型两种方法、根据观测和预报的风场计算了湖区的有效波高,并将计算结果和现场观测值进行了详细比较。结果表明基于观测的风场,利用两种方法所计算的太湖风浪场的精度基本相当;在根据观测的风场、利用SWAN模型计算内陆湖泊的风浪场时,需要精心选择恰当的风场;在根据预报的风场预报湖区风浪场时,SWAN模型的精度要高于规范公式的精度。     

SWAN模型模拟风浪场侧边界失真范围研究

鉴于SWAN模型存在着不能有效地模拟固壁边界附近风浪场的缺点,即在边界附近所模拟的波要素存在失真的现象,研究了在不同水深、风速和风向情况下模型侧边界附近波要素的失真范围,并对计算结果进行了详细的分析。结果表明水深、风速和风向对于侧边界附近波要素的失真范围具有不同的影响,即在风速一定的情况下,失真范围随着水深的增大而增大;水深一定的情况下,失真范围随着风速的增大而减小、随着风向的增大而增大。在利用SWAN模型模拟计算近岸或内陆湖泊风浪场时,必须采取适当的措施以减少实际计算域侧边界附近计算结果的失真范围。     

Evaluation of two spectral wave models for wave hindcasting in the Mackenzie Delta

Climate change, reduced sea ice and increased ice-free waters over extended areas for longer summer periods potentially lead to increased wave energy in the Beaufort Sea (Wang et al., 2015; Khon et al., 2014) [1], [2], which is a major concern for coastal and offshore engineering activities. We compare two spectral wave models SWAN (Simulating WAves Nearshore) and MIKE 21 SW (hereafter MIKE21) in simulations of storm-generated waves in the Mackenzie Delta region of the southern Beaufort Sea. SWAN model simulations are performed using two nested grids system, whereas MIKE21 uses an unstructured grid system. Forcing fields are defined by hourly hindcast winds. Moving ice edge boundaries are incorporated during storm simulations. Modelled wave spectra from four storms are shown to compare well with field observations. Two established whitecapping formulations in SWAN are investigated: one dependent on mean spectral wave steepness, and the other on local spectral steepness. For the Beaufort Sea study area, we suggest that SWAN wave simulations using the latter local spectral steepness formulation are better than those using the former mean spectral steepness formulation. MIKE21 simulations also tend to agree with SWAN results using the latter whitecapping formulation.     

Surface wave simulation during winter with sea ice in the Bohai Sea

Sea ice can attenuate wave energy significantly when waves propagate through ice covers.In this study,a third-generation wave model called simulating wave nearshore(SWAN)was advanced to include damping of wave energy due to friction in the boundary layer below the ice.With the addition of an eddy viscosity wave-ice model,the resulting new SWAN model was applied to simulate wave height in the Bohai Sea during the freezing winter.Its performance was validated with available buoy data near the ice edge,and the new model showed an improvement in accuracy because it considered the ice effect on waves.We then performed a wave hindcast for the Bohai Sea during a freezing period in the winter of 2016 that had the severest ice conditions in recent years and found that the mean significant wave height changed by approximately 16.52%.In the Liaodong Bay,where sea ice concentration is highest,the change reached 32.57%,compared with the most recent SWAN model version.The average influence of sea ice on wave height simulation was also evaluated over a five-year(2013-2017)hindcast during January and February.We found that the wave height decrease was more significant in storm conditions even the eddy viscosity wave-ice model itself showed no advantage on damping stronger waves.     

Spectral modelling of wave energy converters

A spectral model suitable for the representation of wave energy converters is developed. A spectral model is an extension of a frequency-domain model that allows inclusion of non-linear forces and thereby provides improved estimates of wave energy converter performance, without the high computational cost of a time-domain model. The suitability and accuracy of a spectral model representation is demonstrated for a flap-type wave energy converter, by modelling the effect of vortex shedding and large amplitudes of motion. The development of a spectral model of wave energy converters also means that they can be represented in spectral wave models and included explicitly in software tools such as SWAN or Mike21 SW. This means that tools familiar to the industry could be used to determine the environmental impact and energy yield of wave farms efficiently.