Introduction of a new friction routine into the SWAN model that evaluates roughness due to bedform and sediment size changes

The significant loss of wave energy due to seabed interaction in finite depths is a known effect and bottom friction terms are used in the wave models to account for this dissipation. In this paper, a new bottom-interaction function is tested by means of the SWAN model, based on measurements at two field sites, Lake George and Lakes Entrance, both in Australia. The function accounts for dependence of the friction on the formation process of bottom ripples and on the grain size of the sediment. The overall improvement of the model prediction both for the wave height and wave period is demonstrated.     

Weak dependence of the SWAN wave model on hydrodynamic properties of sea bottom

The third generation of the SWAN wave model is modified by the incorporation of new resistance laws for hydrodynamically rough, incompletely rough (smoothly rough), and smooth underlying surfaces. A modified model is used to determine the functional dependences of wave parameters (such as the dimensionless energy of waves and the dimensionless spectral peak frequency) on a dimensionless fetch. The results of calculations are compared to the experimental data obtained in Lake George (northeastern Australia), which has a nearly constant depth and extended, nearly rectilinear segments of coast. The SWAN model is shown to depend weakly on hydrodynamic properties of the sea bottom: distinctions arising from changes in hydrodynamic properties of the sea bottom are smaller than the variances of experimental estimates.     

Comparison of turbulence schemes for prediction of wave-induced near-bed sediment suspension above a plane bed

Based on a wave bottom boundary layer model and a sediment advection-diffusion model, seven turbulence schemes are compared regarding their performances in prediction of near-bed sediment suspension beneath waves above a plane bed. These turbulence algorithms include six empirical eddy viscosity schemes and one standard two-equation k-ε model. In particular, different combinations of typical empirical formulas for the eddy viscosity profile and for the wave friction factor are examined. Numerical results are compared with four laboratory data sets, consisting of one wave boundary layer hydrodynamics experiment and three sediment suspension experiments under linear waves and the Stokes second-order waves. It is shown that predictions of near-bed sediment suspension are very sensitive to the choices of the empirical formulas in turbulence schemes. Simple empirical turbulence schemes are possible to perform equally well as the two-equation k-ε model. Among the empirical schemes, the turbulence scheme, combining the exponential formula for eddy viscosity and Swart formula for wave friction factor, is the most accurate. It maintains the simplicity and yields identically good predictions as the k-ε model does in terms of the wave-averaged sediment concentration.     

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.     

On a theoretical model of rough turbulent wave boundary layers

An analytical theory which describes the motion in a turbulent wave boundary layer near a rough sea bottom by using a two-layer time invariant eddy viscosity model is presented. The eddy viscosity in the inner layer increases quadratically with the height above the sea bottom. In the outer layer the eddy viscosity is taken as a constant. The mean velocity and shear stress profiles, the bottom shear stress and the bottom friction coefficient are presented, and comparisons are made with experimental results.     

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。     

Numerical investigation of wave propagation in the Liverpool Bay, NW England

The computer model for near shore wave propagation,SWAN,was used to study wave climates in Liverpool Bay,northwest England with various input parameters,including bottom friction factor,white capping,wind drag formulation and effects of tidal modulations.Results were compared with in-situ measurements and reveal the impacts from these inputs on the predictions of wave height and propagation distributions.In particular,the model results were found very sensitive to different input formulations,and tend to underestimate the wave parameters under storm conditions in comparison with the observations.It is therefore important to further validate the model against detailed field measurements,particularly under large storms that are often of the primary concern.     

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.     

用两种不同方法计算淀山湖风浪

对淀山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模型计算了湖区风浪场的波高,并将计算结果和现场观测值进行了比较,比较说明两种方法的计算结果存在比较明显的差别。可为今后的相关工作提供借鉴和参考,并可为淀山湖的进一步治理积累必要的工作基础。     

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。     

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.     

A Lagrangian model for wind- and wave-induced near-surface currents

A theory is outlined for time-dependent currents induced near the sea surface in deep water, away from coastal boundaries, by a variable wind stress and deep-water wave field. It is based on the theory of Weber (1983) which uses a second-order perturbation expansion of the Navier-Stokes equations in Lagrangian coordinates and includes the Coriolis effect. It uses an eddy viscosity formulation for both wave dissipation and momentum transfer within the current field: the eddy viscosity ν may be allowed to vary with depth. The wind stress may be time-varying and the wave field may vary in both space and time.For the case of a constant ν, the results agree with those of Ursell (1950), Hasselmann (1970) and Pollard (1970) in the limit ν→0, and the steady-state results agree with those of Weber. For a particular case of depth-varying ν, results (obtained from numerical simulations) are in better general agreement with observations of wind-induced surface drift than when a constant ν is used.An outline is given of the application of the theory to the case of a random sea state. There are good prospects for using output data from numerical wave prediction models to drive the equations of this near-surface current model.     

含变涡动系数的超浅海风暴潮模型

超浅海风暴潮模型提出后[2],对渤海风潮,作为超浅海问题,进行了数值研究[1]。其结果的分析和观测资料的比较都表明了该模型有一定的应用价值;故,对超浅海风暴潮模型作进一步的探讨是有一定意义的。尤其因为我国是一个多浅水域和多风暴潮的国家,这种研究就具有更重要的意义。     

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.     

台风“灿鸿”影响下海浪的数值模拟研究

台风是影响中国黄东海的强天气现象,其引起的强风、巨浪和台风增水严重威胁着沿海地区人民的生命与财产安全。本文以海浪模式SWAN（Simulating Waves Nearshore）与区域海洋模式ROMS（Regional Ocean Modeling System）为基础,构建了中国黄东海海域在201509号台风“灿鸿”影响下的海浪-海洋耦合模式。通过浮标与Jason-2高度计有效波高数据验证了模式结果的准确性。进行了敏感性实验分析,对比耦合（ROMS+SWAN）与非耦合（SWAN）下以及使用不同地形数据（ETOPO1、ETOPO2、GEBCO）、不同物理参数化方案（风能输入、白冠耗散、底摩擦耗散）下的模拟结果差异。结果发现在射阳与前三岛浮标处,使用GEBCO地形数据（15弧秒间隔）下的模拟效果更好且稳定。在空间分布上,台风中心附近的浪流相互作用显著,在其前进方向右侧表现为耦合的有效波高值低于非耦合有效波高值,差值最高可达1米。选择不同风输入与耗散项方案时的模拟差异主要发生在最大波高处,选择不同的风能输入与白冠耗散项方案带来的差异接近0.4米,而底摩擦项方案选择不同带来的差异接近1米。因而在模拟实际的海况时,需要综合考虑这些因素带来的影响,才能达到SWAN海浪模型最好的海浪模拟效果。     

Bottom Boundary Layer Characteristics in the Hooghly Estuary Under Combined Wave-Current Action

The development of a theoretical model for estimating bottom boundary layer characteristics in the Hooghly estuary, located in the east coast of India, under combined effects of waves and currents is reported. Three numerical models, viz a depth averaged hydrodynamic model, SWAN wave model, and bottom boundary layer model, were integrated. In the bottom boundary layer parameters, maximum bottom stress, effective friction factor, and near-bed velocity both during ebb and flood phases of the tidal forcing are investigated and validated for the Haldia channel. The close match seen from results signifies applicability of this model for entire Hooghly basin.     

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.     

Contributions to the dynamics of the Antarctic Circumpolar Current (A. C. C.) II. Integral relationship

Non-dimensional equations of motion are derived for the A.C.C. of the barotropic mode, including the bottom friction and the horizontal eddy viscosity. Integration of the vorticity equation along a streamline leads to the zeroth order stream function which is dependent only on depth divided by Coriolis parameter. Integration of the momentum equation along a streamline yields the relation between the momentum input by wind stress and its dissipation by the bottom friction and by the horizontal eddy viscosity. This relation determines the magnitude of the stream function. It explains differences in the total transport of the A.C.C. obtained byBryan andCox (1972), though it gives only one third of the total transport obtained byKamenkovich (1972) with his vertical eddy viscosity of 10²cm² s^?1. With 1 cm² s^?1 of this viscosity,Bryan andCox obtained the transport of about 650 or less than 32×10⁶m³s^?1 for constant or variable depth models, respectively. The higher transport is mainly due to broadening of the width of the A.C.C., whereas the lower value is due to its narrowing and meandering which in turn make the horizontal eddy viscosity more effective (by exercising friction on both sides of the A.C.C.) and the wind stress input smaller than the almost zonal streamlines for constant depth. In the Appendix dynamics of the bottom boundary layer is treated to give rational estimates of the bottom stress in terms of the geostrophic flow and is compared to the recent observations of the benthic boundary current in the Straits of Florida and off San Diego.     

Large Eddy Simulation for Wave Breaking in the Surf Zone

In this paper, (he large eddy simulation method is used combined with the marker and cell method to study the wave propagation or shoaling and breaking process. As wave propagates into shallow water, the shoaling leads lo the increase of wave height, and then at a certain position, the wave will be breaking. The breaking wave is a powerful agent for generating turbulence, which plays an important role in most of the fluid dynamic processes throughout the surf zone, such as transformation of wave energy, generation of near-shore current and diffusion of materials. So a proper numerical model for describing the turbulence effect is needed. In this paper, a revised Smagorinsky subgrid-scale mode! is used to describe the turbulence effect. The present study reveals that the coefficient of the Smagorinsky model for wave propagation or breaking simulation may be taken as a varying function of the water depth and distance away from the wave breaking point. The large eddy simulation model presented in this pape     

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.