Numerical simulation of wave-induced currents combined with parabolic mild-slope equation in curvilinear coordinates

Researches on breaking-induced currents by waves are summarized firstly in this paper. Then, a combined numerical model in orthogonal curvilinear coordinates is presented to simulate wave-induced current in areas with curved boundary or irregular coastline. The proposed wave-induced current model includes a nearshore current module established through orthogonal curvilinear transformation form of shallow water equations and a wave module based on the curvilinear parabolic approximation wave equation. The wave module actually serves as the driving force to provide the current module with required radiation stresses. The Crank-Nicolson finite difference scheme and the alternating directions implicit method are used to solve the wave and current module, respectively. The established surf zone currents model is validated by two numerical experiments about longshore currents and rip currents in basins with rip channel and breakwater. The numerical results are compared with the measured data and published numerical results.     

渤海湾水位、流场的一个数值预报模式

本文利用普林斯顿海洋模式(POM),建立了渤、黄海风增水预报模式和渤海湾水位海流预报模式;利用正交曲线网格提高重点区域的分辨率;采用美国海洋大气局(NOAA)全球预报风场和气压场作为模式表面强迫场,将计算域边界上的天文潮预报值与风增水模式预报的余水位相叠加构建模式的边界条件,在正压条件下,模拟了渤海湾2002年的水位流场过程。结果表明,模式能够较好地再现计算域内天文潮和综合水位的预报,域内10个潮位站模式与实测分析的m1和M2分潮的振幅与迟角差均不超过5.1cm和6.3°,15个潮流站模式与实测分析的m1和M2分潮流的振幅与迟角差均不超过7.5cm/s和15.8°,模式预报的水位值与塘沽站实测值非常接近,预报精度较单纯的天文潮预报有明显提高。     

非线性流函数在实验风浪场计算中的应用

风作用于水面产生风浪, 其中由于波流紊动产生的动量和能量的交换机制是一个很复杂的过程。风应力一般用来描述这种能量交换, 可以分为3个部分: 水面的剪切力、波生应力以及紊动应力。采用一种有效的非线性波流分离方法——NSFM(Nonlinear Stream Function Method)对波流运动的动量和能量输移进行定性描述。构造能够有效表达非线性波浪的解析流函数, 摄动求解使其满足拉普拉斯方程、动力边界条件和运动边界条件, 结合实验室风浪数据, 分离出波生速度场。通过交叉谱分析, 得到波生雷诺应力在不同风速下对风应力的贡献。结果表明: NSFM对不同工况条件下的风浪的处理具有较高的精度, 模型适应性良好; 且风速越大, 波生应力沿着水深衰减得越快, 且自由面波生应力在动量输移中的比重会逐渐减弱。     

Numerical experiment on the circulation in the Japan Sea

By using a rectangular basin of uniform depth with inflow and outflow openings, the circulation in the Japan Sea is investigated numerically. Heat flux through the sea surface is determined from the annual mean atmospheric conditions for the Japan Sea, but no wind stress is considered.In the transient state, the warm water supplied through an inflow opening travels cyclonically along the coast as a density-driven boundary current in a rotating system. In the quasi-steady state, the warm water flows northward as a western boundary current which corresponds to the East Korean Warm Current and gradually separates from the coast as it flows northward. No strong boundary current corresponding to the nearshore branch of the Tsushima Current exists.Under annual mean atmospheric conditions, formation of the deep water characteristic of the Japan Sea and of the thermal front corresponding to the Polar Front do not take place.     

水动力时空变化对近岸风浪演化的影响——以渤海湾西南岸为例

采用SWAN模型和ADCIRC模型建立了风浪、潮汐和水流联合作用的耦合数值模式,并通过渤海湾西南岸实测资料对该模式进行了验证。利用该模式分析了近岸区水位和流场时空变化对风浪模拟结果的影响,计算结果表明水位变化对近岸区风浪模拟结果有显著影响,特别是中等大风过程高潮位时波高受水位影响的变化幅值可达0.5m以上,且水深越浅影响越大。但在岸滩平缓的近岸海域由于流速、流向的时空变化不太剧烈,流场作用和波浪辐射应力作用对波浪场的影响都基本可以忽略。在模拟近岸风浪过程时,应选用耦合模式。     

A model of profile evolution on wave-dominated mud coast

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远区台风“三巴”对河口波浪增水和波生流影响数值模拟研究

波浪增水和波生流是河口泥沙输运、地貌演变和污染物扩散的重要动力之一,但目前关于远区台风影响下长江口波浪增水和波生流的研究比较缺乏。本文建立了覆盖东中国海的台风-天文潮-波浪耦合三维数值模型,研究了远区台风“三巴”对长江口波浪增水和波生流的影响。结果表明:波浪从台风中心向近岸传播过程中,能量耗散引起波浪作用力的衰减和辐射应力的增大,产生波浪增水,长江口波浪增水在0.05 ~0.20 m之间,占台风总增水值的15%~22%。从NW向入射的台风浪产生自北向南的波生沿岸流,垂向上呈现三维结构,平均流速在0.05~0.20 m/s之间,占风暴潮流的15%~50%,充分说明了远区台风可以对长江口波浪增水和波生流产生明显影响,研究成果可以为河口极值水位和流速计算、泥沙输运、水下三角洲地貌演变等研究提供参考。     

A simple new shoreline change model

A simple new shoreline change model has been developed and calibrated/evaluated with several sets of high quality field data. The model is based upon the general observation that the shoreline tends to approach an equilibrium position exponentially with time when subjected to constant forcing. The model represents the shoreline response to cross-shore processes only and is extremely efficient, requiring only readily obtainable wave and water-level data as input. Shoreline changes are forced by changes in the local water surface elevation due to a combination of local tide, storm surge and wave-induced setup. The model contains three adjustable parameters, representing a baseline condition from which equilibrium shoreline displacements are calculated, and two rate constants, all of which are evaluated by minimizing the error between model hindcasts and several historical shoreline data sets. Several possible forms for the rate parameters, incorporating local wave and sediment properties, were considered and evaluated. At most sites, the model has proven successful in predicting large-scale shoreline response to local water level and wave forcing. The combination of model accuracy and efficiency, along with the minimal data required to drive the model, make it a potentially useful tool in many coastal engineering applications. As more high-quality shoreline, wave and water-level data sets become available, significant improvements can be made in the determination of the rate parameter governing the time scale of the beach response.     

马尔代夫海域水位、海流数值预报研究

基于无结构有限体积法海洋模式(FVCOM),建立了马尔代夫双重嵌套的水位、海流预报模式,并实现了业务化运行。利用三角网格提高重点区域(马尔代夫大桥及岛屿附近海域)的分辨率,最高网格分辨率达到45 m。垂向分层采用σ-s混合坐标的方式划分,分为31层,分别在表层和底层进行加密。采用GFS预报的风场、气压场和热通量结果制作模式表面强迫场文件。在开边界处与HYCOM预报结果进行嵌套,在斜压条件下,采用热启动的方式,业务化模拟了马尔代夫海域2020年的水位流场过程。结果表明,模式能够较好地再现计算海域内天文潮和综合水位的预报,模式预报的水位值与潮位站实测值非常接近。     

Numerical study on vertical structures of undertow inside and outside the surf zone

Nearshore shoaling and breaking waves can drive a complex circulation system of wave-induced currents. In the cross-shore direction, the local vertical imbalance between the gradient of radiation stress and that of pressure due to the setup drives an offshore flow near the bottom, called ‘undertow’, which plays a significant role in the beach profile evolution and the structure stability in coastal regions. A 1DV undertow model was developed based on the relationship between the turbulent shear stress and t...     

Modeling wave�Ccurrent bottom boundary layers beneath shoaling and breaking waves

The boundary layer characteristics beneath waves transforming on a natural beach are affected by both waves and wave-induced currents, and their predictability is more difficult and challenging than for those observed over a seabed of uniform depth. In this research, a first-order boundary layer model is developed to investigate the characteristics of bottom boundary layers in a wave–current coexisting environment beneath shoaling and breaking waves. The main difference between the present modeling approach and previous methods is in the mathematical formulation for the mean horizontal pressure gradient term in the governing equations for the cross-shore wave-induced currents. This term is obtained from the wave-averaged momentum equation, and its magnitude depends on the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient due to spatial variations in the wave field of propagating waves and mean water level fluctuations. A turbulence closure scheme is used with a modified low Reynolds number k-ε model. The model was validated with two published experimental datasets for normally incident shoaling and breaking waves over a sloping seabed. For shoaling waves, model results agree well with data for the instantaneous velocity profiles, oscillatory wave amplitudes, and mean velocity profiles. For breaking waves, a good agreement is obtained between model and data for the vertical distribution of mean shear stress. In particular, the model reproduced the local onshore mean flow near the bottom beneath shoaling waves, and the vertically decreasing pattern of mean shear stress beneath breaking waves. These successful demonstrations for wave–current bottom boundary layers are attributed to a novel formulation of the mean pressure gradient incorporated in the present model. The proposed new formulation plays an important role in modeling the boundary layer characteristics beneath shoaling and breaking waves, and ensuring that the present model is applicable to nearshore sediment transport and morphology evolution.     

Morphodynamics of intertidal bars on a megatidal beach, Merlimont, Northern France

The morphology, bedforms and hydrodynamics of Merlimont beach, in northern France, characterised by intertidal bars and a spring tidal range of 8.3 m, were surveyed over a 10-day experiment with variable wave conditions that included a 2-day storm with significant wave heights of up to 2.8 m. The beach exhibited two pronounced bar-trough systems located between the mean sea level and low neap tide level. Waves showed a cross-shore depth modulation, attaining maximum heights at high tide. The mean current was characterised dominantly by strong tide-induced longshore flows significantly reinforced by wind forcing during the storm, and by weaker, dominantly offshore, wave-induced flows. Vertical tidal water-level variations (tidal excursion rates) showed a bimodal distribution with a peak towards the mid-tide position and low rates near low and high water. The two bar-trough systems in the mid-tide zone remained stable in position during the experiment but showed significant local change. The absence of bar migration in spite of the relatively energetic context of this beach reflects high macro-scale bar morphological lag due to a combination of the large vertical tidal excursion rates in the mid-tide zone, the cross-shore wave structure, and the pronounced dual bar-trough system. The profile exhibited a highly variable pattern of local morphological change that showed poor correlation with wave energy levels and tidal excursion rates. Profile change reflected marked local morphodynamic feedback effects due mainly to breaks in slope associated with the bar-trough topography and with trough activity. Change was as important during low wave-energy conditions as during the storm. Strong flows in the entrenched troughs hindered cross-shore bar mobility while inducing longshore migration of medium-sized bedforms that contributed in generating short-term profile change. The large size and location of the two pronounced bars in the mid-tide zone of the beach are tentatively attributed respectively to the relatively high wave-energy levels affecting Merlimont beach, and to the cross-shore increase in wave height hinged on tidal modulation of water depths. These two large quasi-permanent bars probably originated as essentially breakpoint bars and are different from a small bar formed by swash and surf processes in the course of the experiment at the mean high water neap tide level, which is characterised by a certain degree of tidal stationarity and larger high-tide waves.     

Implementation and modification of a three-dimensional radiation stress formulation for surf zone and rip-current applications

Regional Ocean Modeling System (ROMS v 3.0), a three-dimensional numerical ocean model, was previously enhanced for shallow water applications by including wave-induced radiation stress forcing provided through coupling to wave propagation models (SWAN, REF/DIF). This enhancement made it suitable for surf zone applications as demonstrated using examples of obliquely incident waves on a planar beach and rip current formation in longshore bar trough morphology (Haas and Warner, 2009). In this contribution, we present an update to the coupled model which implements a wave roller model and also a modified method of the radiation stress term based on Mellor (2008, 2011a,b,in press) that includes a vertical distribution which better simulates non-conservative (i.e., wave breaking) processes and appears to be more appropriate for sigma coordinates in very shallow waters where wave breaking conditions dominate. The improvements of the modified model are shown through simulations of several cases that include: (a) obliquely incident spectral waves on a planar beach; (b) obliquely incident spectral waves on a natural barred beach (DUCK'94 experiment); (c) alongshore variable offshore wave forcing on a planar beach; (d) alongshore varying bathymetry with constant offshore wave forcing; and (e) nearshore barred morphology with rip-channels. Quantitative and qualitative comparisons to previous analytical, numerical, laboratory studies and field measurements show that the modified model replicates surf zone recirculation patterns (onshore drift at the surface and undertow at the bottom) more accurately than previous formulations based on radiation stress (Haas and Warner, 2009). The results of the model and test cases are further explored for identifying the forces operating in rip current development and the potential implication for sediment transport and rip channel development. Also, model analysis showed that rip current strength is higher when waves approach at angles of 5° to 10° in comparison to normally incident waves.     

The influence of tides,wind and waves on the redistribution of nourished sediment at Terschelling,The Netherlands

A calibrated morphodynamic model of the barrier island of Terschelling, The Netherlands [Grunnet, N.M., Walstra, D.J.R., Ruessink, B.G., 2004. Process-based modelling of a shoreface nourishment. Coastal Eng. 51/7, 581–607], comprising the island and its two adjacent tidal inlet systems, is applied to identify the relative contribution of tides, wind and waves to the cross-shore and alongshore redistribution of a 2 Mm³ nourishment supplied to the nearshore zone along the island. Several model simulations with varying combinations of horizontal and vertical tide, wind and wave forcing were designed to investigate the effect of each individual forcing on a large spatio-temporal scale (order of kilometres and months, respectively). As expected, stirring and transport by waves and wave-induced currents are predicted to be by far the dominant contributor to the net sediment transport along the coast of Terschelling. Because of the strong obliquity of the winds and the relatively small tidal currents in front of the island (≈ 0.5 m/s), alongshore wind-driven currents increase sediment transport rates and horizontal tides virtually have no net transport capacity. This motivated a local model of the study area along the closed coast of Terschelling, not including tidal inlets and further simplifying tidal boundary definitions by omitting the horizontal tides: morphodynamic simulations of the local model show virtually identical results as the larger model predictions. The reduction in complexity in setting up a local model instead of a regional model coupled with the corresponding significant reduction in computational time points to an increasing applicability of complex process-based models.     

Quasi-3D modelling of nearshore currents

Existing concepts of wave-induced nearshore current models, in the cross-shore vertical plane (2DV) and depth-integrated (2DH), are combined to a quasi-3D mathematical model. This combination is tested for reproducing correct results in 2DV and 2DH situations. The importance of the various contributions to the wave-induced secondary circulation in the vertical plane is investigated for realistic parameter ranges, which leads to the conclusion that both the non-breaking and the breaking fraction of a random wave field in the surf zone generate important secondary currents.Additional computations show the relevance of a 3D-approach of nearshore currents, even in seemingly simple situations like a plane sloping beach with obliquely incident waves.     

Propagation of semi-diurnal internal tides observed off fukushima,along the east coast of Japan

Analysis of current velocity and temperature records obtained from moored buoy systems deployed off the east coast of Japan reveals the intermittent occurrence of semi-diurnal internal tides and their manner of propagation. The internal tidal waves clearly propagate toward the shore, which is confirmed by cross-correlation of the onshore current velocity and temperature between neighboring stations. The propagation speed of the internal tide increases with water depth except in the area furthest offshore. In this area, motions near the second mode seem to occur occasionally, while in the nearshore area the motions for the most part consist of the first mode. Through harmonic analysis, it is shown that theM ₁ internal motions were not vertically homogeneous. That is, the internal motions are greater at the lower level in the nearshore area while they are greater at the upper level in the offshore area. Pathways along which the energy of the internal tide should propagate are estimated in such a way that the characteristic curves pass through the area over which relatively large onshore/offshoreM ₂ velocity is distributed. The movement of the characteristic ray of a certain phase explains the observed phase velocity estimated from the cross-correlation diagrams. Internal motions around the characteristic ray were pronounced in a rather wide area. Thus, it is suggested that the generation region of the internal tide in the present study area might be relatively wide.     

Prediction of wave-induced scour depth under submarine pipelines using machine learning approach

The scour around submarine pipelines may influence their stability; therefore scour prediction is a very important issue in submarine pipeline design. Several investigations have been conducted to develop a relationship between wave-induced scour depth under pipelines and the governing parameters. However, existing formulas do not always yield accurate results due to the complexity of the scour phenomenon. Recently, machine learning approaches such as Artificial Neural Networks (ANNs) have been used to increase the accuracy of the scour depth prediction. Nevertheless, they are not as transparent and easy to use as conventional formulas. In this study, the wave-induced scour was studied in both clear water and live bed conditions using the M5’ model tree as a novel soft computing method. The M5’ model is more transparent and can provide understandable formulas. To develop the models, several dimensionless parameter, such as gap to diameter ratio, Keulegan-Carpenter number and Shields number were used. The results show that the M5’ models increase the accuracy of the scour prediction and that the Shields number is very important in the clear water condition. Overall, the results illustrate that the developed formulas could serve as a valuable tool for the prediction of wave-induced scour depth under both live bed and clear water conditions.     

Sedimentology and morphodynamics of a macrotidal beach, Pendine Sands, SW Wales

The foreshore of Pendine Sands forms the seaward part of an extensive, sandy coastal barrier in a shallow Carmarthen Bay, SW Wales. The sedimentological features of the macrotidal foreshore reflect a tide-induced modification of nearshore wave characteristics. As the tide ebbs, the breaker height may decrease, the surf zone widens and becomes increasingly dissipative, and swash/backwash velocities diminish. A concomitant change from plunging to spilling breakers and increasingly symmetrical swash zone flows are associated with a decreasing beach gradient.

A zero net transport model demonstrates that the beach profile is self-stabilising in the short-term, and periodic levelling has shown that the beach is in long-term equilibrium with prevailing conditions, though this does not preclude a significant dynamic response to changing tides and waves.

The flow regimes of wave-generated currents decline as the tide ebbs, and normal beach processes do not usually affect the lower foreshore. Accordingly, there is an overall seaward-fining of the primary framework component of the sands. In more detail, this framework component displays a slight seaward-coarsening across an upper foreshore dominated by high water swash and surf; a rapid seaward-fining across the mid-foreshore in response to the ebb-attenuating swash zone flow velocities; and a slight seaward-fining across the lower foreshore under the action of nearshore shoaling waves. Bedforms vary from a swash/backwash emplaced flat bed across the upper foreshore to the small ripples of nearshore asymmetric oscillatory flows across the lower foreshore.

The surface sediment veneer is not representative of the subsurface sediments which form in response partly to fairweather conditions, partly to storms. The upper foreshore is characterised by swash/backwash emplaced plane bedding in fine sands frequently disrupted by bubble cavities. The mid-foreshore is composed of coarser-grained shelly traction clogs arranged as landward- and seaward-dipping large-scale cross bedding and/or plane bedding; these are probably storm breaker/surf deposits. The lower foreshore, though partially and sometimes totally bioturbated, shows landward-dipping small-scale cross bedding in very fine sands sorted by nearshore shoaling waves.

Tide- and storm-induced modification of the nearshore flow regimes therefore produces a distinctive shore-normal array of sedimentary facies. Each facies is characterised by diagnostic textural and structural signatures. A prograding sequence of such macrotidal deposits would be similar to, but more extensive than, a comparable microtidal sequence.     

A Kalman Filter Approach to Realize the Lowest Astronomical Tide Surface

In this paper , we present a novel Kalman filter approach to combine a hydrodynamic model-derived lowest astronomical tide (LAT) surface with tide gauge record-derived LAT values. In the approach, tidal water levels are assimilated into the model. As such, the combination is guided by the model physics. When validating the obtained “Kalman-filtered LAT realization” at all tide gauges, we obtained an overall root-mean-square (RMS) difference of 15.1 cm. At the tide gauges not used in the data assimilation, the RMS is 17.9 cm. We found that the assimilation reduces the overall RMS difference by ～ 31% and ～ 22%, respectively. In the Dutch North Sea and Wadden Sea, the RMS differences are 6.6 and 14.8 cm (all tide gauges), respectively. Furthermore, we address the problem of LAT realization in intertidal waters where LAT is not defined. We propose to replace LAT by pseudo-LAT, which we suggest to realize similarly as LAT except that all water level boundary conditions and assimilated tidal water levels have to be enlarged by a constant value that is removed afterward. Using this approach, we obtained a smooth reference surface for the Dutch Wadden Sea that fits LAT at the North Sea boundary within a few centimeters.     

Landward limit of wind setup on beaches

Open coast storm surge water levels consist of a wind shear forcing component generally referred to as wind setup; a wave setup component caused by wind-induced waves transferring momentum to the water column; an atmospheric pressure head component due to the atmospheric pressure deficit over the spatial extent of the storm system; a Coriolis-forced component due to effects of the rotation of the earth acting on the wind-driven alongshore current at the coast; and, if astronomical tides are present, an astronomical tide component. Astronomical tide is considered to be predictable and, therefore, not a meteorological driven component of storm surge although there may be interaction between the tide and meteorological driven water levels. Typically the most important component of storm surge on the US East Coast and Gulf of Mexico shorelines is the wind setup component. The importance of inland flooding due to the wind setup component of storm surge is considered herein with special reference to the effect of subaerial slope on inland flooding where three different linear slopes are considered and storm surge is calculated for the region above still water level, using an analytic solution. The present study findings show that the inland storm surge from the wind setup component can be of considerable importance and lead to significantly higher storm surges than found for storm surge at the still water level intersection of the beach/land. It is shown that mild slopes can lead to very high water levels at the land–water interface (i.e. above the still water level intersection of the beach).