Numerical study of wave and longshore current interaction

Wave and longshore current interaction was examined based on the numerical models.In these models,water waves in the presence of longshore currents were modeled by parabolic mild slope equation,and wave breaking induced longshore currents were modeled by shallow water equation.Water wave provided the radiation stress gradients to drive current.Wave and longshore current interactions were considered by cycling the wave and longshore current models to a steady state.The experiments for regular and irregular breaking wave induced longshore currents by Hamilton and Ebersole（2001） and Reniers and Battjes（1997） were simulated.The numerical results indicate that the present models are effective for simulating the interaction of wave and breaking wave induced longshore currents,and the numerically simulated longshore current at wave breaking point considering wave and longshore current interaction show some disagreement with those neglecting the wave-current interaction,and the breaking wave induced longshore current effect on wave transformation is not obvious.     

A swell model of the German Bight

A numerical model is presented, which investigates the contribution of wave-induced currents to the tidal residual circulation in the German Bight. The momentum transfer, by swell decaying to the mean circulation, is calculated including wave-current interaction without refraction. The model couples deep-water and shallow-water energy dissipation mechanisms such as wave attenuation and wave breaking. The model computes wave set-up, wave set-down and a longshore current as well. The pure wave-induced circulation is calculated, and also the residual circulation due to the interaction between waves and tide. The results suggest that the wave-induced currents can be neglected for the calculation of transport of near-surface pollutants.     

One-dimensional modelling of individual waves and wave-induced longshore currents in the surf zone

A probabilistic model ( -model) was developed to describe the propagation and transformation of individual waves (wave by wave approach). The individual waves shoal until an empirical criterion for breaking is satisfied. Wave height decay after breaking is modelled by using an energy dissipation method. Wave-induced set-up and set-down and breaking-associated longshore currents are also modelled. Laboratory and field data were used to calibrate and verify the model. The model was calibrated by adjusting the wave breaking coefficient (as a function of local wave steepness and bottom slope) to obtain optimum agreement between measured and computed wave height. Four tests carried out in the large Delta flume of Delft Hydraulics were considered. Generally, the measured H_1/3-wave heights are reasonably well represented by the model in all zones from deep water to the shallow surf zone. The fraction of breaking waves was reasonably well represented by the model in the upsloping zones of the bottom profile. Verification of the model results with respect to wave-induced longshore current velocities was not extensive, because of a lack of data. In case of a barred profile the measured longshore velocities showed a relatively uniform distribution in the (trough) zone between the bar crest and the shoreline, which could to some extent be modelled by including space-averaging of the radiation force gradient, horizontal mixing and longshore water surface gradients related to variations in set-up. In case of a monotonically upsloping profile the cross-shore distribution of the longshore current velocities is reasonably well represented.     

Numerical study on water waves and wave-induced longshore currents in Obaky coastal water

In this paper, the water waves and wave-induced longshore currents in Obaky coastal water which is located at the Mediterranean coast of Turkey were numerically studied. The numerical model is based on the parabolic mild-slope equation for coastal water waves and the nonlinear shallow water equation for the wave-induced currents. The wave transformation under the effects of shoaling, refraction, diffraction and breaking is considered, and the wave provides radiation stresses for driving currents in the model. The numerical results for the water wave-induced longshore currents were validated by the measured data to demonstrate the efficiency of the numerical model. Then the water waves and longshore currents induced by the waves from main directions were numerically simulated and analyzed based on the numerical results. The numerical results show that the movement of the longshore currents was different while the wave propagated to a coastal zone from different directions.     

Two-dimensional wave-current interaction with a locally enriched quadtree grid system

Wave-induced currents may drive nearshore mixing and transport processes, including coastal pollutant dispersion, littoral drift, and long-term morphological changes through beach erosion and accretion. In this study, a numerical model is newly developed to simulate wave climate and localized currents in complicated coastal environments. The model developed is based on a quadtree grid system. The two-dimensional hydrodynamic governing equations are solved by using an explicit Adams-Bashforth finite difference scheme. Effects of wave breaking, shoaling, refraction, diffraction, wave-current interaction, set-up and set-down, turbulent mixing, bed friction, and shoreline movement are incorporated in the model. Results are presented for set-up at a beach in a flume due to normally incident waves, and longshore currents generated by oblique waves on a plane beach.     

Establishing uniform longshore currents in a large-scale sediment transport facility

A large-scale laboratory facility for conducting research on surf-zone sediment transport processes has been constructed at the U.S. Army Engineer Research and Development Center. Successful execution of sediment transport experiments, which attempt to replicate some of the important coastal processes found on long straight beaches, requires a method for establishing the proper longshore current. An active pumping and recirculation system comprised of 20 independent pumps and pipelines is used to control the cross-shore distribution of the mean longshore current. Pumping rates are adjusted in an iterative manner to converge toward the proper settings, based on measurements along the beach. Two recirculation criteria proposed by Visser [Coastal Eng. 15 (1991) 563] were also used, and they provided additional evidence that the proper total longshore flow rate in the surf zone was obtained. The success of the external recirculation system and its operational procedure, and the degree of longshore uniformity achieved along the beach, are the subjects of this paper. To evaluate the performance of the recirculation system, and as a precursor to sediment transport experiments, two comprehensive test series were conducted on a concrete beach with straight and parallel contours (1:30 slope), one using regular waves and the other using irregular waves. In the regular wave case, the wave period was 2.5 s and the average wave height at breaking was approximately 0.25 m. In the irregular wave case, the peak wave period was 2.5 s and the significant breaking wave height was approximately 0.21 m. The longshore current recirculation system proved to be very effective in establishing uniform mean longshore currents along the beach in both cases. This facility and the data presented here are unique for the following reasons: (1) the high cross-shore resolution of the recirculation system and the ease with which changes can be made to the longshore current distribution, (2) the degree of longshore uniformity achieved as a percentage of the length of the basin (even near the downdrift boundary), (3) the scale of the wave conditions generated, and (4) the relatively gentle beach slope used in the experiments (compared to previous laboratory studies of the longshore current). Measured data are provided in an appendix for use in theoretical studies and numerical model development and validation.     

结合椭圆型缓坡方程模拟近岸波流场

波浪向近岸传播的过程中,由波浪破碎效应所产生的近岸波流场是近岸海域关键的水动力学因素之一.结合近岸波浪场的椭圆型缓坡方程和近岸波流场数学模型对近岸波浪场及由斜向入射波浪破碎后所形成的近岸波流场进行了数值模拟.计算中考虑到波浪向近岸传播中由于波浪的折射、绕射、反射等效应使局部复杂区域波向不易确定,采用结合椭圆型缓坡方程所给出的波浪辐射应力公式来计算波浪产生的辐射应力,在此基础上耦合椭圆型缓坡方程和近岸波流场数学模型对近岸波流场进行数值模拟,从而使模型综合考虑了波浪的折射、绕射、反射等效应且避免了对波向角的直接求解,可以应用于相对较复杂区域的近岸波流场模拟.     

Longshore sediment transport estimation using a fuzzy inference system

Accurate prediction of longshore sediment transport in the nearshore zone is essential for control of shoreline erosion and beach evolution. In this paper, a hybrid Adaptive-Network-Based Fuzzy Inference System (ANFIS), Fuzzy Inference System (FIS), CERC, Walton–Bruno (WB) and Van Rijn (VR) formulae are used to predict and model longshore sediment transport in the surf zone. The architecture of ANFIS consisted of three inputs (breaking wave height), (breaking angle), (wave period) and one output (longshore sediment transport rate). For statistical comparison of predicted and measured sediment transport, bias, root mean square error and scatter index are used. The longshore sediment transport rate (LSTR) and wave characteristics at a 4 km-long beach on the central west coast of India are used as case studies. The CERC, WB and VR methods are also applied to the same data. Results indicate that the errors of the ANFIS model in predicting wave parameters are less than those of the empirical formulas. The scatter index of the CERC, WB and VR methods in predicting LSTR is 51.9%, 27.9% and 22.5%, respectively, while the scatter index of the ANFIS model in the prediction of LSTR is 17.32%. A comparison of results reveals that the ANFIS model provides higher accuracy and reliability for LSTR estimation than the other techniques.     

Evolution of waves and currents over a submerged laboratory shoal

The vertically-integrated effect of interaction between waves and wave-induced currents on wave transformation over a submerged elliptic shoal was investigated based on numerical simulations of the Vincent and Briggs experiment [Vincent, C.L., Briggs, M.J., 1989. Refraction- diffraction of irregular waves over a mound. Journal of Waterway, Port, Coastal and Ocean Engineering, 115(2), pp. 269–284.]. The numerical simulations were performed using two numerical wave-current model systems: one, a combination of the wave model SWAN and the current model SHORECIRC, and the other, a combination of the wave model REF/DIF and the same current model. A time-dependent, phase-resolving wave and current model, FUNWAVE, was also utilized to simulate the experiment. In the simulations, the developed wave-induced currents defocused waves behind the shoal and brought on a wave shadow zone that showed relatively low wave height distributions. For the breaking case of monochromatic waves, the wave heights computed using FUNWAVE showed good agreement with the measurements and the resulting wave-induced currents showed a jet-like velocity distribution in transverse direction. And the computed results of the two model combinations agreed better with the measurements than the computed results obtained by neglecting wave-current interaction. However, it was found that for the case in which transverse interference pattern caused by refracted waves was strong, REF/DIF-SHORECIRC did not correctly evaluate radiation stresses, the gradients of which generate wave-induced currents. SWAN-SHORECIRC, which cannot deal with the interference patterns, predicted a jet-like wave-induced current. For breaking random wave cases, the computed results of the two model combinations and FUNWAVE agreed well with the measurements. The agreements indicate that it is necessary to take into account the effect of wave-induced current on wave refraction when wave breaking occurs over a submerged shoal.     

A morphological stability analysis for a long straight barred coast

A morphological stability analysis is carried out for a long straight coast with a longshore bar. The situation with oblique wave incidence and a wave-driven longshore current is considered. The flow and sediment transport are described by a numerical modelling system. The models comprise: (i) a wave model with depth refraction, shoaling and wave breaking, (ii) a depth integrated model for wave driven currents and (iii) a sediment transport model for the bed load transport and the suspended load transport in combined waves and current. The direction of the sediment transport is taken to be parallel to the depth integrated mean current velocity, neglecting the effects of a bed slope and secondary currents. An instability is found to develop around the bar crest. The instability is periodic in the alongshore direction, and tends to form rip channels and to steepen the offshore face of the bar between the rip channels. The alongshore wave length of the most unstable perturbation is determined for different combinations of the wave conditions and the geometry of the profile.     

On Radiation Boundary Conditions and Wave Transformation Across the Surf Zone

The purpose of this paper is to extend the validity of Li's parabolic model (1994) by incorporating a combined energy factor in the mild-slope equation and by improving the traditional radiation boundary conditions. With wave breaking and energy dissipation expressed in a direct form in the equation, the proposed model could provide an efficient numerical scheme and accurate predictions of wave transformation across the surf zone. The radiation boundary conditions are iterated in the model without use of approximations. The numerical predictions for wave height distributions across the surf zone are compared with experimental data over typical beach profiles. In addition, tests of waves scattering around a circular pile show that the proposed model could also provide reasonable improvement on the radiation boundary conditions for large incident angles of waves.     

Modelling the wave-current interactions in an offshore basin using the SWAN model

The theoretical background of the wave-current interactions, including the transformation of the wave spectrum and breaking waves due to currents, are first presented in this work. In the next part of the work, experimental data resulted from studies performed in an offshore wave basin of the Danish Hydraulic Institute concerning the wave-current interactions were presented in parallel with some wave model simulations performed in similar conditions. SWAN, which is presently the state-of-the-art spectral model for the wave transformations, was adopted for performing numerical simulations. In general, a good agreement was encountered between the experimental data and the simulation results.     

Simulation of three-dimensional cohesive sediment transport in Hangzhou Bay, China

Sediment transport in the Hangzhou Bay is extremely complicated due to its bathymetry and hydrodynamic conditions. The ECOMSED model is employed to simulate three-dimensional (3-D) cohesive sediment transport in Hangzhou Bay. Dynamical factors such as Coriolis force, tides, salinity, river discharges, and waves are considered in the model. The wave parameters, including the significant wave height, period, and direction, are calculated with the SWAN model. The Grant-Madsen model is introduced for the bed shear stress due to the combined effect of waves and currents. The formulation of bed shear stress used to calculate the sink/source terms is modified based on previous research that sufficiently validated the formulation with measurement data. The integrated model of the above-mentioned models is applied to simulate sediment transport in Hangzhou Bay. The results of the simulation agree well with field observations concerning the distribution of suspended sediment, indicating that the sediments are remarkably suspended in Hangzhou Bay under the action of waves and currents.     

基于激波捕捉类Boussinesq模型对岛礁地形上波浪传播的数值模拟

为了探究激波捕捉类Boussinesq模型在模拟岛礁地形上规则波和不规则波传播的可行性,采用基于完全非线性Boussinesq方程并具有激波捕捉能力的数值模型Funwave-TVD对规则波和不规则波在岛礁地形上的传播进行了数值模拟,通过与试验数据对比,分析模型中空间步长的影响,验证模型在模拟波高、平均水位分布以及波谱空间演变的能力,结果表明:采用合适的空间步长,模型能较好地模拟规则波和不规则波在岛礁地形上的传播和演化过程。对于规则波,较小的空间步长可改善破碎点处波高峰值的预测,并能更好地预测波浪破碎后波高的空间分布,相比结合经验破碎的Boussinesq模型,Funwave-TVD能更好地模拟规则波在岛礁地形上的破碎,以及破碎以后行进涌波的再生成过程;对于不规则波,Funwave-TVD总体而言能较好地模拟涌浪有效波高、次重力波的生成及空间演化和平均水位,但会低估礁坪上次重力波波高,较粗的空间步长也会低估礁坪上涌浪有效波高。     

Examination of the influence of several factors on longshore current computation with random waves

Influence of various factors affecting the longshore currents induced by obliquely incident random waves is examined through numerical calculation. Seven numerical models for random wave breaking process are found to yield large differences in the wave heights in the surf zone and longshore current velocities. The turbulent eddy viscosity formulation by Larson and Kraus [Larson, M. and Kraus, N.C. (1991): Numerical model of longshore current for bar and trough beaches, J. Waterway, Port, Coastal, and Ocean Eng., ASCE, 117 (4), pp. 326-347.] functions almost equal to that by Battjes [Battjes, J.A. (1975): Modeling of turbulence in the surf zone, Proc. Symp. Modeling Techniques, pp. 1050–1061.], but the formulation by Longuet-Higgins [Longuet-Higgins, M.S. (1970): Longshore current generated by obliquely incident sea waves, 1 and 2, J. Geophys. Res., 75 (33), pp. 6779–6801.] produces excessive diffusion of longshore currents into the offshore zone. The generation and decay process of the surface roller is indispensable in the longshore current analysis. The random wave transformation model called PEGBIS (Parabolic Equation with Gradational Breaker Index for Spectral waves) by Goda [Goda, Y. (2004): A 2-D random wave transformation model with gradational breaker index, Coastal Engineering Journal, JSCE and World Scientific, 46 (1), pp. 1–38.] produced good agreement with several laboratory and field data of longshore currents.     

The Relative Trough Froude Number for initiation of wave breaking: Theory,experiments and numerical model confirmation

It is important to accurately locate the wave breaking region for the calculation of nearshore hydrodynamics. Energy from breaking waves drives hydrodynamic phenomena such as wave set-up, set-down, wave run-up, longshore currents, rip currents, and nearshore circulation. Numerous studies have been undertaken to describe when and where wave breakings occurs. Recent development of computer resources permits the use of phase-resolving numerical models for the study of wave propagation, transformation, and nearshore hydrodynamics. This requires new types of wave breaking criteria for the numerical model. The Relative Trough Froude Number (RTFN) is a new wave breaking criterion. This model is based on the moving hydraulic jump concept, therefore it satisfies properly posed boundary-value conditions. It has been experimentally proved that a critical RTFN at the initiation of wave breaking is consistent with and without the presence of an opposing current, but previous efforts did not investigate the theory for the critical value. This paper provides a theoretical analysis and a numerical analysis to demonstrate why the RTFN theory works as a wave breaking initiation (trigger) index. The theoretical analysis provides a universal constant for the initiation of wave breaking for all water depths assuming the Miche formula properly describes the wave breaking condition. A subroutine for wave breaking in a numerical model, FUNWAVE was modified to include the RTFN trigger. The numerical model was calibrated with data from wave tank experiments, and it was found that the critical condition is very close to the theoretical number, CTFN = 1.45. A second paper (in preparation) provides details of the theory and experiments for a second criterion for termination of wave breaking. The time scale for the establishment of the breaking region i.e., between the initiation position and termination position, depends upon the additional momentum present under turbulent condition within the breaking wave. This subject is not considered herein.     

波浪-海流-微地形耦合的沉积动力模式建立及应用

沙纹微地形普遍存在于海底,沙纹的消长能改变底部应力进而影响泥沙的运移。以往研究较多侧重于波致沙纹,并已应用于波浪模式的底摩擦计算,而较少考虑波流联合效应产生的沙纹,也未将其应用于综合的水动力模式和沉积物输运模式。本文在POM水动力模式中嵌入新南威尔士大学泥沙模式,通过耦合波流共同作用的微地形模型与波流相互作用底边界层模型,发展了波浪-海流-微地形（沙纹）耦合的沉积动力模式。本文将该模式应用于澳大利亚Jervis湾,针对波主导和波流联合主导沙纹两种类型,分别进行了沙纹发展状态、几何形态的分布及悬浮泥沙的模拟。结果表明:波致沙纹比波流联合作用的沙波具有更大的波高和波长,因此当波主导时沙纹对悬浮泥沙起着关键作用。通过考虑随沙纹变化的粗糙度,相比于以往模式设置均一的粗糙度,该模型能对悬浮物浓度的骤升过程进行更精细的预测。     

波浪作用下近岸区污染物输移扩散的数学模型及其实验验证

在近岸缓坡浅水海岸,波浪破碎产生沿岸流是近岸海域流场的重要组成部分,它对污染物输移扩散规律的影响重大,在高阶近似抛物化缓坡方程求解大面积波浪场基础上,建立了波浪作用下污染物输移扩散数学模型.计算结果与不同坡度均匀斜坡地形上具有不同波高、周期的规则波及不规则波浪作用下污染物输移扩散实验结果进行了比较,分析了各种因素对波浪作用下沿岸流分布规律影响,所得结论认为地形坡度及入射波高对污染物输移扩散的影响较大,波浪作用将使缓坡海滩上污染物的输移扩散平行岸线方向.