Longshore current and sediment transport on composite beach profiles

Natural beaches tend to exhibit an equilibrium profile that is planar nearshore and nonplanar, concave-up offshore. The longshore current on this type of beach profile depends on the horizontal distance to the location of the intersection between the planar and nonplanar profiles. As the width of the planar beach face decreases, the location of the maximum longshore current moves closer to the shore. The dependency of the corresponding longshore sediment transport rate on the location of the intersection between the two profiles is demonstrated for two energetics-based sediment transport models. Again, a narrower beach face results in the maximum sediment transport being closer to the shore. Total sediment transport rates are also a function of the planar beach face width. This suggests that longshore transport rates are modulated by the tidal elevation.     

Wave setup/setdown and longshore current on non-planar beaches

Wave-induced setup/setdown and longshore currents are examined theoretically for non-planar, concave-up beaches. A beach profile in which the still-water-depth is proportional to the horizontal distance offshore raised to the $\text{2}\text{3}$ power is examined in detail. The total mean-water-depth, which includes the sum of the still-water-depth for this $\text{2}\text{3}$ power beach profile plus the wave-induced setup/setdown, may be approximated shoreward of the breaker line in a best least-squares sense by a profile that is proportional to the horizontal distance offshore raised to the $\text{1}\text{2}$ power. The longshore current profile for this non-planar beach is found to differ significantly from that predicted analytically for a planar beach. The longshore current velocity does not vanish at the shoreline as in the planar beach case. In addition, the peak velocities and the total longshore transport of water are found to be less than for the corresponding planar beach cases. For a given concave-up beach profile, the influence of the lateral mixing increases as the wave height decreases.     

沙坝海岸沿岸流速度剖面特征研究

通过对两个坡度沙坝地形沿岸流实验测量和基于能量方程的沿岸流数值模拟,研究了沙坝海岸平均沿岸流速度剖面的双峰剖面特征,重点分析了第二个峰值的特征和两峰值的比值。综合考虑入射波高、入射波类型和坡度对波生沿岸流垂直岸线速度剖面的影响。结果表明,平均沿岸流速度剖面出现双峰剖面特征:第一峰值发生在沙坝向岸侧面的中部,第二个峰值发生在靠近岸线处;同一坡度情况两个峰值的位置和比值,不受入射波类型、入射波高的影响。数值模型中包括了侧混、底摩擦和水滚等因素,其数值模拟结果和实验值拟合较好,并讨论了有无侧混和水滚对速度剖面的影响。     

Laboratory measurements of uniform longshore currents

Experiments on uniform longshore currents in a wave basin are described. The measurements were performed in a basin with a pumped recirculation through openings in the wave guides. Minimal return flows in the offshore region of the basin are found to be accompanied with longshore currents which are virtually uniform alongshore. Three-dimensional longshore current velocity distributions were measured with much attention to quality control. Detailed experimental results are presented for different wave fields, two beach slopes and two beach roughnesses.     

Longshore Current on an Equilibrium Beach

Natural beaches tend to be concave-up rather than planar and are reasonable to be modeled by an equilibrium beach profile. A governing equation for longshore current on an equilibrium beach is derived and its analytical solution is given in this paper. Through comparisons of the present solution and field data of longshore current for a step-type beach, the present solution is found to have fairly agreeable prediction to longshore current inside the surf zone. The effects of the shape of a concave-up beach and turbulent mixing stress on longshore current inside the surf zone are discussed in the present paper.     

沿岸流中混合系数的实验研究

进行了在规则波作用下破波带内水平混合系数测量的物理模型实验。通过在沿岸流流场中投放墨水点源和采用CCD摄像机摄像,测量了点源扩散过程。利用水深平均二维扩散方程近似解析解得到了由实验结果计算混合系数的方法。实验结果表明:扩散系数仅依赖于当地水深,与波浪参数(周期和波高)无关。沿岸流沿水深变化产生的离散作用导致顺流方向(纵向)混合系数远大于横流方向(横向)混合系数。横流方向混合系数中由波浪产生的扩散系数占总扩散系数约40%,其余为波浪破碎引起的湍流产生的扩散系数。     

Boussinesq modelling of transient rip currents

The flow on a plane beach with a random, directionally spread wave field was simulated with a Boussinesq model. The random wave spectra were directionally symmetric with their central direction perpendicular to the beach, so no constant longshore current was generated. Variable wave-averaged currents were generated because of the spatially variable wave field, and sometimes formed offshore directed rip currents that appear in variable longshore locations. The rip currents are associated with a vortex pair which is generated within the surfzone and subsequently propagates offshore. Analysis of the vorticity balance show that the main vorticity input occurs within the inner surfzone. Three different beach slopes and four different wave spectra are simulated. The frequency, duration, and intensity of the transient rips depend on both the beach slope and the incident wave spectra. The results have important engineering implications for the transport of material in the nearshore zone, in particular on longshore uniform beaches.     

Longshore Currents over Barred Beach with Mild Slope

The laboratory experiment and numerical simulations of wave-driven longshore currents by random waves on barred beaches with slopes of 1:100 and 1:40 were conducted to investigate the bimodal feature of mean longshore currents, with emphasis on the location and ratio of two peaks of longshore currents. The location and ratio of two peaks are controlled by the sand bar. The influences of wave heights and beach slopes on the longshore currents are discussed. Numerical simulations were also performed to compute the measured velocity profile, with the emphasis on the effect of lateral mixing, bottom friction and surface rollers on numerical results.     

Beach profiles characteristics along Giao Thuy and Hai Hau coasts, Vietnam: A field study

Giao Thuy and Hai Hau coasts are located in Nam Dinh province, Vietnam, with a total coastline of 54.42 km in length. The sea-dike system has been seriously damaged and there have been many dike breaches which caused floods and losses. This situation is considered of a general representative for coastal area in the northern part of Vietnam. A variety of studies have shown that the gradient in the longshore sediment transport rate and the offshore ?ne sediment lost are the main mechanisms causing the beach erosion. This study presents a field investigation of the beach profiles at Giao Thuy and Hai Hau beaches. Three types of empirical functions for the equilibrium beach profile are applied and compared with the observations. Results show that all observed beach pro?les can be described by a single function. However, one specific equilibrium pro?le equation is not sufficient to assess all beach pro?les. In Section 1 of Giao Thuy and Section 3 of Hai Thinh beaches, beach profiles are consistent with the logarithmic function, while the exponential function fits well in Section 2. This difference is explained with respect to coastal morphology, sediment characteristics and hydrodynamic conditions which vary in site. An analysis of the validity of the beach profile functions is recommended for the numerical modeling and engineering designs in this area.     

Numerical Simulation of the Three-Dimensional Wave-Induced Currents on Unstructured Grid

By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three-dimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.     

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.     

A Numerical Model for Edge Waves on A Compound Slope

An edge wave is a kind of surface gravity wave basically travelling along a shoaling beach. Based on the periodic assumption in the longshore direction, a second order ordinary differential equation is obtained for numerical simulation of the cross-shore surface elevation. Given parameters at the shoreline, a cross-shore elevation profile is obtained through integration with fourth-order Runge-Kutta technique. For a compound slope, a longshore wavenumber is obtained by following a geometrical approach and solving a transcendental equation with an asymptotic method. Numerical results on uniform and compound sloping beaches with different wave periods, slope angles, modes and turning point positions are presented. Some special scenarios, which cannot be predicted by analytical models are also discussed.     

企望湾砂质海滩剖面冲淤幅度的估算

以海滩沉积地貌现场观测资料为基础 ,通过海滩剖面形态组合 ,历史地形资料比较和特征地貌形态变化理论计算分析 ,对汕头南部企望湾弧形砂质海岸切线段的海滩剖面冲淤幅度进行了估算。结果表明 ,该海滩剖面冲淤幅度具有区段变化 ,低潮阶地和槽谷部位约 1 .5～ 2 .0m,滩肩和水下沙坝部位可达 3 .0 m。近 3 0年来 ,海滩剖面总体上趋于微冲刷 ,平均冲刷强度约为 1～ 2 cm/a,可能与近期人工挖砂有关。     

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.     

Development of A Depth-Integrated Longshore Current Model with Unstructured Grids

A depth-integrated model for simulating wave-induced longshore current was developed with unstructured grids. Effects of surface roller and horizontal mixing under combined waves and currents were incorporated in the numerical model. Recommended values of model coefficients were also proposed based on sensitivity analysis. Field observations and three series of laboratory measurements including two cases conducted on the plane beach and one implemented on the ideal inlet were employed to examine the predictive capability of this model. For the field case and laboratory cases conducted on the plane beach, numerical results were compared favorably with the measured data. For the case with an ideal inlet, simulated circulation pattern is supposed to be reasonable although some deviations between numerical results and measured data still can be detected.     

Longshore sediment transport on non-planar beaches

For a concave-up $\text{2}\text{3}$ power Bruun beach profile, the following two energetics-based sediment transport models are developed: (1) a Bagnold-type model and (2) a combined wave-current stress model. The stress model is calibrated with the Bagnold model using observed transport rates on planar beaches. The sediment transport profiles for the two models are in agreement within the surf zone for the planar beach case; but the stress model is also applied seaward of the breaker line where the Bagnold model is not. A mean swash transport of sand is predicted by the Bagnold model for a $\text{1}\text{2}$ power least-squares approximation to total depth including setup/setdown on a Bruun beach profile. The total longshore transport of sand is determined for each transport model as a function of the turbulent lateral mixing strength. The total sand transport is found to be less on a concave-up beach profile than for the corresponding planar beach case.     

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.     

Longshore currents of regular waves on different beaches

The experiment and numerical computations of longshore currents produced by regularwaves on the two beaches with the slopes of 1:100 and 1:40 are made. The cross-shore distributions of longshore current velocities and wave heights are given and the influences of wave heights, wave periods and beach slopes on the longshore currents are discussed. The discussion is also made for the influences of different eddy viscosity coefficients on the numerical results of longshore current velocities.     

沿岸流不稳定运动传播特性的小波相干谱分析

沿岸流不稳定运动属于超低频运动,研究它的传播特性,有助于深入理解其对岸滩演变、污染物、鱼卵等输移、迁移的影响。本文基于小波相干谱对所选实验波况进行了研究,分析了规则波、随机波入射情况下沿岸流不稳定运动传播特性,并讨论了入射波高、周期、坡度等对其的影响。结果表明,不规则波更易诱导出沿岸流不稳定运动,且在不规则波情况下,不稳定运动在沿岸方向相距4 m的两个断面上产生的相位差都约为±30°,与波浪入射角相近;随着入射波高的增加,非线性随之增强,更易诱导出不稳定运动,生成的沿岸流不稳定运动周期范围将增大;入射波周期对沿岸流不稳定运动的传播特性影响较小;坡度越陡越易诱导出超低频的不稳定运动。     

Investigation and Discussion on the Beach Morphodynamic Response Under Storm Events Based on A Three-Dimensional Numerical Model

A well-established 3D phase-averaged beach morphodynamic model was applied to investigate the morphodynamics of a typical artificial beach,and a series of discussions were made on the surfzone hydro-sedimentological processes under calm and storm events.Model results revealed that the nearshore wave-induced current presents a significant 3D structure under stormy waves,where the undertow and longshore currents exist simultaneously,forming a spirallike circulation system in the surfzone.Continuous longshore sediment transport would shorten the sediment supply in the cross-shore direction,subsequently suppress the formation of sandbars,showing that a typical recovery profile under calm waves does not necessarily develop,but with a competing process of onshore drift,undertow and longshore currents.Sediment transport rate during storms reaches several hundreds of times as those under calm waves,and two storm events contribute approximately 60%to the beach erosion.Sediment transport pattern under calm waves is mainly bed load,but as the fine sands underneath begin to expose,the contribution of suspended load becomes significant.