Longshore sorting on a beach under wave action

Sorting of sediment on a beach under wave action takes several forms. Stratified layers of finer and coarser sediment, which depend on wave climate, grain size and beach slope are formed. This complex problem can be simplified by defining the cross-shore and longshore sorting according to the angle between the breaking wave and the coast. In the present study, longshore distribution of sediment as well as corresponding beach profiles was measured in a wave basin. Three-dimensional hydraulic model experiments were performed with regular waves. Eighteen sets of experiments performed in longshore sorting mechanism using two different sand beds. The sorting of the bed material and the formation of armour coats along the beach were defined by grain size distributions and dimensionless parameters for sandy beaches.The rate of sediment transport with grain size sorting was measured in a wave basin. A method introduced sorting process was presented in this study. The sediment rate based on sorting mechanism was also discussed with known methods. It has been found that the non-uniformity of the grain size and hence sorting of the beaches play a very important role in the sand transport due to wave motion in a similar way to the case of steady flow in alluvial channels.     

Calculations of wave transformation across the surf zone

The accuracy of predicting wave transformation in the nearshore is very important to wave hydrodynamics, sediment transport and design of coastal structures. An efficient numerical model based on the time-dependent mild-slope equation is presented in this paper for the estimation of wave deformation across the surf zone. This model incorporates an approximate nonlinear shoaling formula and an energy dissipation factor due to wave breaking to improve the accuracy of the calculation of wave height deformation prior to wave breaking and also in the surf zone. The model also computes the location of first wave breaking, wave recovery and second wave breaking, if physical condition permits. Good agreement is found upon comparison with experimental data over several one-dimensional beach profiles, including uniform slope, bar and step profiles.     

季节性波浪动力作用下南湾弧形岸滩泥沙横向输运特征

响应季节性波候作用的泥沙输运特征是研究弧形海滩地貌变化及港工建筑的重要内容。基于南湾弧形海滩实际测量的冬、夏各11条剖面高程变化资料,将其划分为低潮间带、低中潮带、中潮带、高潮间带、低冲流带、中冲流带及其海滩后滨等7带,在此基础上利用经验正交函数(EOF)方法对各个带的体积变化进行分析,结果表明:1)南湾弧形海滩的泥沙以单向输运为主,并具有季节性变化特征,其中冬季泥沙在东南浪作用下,自陆向海输运,夏季泥沙在西南浪作用下自海向陆输运;2)南湾弧形海滩的泥沙分别在高潮带与中潮带、低冲流带与中冲流带之间存在频繁的双向输运;3)南湾弧形海滩不同岸段泥沙的横向输运因岬角的遮蔽能力、地形以及波浪作用的方向而有所差异。     

On the cross-shore profile change of gravel beaches

This paper investigates cross-shore profile changes of gravel beaches, with particular regard to discussing the tendency for onshore transport and profile steepening in the swash zone. The discussion includes observed morphological changes on a gravel beach from experimental investigations at the Large Wave Flume (GWK) in Hanover, Germany. During the tests all the profile changes occurred in the swash zone, resulting in erosion below the still water line (SWL) and formation of a berm above the SWL. We investigate the profile evolution evaluating the transport rates from a bed load sediment transport formulation coupled with velocities calculated from a set of Boussinesq equations that have been validated for its use in the surf and swash zones [Lynett, P.J., Wu, T.-R., and Liu, L.-F., P., 2002. Modelling wave runup with depth-integrated equations. Coastal Engineering, 46, 89–107; Otta, A.K., and Pedrozo-Acuña, A., 2004. Swash boundary and cross-shore variation of horizontal velocity on a slope. In: J.M. Smith (Editor), Proceedings 29th International Conference on Coastal Engineering. World Scientific, Lisbon, Portugal, pp. 1616–1628]. We discuss the influence of bottom friction on the predicted profiles, using reported friction factors from experimental studies. It is shown that the use of a different friction factor within a realistic range in each phase of the swash (uprush and backwash) improves prediction of the beach profiles, although quantitative agreement between the measured and computed profile evolutions is not satisfactory. Furthermore, if the friction factor and the transport efficiency (C) of the sediment transport formulation are kept the same in the uprush and backwash, accurate representation of profile evolution is not possible. Indeed, the features of the predicted profiles are reversed. However, when the C parameter is set larger during the uprush than during the backwash, the predicted profiles are closer to the observations. Differences between the predicted profiles from setting non-identical C-values and friction factors for the swash phase, are believed to be linked to both the infiltration effects on the flow above the beachface and the more accelerated flow in the uprush.     

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.     

Prediction of offshore bar-shape parameters resulted by cross-shore sediment transport using neural network

In order to understand the features of coastal zone and to utilize the coastal areas, it is necessary to determine the sediment movement and the resulting transport. Waves, topographic features, and material properties are known as the most important factors affecting the sediment movement and coastal profiles. In this study, by taking into consideration of wave height and period (H₀, T), bed slope (m) and sediment diameter (d₅₀), cross-shore sediment movement was studied in a physical model and various bar-shape parameters of the resultant erosion type profile were determined. Using 80 experimental data which are obtained from physical model studies, a neural network (NN) has been calibrated to predict bar-shape parameters of beach profiles. A sensitivity analysis was firstly carried out to decide data of training and test sets. Four different models, in which the rates of their training and testing set data were 80% and 20%, 70% and 30%, 60% and 40%, 50% and 50% were constituted and their performances were compared. It was determined that the model, in which the rate of its training and testing set data was 80% and 20%, respectively, has the best results. Therefore, a total of 64 experimental data were used as training set and the remainders of the experimental data were used as a testing set for the model. The performance of the NN model was compared with the regression equations developed in a previous study and the equations cited in literature indicating better performance over the equations.     

The effects of sediment characteristics and wave height on shape-parameter for representing equilibrium beach profiles

The shape parameter helps determining the shape of equilibrium beach profile in terms of offshore distance and water depth. The shape parameter therefore, should represent the effect of all the environmental factors involved in beach profile formation, such as wave climate and sediment properties. However, all the previous studies carried out to define shape parameter only consider the effects of sediment characteristics in their definitions. The aim of this study is to add the effect of wave climate also in the definition of shape parameter. This is achieved by integrating wave energy dissipation rate per unit volume at the surf zone. The result yields equilibrium wave energy dissipation rate that leads to theoretical definition of equilibrium beach profiles involving the effects of both the grain size and the wave climate parameters. It is found that the sediment grain size and the incoming wave height affect the value of shape parameter; whereas, the effects of wave period can be neglected. By means of energy equation, it is also possible to observe in macro scale the strength of wave energy on beach profile for different grain sizes. The findings also bring about the possibility of defining shape parameter such that any two arbitrary beach profiles owning the same sediment grain sizes can have the opportunity to have different beach profile formations. Finally, by adding the effect of wave height in the definition of shape parameter the graphical representation of the parameter, previously given by Moore (1982) is improved herein.     

A phase-resolving cross shore sediment transport model for beach profile evolution

A phase-resolving wave transformation module is combined with an intra-wave sediment transport module to calculate the on-/offshore sediment transport rates. The wave module is based on the Boussinesq equations extended into the surf zone. The vertical variation of the mean undertow and the intra-wave sediment concentrations are calculated. The net sediment transport rates are calculated, and the equation for conservation of sediment is solved to predict the beach profile evolution. The results of the present paper showed that the undertow contribution to the sediment transport rates is not dominating in all parts of the surf zone, even for eroding beaches, suggesting that other contributions should not be neglected. The present model also showed that for the same offshore wave energy the time series of the oscillatory motion is important and that the effect of wave groups cannot be disregarded.     

Equilibrium beach profiles under breaking and non-breaking waves

Simple theoretical models to determine the equilibrium profile shape under breaking and non-breaking waves are presented. For the case of breaking waves, it is assumed that the seaward transport in the undertow is locally balanced by a net vertical sedimentation, so that no bottom changes occur at equilibrium. The parameterization of the water and sediment flux in the surf zone yields a power curve for the equilibrium profile with a power of 2/3, which is in agreement with previous field investigations on surf zone profile shapes. Three different models were developed to derive the profile shape under non-breaking waves, namely (1) a variational formulation where the wave energy dissipation in the bottom boundary layer is minimized over the part of the profile affected by non-breaking waves, (2) an integration of a small-scale sediment transport formula over a wave period where the slope conditions that yield zero net transport determine equilibrium, and (3) a conceptual formulation of mechanisms for onshore and offshore sediment transport where a balance between the mechanisms defines equilibrium conditions. All three models produced equilibrium profile shapes of power-type with the power typically in the range 0.15–0.30. Comparison with field data supported the results obtained indicating different powers for the equilibrium profile shape under breaking and non-breaking waves.     

An estimate of the cross-shore sediment flux at the boundary of the coastal zone

A method based on mathematical modeling of the near-shore dynamics is suggested to calculate the annual mean cross-shore sediment flux q* at the coastal zone boundary. This method is applied to several sand coast profiles located in various geographical regions and exposed to energetic impacts of different scale. It is shown that the fluxes can be either positive (directed to the shore) or negative, and the magnitudes found agree with the known estimates based on other approaches. A conclusion is made that the resulting direction of q* is controlled by moderate storms with regime cumulative exedence from 1 to 10%. The wave periods, bottom slope, and sediment grain size play a special role in the process. An empirical criterion is found that allows one to predict the direction of the sediment flux crossing the coastal zone boundary.     

Process-based model for nearshore hydrodynamics, sediment transport and morphological evolution in the surf and swash zones

Hydrodynamics and sediment transport in the nearshore zone were modeled numerically taking into account turbulent unsteady flow. The flow field was computed using the Reynolds Averaged Navier–Stokes equations with a k–ε turbulence closure model, while the free surface was tracked using the Volume-Of-Fluid technique. This hydrodynamical model was supplemented with a cross-shore sediment transport formula to calculate profile changes and sediment transport in the surf and swash zones. Based on the numerical solutions, flow characteristics and the effects of breaking waves on sediment transport were studied. The main characteristic of breaking waves, i.e. the instantaneous sediment transport rate, was investigated numerically, as was the spatial distribution of time-averaged sediment transport rates for different grain sizes. The analysis included an evaluation of different values of the wave friction factor and an empirical constant characterizing the uprush and backwash. It was found that the uprush induces a larger instantaneous transport rate than the backwash, indicating that the uprush is more important for sediment transport than the backwash. The results of the present model are in reasonable agreement with other numerical and physical models of nearshore hydrodynamics. The model was found to predict well cross-shore sediment transport and thus it provides a tool for predicting beach morphology change.     

波浪作用下岸坡和海底平衡条件的研究

提出波浪作用下岸坡和海底动态和静态平衡条件的数学模型。在已建立的推移质泥沙体积输沙率基本关系式的基础上,根据连续方程,计算出底坡、泥沙、波浪三要素在动态和静态平衡情况下的关系式,得出反映这种关系的底坡平衡函数曲线图。用实际资料对这一函数曲线进行了验证,并对实际资料相对模型的某些差异作出解释。     

海南岛西部岸外沙波的高分辨率形态特征

利用SIMRAD-EM3000多波束探测系统和DGPS定位系统,对海南岛东方岸外的沙波沙脊区进行了高精度探测,分析结果表明:从海岸到陆架底形具有明显的分带性,依次出现弱侵蚀底形段、沙波沙脊底形段和平坦底形段。沙波仅发育于沙波沙脊段,介于水深20~50 m之间,沙波形态有二维与三维两种,沙波波高多为0.7~2.5 m,波长20~70 m,沙波指数(L/H)为20~60,对称指数为1~3;沙波沙脊区沉积物的搬运方向有明显的规律性,在沙脊的西侧,沉积物主要向北搬运;在沙脊的东侧,沉积物主要向南搬运;沙波的形成和发育主要受潮流场控制,热带风暴对其有改造作用。     

Numerical simulation of time-dependent beach and dune erosion

A computational procedure is developed for predicting the time-dependent, two-dimensional beach and dune erosion during severe storms due to elevated water levels and waves. The model employs the equation of sediment continuity and a dynamic equation governing the cross-shore sediment transport due to a disequilibrium of wave energy dissipation levels. These equations are solved numerically by an implicit, double-sweep procedure to determine the change in position of elevation contours in the profile. Given sufficient time, the profile will evolve to a form where the depth, h, in the surf zone is related to the distance seaward of the waterline by the relationship: $\text{h = Ax}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$, which is consistent with many natural profiles and in which A depends on sediment characteristics.The model is verified qualitatively and quantitatively through application to several idealized cases and through a preliminary simulation of erosion during Hurricane Eloise. In general, the time scales for shoreline response were found to be quite long relative to natural storm systems and erosion in the early response stages was found to be sensitive to storm surge height, but much less sensitive to wave height. The model response characteristics for simulation of erosion due to time-varying storm conditions show a lag between the maximum storm surge elevation and maximum erosion with the maximum erosion rate occurring at the time of the peak surge. For the simulated erosion due to Hurricane Eloise, reasonable agreement was found between the post-hurricane dune profiles and those calculated. However, the eroded volumes were in better agreement than the profile forms as the steepening of the natural dune profiles was not reproduced in the model.     

卷破波作用下沙质岸滩剖面形态判别式初探

通过波浪水槽实验,开展不同类型波浪作用下的沙质岸滩演化规律研究工作。本次实验研究不考虑比尺,采用1:10与1:20组成的复合沙质斜坡对岸滩进行概化,选取规则波和椭圆余弦波两种典型波浪作用,对波浪的传播、变形和破碎、上爬、回落过程以及波浪作用前后沙质岸滩床面地形进行了观测,探讨波浪作用下沙质岸滩剖面演化规律。本文实验工况中,规则波作用下,岸滩剖面呈现出沙坝剖面和滩肩剖面,椭圆余弦波作用下的岸滩剖面均呈滩肩形态,发现岸滩剖面形态不仅与波浪作用类型、强度、周期等因素相关,还与波浪破碎的强度等因素有关。通过对实验过程中现象的进行观察和分析,引入了卷破波水舌冲击角的概念。对波浪卷破破碎后形成的水流挟沙运动与岸滩剖面形态的关系进行定性分析,对水舌冲击角与Irribarren参数之间的关系进行定量分析,基于Irribarren参数与岸滩剖面形态的关系初步建立了波浪作用下沙质岸滩剖面形态判别关系式。通过本文实验结果和前人实验结果对趋势线进行拟合,求得其判别系数,判别式能够较好地划分淤积型岸滩、侵蚀型岸滩及过渡型岸滩三种岸滩形态。     

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.     

Dynamics of surf-zone turbulence in a strong plunging breaker

The characteristics of turbulence created by a plunging breaker on a 1 on 35 plane slope have been studied experimentally in a two-dimensional wave tank. The experiments involved detailed measurements of fluid velocities below trough level and water surface elevations in the surf zone using a fibre-optic laser-Doppler anemometer and a capacitance wave gage. The dynamical role of turbulence is examined making use of the transport equation for turbulent kinetic energy (the k-equation). The results show that turbulence under a plunging breaker is dominated by large-scale motions and has certain unique features that are associated with its wave condition. It was found that the nature of turbulence transport in the inner surf zone depends on a particular wave condition and it is not similar for different types of breakers. Turbulent kinetic energy is transported landward under a plunging breaker and dissipated within one wave cycle. This is different from spilling breakers where turbulent kinetic energy is transported seaward and the dissipation rate is much slower. The analysis of the k-equation shows that advective and diffusive transport of turbulence play a major role in the distribution of turbulence under a plunging breaker, while production and dissipation are not in local equilibrium but are of the same order of magnitude. Based on certain approximate analytical approaches and experimental measurements it is shown that turbulence production and viscous dissipation below trough level amount to only a small portion of the wave energy loss caused by wave breaking. It is suggested that the onshore sediment transport produced by swell waves may be tied in a direct way to the unique characteristics of turbulent flows in these waves.     

Numerical study on wave-induced filtration flow across the beach face and its effects on swash zone sediment transport

A numerical model, coupling an analysis of beach groundwater flow with an analysis of swash wave motion over a uniform slope, is presented. Model calculations are performed to investigate the variations of swash-induced filtration flows across the beach face for different input parameters. Swash zone sediment transport under the influence of such filtration flow across the beach face is investigated through modification of effective weight of sediment particle and modification of swash boundary layer thickness. These effects are quantified based on a bed load transport model with a modified Shields parameter.     

Verification of sediment transport rate parameter on cross-shore sediment transport analysis

The sediment transport parameter helps determining the amount of sediment transport in cross-shore direction. The sediment transport parameter therefore, should represent the effect of necessary environmental factors involved in cross-shore beach profile formation. However, all the previous studies carried out for defining shape parameter consider the parameter as a calibration value. The aim of this study is to add the effect of wave climate and grain size characteristics in the definition of transport rate parameter and thus witness their influence on the parameter. This is achieved by taking the difference in between “the equilibrium wave energy dissipation rate” and “the wave energy dissipation rate” to generate a definition for the bulk of sediment, dislocating within a given time interval until the beach tends reach an equilibrium conditions. The result yields that empirical definition of transport rate parameter primarily governs the time response of the beach profile. Smaller transport rate value gives a longer elapsed time before equilibrium is attained on the beach profile. It is shown that any significant change in sediment diameter or wave climate proportionally increases the value of the shape parameter. However, the effect of change in wave height or period on sediment transport parameter is not as credit to as mean sediment characteristics.