Calculation of beach change under interacting cross-shore and longshore processes

This paper presents a mathematical approach and numerical model that simulates beach and dune change in response to cross-shore processes of dune growth by wind and dune erosion by storms, and by gradients in longshore sand transport that will alter shoreline position. Sub-aerial transport processes are represented, whereas sub-aqueous transport is neglected. The system is tightly coupled morphologically, with the berm playing a central role. For example, the potential for sand to be transported to the dune by wind depends on berm width, and sand lost in erosion of the dune during storms can widen the berm. Morphologic equilibrium considerations are introduced to improve reliability of predictions and stability of the non-linear model. An analytical solution is given under simplification to illustrate properties of the model. Sensitivity tests with the numerical solution of the coupled equations demonstrate model performance, with one test exploring beach and dune response to potential increase in storm-wave height with global warming. Finally, the numerical model is applied to examine the consequences of groin shortening at Westhampton Beach, Long Island, New York, as an alternative for providing a sand supply to the down-drift beach. Results indicate that the sand will be released over several decades as the shoreline and dune move landward in adjustment to the new equilibrium condition with the shortened groins.     

Temporal assessment of sediment transport from beach nourishments by using foraminifera as natural tracers

This paper presents the application of a technique that can be easily applied in monitoring programs following beach fills, where sand is dredged from subtidal zones, seabed or bays, usually rich in foraminifera shells. Its utility lies in a simple and rapid estimation of the prevailing longshore transport paths and determination of the main eroding/accreting zones. A beach monitoring program was undertaken in a embayment on the South Atlantic Spanish coast, where several nourishments were carried out in order to recover an eroding beach. Once the nourishment was complete, a temporal analysis of foraminifera shell distribution was made in a nearby beach inside the embayment by monthly sediment sampling. Foraminifera shells were used as natural tracers for estimating sediment pathways. The results showed a complex pattern of sedimentary transport between both beaches, where wind action and reflected/diffracted waves interfered with the dominant longshore current, depending on the prevailing hydrodynamic regime. These results were later confirmed by a 3-year morphodynamic study. Although foraminifera dispersion only accounts for the behaviour of fine fractions, the monitoring of shell dispersion after dumping demonstrated to be a useful tool for studying the stability of nourished beaches. In the case of nourished beaches foraminifera shells could be considered as mixed tracers, with many advantages over both natural and artificial traditional tracers.     

Large-wave simulation of three-dimensional,cross-shore and oblique,spilling breaking on constant slope beach

In this work, the large-wave simulation (LWS) method is adapted for application in spilling wave breaking over a constant slope beach. According to LWS, large scales of velocities, pressure and free-surface elevation are numerically resolved, while the corresponding unresolved scale effects are taken into consideration by a subgrid scale (SGS) model for wave and eddy stresses. The model may be not fully applicable in very shallow water, close to the shoreline, where the unresolved, turbulent, free-surface oscillation is of the same order with the water depth. Time integration of the Euler equations is achieved by a two-stage fractional scheme, combined with a hybrid scheme for spatial discretization, consisting of finite difference and pseudospectral approximation methods. Model parameters are calibrated by comparison to available experimental data of free-surface elevation and velocities in the surf zone for cross-shore incoming waves. The action of the wave SGS stresses in the outer coastal and surf zones initiates breaking and generates appropriate vorticity, in the form of an eddy structure (surface roller), at the breaking wavefront. At incipient breaking, both advection and gravity contribute to the vorticity flux at the free surface, while only after the full development of the surface roller, the effect of advection becomes stronger. The SGS model is also utilized to simulate propagation, refraction and breaking of oblique incoming waves. The gradual breaking and dissipation of wave crestlines and the surface roller structure along the breaking wavefront are automatically captured without any empirical input, such as data for the roller shape or the wave propagation angle at breaking.     

Effects of cross-shore boundary condition errors in nearshore circulation modeling

The paper analyzes the effect which prescribed errors in the cross-shore boundary conditions for a computational domain along a beach have on the flow field predicted inside the domain. This problem is relevant because errors in boundary conditions are unavoidable when modeling limited domains of a nearshore region. For simplicity, we consider a longshore uniform plane beach with monochromatic, obliquely incident waves, and assume depth uniform currents. It is then studied analytically and numerically how small perturbations of the boundary conditions along both upstream and downstream cross-shore boundaries spread inside the computational domain. It is found that the errors at the upstream cross-shore boundary tend to spread over a long distance downstream of the boundary, while the influence of the errors in the downstream boundary condition is limited to the adjacent upstream area of the computational domain. Both the numerical and analytical solutions show that the errors introduced at the upstream boundary decay exponentially in the surf zone at a rate proportional to the bottom friction. A simple formula is developed to estimate the influence distance of the upstream errors. If we consider the mismatch in the volume flux at the upstream boundary, the error merely redistributes in the cross-shore direction to conserve volume. In the case of excessive flux or velocity specified at the cross-shore boundaries, a circulation cell tends to appear in the offshore region where the errors caused by the boundary mismatch increase with the cross-shore width of the model domain.     

Integrated monitoring of the hydro-morphodynamics of a beach protected by low crested detached breakwaters

The aim of this paper is to propose an integrated low cost system for monitoring the performance of beach defence works during storms. For this purpose, the site of Igea Marina, Northern Adriatic Sea, Italy, which is protected by low crested detached breakwaters, is selected. The monitoring system is composed by a video installation, for the identification of the shoreline position and of the intertidal bathymetry at high space and time resolution, and a 2DH numerical model, to reconstruct the hydrodynamics induced by coastal defenses. The accuracy of the monitoring system is verified against available measurements of waves and currents performed during a field campaign with acoustic Doppler profilers. Assimilation of data on the shoreline position in 2DH model operatively working is challenging in the improvement of the production of risk maps. These show the current intensities and flooded areas during forecasted storms. First promising results suggest the possibility of setting up an early warning tool.     

泥沙粒径组成的不均匀性对海岸地形演变的影响

海岸的泥沙输沙模式决定着海岸地形的演变特征,不同的输沙模式会导致形成横向和倾斜沙坝、裂流沟槽等不同的地貌特征。本研究提出了一种考虑泥沙分布不均匀性的新输沙率公式,该公式包含了反映泥沙粒径不均匀性的概率加权和考虑泥沙颗粒遮蔽效应的加权。该公式所给出的载沙量与传统输沙率公式的对比表明,相同中值粒径下,二者有明显差异。将该输沙率公式应用于地形线性不稳定分析,所得到的地形不稳定性增长率不同于假定泥沙为均匀的结果,对应的地形变形波长也有所差别。     

Hindcast of short-term shoreline evolution

A mathematical procedure is described with the aim of estimating short-term shoreline variations. The approach is fully deductive; the procedure being composed of different models that, starting from the atmospheric pressure distribution, evaluate in sequence the wind, current, wave fields, the breaking conditions, the coastal currents and finally the littoral transport. A comparison is made between visual observations of the shoreline evolution and, at one location, the variation of the bottom profile.     

人工砾石海滩变化及输移率研究

在我国采用砾石海滩在某些强动力区域进行海滩养护是一种新的尝试,具有很好的适用性。以厦门天泉湾人工砾石滩为研究对象,对2015年至2016年间10条海滩剖面开展了5次周期性监测,通过综合分析,得出在人工砾石滩竣工完成后的一年时间内,滩肩外沿线、岸线及滩面底角的砂砾分界线大幅度后退,滩肩宽度变窄;滩肩外沿线明显隆起,形成滩肩脊线;滩面坡度变大,且上游侧海滩的滩面普遍比下游侧海滩的滩面陡,一年后,岸滩整体变化趋于稳定。针对砾石滩不断向西南方向运移的现状,采用Leo C.van Rijn输移率公式计算砾石滩年平均输移率,并通过测量断面法、体积变化量法对Leo C.van Rijn公式计算结果进行验证,得出砾石滩年平均输移率的范围约为1 015.66~2 392.5 m~3/a。     

波浪动力因素变化对沙质岸滩演变的影响

通过波浪水槽实验,对海平面变化造成的波浪动力因素改变引起的沙质岸滩形态响应开展机理性研究。实验采用1∶10单一沙质斜坡概化岸滩,利用3种不同实验水深模拟海平面变化,考虑椭圆余弦波、非规则波、规则波和孤立波4种类型波浪作用。实验对波浪在斜坡上的传播变形、破碎、上爬和回落过程的波高及波浪作用后的岸滩地形进行了测量。实验结果表明,椭圆余弦波、规则波和非规则波作用下,平衡岸滩呈现出滩肩形态,孤立波作用下则呈沙坝形态。海平面上升造成波浪动力增强,沙质岸滩平衡剖面形状基本保持不变向岸平移,槽谷、滩肩、沙坝位置以及岸线蚀退距离,均呈现出良好规律性。     

Field experiment on secondary wave generation on a barred beach and the consequent evolution of energy dissipation on the beach face

A field experiment, conducted on a sandy, barred beach situated on the southern part of the French Atlantic coastline, allowed us to investigate the formation of secondary waves when a moderate (significant wave height of about 0.8 m in 3.7-m water depth), long (11–14 s) narrowband swell propagated over an intertidal ridge and runnel system, in both breaking and nonbreaking conditions. Field evidence using higher spectral analysis is given for the sum interactions between pairs of waves at the primary spectral peak and the consequent energy transfer to nearly harmonic wave components. Although wave breaking appears to weaken the strength of nonlinear couplings, the generation of high-frequency energy is hardly affected by wave breaking. The phenomenon of harmonic decoupling, which takes place behind the bar, cannot be completely ascribed to the increase in water depth and the so-called deshoaling effect. Indeed, the variation in the values of the maximum bicoherence was very moderate when no breaking occurred. Finally, the doubling in the number of wave crests and the consequent decrease in the significant wave period delay the energy dissipation on the beach face.     

Numerical modelling of sand beach evolution around coastal structures

I~crIOWIn the coastal area, especially at the sandy seashore, wave and nearshore current are the major factors which affect sediment transPOrt and the motyhChdynamics.The numerical models of predicting the beach evolution can be classified intO the medi~term and long-term models according to their space and time scales (De Briend et al., 1993;Watanabe, 1990; Watanabe et al., 1986; Tao, 1996). In the medium-term model the effects ofwave, nearshore current and sediment transport are conside…     

On the evolution and run-up of breaking solitary waves on a mild sloping beach

This paper presents new laboratory experiments carried out in a supertank (300 m × 5 m × 5.2 m) of breaking solitary waves evolution on a 1:60 plane beach. The measured data are employed to re-examine existing formulae that include breaking criterion, amplitude evolution and run-up height. The properties of shoreline motion, underwater particle velocity and scale effect on run-up height are briefly discussed. Based on our analyses, it is evidently found that there exist five zones during a wave amplitude evolution course on the present mild slope. A simple formula which is capable of predicting maximum run-up height for a breaking solitary wave on a uniform beach with a wide range of beach slope (1:15–1:60) is also proposed. The calculated results from the present model agree favorably with available laboratory data, indicating that our method is compatible with other predictive models.     

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.     

Probabilistic modelling of long-term beach evolution near segmented shore-parallel breakwaters

This paper presents a new framework for probabilistic modelling of long-term beach evolution in the vicinity of detached breakwaters. The study focuses on the key physical processes contributing to beach variability over a range of spatial and temporal scales. Based on a one-line model, the framework is enhanced with sophisticated solutions for beach-wave-structure interaction, diffraction together with a treatment of varying tide level. The sediment transport rate is calibrated at regional and local levels using data from bespoke field campaigns and site-specific coefficients are proposed. Monte Carlo simulation is conducted for long-term shoreline simulation under a sequence of time varying sequence of waves, currents and tidal levels. The results of the Monte Carlo simulation give an insight into the statistical characteristics of beach behaviour within the defence system. In particular, regions within the scheme that are relatively stable and those that exhibit greater natural fluctuations are identified.     

Development of a medium–long term beach evolution model

A new medium–long term beach evolution model is proposed. This model is based on an analytically integrated sediment conservation equation and on a beach profile evolution model. The sediment conservation equation provides the sediment supplies or losses. The beach profile evolution model redistributes the sediment supplies or losses along the beach profile. In the beach profile evolution model, the definition of the complete profile is incorporated (breaking zone, transition zone, exterior zone and geological zone). The proposed model has been applied to several theoretical cases and to field data, showing the advantages of this model compared to classical “one-line models”.     

Artificial neural network modeling of cross-shore profile on sand beaches: The coast of the province of Valencia (Spain)

The paper describes the training, validation, testing, and application of models of artificial neural networks (ANN) for computing the cross-shore beach profile of the sand beaches of the province of Valencia (Spain). Sixty ANN models were generated by modifying both the input variables as the number of neurons in the hidden layer. The input variables consist of wave data and sedimentological data. To select and evaluate the performance of the optimal model, the following parameters were used: R², absolute error, mean absolute percentage error, and percentage relative error. Finally, the results are compared with the numerical model proposed by Aragonés et al. (2016b Aragonés, L., Y. Villacampa, F. J. Navarro-González, and I. López. 2016b. Numerical modelling of the equilibrium profile in Valencia (Spain). Ocean Engineering, 123:164–73. doi:10.1016/j.oceaneng.2016.07.036[Crossref], [Web of Science ®] , [Google Scholar]) for the equilibrium profile in the study area. The results show a mean absolute error of 0.21?m compared to 0.33?m Aragones’ model, significantly improving the results of the numerical model in the bar area around de Valencia Port. In addition, when comparing the results with other methods currently used (Dean’s or Vellinga formulation), the errors of these compared to ANN are of the order of 167 and 1538% higher, respectively.     

Comparison of long-, medium- and short-term variations of beach profiles with and without submerged geological control

Victoria Beach (Cadiz, Spain) comprises a rocky flat outcrop in its northern zone and a sand-rich southern zone. These natural features allowed for a 5-year monitoring period and subsequent analysis of two different profiles (one in each zone) based on differences in bottom contours. Topo-bathymetric data were analysed using empirical orthogonal functions (EOFs) to determine changes over the short-, medium- and long-term. Several morphologic phenomena were identified (generalised erosion, seasonal or summer–winter tilting of the profile around different hinge points, berm development and its posterior destruction, etc.) in terms of their importance in explaining the variability of the collected data for both profiles. It is worth mentioning that both profiles undergo parallel regression in the medium-term. Thus, the 1st eigenfunction enabled us to identify the true regression of the beach shoreline, independent of seasonal or summer–winter slope changes. Reconstruction of profiles using EOF components demonstrated that though accretion periods in the medium-term were similar for both types of profiles, the accretion speed was much faster in the sand-rich profile than in the reef-protected profile (1.01 m³/day versus 0.33 m³/day). Moreover, the seasonal erosion rate and the subsequent shoreline retreat for the sand-rich profile were much larger than for the reef-protected profile (121 m³/year versus 29 m³/year). Analysis in the short-term (changes induced by a single day's storm) showed an instantaneous tilting of the profile, with the mobilised sand volume being much greater for the sand-rich than for the reef-protected profile (68 m³/m versus 12 m³/m).     

Immediate profile and planform evolution of a beach nourishment project with hurricane influences

In this study, planform adjustment began during a period of calm weather immediately after nourishment and then the passage of one strong storm caused a substantial portion of the total profile equilibration. Weekly beach profiles, shoreline surveys, and nearshore wave measurements were conducted before, during, and immediately after construction of the 1100-m long Upham Beach nourishment project on the low-energy, west coast of Florida. This project was constructed in three segments: the wide north segment, the central segment, and the narrow south segment. With the exception of the relatively distant passage of Hurricane Charley, calm weather prevailed for 45 days following completion of the south and central segments. Construction of the wide north segment was completed on August 27, 2004. Substantial planform diffusion occurred prior to construction completion via formation of a 300-m long spit extending from the wide north segment. The shoreline orientation was changed abruptly due to this diffusion spit formation, as opposed to the gradual adjustment predicted by most long-term models. Planform adjustment was initiated prior to profile equilibration, and it did not require high-energy conditions. A simple vector sum model for determining the orientation of a potential diffusion spit was developed. This study recommends designing end transitions at the predicted diffusion spit orientation to avoid post-nourishment spit formation during future projects.     

Physical modeling of long-range infrasonic propagation in the atmosphere

The results of experiments on the physical modeling of long-range infrasonic propagation in the atmosphere are given. Such modeling is based on the possible coincidence between the forms of the vertical profiles of the effective sound speed stratification in the atmospheric boundary layer (between 0 and 600 m for the case under consideration) and in the atmosphere as a whole (from the land surface up to thermospheric heights (about 150 km)). The source of acoustic pulses was an oscillator of detonation type. Owing to the detonation of a gas mixture of air (or oxygen) and propane, this generator was capable of producing short, powerful (the maximum acoustic pressure was on the order of 30 to 60 Pa at a distance of 50 to 100 m from the oscillator), and sufficiently stable acoustic pulses with a spectral maximum at frequencies of 40 to 60 Hz and a pulsing period of 20 to 30 s. The sites of acoustic-signal recording were located at different distances (up to 6.5 km) from the source and in different azimuthal directions. The temperature and wind stratifications were monitored in real time during the experiments with an acoustic locator—a sodar—and a temperature profiler. The data on the physical modeling of long-range sound propagation in the atmosphere are analyzed to verify the physical and mathematical models of predicting acoustic fields in the inhomogeneous moving atmosphere on the basis of the parabolic equation and the method of normal waves. A satisfactory agreement between calculated and experimental data is obtained. One more task was to compare the theoretical relations between variations in the azimuths and angles of tilting of sound rays about the horizon and the parameters of anisotropic turbulence in the lower troposphere and stratosphere with the experimental data. A theoretical interpretation of the experimental results is proposed on the basis of the theory of anisotropic turbulence in the atmosphere. The theoretical and experimental results are compared, and a satisfactory agreement between these results is noted.     

近岸波、流作用下结构物附近海岸演变的数值模拟

针对与砂质海岸在波浪作用下的演变有关的波浪、近岸流及输沙问题进行了系统的研究,并对结构物附近海岸演变进行了数值模拟。考虑了波浪折射-绕射及波浪破碎的综合作用,在近岸流场的模拟中用沿水深积分形成的K方程模型确定涡粘系数。计算岸滩地形变化时,综合波浪、近岸流作用的底沙和悬沙输沙率,并考虑波浪对泥沙作用的影响。模型对防波堤和近岸沉船附近地形变化进行了模拟,效果良好。