Numerical experiments of swash oscillations on steep and gentle beaches

A weakly non-linear Boussinesq model with a slot-type shoreline boundary is used to simulate swash oscillations on beaches. Numerical simulations of swash were compared with laboratory measurements and in general good agreement found (less than 15% root-mean-square error of surface elevation except in regular waves). A series of numerical experiments on shoreline movement were then performed for a range of beach slopes and incident wave conditions. The resulting swash characteristics are then discussed in terms of their physical nature and spectral properties. On steep slopes, both individual bores and infragravity waves are equally significant in driving the swash while infragravity waves alone drive them on mild slopes. Swash excursions on any given slope are found to be highest when individual bores from a partially saturated surf zone ride on top of low-frequency waves. This is confirmed by the relationship found between swash excursion and wave groupiness in the surf zone. Swash excursions increase with increasing incident wave energy, even in fully saturated surf zones. However, a poor correlation is found between swash excursion and the surf similarity parameter due to the involvement of infragravity wave energy in the swash.     

Extreme value statistics for wave run-up on a natural beach

Statistics of wave run-up maxima have been calculated for 149 35-minutes data runs from a natural beach. During the experiment incident wave height varied from 0.4 to 4.0 m, incident wave period from 6 to 16 s, and beach face slope from 0.07 to 0.20. Four extreme statistics were calculated; the maximum run-up height during each run, the 2% exceedence level of shoreline elevation, the 2% exceedence height for individual run-up peaks, and the 2% exceedence level for swash height as determined by the zero-upcrossing method. These statistics were best parameterized when normalized by the incident significant wave height and plotted against the Iribarren number, ξ = β/(H/L₀)^1/2. The swash data (with set-up removed) showed less scatter than total run-up (with set-up included). For Iribarren number greater than 1.5 the run-up was dominated by the incident frequencies, for lower Iribarren number longer period motions dominated the swash. A reasonable value of wave steepness for a fully developed storm sea is 0.025 so that a storm Iribarren number can be estimated as 6.3 times the beach slope. Using this and an offshore design wave height, the included graphs may provide guidance in determining a design run-up height.     

Swash–groundwater dynamics in a sandy beach laboratory experiment

Experiments are carried out in a wave basin in order to study the swash–groundwater interaction. A set of wave gages and pressure sensors are used to monitor the free surface and groundwater dynamics. The study is based on the comparison of two selected cases which differ by the gravity and infragravity forcing conditions, the features of wave breaking in the surf zone, the presence of a standing wave attached to the beach face and the wave setup at the shoreline. Significant differences are observed in the response of the swash–groundwater system. The water table overheight appears to be controlled by the amount of infragravity energy available at the shore. Cyclic beach drainage processes can be observed when the water table is low. Significant time-averaged and time-resolved flows are observed into the sand, depending on the swash hydrodynamics. The presence of a gravity standing wave modulation attached to the shore is shown to affect swash and groundwater dynamics. Most of the pressure gradients observed under the swash zone are related to infiltration flows and are thus related to moderate increase of the sediment relative weight.     

A Numerical Investigation of the Reduction of Solitary Wave Runup by A Row of Vertical Slotted Piles

To improve the current understanding of the reduction of tsunami-like solitary wave runup by the pile breakwater on a sloping beach, we developed a 3D numerical wave tank based on the CFD tool OpenFOAM in this study. The Navier Stokes equations were applied to solve the two-phase incompressible flow, combined with an LES model to solve the turbulence and a VOF method to capture the free surface. The adopted model was firstly validated with existing empirical formulas for solitary wave runup on the slope without the pile structure. It is then validated using our new laboratory observations of the free surface elevation, the velocity and the pressure around a row of vertical slotted piles subjected to solitary waves, as well as the wave runup on the slope behind the piles. Subsequently, a set of numerical simulations were implemented to analyze the wave reflection, the wave transmission, and the shoreline runup with various offshore wave heights, offshore water depths, adjacent pile spaces and beach slopes. Finally, an improved empirical equation accounting for the maximum wave runup on the slope was proposed by taking the presence of the pile breakwater into consideration.     

Statistical characteristics of long waves nearshore

The random long wave runup on a beach of constant slope is studied in the framework of the rigorous solutions of the nonlinear shallow water theory. These solutions are used for calculation of the statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. It is shown that probability characteristics of the runup heights and extreme values of the shoreline velocity coincide in the linear and nonlinear theory. If the incident wave is represented by a narrow-band Gaussian process, the runup height is described by a Rayleigh distribution. The significant runup height can also be found within the linear theory of long wave shoaling and runup. Wave nonlinearity nearshore does not affect the Gaussian probability distribution of the velocity of the moving shoreline. However the vertical displacement of the moving shoreline becomes non-Gaussian due to the wave nonlinearity. Its statistical moments are calculated analytically. It is shown that the mean water level increases (setup), the skewness is always positive and kurtosis is positive for weak amplitude waves and negative for strongly nonlinear waves. The probability of the wave breaking is also calculated and conditions of validity of the analytical theory are discussed. The spectral and statistical characteristics of the moving shoreline are studied in detail. It is shown that the probability of coastal floods grows with an increase in the nonlinearity. Randomness of the wave field nearshore leads to an increase in the wave spectrum width.     

An empirical model for infragravity swash on barred beaches

Idealized computational simulations with the nearshore model XBeach were carried out for a series of barred beach configurations in order to quantify the impact of nearshore bars on infragravity swash. Results show that nearshore bar systems reduce infragravity swash energy at the shoreline. The amount of swash reduction was found to correlate with both bar depth and rip width, when a rip channel is present. In order to develop a generalized empirical model for significant infragravity swash for barred beaches, the simulations were used to extend the empirical swash model of Stockdon et al. (2006) to include bar characteristics. The developed empirical model relates significant infragravity swash to incident wave conditions and nearshore bar depth. With respect to Stockdon et al. (2006), this new model improves predictive skill by reducing root-mean-square error by 50% for the computational simulations and by 15% when applied to a range of field data.     

Probability distributions for wave runup on beaches

Measured probability distributions of shoreline elevation, swash height (shoreline excursion length) and swash maxima and minima from a wide range of beach types are compared to theoretical probability distributions. The theoretical distributions are based on assumptions that the time series are weakly steady-state, ergodic and a linear sum of random variables. Despite the swash process being inherently non-linear, results indicate that these assumptions are not overly restrictive with respect to modeling exceedence statistics in the upper tail of the probability distribution. The RMS-errors for a range of exceedence level statistics (50, 10, 5, 2, and 1%) were restricted to < 10 cm (and often < 5 cm) for all of the swash variables that were investigated. The results presented here provide the basis for further refinement of coastal inundation modeling as well as stochastic-type morphodynamic modeling of beach response to waves. Further work is required, however, to relate the parameters of swash probability distributions to wave conditions further offshore.     

Wave-induced water table fluctuations,sediment transport and beach profile change: Modeling and comparison with large-scale laboratory experiments

Coastal groundwater systems can have a considerable impact on sediment transport and foreshore evolution in the surf and swash zones. Process-based modeling of wave motion on a permeable beach taking into account wave-aquifer interactions was conducted to investigate the effects of the unconfined coastal aquifer on beach profile evolution, and wave shoaling on the water table. The simulation first dealt with wave breaking and wave runup/rundown in the surf and swash zones. Nearshore hydrodynamics and wave propagation in the cross-shore direction were simulated by solving numerically the two-dimensional Navier–Stokes equations with a k–ε turbulence closure model and the Volume-Of-Fluid technique. The hydrodynamic model was coupled to a groundwater flow model based on SEAWAT-2000, the latter describing groundwater flow in the unconfined coastal aquifer. The combined model enables the simulation of wave-induced water table fluctuations and the effects of infiltration/exfiltration on nearshore sediment transport. Numerical results of the coupled ocean/aquifer simulations were found to compare well with experimental measurements. Wave breaking and infiltration/exfiltration increase the hydraulic gradient across the beachface and enhance groundwater circulation inside the porous medium. The large hydraulic head gradient in the surf zone leads to infiltration across the beachface before the breaking point, with exfiltration taking place below the breaking point. In the swash zone, infiltration occurs at the upper part of the beach and exfiltration at the lower part. The simulations confirm that beaches with a low water table tend to be accreted while those with a high water table tend to be eroded.     

防浪建筑物影响下珊瑚礁海岸波浪传播变形试验

通过测试一系列不规则波工况研究了防浪建筑物存在下珊瑚礁海岸附近短波、低频长波和增水的变化规律,并对比了防浪建筑物的不同位置情况。分析结果表明：波浪在沿礁传播过程中,短波波高沿礁坪持续衰减,低频长波波高沿礁坪逐渐增大,波浪增水则沿礁坪基本保持不变;海岸附近短波随着防浪建筑物与礁缘距离的变大而减小,低频长波则在防浪建筑物处于礁坪后部时达到最大,防浪建筑物位置的变化对于礁坪波浪增水的影响可以忽略。通过理论分析证明了珊瑚礁地形上低频长波是由于群波破碎造成的破碎点移动而产生的;当特定波况作用于特定位置的防浪建筑物时,低频长波在礁坪上会发生一阶共振效应导致其能量在海岸附近达到最大值。     

Prediction of swash motion and run-up including the effects of swash interaction

Modifications to a model describing swash motion based on solutions to the non-linear shallow water equations were made to account for interaction between up-rush and back-wash at the still water shoreline and within the swash zone. Inputs to the model are wave heights and arrival times at the still water shoreline. The model was tested against wave groups representing idealized vessel-generated wave trains run in a small wave tank experiment. Accounting for swash interaction markedly improved results with respect to the maximum run-up length for cases with rather gentle foreshore slopes (tanβ=0.07). For the case with a steep foreshore slope (tanβ=0.20) there was very little improvement compared to model results if swash interaction was not accounted for. In addition, an equation was developed to predict the onset and degree of swash interaction including the effects of bed friction.     

Field investigation on the results of non-linear shallow water equations in the Swash Zone

For the study of the cross-shore wave-induced hydrodynamics in the swash zone, a numerical model is developed based on the one-dimensional non-linear shallow water (NSW) equations for prediction of hydrodynamic parameters in the swash zone. In order to evaluate the accuracy of the outputs of the numerical model, the model's predictions in terms of water surface elevations and cross-shore velocities, are compared to field data from full-scale experiments conducted on three sites with different beach slope; mild and steep, several bed particle sizes and under various incident wave conditions. The quantitative and qualitative comparison of the results of the numerical model and the full-scale data reveals that the model can generally predict many aspects of the flow in the surf and swash zone on both types of beach. The accuracy is adequate for application in a sediment transport study. Considering the time-history and probability distribution of water surface elevation, the model is generally more accurate on steep beaches than on the mild beach. The model can adequately simulate the dominant frequency across the beach and saturation of higher frequencies on both mild and steep beaches for various incident wave energy characteristics. With regard to the horizontal (cross-shore) velocity, the sawtooth shape of time-history and negative acceleration of water are well predicted by the model for both mild and steep beaches. Due to the uncertainties in maximum and minimum values of velocity data, clear judgement about the accuracy of the numerical model in this matter was not possible. However, the comparison of the minimum velocities (offshore direction) revealed that the application of friction factors below the range which is suggested by literature best match the data.     

Haeundae Beach in Korea: Seasonal-to-decadal wave statistics and impulsive beach responses to typhoons

Haeundae Beach represents Korean pocket beaches that are currently erosional and dominated by summertime typhoons. The decadal wave characteristics 9 km offshore of Haeundae Beach were analyzed using the WAM model that was validated through the 2007 wave observations. The wave statistics modelled for 1979–2007 indicates that the seasonal mean significant wave height (H _s ) is highest (0.6–0.7 m) in summer due to typhoons, in contrast to the lowest (around 0.5 m) autumn analog. The wave direction is also pronouncedly seasonal with the principal bearings of SSW and NE in the summer and winter seasons, respectively. The WAM results additionally show that the H _s has gradually increased over the region of Haeundae Beach since 1993. Beach profiling during June–November 2014 shows the opposite processes of the typhoon and fair-weather on beach sands. During a typhoon, foreshore sands were eroded and then accumulated as sand bars on the surf zone. In the subsequent fair-weather, the sand bars moved back to the beach resulting in the surf-zone erosion and foreshore accretion. A total of 5 cycles of these beach-wide sand movements yielded a net retreat (up to 20 m) of the shoreline associated with large foreshore erosion. However, the surf zone only slightly accumulated as a result of the sand cycles. This was attributed to the sand escape offshore from the westernmost tip of the beach. The present study may provide an important clue to understanding the erosional processes in Haeundae Beach.     

珊瑚礁礁坪宽度对波浪传播变形及增水影响的实验研究

通过在波浪水槽中进行一系列物理模型实验, 研究珊瑚礁礁坪宽度变化对珊瑚礁海岸附近波浪传播变形及礁坪上波浪增水的影响。物理实验采用理想化的珊瑚礁模型, 测试了3种礁坪宽度下的一系列不规则波工况。实验结果分析表明: 波浪沿礁传播过程中, 短波持续衰减; 低频长波波高沿礁逐渐增大, 直到海岸线附近达到最大; 随着礁坪宽度的增加, 海岸线附近的短波波高呈下降趋势, 低频长波波高的变化规律不显著; 礁坪上的波浪增水受礁坪宽度变化的影响不明显; 通过对海岸线附近的波浪进行频谱分析发现, 礁坪上低频长波的运动存在着一阶共振模式, 且共振放大效应强度受礁坪水深、入射波峰周期和礁坪宽度共同影响。     

Runup estimations on a macrotidal sandy beach

This paper presents a methodological approach to calculate runup from the analysis of morphodynamic conditions on a macrotidal sandy beach. The method is based on measurements of the elevation of high-tide deposits and on the analysis of morphological and hydrodynamic changes. A series of measurements has been carried out on the beach of Vougot (Brittany, France) under different wave conditions. This allowed to assess runup formula effectiveness on a macrotidal sandy beach and to determine the best slope parameters to estimate runup. The results suggest that on that macrotidal sandy beach the slope of the active section of the upper beach should be used instead of the entire slope of the foreshore, the latter resulting in an underestimation of runup elevations when used in predictive equations from the literature. Results obtained with widely used equations are relatively well correlated with observed values (r² = 0.63). An analysis of the relationship between observed runup elevations and various variables has enabled the establishment of a runup estimation formula with a relatively good fit to the study site (r² = 0.86).     

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.     

Numerical analysis of run-up oscillations under dissipative conditions

This paper presents laboratory and numerical simulations of run-up induced by irregular waves breaking on a gentle-sloping planar beach. The experimental data are well reproduced by a numerical model based on the nonlinear shallow water equations. By extending the incoming wave conditions considered in the laboratory experiments, the model is applied to study the run-up variability under highly energetic incoming conditions. The numerical results support the idea that, for cases characterized by the same incident peak frequency, infragravity run-up increases almost linearly with the offshore significant wave height. Moreover, the most energetic conditions lead to an upper limit of the swash similarity parameter of about 1.8.     

粤东后江湾冲流带滩面高频振动及动力作用分析

利用涌浪影响下短时段内的冲流带滩面高频高程数据和碎波带波流资料,在奇异谱分析(SSA)的基础上,对比研究了不同形态滩面的冲淤变化趋势、趋势分布形状、冲淤变化周期和冲淤变化强度,以及同一条剖面不同桩点间各因素间的变化关系;用交叉谱方法探索了每分钟滩面高频冲淤变化与碎波带长重力波间的作用关系。分析结果表明,滩角韵律地形引起的冲流分流作用促进了滩脊向滩谷的泥沙转运,冲流带滩面存在明显的长重力波频段的周期性冲淤振动,滩面冲淤振动强度由滩面下部向上部递减,碎波带长重力波对滩面高频冲淤变化起重要作用。     

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.     

人工采掘坑影响下珊瑚礁海岸波浪传播变形试验

基于礁坪上高分辨率的波浪测量,通过波浪水槽试验分析了短波、低频长波、平均水位、波形参数和非线性参数的沿礁变化规律,重点探讨礁坪中部存在人工采掘坑对上述波浪传播变形特征的影响,并与无坑的情况进行对比.研究表明:当人工采掘坑存在时,短波波高在坑前和坑内分别增大和减小,在礁后岸滩附近却无显著变化;低频长波波高在坑附近变化不大...     

Alongshore fluid motions in the swash zone of a sandy and gravel beach

Field experiments were conducted on a low-gradient, high-energy sandy beach (Truc Vert, France) and a steep, low-energy gravel beach (Slapton, UK) to examine alongshore-directed currents within the swash zone. At Truc Vert, data were collected over 33 tidal cycles with offshore significant wave heights of 1–4 m and periods of 5–12 s. At Slapton data were collected during 12 tides with wave heights of 0.3–1 m and periods of 4–9 s. The swash motion was predominantly at infragravity frequencies at Truc Vert and incident frequencies at Slapton.