Simulation and prediction of swash oscillations on a steep beach

This paper presents numerical simulations and analytical predictions of key aspects of swash oscillations on a steep beach. Simulations of the shoreline displacement based on bore run-up theory are found to give excellent agreement with recent experimental data for regular waves, wave groups and random waves. The theory is used to derive parameters that predict the onset of swash saturation and the spectral characteristics of the saturated shoreline motion. These parameters are again in good agreement with the measured laboratory data and are also consistent with previous experimental data. Simulation of irregular wave run-up using a series of overlapping monochromatic swash events is found to reproduce typical features of swash oscillations and can accurately describe both the low and high frequency spectral characteristics of the swash zone. In particular, the low frequency components of the run-up can be modelled directly using a sequence of incident short wave bores, with no direct long wave input to the numerical simulations. This suggests that wave groupiness must be accounted for when modelling shoreline oscillations.     

Beach morphology and shoreline evolution: Monitoring and modelling medium-term responses (Portuguese NW coast study site)

Numerical models for shoreline evolution have been used for coastal management planning for several decades. The model calibration is a start point to project shoreline scenarios and in this aim the use of data acquired within the scope of monitoring programmes provides the opportunity to assess the models' capabilities under real condition. This work applies calibration data (retrieved from field surveys) to numerical models to predict medium-term shoreline evolution using, as a case study, a beach stretch named AC, about 3.5 km long and located downdrift of a groin on the northwest Portuguese coast. A smaller stretch AB (2.4 km long), included in the total one, which exhibits a pronounced erosive tendency usually better reproduced in shoreline evolution models, was also analysed. Based on topographic surveys, associated wave climate conditions registered between 2003 and 2008 and typical wave conditions registered over a longer wave climate time period, this work compares the calibration of two different shoreline evolution models, Long-term Configuration (LTC) and GENESIS for this period. Then, considering the 2003 topographic conditions for the models' calibration, the results of both models are discussed with respect to simulation scenarios after 10, 15 and 20 years of evolution. The 10-year evolution projections of the models are also compared to the results of a survey performed in February 2012. For the wave data calibration period (2003–2008), the average shoreline retreat of the analysed coastal stretch was reproduced with small differences (around 1% and 10% for LTC and 15% and 14% for GENESIS, considering stretches AB or AC, respectively), though local differences along the AB coastal stretch represent root mean square errors reaching up to 52% and 88% for GENESIS and LTC, respectively, and were above 118% for both models along the AC coastal stretch.     

Transformation and Breaking of Irregular Waves on Very Gentle Slopes

—Based on theoretical analysis.numerical calculation.and experimental study,this paper dis-cusses breaker indices of irregular waves.transformation of wave spectrum.characteristics and computa-tion of breaking waves.as well as the critical beach slope under which waves will not break.Computed re-sults are in good agreement with laboratory physical model test data and ocean wave field measurements.     

大尺度圆柱墩群周围的波流场的数值模拟

本文对波流共同作用下大尺度圆柱墩群周围的波流场进行了数值研究。利用波浪弥散关系的迭代计算求得波向与流向的夹角以及波浪的相对频率。流场通过求解浅水环流方程得到,波浪场通过求解含流的缓坡方程得到,通过二者的迭代计算得到大尺度圆柱墩群周围的波流场的耦合解。用有限元法建立了数值模型,并将本文的计算数据与试验数据以及其他学者计算数据进行了比较,结果较为合理。     

Boundary integral equation solutions for solitary wave generation, propagation and run-up

The boundary integral equation method (BIEM) is developed as a tool for studying two-dimensional, nonlinear water wave problems, including the phenomena of wave generation, propagation and run-up. The wave motions are described by a potential flow theory. Nonlinear free-surface boundary conditions are incorporated in the numerical formulation. Examples are given for either a solitary wave or two successive solitary waves. Special treatment is developed to trace the run-up and run-down along a shoreline. The accuracy of the present scheme is verified by comparing numerical results with experimental data of maximum run-up.     

Numerical Modeling of the Undertow Structure and Sandbar Migration in the Surfzone

A process-based 3D numerical model for surfzone hydrodynamics and beach evolution was established. Comparisons between the experimental data and model results proved that the model could effectively describe the hydrodynamics, sediment transport feature and sandbar migration process in the surfzone with satisfactory precision. A series of numerical simulations on the wave breaking and shoaling up to a barred beach were carried out based on the model system. Analyzed from the model results, the wave-induced current system in the surfzone consists of two major processes, which are the phase-averaged undertow caused by wave breaking and the net drift caused by both of the nonlinear wave motion and surface roller effect. When storm waves come to the barred beach, the strong offshore undertow along the beach suppresses the onshore net drift, making the initial sandbar migrate to the seaside. Under the condition of calm wave environment, both the undertow and net drift flow to the shoreline at the offshore side of the sandbar, and then push the initial sandbar to the shoreline. The consideration of surface roller has significant impact on the modeling results of the sandbar migration. As the roller transfer rate increases, the sandbar moves onshore especially under the storm wave condition.     

Reflection of Short Waves

—According to the energy equation,the relation between reflection and energy losses for shortwaves from mild beaches is established and analysed.A reflection coefficient varying with position and en-ergy losses is proposed.Different reflection tests are conducted to check the theoretical analysis.A modi-fied method to estimate the reflection coefficient at varied water depths is suggested based on the linearwave theory.The study indicates that the reflection coefficient from mild beaches has a changing trend forshort waves approaching shoreline.     

Beach response to a fixed sand bypassing system

Indian River Inlet is located at roughly the mid-point of the Atlantic coast of Delaware and connects the ocean to two Delaware inland bays. Jetties constructed in 1940 have maintained the inlet for navigation purposes but have also acted as a barrier to net northerly alongshore sediment transport causing downdrift erosion. A mobile, land-based bypassing system was initiated in 1990 in an effort to counteract this erosion. Beach profile data from 1985 (pre-bypassing) until 2008 are used to investigate the effect of the sand bypassing system on beaches adjacent to the inlet. The downdrift beach experienced horizontal shoreline erosion between 10 and 60 m during the pre-bypassing period but accreted 10–20 m during the bypassing period. The mean shoreline location on the updrift beach during bypassing is 10–20 m landward (erosion) of its position during the pre-bypassing period. Empirical orthogonal function (EOF) amplitudes from analyses performed on mean-removed elevation surfaces during the periods of highest bypassed volume (average of 83% of design rate) showed that the influence of the bypassing system on the downdrift beach extends to about 1500 m of the inlet. An EOF analysis showed that different morphologic responses were evident following the initiation of bypass operations. Temporal variations of shoreline and beach morphology were correlated to the temporal variations in bypassing rates on the downdrift beach only. The downdrift beach response was greatest near the inlet for larger bypassing volumes. Correlation in these instances occurred with a roughly 1-year time lag suggesting that the beach quickly redistributes the bypassed sand. EOF amplitude and shoreline response are weakly correlated to bypassed volumes when the system bypassed smaller volumes (average of 56% of design rate) of sand suggesting that there is a minimum bypassing rate, regardless of yearly variability, below which the effect on the downdrift beach is obscured.     

Nonlinear Model of Mean Free Surface of Waves

-A nonlinear model of mean free surface of waves or wave set-up is presented.The model isbased on that of Roelvink(1993),but the numerical techniques used in the solution are based on theWeighted-Average Flux(WAF)method(Watson et al,1992),with Time-Operator-Splitting(TOS)usedfor the treatment of the source terms.This method allows a small number of computational points to beused,and is particularly efficient in modeling wave set-up.The short wave(or primary wave)energy equa-tion is solved by use of a more traditional Lax-Wendroff technique.A nonlinear wave theory(James,1974)is introduced.The model described in this paper is found to be satisfactory in most respects whencompared with the measurements conducted by Stive(1983)except in modeling the mean free surface veryclose to the mean shoreline.     

A numerical study of swash flows generated by bores

The dynamic processes of bore propagation over a uniform slope are studied numerically using a 2-D Reynolds Averaged Navier–Stokes (RANS) solver, coupled to a non-linear k − ε turbulence closure and a volume of fluid (VOF) method. The dam-break mechanism is used to generate bores in a constant depth region. Present numerical results for the ensemble-averaged flow field are compared with existing experimental data as well as theoretical and numerical results based on non-linear shallow water (NSW) equations. Reasonable agreement between the present numerical solutions and experimental data is observed. Using the numerical results, small-scale bore behaviors and flow features, such as the bore collapse process near the still-water shoreline, the ‘mini-collapse’ during the runup phase and the ‘back-wash bore’ in the down-rush phase, are described. In the case of a strong bore, the evolution of the averaged turbulence kinetic energy (TKE) over the swash zone consists of two phases: in the region near the still-water shoreline, the production and the dissipation of TKE are roughly in balance; in the region farther landwards of the still-water shoreline, the TKE decay rate is very close to that of homogeneous grid turbulence. On the other hand, in the case of a weak bore, the bore collapse generated turbulence is confined near the bottom boundary layer and the TKE decays at a much slower rate.     

Numerical Simulation of Waves Generated by Seafloor Movements

Waves generated by vertical seafloor movements are simulated by use of a fully nonlinear two-dimensional numerical wave tank. In the souree region, the seafloor lifts to a designated height by a generation function. The numerical tests show that the linear theory is only valid for estimating the wave behaviors induced by the seafloor movements with a small amplitude, and the fully nonlinear numerical model should be adopted in the simulation of the wave generation by the large amplitude seafloor movements. Without the background surface waves, many numerical tests on the stable maximum elevations η0^max are carried out by beth the linear theory and the fully nonlinear model. The results of two models are compared and analyzed. For the fully nonlinear model, the influences of the amplitudes and the horizontal lengths on η^max are stronger than that of the characteristic duration times. Furthermore, results reveal that there are significant differences be- tween the linear theory and the fully nonlinear model. When the influences of the background surface waves are considered, the corresponding numerical analyses reveal that with the fully nonlinear model the η0^max near-linearly varies with the wave amplitudes of the surface waves, and the η0^max has significant dependences on the wave lengths and the wave phases of the surface waves. In addition, the differences between the linear theory and the fully nonlinear model are still obvious, and these differences are significantly affected by the wave parameters of the background surface waves, such as the wave amplitude, the wave length and the wave phase.     

Wave setup and setdown generated by obliquely incident waves

An analytical theory is developed for the wave setup and setdown induced by obliquely incident waves on an impermeable swell-built beach profile. The wave setup and setdown are found to decrease as wave obliquity increases. The incorporation of wave obliquity in wave setup and setdown formulation offers the physical reality in engineering applications. The general solutions presented in this paper yield the limiting case of normal wave incidence and the result is consistent with the classical theories published. The present theory is primarily applicable to the spilling and plunging breaker across the surf zone, within which wave amplitude is assumed to be linearly related to the local water depth. Experiments were conducted in a large-scale wave basin to compare with theoretical results and especially to investigate the applicability of this assumption to the case of obliquely incident waves. The dimensionless setup versus the distance offshore within the surf zone is found to depend on wave breaking angle and the shape of the beach profile; and it has a non-zero value at the original shoreline position. This implies that the original shoreline will advance landwards, and that the extent of this movement can be related to wave angle at breaking and the beach profile under consideration. The results of the present theory are in good agreement with experimental data and field measurements available.     

Numerical Study of Two-Dimensional Focusing Waves

Two-dimensional focusing waves are generated and investigated by numerical method. The numerical model is developed by introducing the wave maker boundary on the high-order spectral （HOS） method proposed by Dommermuth and Yue in 1987 and verified by theoretical and experimental data. Some cases of focusing waves considering different parameters such as assumed focusing amplitudes, frequency bandwidth, central frequency and frequency spectrum are generated. Characteristics of the focusing wave including surface elevations, the maximum crest, shift of focusing points and frequency spectra are discussed. The results show that the focusing wave characteristics are strongly affected by focusing amplitudes, frequency bandwidth, central frequency and frequency spectrum.     

A Model for Nonlinear Irregular Waves in Coastal Area

Based on the refraction-diffraction theory of irregular waves in the waters of slowly-varying cur-rents and depths,and the generation dissipation theory of wind wave,a model for nonlinear irregular wavesin coastal area is developed.In light of the specific conditions of coastal wave character and engineering ap-plication,a practical mathematical model for the nonlinear irregular waves is presented.with directional spec-trum in coastal area.Coast effect,refraction,whitecapping.bottom friction.current,wind and nonlinearaction are considered in this model.The numerical methods and schemes for wave refraction ray,energy con-servation of propagation,energy balance of the generation and dissipation of wind waves have been studied.Finally,the model is used for the directional wave spectrum computation in the Daya Bay.Compared withthe measured data with 956 wave bouys in the Daya Bay,the model results are in good agreement with themeasured results.     

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.     

Numerical Simulation of Hydrodynamic Behaviors of Gravity Cage in Waves

This paper aims at investigation of the dynamic properties of gravity cage exposed to waves by use of a numerical model. The numerical model is developed, based on lumped mass method to set up the equations of motion of the whole cage; meanwhile the solutions of equations are solved by the Runge-Kutta-Verner fifth-order and sixth-order method. Physical model tests have been carried out to examine the validity of the numerical model. The results by the numerical simulation agree well with the experimental data.     

On low-frequency waves in the surf and swash

Low-frequency waves in the surf and swash zones on various beach slopes are discussed using numerical simulations. Simulated surface elevations of both primary waves and low-frequency waves across the surf zone were first compared with experimental data and good agreement found. Low-frequency wave characteristics are then discussed in terms of their physical nature and their relationship to the primary wave field on a series of sea bottom slopes. Unlike primary waves, low-frequency wave energy increases towards the shoreline. Low-frequency waves in the surf and swash are a function of incident waves and the sea bottom slope and hence the saturation level of the surf zone. Wave energy on a gently sloping beach is dominated by low-frequency waves while primary waves play a significant role on a steep beach. Low-frequency wave radiation from the surf zone on a given beach depends on primary wave frequency and beach slope. However, a very poor correlation was found between surf similarity parameter and low-frequency wave radiation.     

边缘波研究进展

由于折射作用,在波浪近岸传播过程中会出现一种特殊的、沿着岸线传播的波浪,这种波浪被称为边缘波。边缘波平行于岸线传播,其振幅在岸线处最大,在远离岸线的方向,其振幅呈指数型减小,它们的能量基本被限制在离海岸一波长的距离之内,因此边缘波对近岸地区工程、地貌等有着重要影响。本文对边缘波的研究历史、研究进展进行了阐述,主要介绍了以下几个方面：（1）基于不同控制方程、不同地形上的边缘波理论;（2）实际观测到的边缘波特性;（3）物理模型试验中边缘波的造波方式以及观测到的边缘波特性;（4）数值模拟方法在边缘波研究中的应用。最后,展望了边缘波在未来的研究趋势。     

Analysis of Interaction of Plane Waves with Multiple Circular Cylinders

The interaction of water waves with multiple circular cylinders is analysed briefly in this paper.The formula obtained by Linton and Evans is improved to introduce a relation of phase between cylinders.The condition for the existence of the solution has been proved.The numerical results are compared with ana-lytic solutions(Linton and Evans),numerical solutions and experimental data(Isaacson),and good agree-ment has been found.