Study of irregular wave run-up over fringing reefs based on a shock-capturing Boussinesq model

This paper presents the results of a parametric study of irregular wave run-up over fringing reefs using the shock-capturing Boussinesq wave model Funwave-TVD to better understand the role of fringing reefs in the mitigation of wave-driven flooding. Laboratory experiments were newly performed with a typical fringing reef profile and typical hydrodynamic conditions to validate the model. Experimental data shows irregular wave run-ups are dominated by the low-frequency motions and confirms the run-up resonant phenomenon over the back-reef slope, which has been revealed in previous numerical studies. It is demonstrated that irregular wave evolution and run-up over fringing reefs are reasonably reproduced by the present model with a proper grid size. However, the infragravity run-up height and highest 2% run-up height over the back-reef slope are under-predicted due to the underestimation of the infragravity wave height over the reef flat. The validated model was then utilized to model irregular wave transformations and run-ups under different conditions. Through a series of numerical experiments, the effects of key hydrodynamic and reef geometry parameters, including the reef flat width, water depth over the reef flat, fore-reef slope angle and back-reef slope angle, on the irregular wave run-up were investigated. Variations of spectral components of irregular wave run-ups were examined to better understand the physical process underlying the effect of each parameter.     

片状分布植被对孤立波爬高影响的数值模拟研究

近岸植被对波浪爬坡具有一定的衰减作用。在自然界中,由于植被的死亡、再生或人为破坏等原因,近岸植被通常呈片状分布,且其内部分布也是不均匀的。本文以完全非线性Boussinesq方程为基础,引入植被作用项,建立了模拟近岸植被区波浪传播的数值模型,验证了模型可靠性,进而采用该模型模拟分析了片状分布植被对孤立波爬高的影响。数值模拟结果表明,片状分布植被能有效减小孤立波爬高;对于均匀分布的片状植被,高密度片状植被对孤立波爬高的消减效果优于低密度片状植被;对于相同密度、不同分布形式的片状植被,均匀分布的片状植被对孤立波的消减效果优于不均匀分布的片状植被;对于不均匀分布的片状植被,前密后疏的片状植被对孤立波的消减效果优于前疏后密的片状植被。     

Three-dimensional numerical simulation of solitary wave run-up using the IB method

Although the finite difference method is computationally efficient, it is acknowledged to be inferior when dealing with flow-over on structures with a complex geometry because of its rectilinear grid system. Therefore, we developed a numerical procedure that can cope with flow over structures with complex shapes while, at the same time, retaining the simplicity and efficiency of a rectilinear grid system. We used the immersed boundary method, which involves application of immersed boundary forces at solid boundaries rather than conventional boundary conditions, to investigate wave interactions with coastal structures in a three-dimensional numerical wave tank by solving the Navier–Stokes equations for two-phase flows. We simulated the run-up of a solitary wave around a circular island. Maximum run-up heights were computed around the island and compared with available laboratory measurements and previous numerical results. The three-dimensional features of the run-up process were analyzed in detail and compared with those of depth-integrated equations models.     

Numerical study of vegetation damping effects on solitary wave run-up using the nonlinear shallow water equations

Vegetation damping effects on propagating water waves have been investigated by many researchers. This paper investigates the effects of damping due to vegetation on solitary water wave run-up via numerical simulation. The numerical model is based on an implementation of Morison's formulation for vegetation induced inertia and drag stresses in the nonlinear shallow water equations. The numerical model is solved via a finite volume method on a Cartesian cut cell mesh. The accuracy of the numerical scheme and the effects of the vegetation terms in the present model are validated by comparison with experiment results. The model is then applied to simulate a solitary wave propagating on a plane slope with vegetation. The sensitivity of solitary wave run-up to plant height, diameter and stem density is investigated by comparison of the numerical results for different patterns of vegetation. The numerical results show that vegetation can effectively reduce solitary wave propagation velocity and that solitary wave run-up is decreased with increase of plant height in water and also diameter and stem density.     

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.     

Third-order interactions,wave run-up and hydrodynamic loading on a vertical plate in an infinite wave field

The nonlinear wave interaction problem with a vertical plate of finite length is considered. Reference is made to previous experimental and numerical studies reported in Molin et al. [1–3], where it was shown that the observed run-up phenomena are due to third-order (or tertiary) interactions between the incoming and reflected wave systems. In this paper a new numerical model is proposed where the presence of lateral walls is relaxed. Run-up computations, with and without confinement effects, are compared. It is found that, in the model tests reported in Molin et al. [3], the effect of confinement was relatively small. The time-varying and steady wave loads which are exerted on the plate are also investigated. The dedicated numerical predictions show that as the wave steepness is increased the response amplitude operators of the time-varying loads first increase, reach a maximum and then decrease dramatically, due to phasing effects.     

Numerical investigation on the dynamics of a vertical wall defenced by an offshore breakwater

The numerical and experimental investigations on the performance of an offshore-submerged breakwater in reducing the wave forces and wave run-up on vertical wall are presented. A two-dimensional finite-element model is employed to study the hydrodynamic performance of the submerged breakwater under the action of regular and random waves. The numerical prediction has been supported with experimental measurements. The wave forces and wave run-up on the vertical wall were measured for different breakwater configurations. The applicability of linear theoretical model in the prediction of wave forces on the wall by a submerged breakwater has been discussed.     

Comparative Experimental and Numerical Study of Wave Loads on A Monopile Structure Using Different Turbulence Models

This study numerically and experimentally investigates the effects of wave loads on a monopile-type offshore wind turbine placed on a 1: 25 slope at different water depths as well as the effect of choosing different turbulence models on the efficiency of the numerical model. The numerical model adopts a two-phase flow by solving Unsteady Reynolds-Averaged Navier-Stokes(URANS) equations using the Volume Of Fluid(VOF) method and three different turbulence models. Typical environmental conditions from the East China Sea are studied. The wave run-up and the wave loads applied on the monopile are investigated and compared with relevant experimental data as well as with mathematical predictions based on relevant theories. The numerical model is well validated against the experimental data at model scale. The use of different turbulence models results in different predictions on the wave height but less differences on the wave period. The baseline turbulence model and Shear-Stress Transport(SST) turbulence model exhibit better performance on the prediction of hydrodynamic load, at a model-scale water depth of 0.42 m, while the laminar model provides better results for large water depths. The SST turbulence model performs better in predicting wave run-up for water depth 0.42 m, while the laminar model and standard model perform better at water depth 0.52 m and 0.62 m, respectively.     

Wave Run-up on A Vertical Seawall Protected by An Offshore Submerged Barrier

Submerged barriers are constructed in coastal zones for shoreline or harbor protection or to prevent the beach erosion. In the present study, the wave run-up on a vertical seawall protected by a submerged barrier is analyzed. The physical configurations include a rigid barrier and a long channel of finite depth. For linear water waves, by matching the velocity along the barrier and along the gap, the systems of linear equations about the velocity potentials are obtained. The wave run-up is further analyzed for various settings of barrier height and distance between the barrier and the wall, i.e. the chamber length. For nonlinear waves and random sea waves, a numerical model is extended to investigate the effect parameters of the barrier on the wave run-up against the seawall. Not only the numerical simulations, but also the analytical results illustrate that the wave run-up on the seawall depends very much on the distance between the barrier and the vertical seawall.     

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.     

Forecast of wave run-up on coastal structure using offshore wave forecast data

In this paper, first we introduce the wave run-up scale which describes the degree of wave run-up based on observed sea conditions near and on a coastal structure. Then, we introduce a simple method which can be used for daily forecast of wave run-up on a coastal structure. The method derives a multiple linear regression equation between wave run-up scale and offshore wind and wave parameters using long-term photographical observation of wave run-up and offshore wave forecasting model results. The derived regression equation then can be used for forecasting the run-up scale using the offshore wave forecasting model results. To test the implementation of the method, wave run-up scales were observed at four breakwaters in the East Coast of Korea for 9 consecutive months in 2008. The data for the first 6 months were used to derive multiple linear regression equations, which were then validated using the run-up scale data for the remaining 3 months and the corresponding offshore wave forecasting model results. A comparison with an engineering formula for wave run-up is also made. It is found that this method can be used for daily forecast and warning of wave run-up on a coastal structure with reasonable accuracy.     

Nonlinear wave interaction with a vertical circular cylinder. Part II: Wave run-up

Theoretical results for second-order wave run-up around a large diameter vertical circular cylinder are compared to results of 22 laboratory experiments conducted in regular nonlinear waves. In general, the second-order theory explains a significant portion of the nonlinear wave run-up distribution measured at all angles around the cylinder. At the front of the cylinder, for example, measured maximum run-up exceeds linear theory by 44% on average but exceeds the nonlinear theory by only 11% on average. In some cases, both measured run-up and the second-order theory exceed the linear prediction by more than 50%. Similar results are found at the rear of the cylinder where the second-order theory predicts a large increase in wave amplitude for cases where the linear diffraction theory predicts little or no increase. Overall, the nonlinear diffraction theory is found to be valid for the same relative depth and wave steepness conditions applicable to Stokes second-order plane-wave theory. In the last section of the paper, design curves are presented for estimating the maximum second-order wave run-up for a wide range of conditions in terms of the relative depth, relative cylinder size, and wave steepness.     

Numerical study on cnoidal wave run-up around a vertical circular cylinder

A finite element model of Boussinesq-type equations was set up, and a direct numerical method is proposed so that the full reflection boundary condition is exactly satisfied at a curved wall surface. The accuracy of the model was verified in tests. The present model was used to further examine cnoidal wave propagation and run-up around the cylinder. The results showed that the Ursell number is a nonlinear parameter that indicates the normalized profile of cnoidal waves and has a significant effect on the wave run-up. Cnoidal waves with the same Ursell number have the same normalized profile, but a difference in the relative wave height can still cause differences in the wave run-up between these waves. The maximum dimensionless run-up was predicted under various conditions. Cnoidal waves hold entirely distinct properties from Stokes waves under the influence of the water depth, and the nonlinearity of cnoidal waves enhances rather than weakens with increasing wavelength. Thus, the variations in the maximum run-up with the wavelength for cnoidal waves are completely different from those for Stokes waves, and there are even significant differences in the variation between different cnoidal waves.     

Numerical Study of the Impact of Climate Change on Irregular Wave Run-up Over Reef-Fringed Coasts

Wave hydrodynamics over fringing reefs is largely controlled by the reef surface roughness and hydrodynamic forcing. It is believed that climate change will result in a net increase in the water depth over the reef flat, a degrading of the surface roughness of coral reefs and changes in extreme incident wave heights. For an accurate assessment of how climate change affects the safety of reef-fringed coasts, a numerical study of the impact of climate change on irregular wave run-up over reef-fringed coasts was carried out based on a Boussinesq wave model,FUNWAVE-TVD. Validated with experimental data, the present model shows reasonable prediction of irregular wave evolution and run-up height over fringing reefs. Numerical experiments were then implemented based on the anticipated effects of climate change and carried out to investigate the effects of sea level rise, degrading of the reef surface roughness and increase of extreme incident wave height on the irregular wave run-up height over the backreef beach respectively. Variations of run-up components(i.e., spectral characteristics of run-up and mean water level) were examined specifically and discussed to better understand the influencing mechanism of each climate change-related effect on the run-up.     

Extreme wave run-up and pressure on a vertical seawall

The performance of coastal vertical seawalls in extreme weather events is studied numerically, aiming to provide guidance in designing and reassessing coastal structures with vertical wall. The extreme wave run-up and the pressure on the vertical seawall are investigated extensively. A time-domain higher-order boundary element method (HOBEM) is coupled with a mixed Eulerian-Lagrangian technique as a time marching technique. Focused wave groups are generated by a piston wave-maker in the numerical wave tank using a wave focusing technique for accurately reproducing extreme sea states. An acceleration-potential scheme is used to calculate the transient wave loads. Comparisons with experimental data show that the extended numerical model is able to accurately predict extreme wave run-ups and pressures on a vertical seawall. The effects of the wave spectrum bandwidth, the wall position and the wave nonlinearity on the wave run-up and the maximum wave load on the vertical seawall are investigated by doing parametric studies.     

多向不规则波浪作用下群墩结构上爬高的计算研究

波浪的方向分布对波浪的传播及其与工程结构物的作用都具有明显影响,目前现有的研究大多是基于单向波浪进行的。为了研究方向分布对群墩结构上的爬高影响,基于规则波浪与群墩作用的理论解,结合多向不规则波浪的造波方法,建立了多向不规则波浪与群墩作用的计算模型,同时进行了物理模型试验对模型的有效性进行了验证。系统地对群墩周围及表面上的波浪爬高进行了计算分析,结果表明,方向分布对波浪爬高具有较大的影响,且不同位置处的影响并不相同,在实际的工程设计中如果按照单向波浪计算,可能低估或者高估群墩周围的爬高。     

Benchmark computations of wave run-up on single cylinder and four cylinders by naoe-FOAM-SJTU solver

The benchmark simulations of wave run-up on a fixed single truncated circular cylinder and four circular cylinders are presented in this paper. Our in-house CFD solver naoe-FOAM-SJTU is adopted which is an unsteady two-phase CFD code based on the open source package OpenFOAM. The Navier-Stokes equations are employed as the governing equations, and the volume of fluid (VOF) method is applied for capturing the free surface. Monochromatic incident waves with the specified wave period and wave height are simulated and wave run-up heights around the cylinder are computed and recorded with numerical virtual wave probes. The relationship between the wave run-up heights and the incident wave parameters are analyzed. The numerical results indicate that the presented naoe-FOAM-SJTU solver can provide accurate predictions for the wave run-up on one fixed cylinder and four cylinders, which has been proved by the comparison of simulated results with experimental data.     

Wave run-up and rundown on ACB Mats under granular and geotextile filters’ condition

Articulated concrete block mattress revetment (ACB Mats) is an appropriate revetment for shore protection and breakwater. ACB Mats act as an integrated and flexible revetment against waves. There is a necessary need of investigation due to the lack of exact ACB Mat design relations in the estimation of hydrodynamic processes including wave run-up and run-down parameters. In the present study, using proper laboratory equipment, run-up and run-down processes were investigated under irregular waves and also granular and geotextile filters’ conditions. In this study, wave run-up and run-down estimation relations in ACB Mat revetment with the open area were explored for the first time. As the obtained results showed, relative maximum wave run-up and rundown are desirable for all conditions. Using a geotextile layer under ABC Mat caused a 14% increase in relative wave run-up values compared to granular filter. Further, in the run-down process, geotextile filter caused a 40% decrease in relative wave run-down values. The intensive decrease in run-down value occurred due to the outflow rate of the water from inside the filter with delay during water attack toward downward, which can be effective on structure stability significantly and should be considered in designs.     

Effect of Wave Groups on Wave Run-up

-The effect of wave group on wave run-up on a slope dike is mainly discussed in this paper. Two simulating methods of wave group and their applications in laboratory are introduced. Synthesizing the research results of wave run-up on a slope dike, the effect of wave group on wave run-up on a slope dike in coastal protection engineering is studied as the main point.     

孤立波与带窄缝双箱相互作用模拟研究

针对孤立波与带窄缝双箱的作用问题,应用时域高阶边界元方法建立了二维数值水槽。其中,自由水面满足完全非线性运动学和动力学边界条件,对瞬时自由表面流体质点采用混合欧拉-拉格朗日法追踪,采用四阶龙格库塔法对下一时刻的自由水面的速度势和波面升高进行更新。采用加速度势法求解物体湿表面的瞬时波浪力。采用推板方法生成孤立波。通过模拟孤立波在直墙上的爬高以及施加在直墙上的波浪力,并与已发表的实验和数值结果对比,验证本数值模型的准确性。通过数值模拟计算研究了窄缝宽度、方箱尺寸对波浪在箱体迎浪侧爬高,窄缝内波面升高,箱体背浪侧透射波高及箱体受波浪荷载的影响。同时研究了有一定时间间隔的双孤立波与带窄缝双箱系统作用问题。