Run-up of tsunamis and long waves in terms of surf-similarity

In this paper we review and re-examine the classical analytical solutions for run-up of periodic long waves on an infinitely long slope as well as on a finite slope attached to a flat bottom. Both cases provide simple expressions for the maximum run-up and the associated flow velocity in terms of the surf-similarity parameter and the amplitude to depth ratio determined at some offshore location. We use the analytical expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that extreme run-up combined with extreme flow velocities occurs for surf-similarity parameters of the order 3–6, and for typical tsunami wave periods this requires relatively mild beach slopes. Next, we compare the theoretical solutions to measured run-up of breaking and non-breaking irregular waves on steep impermeable slopes. For the non-breaking waves, the theoretical curves turn out to be superior to state-of-the-art empirical estimates. Finally, we compare the theoretical solutions with numerical results obtained with a high-order Boussinesq-type method, and generally obtain an excellent agreement.     

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.     

Wave-induced drag force on vegetation under shoaling random waves

This paper provides a practical method for estimating the drag force on a vegetation field in shoaling conditions beneath non-breaking and breaking random waves. This is achieved by using a simple drag formula based on two empirical drag coefficients given by Méndez et al. (1999) and Méndez and Losada (2004), respectively, in conjunction with a stochastic approach. Here the waves are assumed to be a stationary narrow-band random process and propagating in shallow waters. The effects of shoaling and breaking waves are included by adopting the Méndez et al. (2004) wave height distribution. Results are presented and discussed for different slopes, and an example of calculation is also provided to demonstrate the application of the method.     

Effects of Wave Breaking on Freak Wave Generation in Random Wave Train

The experimental studies of the wave breaking effects on freak wave generation are presented within a finite-depth random wave train in a laboratory wave tank. The main attention is paid to the abnormal index,AI=Hmax/Hs,being used to characterize the freak waves,and the changes of the coefficient due to wave breaking. The results show that the occurrence probability of freak wave events in non-breaking waves is much larger than that in breaking waves and such occurrence in deep water is larger than that in ...     

Forces on a single pile caisson in breaking waves and current

The effect of breaking and steep non-breaking waves on a vertical pile such as found in minimal caisson structures in the Gulf of Mexico shallow water environment was studied in a wave tank testing. The waves generated were both regular and irregular. The irregular waves were of Bretschneider type. In some tests current was combined in the direction of waves. Specially steep waves in the recorded wave profile were chosen for the analysis of wave forces. It was observed that the forces on the caisson at the wave frequency due to breaking waves were no higher in general than those in nonbreaking steep waves. The drag coefficients in waves alone were much higher than those in a combined wave-current field. The wave-current drag coefficients approached those found in the steady current alone.     

海啸波传播的线性和非线性特征及近海陆架效应影响的数值研究

浅水方程被广泛应用于海啸预警报业务及研究,而针对线性浅水方程与非线性浅水方程在不同海区水深地形条件下的适用范围、计算效率问题是海啸研究人员急需了解的。本文应用基于浅水方程的海啸数值预报模型就海啸波在南海、东海传播的线性、非线性特征以及陆架对其传播之影响进行了数值分析研究。海啸波在深水的传播表征为强线性特征,此时线性系统对海啸波幅的模拟计算具有较高的精度和效率,而弱的非线性特征及弱的色散特征对海啸波幅的预报影响甚微,可以忽略不计。海啸波传播至浅水大陆架后受海底坡度变化、海底粗糙度等因素影响,波动的非线性效应迅速传播、积累,与线性浅水方程计算的海啸波相比表现出较大差异,主要表现为:在南海区,水深小于100m时,海啸波首波以后的系列波动非线性特征比较明显,两者波幅差别较大,但首波波幅的区别不大,因此对于该区域在不考虑海啸爬高的情况下,应用线性系统计算得到的海啸波幅也可满足海啸预警报的要求;在东海区由于陆架影响,海啸波非线性特征明显增强,水深小于100m区域,首波及其后系列波波幅均差异较大,故在该区域必须考虑海啸波非线性作用。本文就底摩擦项对海啸波首波波幅的影响进行了数值对比分析,结果表明:底摩擦作用对海啸波首波波幅影响仅作用于小于100m水深。最后,该文通过敏感性试验,初步分析了陆架宽度及陆架边缘深度对海啸波波幅的影响,得出海啸波经陆架传播共振、变形后,海啸波幅的放大或减小与陆架的宽度及陆架边缘水深有关。     

破碎波群的显著特征指标

群发性是风浪破碎的显著特征,最近的研究表明风浪破碎研究应该基于波群而不是单个波。本文探讨破碎波群区别于非破碎波群的显著特征指标。依据一系列风浪破碎实验数据,采用多种判据与实验现场目测的破碎标记信号相结合的原则划分破碎波群与非破碎波群,考查波群特征量、单个波几何特征量、局地破碎判据指标、波包络几何特征量以及波群能量结构特征量等5大类28个指标在破碎波群与非破碎波群上的分布差异。结果表明:波陡、峰前波陡、瞬时波面斜率、运动学判据指标和动力学判据指标等在破碎非破碎波群上的分布几乎没有交叠;后两者尤为理想,分布明显分离,是破碎波群区别于非破碎波群的显著指标;而其它各指标在破碎波群非破碎波群上的分布都有不同程度的交叠,不能单独依据它们区分破碎波群与非破碎波群。     

Scour below marine pipelines in shoaling conditions for random waves

This paper provides an approach by which the scour depth below pipelines in shoaling conditions beneath non-breaking and breaking random waves can be derived. Here the scour depth formula in shoaling conditions for regular non-breaking and breaking waves with normal incidence to the pipeline presented by Cevik and Yüksel [Cevik, E. and Yüksel, Y., (1999). Scour under submarine pipelines in waves in shoaling conditions. ASCE J. Waterw., Port, Coast. Ocean Eng., 125 (1), 9–19.] combined with the wave height distribution including shoaling and breaking waves presented by Mendez et al. [Mendez, F.J., Losada, I.J. and Medina, R., (2004). Transformation model of wave height distribution on planar beaches. Coast. Eng. 50 (3), 97–115.] are used. Moreover, the approach is based on describing the wave motion as a stationary Gaussian narrow-band random process. An example of calculation is also presented.     

Implementation and modification of a three-dimensional radiation stress formulation for surf zone and rip-current applications

Regional Ocean Modeling System (ROMS v 3.0), a three-dimensional numerical ocean model, was previously enhanced for shallow water applications by including wave-induced radiation stress forcing provided through coupling to wave propagation models (SWAN, REF/DIF). This enhancement made it suitable for surf zone applications as demonstrated using examples of obliquely incident waves on a planar beach and rip current formation in longshore bar trough morphology (Haas and Warner, 2009). In this contribution, we present an update to the coupled model which implements a wave roller model and also a modified method of the radiation stress term based on Mellor (2008, 2011a,b,in press) that includes a vertical distribution which better simulates non-conservative (i.e., wave breaking) processes and appears to be more appropriate for sigma coordinates in very shallow waters where wave breaking conditions dominate. The improvements of the modified model are shown through simulations of several cases that include: (a) obliquely incident spectral waves on a planar beach; (b) obliquely incident spectral waves on a natural barred beach (DUCK'94 experiment); (c) alongshore variable offshore wave forcing on a planar beach; (d) alongshore varying bathymetry with constant offshore wave forcing; and (e) nearshore barred morphology with rip-channels. Quantitative and qualitative comparisons to previous analytical, numerical, laboratory studies and field measurements show that the modified model replicates surf zone recirculation patterns (onshore drift at the surface and undertow at the bottom) more accurately than previous formulations based on radiation stress (Haas and Warner, 2009). The results of the model and test cases are further explored for identifying the forces operating in rip current development and the potential implication for sediment transport and rip channel development. Also, model analysis showed that rip current strength is higher when waves approach at angles of 5° to 10° in comparison to normally incident waves.     

破碎波冲击直立桩柱的大比尺试验研究

波浪破碎是海洋中最常见的现象之一,其能够对海洋中的结构物产生巨大的波浪力作用。本文在大比尺波浪水槽通过聚焦波的方法生成了极端波浪和不同破碎阶段的破碎波浪,并对其冲击桩柱过程中的点压力进行了测量,进而采用连续小波变换的方法,对桩柱上点压力的分布及大小进行了细致分析。结果表明,多次重复试验下,相比非破碎极端波浪,破碎极端波浪产生的点压力离散性更强;波浪破碎程度越大,测点位置越靠近波峰,则点压力离散程度越大;破碎波的最大点压力出现在1.2倍的最大波面附近,且其大小可达3倍的最大静水压力;基于点压力小波谱,不同破碎阶段破碎波产生冲击作用不同,对于波浪作用桩柱前波浪已经发生破碎的情况,其冲击区域更大,点压力分布更复杂;而对于桩面破碎的情况,其造成的波浪总力更大。     

Numerical experiments on low-frequency fluctuations on a submerged coastal reef

Low-frequency fluctuations on a reef coast are studied through a numerical model based on nonlinear conservation equations of mass and momentum. The model is used to investigate the long wave generation and propagation phenomena under both breaking and non-breaking incident short wave groups. The effects of incident wave characteristics and reef topography on the long wave phenomena are discussed. The results show that the long wave elevations on reef coasts are substantial, which explains the large water level fluctuations observed at certain occasions.     

Kinematics of breaking tsunami wavefronts: A data set from large scale laboratory experiments

This paper provides an overview of a new large scale laboratory data set on the kinematics of breaking tsunami wavefronts. The aim of the experiments was to provide an open access data set for model testing, calibration and verification, with particular emphasis on fluid kinematics in the wave breaking and run-up (swash) zones. The experiments were performed over a composite slope in the tsunami wave basin at the O. H. Hinsdale Wave Research Laboratory at Oregon State University. Data for ten different wave conditions were collected, including non-breaking and breaking waves, and both shore breaks and fully developed long bores.Surface elevation and fluid kinematics were measured with a closely spaced array of surface piercing wave gauges, non-contact ultrasonic wave gauges and four 3-D side-looking Acoustic Doppler Velocimeters. The array was traversed from the nearshore (depth = 0.2 m) to the middle and upper run-up zone, providing kinematic data at 30 cross-shore locations. Video was also recorded from 4 cameras covering the propagation, breaking and run-up zones. Surface elevation, flow velocities and the wave maker displacement were also recorded to provide offshore boundary conditions.The experiments include conditions with wave heights up to 0.55 m, notional wave periods up to 20 s and run-up lengths of up to 15.2 m on a 1/30 slope. In terms of the slope in the shoaling and breaker zones, the data correspond to Iribarren numbers in the range of 0.26–5.6. Raw, calibrated and processed data are stored with open access within the OSU Tsunami Wave Basin Experiment Notebook, which provides full access to all the wave maker control signals, data, instrument coordinates, and processing and plotting software. This paper serves as an introduction to the data set, demonstrates data quality and provides an initial analysis of some key parameters that govern the impact of tsunami events, including run-up versus offshore wave conditions and nearshore bore height, the maximum inundation depths at the original shoreline position, and the time to maximum inundation depth and flow reversal. Examples of temporal and convective accelerations and turbulent flow components are also presented to illustrate further details of the kinematics.     

植被斜坡岸滩海啸波消减数值模拟研究

An explicit one-dimensional model based on the shallow water equations(SWEs) was established in this work to simulate tsunami wave propagation on a vegetated beach. This model adopted the finite-volume method(FVM)for maintaining the mass balance of these equations. The resistance force caused by vegetation was taken into account as a source term in the momentum equation. The Harten–Lax–van Leer(HLL) approximate Riemann solver was applied to evaluate the interface fluxes for tracing the wet/dry transition boundary. This proposed model was used to simulate solitary wave run-up and long-periodic wave propagation on a sloping beach. The calibration process suitably compared the calculated results with the measured data. The tsunami waves were also simulated to discuss the water depth, tsunami force, as well as the current speed in absence of and in presence of forest domain. The results indicated that forest growth at the beach reduced wave energy loss caused by tsunamis. A series of sensitivity analyses were conducted with respect to variable parameters(such as vegetation densities, wave heights, wave periods, bed resistance, and beach slopes) to identify important influences on mitigating tsunami damage on coastal forest beach.     

Threshold of motion of coarse-grained sediment under waves in shallow water

This paper considers the threshold of motion of sediment in shallow coastal waters under breaking and non-breaking waves. A simple model, representing conditions at the fluid/sediment interface, is developed. The representation of a breaking wave is based on bore theory, and the shear stress at the bed is based on the friction formula of O'Connor and Yoo. A threshold formula is presented based on the use of energy dissipation. The threshold data is also related to the Shields threshold criterion.     

孤立波特性的实验室模拟

孤立波是浅海水域中经常出现的一种波动现象,常用来描述海啸和风暴等引起的巨浪以及波长较长的表面波的某些特性。采用"水体瞬间坍塌"的方法产生孤立波,在二维波浪水槽内进行系列实验。实验结果表明,产生的孤立波波高与水深之比可达1.29;箱体宽度及箱内水体高度对波高影响较大;得到孤立波波高计算公式,可较好地反映孤立波波高与箱体宽度、水深和箱内水体高度之间的变化关系,并给出了公式的适用范围。     

Breaking of Solitary Waves on Uniform Slopes

The propagation,shoaling and breaking of solitary waves on mild slopes are simulated byboundary element method.In this paper,the criterion of breaking solitary waves on mild slopes is discussed.The criterion is that the ratio of horizontal velocity of water particles on the wave crest to wave celerity equalsone.However,the case that the ratio of horizontal velocity of water particles on the wave crest to wave ce-lerity is below one but the front face of wave profile becomes vertical is also considered as a breaking criteri-on.According to the above criteria,the breaking index for slopes 1:10 to 1:25 is studied.The result is com-pared to other researchers'.The deformation of solitary waves on slopes is discussed and the distribution offluid velocities at breaking is shown.     

Physical modelling of tsunami using a new pneumatic wave generator

The physical simulation of tsunami in the laboratory has taken a major leap forward with the construction and testing of a new wave generator, capable of recreating scaled tsunami waves. Numerical tools fail to reproduce tsunami nearshore and onshore processes well, and physical experiments in large scale hydraulic facilities worldwide have been limited to the generation of solitary waves as an (controversial) approximation for evolved forms of tsunami. The new concept in wave generation presented herein is born of collaboration between UCL's Earthquake and People Interaction Centre (EPICentre) and HR Wallingford. It allows for the first time the stable simulation of extremely long waves led either by a crest or a trough (depressed wave). This paper presents the working concepts behind the new wave generator and the first stages of testing for verifying its capacities and limitations. It is shown that the new wave generator can not only reproduce solitary waves and N-waves with large wavelengths, but also the 2004 Indian Ocean Tsunami as recorded off the coast of Thailand (“Mercator” trace).     

Onshore sandbar migration at Tairua Beach (New Zealand): Numerical simulations and field measurements

We observed the onshore migration (3.5 m/day) of a nearshore sandbar at Tairua Beach, New Zealand during 4 days of low-energy wave conditions. The morphological observations, together with concurrent measurements of waves and suspended sediment concentrations, were used to test a coupled, wave-averaged, cross-shore model. Because of the coarse bed material and the relatively low-energy conditions, the contribution of the suspended transport to the total transport was predicted and observed to be negligible. The model predicted the bar to move onshore because of the feedback between near-bed wave skewness, bedload, and the sandbar under weakly to non-breaking conditions at high tide. The predicted bathymetric evolution contrasts, however, with the observations that the bar migrated onshore predominantly at low tide. Also, the model flattened the bar, while in the observations the sandbar retained its steep landward-facing flank. A comparison between available observations and numerical simulations suggests that onshore propagating surf zone bores in very shallow water (< 0.25 m) may have been responsible for most of the observed bar behaviour. These processes are missing from the applied model and, given that the observed conditions can be considered typical of very shallow sandbars, highlight a priority for further field study and model development. The possibility that the excess water transported by the bores across the bar was channelled alongshore to near-by rip-channels further implies that traditional cross-shore measures to judge the applicability of a cross-shore morphodynamic model may be misleading.     

强非线性和色散性Boussinesq方程数值模型检验

采用同位网格有限差分法,建立了强非线性和色散性Boussinesq方程数值计算模型。以稳恒波Fourier近似解给定入射波边界条件,对均匀水深深水和浅水域不同非线性的行进波、缓坡地形上深水至浅水域的浅水变形波、以及缓坡和陡坡地形上的波浪水槽实验进行了数值计算,并将计算结果与解析解、解析数值解以及实验值进行了较为详细的比较,从而检验了模型的色散性、非线性以及不同底坡下非线性波的浅水变形性能。     

Simulation of nearshore wave processes by a depth-integrated non-hydrostatic finite element model

This paper presents CCHE2D-NHWAVE, a depth-integrated non-hydrostatic finite element model for simulating nearshore wave processes. The governing equations are a depth-integrated vertical momentum equation and the shallow water equations including extra non-hydrostatic pressure terms, which enable the model to simulate relatively short wave motions, where both frequency dispersion and nonlinear effects play important roles. A special type of finite element method, which was previously developed for a well-validated depth-integrated free surface flow model CCHE2D, is used to solve the governing equations on a partially staggered grid using a pressure projection method. To resolve discontinuous flows, involving breaking waves and hydraulic jumps, a momentum conservation advection scheme is developed based on the partially staggered grid. In addition, a simple and efficient wetting and drying algorithm is implemented to deal with the moving shoreline. The model is first verified by analytical solutions, and then validated by a series of laboratory experiments. The comparison shows that the developed wave model without the use of any empirical parameters is capable of accurately simulating a wide range of nearshore wave processes, including propagation, breaking, and run-up of nonlinear dispersive waves and transformation and inundation of tsunami waves.