Reconstructing tsunami run-up from the characteristics of tsunami deposits on the Thai Andaman Coast

Tsunamis can leave deposits on the land surface they inundate. The characteristics of tsunami deposits can be used to calculate tsunami run-up height and velocity. This paper presents a reconstruction of tsunami run-up from tsunami deposit characteristics in a simple mathematical model. The model is modified and applied to reconstruct tsunami run-ups at Ao Kheuy beach and Khuk Khak beach, Phangnga province, Thailand. The input parameters are grain-size and maximum run-up distance of the sediment. The reconstructed run-up heights are 4.16–4.91 m at Ao Kheuy beach and 5.43–9.46 m at Khuk Khak beach. The estimated run-up velocities (maximum velocity) at the still water level are 12.78–19.21 m/s. In the area located 70–140 m inland to the end of run-up inundation, estimated mean run-up velocities decrease from approximately 1.93 m/s to 0 m/s. Reasonably good agreements are found between reconstructed and observed run-up heights. The tsunami run-up height and velocity can be used for risk assessment and coastal development programs in the tsunami affected area. The results show that the area from 0 to 140 m inland was flooded by high velocity run-ups and those run-up energies were dissipated mainly in this area. The area should be designated as either an area where settlement is not permitted or an area where effective protection is provided, for example with flood barriers or forest.     

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.     

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.     

礁面大糙率存在下孤立波传播变形及爬高实验研究

本文采用圆柱体阵列来模拟珊瑚礁面的大糙率,通过波浪水槽实验研究礁面糙率对孤立波传播变形及岸滩爬高的影响.结果表明,粗糙礁面的存在显著削弱了礁坪上孤立波的首峰和礁后岸滩反射造成的次峰,同时降低了波浪在珊瑚礁面的传播速度;垂直于岸线方向沿礁相对波高随着入射波增大而减小,随着礁坪水深的增大而增大,粗糙礁面上波高沿礁的衰减更为...     

Wave run-up on slender circular cylindrical foundations for offshore wind turbines in nonlinear random waves

A practical method for estimating the wave run-up height on a slender circular cylindrical foundation for wind turbines in nonlinear random waves is provided. The approach is based on the velocity stagnation head theory and Stokes second order wave theory by assuming the basic harmonic wave motion to be a stationary Gaussian narrow-band random process. Comparisons are made with measurements by De Vos et al. (2007), and some of the highest wave run-up events that were predicted agree with those measured.     

Historical tsunami in the Makran Subduction Zone off the southern coasts of Iran and Pakistan and results of numerical modeling

Tsunami hazard in the Makran Subduction Zone (MSZ), off the southern coasts of Iran and Pakistan, was studied by numerical modeling of historical tsunami in this region. Although the MSZ triggered the second deadliest tsunami in the Indian Ocean, among those known, the tsunami hazard in this region has yet to be analyzed in detail. This paper reports the results of a risk analysis using five scenario events based on the historic records, and identifies a seismic gap area in western Makran off the southern coast of Iran. This is a possible site for a future large earthquake and tsunami. In addition, we performed numerical modeling to explain some ambiguities in the historical reports. Based on the modeling results, we conclude that either the extreme run-up of 12–15 m assigned for the 1945 Makran tsunami in the historical record was produced by a submarine landslide triggered by the parent earthquake, or that these reports are exaggerated. The other possibility could be the generation of the huge run-up heights by large displacements on splay faults. The results of run-up modeling reveal that a large earthquake and tsunami in the MSZ is capable of producing considerable run-up heights in the far field. Therefore, it is possible that the MSZ was the source of the tsunami encountered by a Portuguese fleet in Dabhul in 1524.     

Laboratory modeling of the propagation of periodic internal waves over bottom slopes

The experimental investigation of the run-up of periodic internal waves in a two-layer fluid on the coastal slope is performed in an open hydrochannel at the Physical Department of the Lomonosov Moscow State University. The waves are produced by a wave generator. We study the transformation of waves, the vertical structure of the field of velocities of mass transfer, and the behavior of the parameters of internal waves propagating over the sloping bottom. It is shown that the run-up and breaking of internal waves are accompanied by periodic emissions of portions of the heavier fluid from the bottom layer upward along the slope. The Stokes drift velocity changes its sign as a function of depth. Moreover, both the wave length (the horizontal distance between the neighboring crests) and the height of waves over the sloping bottom (the elevation of the crest over the slope along the vertical) decrease as the wave approaches the coast.     

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.     

Run-up of long waves on a beach: The influence of the incident wave form

The influence of the incident wave form on the extreme (maximal) characteristics of a wave at a beach (run-up and draw-down heights, run-up and draw-down velocities, and the breaking parameter) is studied. It is suggested to use in the calculations the definition of wavelength at a level of 2/3 of the maximal height, which to a certain degree correlates with the definition of the significant wavelength accepted in oceanology. Such a definition allows us to unify the relations for extreme run-up characteristics so that the influence of the incident wave form becomes insignificant. The obtained universal relations can be used for the estimates of run-up characteristics when the exact information about the form of the incident wave is not available.     

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.     

Run-up of long solitary waves of different polarities on a plane beach

We study the run-up of long solitary waves of different polarities on a beach in the case of composite bottom topography: a plane sloping beach transforms into a region of constant depth. We confirm that nonlinear wave deformation of positive polarity (wave crest) resulting in an increase in the wave steepness leads to a significant increase in the run-up height. It is shown that nonlinear effects are most strongly pronounced for the run-up of a wave with negative polarity (wave trough). In the latter case, the run-up height of such waves increases with their steepness and can exceed the amplitude of the incident wave.     

Run-up of solitary waves on slopes with different profiles

The problem of sea-wave run-up on a beach is discussed within the framework of exact solutions of a nonlinear theory of shallow water. Previously, the run-up of solitary waves with different forms (Gaussian and Lorentzian pulses, a soliton, special-form pulses) has already been considered in the literature within the framework of the same theory. Depending on the form of the incident wave, different formulas were obtained for the height of wave run-up on a beach. A new point of this study is the proof of the universality of the formula for the maximum height of run-up of a solitary wave on a beach for the corresponding physical choice of the determining parameters of the incident wave, so that the effect of difference in form is eliminated. As a result, an analytical formula suitable for applications, in particular, in problems related to tsunamis, has been proposed for the height of run-up of a solitary wave on a beach.     

Wave run-up on cylindrical and cone shaped foundations for offshore wind turbines

During the last decade, several offshore wind-farms were built and offshore wind energy promises to be a suitable alternative to provide green energy. However, there are still some engineering challenges in placing the foundations of offshore wind turbines. For example, wave run-up and wave impacts cause unexpected damage to boat landing facilities and platforms. To assess the forces due to wave run-up, the distribution of run-up around the pile and the maximum run-up height need to be known. This article describes a physical model study of the run-up heights and run-up distribution on two shapes of foundations for offshore wind turbines, including both regular and irregular waves. The influence of wave steepness, wave height and water depth on run-up is investigated. The measured run-up values are compared with applicable theories and previous experimental studies predicting run-up on a circular pile.     

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.     

Dynamic pressures and run-up on semicircular breakwaters due to random waves

The dynamic pressures due to random waves of predefined spectral characteristics exerted on a semicircular breakwater model at five different elevations along the depth are measured. In addition, the wave run-up on the model and its reflection characteristics are measured. The results on the variation of the frequency pressure spectra along the depth and the run-up spectra are reported in this paper. The average spectral characteristics as well as statistical properties of the above two parameters are presented. The average reflection coefficient is reported as a function of the wave steepness, described as the ratio of the significant wave height to the square of the peak period.     

Wave run-up and overtopping on smooth and rough slopes of coastal structures

A series of hydraulic model tests has been carried out in a glass wave flume to investigate the influences of wave height, wave period, wave steepness, surf similarity parameter, roughness, layer thickness and porosity on wave run-up and overtopping of 1:2 sloped impermeable and permeable breakwaters fronted by a 1:10 gentle, smooth beach slope. The analysis of results involves the correlation between the overtopping energy transfer with the relative wall height and the relationship between wave run-up and overtopping rate. Further, measured wave run-up and overtopping rates are compared with the results given in the Shore Protection Manual (1984), Automated Coastal Engineering System (1992)and results of other investigators.     

畸形波作用下半潜式平台波浪爬升与气隙响应特性

半潜平台的波浪爬升与气隙响应是设计过程中的重要考量因素。为探究随机波浪场中畸形波对半潜平台波浪爬升及气隙响应的影响,将含畸形波的随机波浪试验与一般随机波浪试验结果进行了对比研究分析。对模型试验测得的运动以及监测点处的波浪爬升及气隙进行频谱分析以及极值统计分析。研究发现,纵荡和纵摇的极大值主要受畸形波的影响而显著增大,纵荡、垂荡以及纵摇响应谱几乎不受单个畸形波影响;波浪爬升与气隙的极大值受到畸形波的影响而增大,同时,畸形波对气隙响应谱造成极大影响,增强了波浪爬升与气隙响应的非线性性。     

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.     

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.     

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.