Numerical simulation of wave transformation and runup incorporating porous media wave absorber and turbulence models

A numerical wave tank is first established using the Navier–Stokes equations and the VOF method assuming laminar flow. The standard k–ε, realizable k–ε and RNG k–ε turbulent models are then incorporated to the numerical tank. An effective numerical method for wave absorption utilizing the energy-dissipating property of porous media is also included. To validate the accuracy of the proposed models, the propagation of a solitary wave, where analytical solution is available for comparison, is first simulated. This is followed by the simulation of irregular wave runup on a composite seawall, wave propagation over submerged bars and wave refraction and diffraction over an elliptic shoal, where experimental data are available for comparison. All computed results agree well with either the analytical solution or the experimental data.     

Static wave setup with emphasis on damping effects by vegetation and bottom friction

Wave setup can contribute significantly to elevated water levels during severe storms. In Florida we have found that wave setup can be 30% to 60% of the total 100-year storm surge. In areas with relatively narrow continental shelves, such as many locations along the Pacific Coast of the United States, wave setup can be an even larger proportionate contributor of anomalous water levels during major storms. Wave setup can be considered as comprising two components, with the first being the well-known static wave setup resulting from the transfer of breaking wave momentum to the water column. The second, oscillating component, is a result of nonlinear transfer of energy and momentum from the primary (linear) spectrum to waves with length and time scales on the order of the wave groups.Static wave setup is the focus of this paper with emphasis on effects due to internal or surface forces that act on the wave system and cause both dissipation of wave energy and transfer of momentum. In particular, the effects of wave damping by vegetation and bottom friction are considered. Linear wave theory is applied to illustrate these effects and, for shallow water waves, the setup is reduced by two-thirds the amount that would occur if the same amount of energy dissipation occurred in the absence of forces. Effects of nonlinear waves are then considered and it is found, for a shallow water wave of approximately one-half breaking height, that a wave setdown rather than setup occurs due to damping by vegetation and bottom friction.The problem of wave setup as waves propagate through vegetation was stimulated by studies to establish hazard zones associated with 100-year storm events along the shorelines of the United States. These storms can generate elevated water levels exceeding 4 to 6 m and can result in overland wave propagation. As these waves propagate through vegetation and damp, the question arose as to the contribution of this process to elevated mean water levels through additional wave setup.     

Boundary layer approach in the modeling of breaking solitary wave runup

The boundary layer is very important in the relation between wave motion and bed stress, such as sediment transport. It is a known fact that bed stress behavior is highly influenced by the boundary layer beneath the waves. Specifically, the boundary layer underneath wave runup is difficult to assess and thus, it has not yet been widely discussed, although its importance is significant. In this study, the shallow water equation (SWE) prediction of wave motion is improved by being coupled with the k–ω model, as opposed to the conventional empirical method, to approximate bed stress. Subsequently, the First Order Center Scheme and Monotonic Upstream Scheme of Conservation Laws (FORCE MUSCL), which is a finite volume shock-capturing scheme, is applied to extend the SWE range for breaking wave simulation. The proposed simultaneous coupling method (SCM) assumes the depth-averaged velocity from the SWE is equivalent to free stream velocity. In turn, free stream velocity is used to calculate a pressure gradient, which is then used by the k–ω model to approximate bed stress. Finally, this approximation is applied to the momentum equation in the SWE. Two experimental cases will be used to verify the SCM by comparing runup height, surface fluctuation, bed stress, and turbulent intensity values. The SCM shows good comparison to experimental data for all before-mentioned parameters. Further analysis shows that the wave Reynolds number increases as the wave propagates and that the turbulence behavior in the boundary layer gradually changes, such as the increase of turbulent intensity.     

Ocean depth effects on tsunami amplitudes used in source models in linearized shallow-water wave theory

The aim of this study is to determine the effects of ocean depth on tsunami amplitudes used in source models for use in linear shallow-water wave theory. To determine the effects, 19 ocean depths ranging from 200–2000 m are studied. The results show that it is possible to establish a series-type exploration function to define the depth-amplitude effects. This function with the unknown coefficients related to ruptures of the ocean floor involves the normalized maximum tsunami amplitude. Results obtained from this series-function give good approximations for four or more terms in the series. Two basic source models are considered. Numerical examples are presented.     

带有侧摩擦和底摩擦的绕岛理论

绕岛理论来自于Sverdrup理论,被广泛用于估计和分析通过岛屿之间海峡的输运情况。以往的研究得到了带有侧摩擦或底摩擦的单岛理论或多岛理论。本文在线性情况下考虑了风驱动环流下的解析模型。在同时考虑侧摩擦和底摩擦的情况下,推导出了岛屿周围输运流函数的解析解,并给出了通过岛屿之间通道的流量输运。其结果与Wajsowicz相似,但摩擦常数表示不同的值。从解析解上看,摩擦常数与侧摩擦和底摩擦之间的关系比较复杂,为了推导出它们之间的相互作用原理,本文在正压β平面上随机选取了一些侧摩擦和底摩擦的值。结果表明,在构成摩擦常数方面,侧摩擦和底摩擦近似呈线性关系。我们研究了宽度对通道输运值的影响,结果表明摩擦在一定宽度内提高了流量,这种现象和只考虑侧摩擦时比较相似。本文也比较了在不同深度下的流量,发现当水平涡粘性系数和底部拖曳系数固定时,水深越大,输运减少率越小。为了进一步揭示侧摩擦和底摩擦耗散的联合作用,在两个岛屿的情况下,本文在不同宽度的通道中与Wajsowicz的只考虑底摩擦或侧摩擦的模型进行了比较。结果表明,当通道比较窄,尤其是在小于Munk边界层厚度时,侧摩擦的作用大于底摩擦。当通道宽度远大于Munk边界层厚度时,底摩擦的作用大于侧摩擦。将模型应用到印尼贯穿流,得到大约20%的输运减少量。     

Numerical modeling of wave runup and forces on an idealized beachfront house

In this paper, a numerical wave model based on the incompressible Reynolds-averaged Navier–Stokes (RANS) and k–ε equations is used to estimate the impact of a solitary wave on an idealized beachfront house located at different elevations on a plane beach. The locations of the free surface are reconstructed by volume of fluid (VOF) method. The model is satisfactorily tested against the experimental data of wave runup, and the analytical solution of wave forces on vertical walls. The time histories of wave profiles, forces, and overturning moments on the idealized house are demonstrated and analyzed. The variations of wave forces and overturning moments with the elevation of the idealized beachfront house are also investigated.     

The long wave climbing a shore in a bay of variable cross-section

The long wave climbing a shore is studied assuming the shelf surface to be a tilted parabolic cylinder. Asymptotic formulae have been derived which permit extreme values of water surface elevation and velocity at the water's edge to be calculated, when the incident wave has an arbitrary form. For the case where the impinging wave is a simple harmonic, we have derived an accuration solution for evolution of the wave height at the water's edge.Translated by V. Puchkin.     

珊瑚岛礁孤立波爬坡的平面二维数值模拟研究

为了探究岛屿周围珊瑚礁在抵御海啸灾害中的作用,采用激波捕捉类Boussinesq模型FUNWAVE-TVD,对孤立波在理想化三维岛礁地形上的传播及爬坡开展了现场尺度的平面二维数值模拟,分析了入射波高、礁坪水深、礁坪宽度、礁前斜坡坡度、礁后斜坡坡度、珊瑚礁糙率对岛屿四周孤立波爬高分布的影响。结果表明,珊瑚礁的存在总体上可有效降低岛屿四周孤立波的最大爬坡高度;入射波高、礁坪水深、礁坪宽度、珊瑚礁糙率是影响珊瑚岛礁四周孤立波爬坡分布的主要因素,岛礁四周最大爬坡高度会随入射波高和礁坪水深的增大、礁坪宽度和珊瑚礁糙率的减小而不断增大;当礁坪水深增大到一定程度时,珊瑚礁主要会对岛屿背浪面的爬高失去影响,而当礁坪宽度和珊瑚礁糙率减小至一定程度时,会出现岛礁四周最大爬高高于无珊瑚礁时爬高的现象;礁后斜坡的变缓会使岛礁周围的最大爬高有所减小,而礁前斜坡坡度对珊瑚岛礁周围的最大爬高几乎没有影响。     

Numerical modelling of the tsunami generation process by the moving sea bottom displacement

The process of tsunami generation by the moving horizontal bottom displacement is studied numerically. The influence produced by the displacement rate and the range of the run on the parameters of the wave generated is studied. A comparison with the results derived using the linear theory of long waves is made.Translated by Mikhail M. Trufanov.     

The application of wave refraction-diffraction model with friction

In this paper a refraction-diffraction model with friction is used to compute wave characteristics in a region near a certain port. Comparing with the results from refraction model, and with the data observed during a typhoon in 1985, it is found that the characteristics from the refraction-diffraction model with friction are reasonable, and that the results are in rather good agreement with observations. Thus it can be concluded that the model is effective for computing coastal wave characteristics over complicated bottom topography.     

Experimental study on the mitigation effect of mangroves during tsunami wave propagation

Mangroves are crucial for protecting coastal areas against extreme disasters such as tsunamis and storm surges.An experimental study was conducted to determine how mangroves can mitigate the tsunami wave propagation.The test was performed in a flume, where mangrove models were installed on a slope, and dam-burst waves were used to simulate tsunami waves. To study how mangrove forests reduce the impact of tsunamis, this paper measured the heights of the incoming waves under different initial cond...     

On the numerical modeling of tsunami wave generation and propagation

Abstract

In this article three main stages of tsunami wave evolution are investigated. At first, the development of disturbances from a given patched elevation of the bottom surface in an incompressible nonviscous fluid of the uniform depth is considered. Then, a tsunami wave diffraction by underwater bottom elevation or cavity is investigated. In this case the shallow water equations are already used, and it is supposed that a cylindrical wave is spread from patched water elevation over the epicentrum. Last, the tsunami propagation and transformation in a shallow water region and its run‐up on a beach are investigated on the basis of the improved shallow water theory, taking into consideration the nonlinear and dispersive terms of higher order. The proposed theory is tested in a problem of collisions of two solutions. Solutions of the first and the second problems are obtained by the method of integral Laplace's transformation with following numerical inversion of transformations. A finite difference method for a solution of the last problem is used.     

Influence of the wave spectrum form on the bottom sediment dynamics

This paper is dedicated to the investigation of the influence of the irregular wave spectrum form on the regularities of the bottom suspension and formation of the bottom topographic microforms (ripples). It is shown that the vertical profile of the suspended matter concentration and the possible partial deformation of the bottom ripples are related to the peculiarities of the frequency distribution of the energy in the wave spectrum (at the constant energy of the process).     

Mathematical analysis of long-wave breaking on open channels with bottom friction

In this paper we study the breaking of long waves propagating along an open channel with linear friction on the bottom. The equations governing the wave propagation consist of a pair of first-order nonlinear hyperbolic partial differential equations (PDEs). We first transformed the PDEs into a pair of ordinary differential equations (ODEs) along the characteristic directions by means of a pair of Riemann invariants. By analyzing the ODEs, we found that the breaking of waves can be identified by the singularity of the derivative of the Riemann invariants. Thus, we derived an analytical solution for the derivative of the Riemann invariants. Then, a breaking criterion and an analytical formula for the estimation of breaking time were developed and validated through numerical experiments. It is also shown in the paper that the present model includes the previous model neglecting bottom friction as a special case.     

On the role of bottom roughness in overflows

Overflows play an important role in the downwelling limb of the oceanic thermohaline circulation. In light of the recognition that some overflows are not homogenous but exhibit a vertical density structure, and details of topography influence the pathways of some overflows, the impact of topographic roughness on the product property distribution is explored using the 3D non-hydrostatic spectral element model Nek5000. Numerical experiments are carried out by varying bottom roughness amplitude and ambient stratification parameters, in a regime where equilibrated product water masses are formed in a non-rotating environment.Our main finding is that bottom roughness can influence the overflow product distribution such that the highest salinity classes are removed and neutral buoyancy level is attained higher up in the stratified ambient water column. It is also shown that the form drag coefficients in overflows over rough bottom can be much larger than the skin drag coefficient over smooth bottom. To our knowledge, form drag has never been measured in oceanic overflows. As such, these numerical experiments imply that such measurements would be useful for a better understanding of overflow dynamics. It is also found that the ratio of source and product overflow mass transports is robust to changes in bottom roughness. This appears to happen because the distribution of entrainment is totally different in the case of rough bottom. Entrainment tends to initiate earlier (due to vertical motion induced by topography) and terminate earlier (due to development of form drag) than that over smooth topography.     

沙质岸坡上波浪传播变形及动力响应特性研究

波浪作用对水库岸坡稳定性有重要影响。为了解波浪在岸坡地形中的传播演变机制和孔隙水压力响应特性,在波浪水槽末端铺设长6 m、坡度1∶16的斜坡沙床进行试验。通过改变入射波浪参数,测量斜坡段各处波面形态,采集斜坡段不同位置处孔隙水压力,分析了波浪在沙质岸坡上浅水变形区域内波面变化特征、波能演变规律以及岸坡土体孔压特征。结果表明：随着入射波浪厄塞尔数的增大,波浪浅水变形更加明显,波形不对称性加剧,各阶谐波之间互相作用更加强烈;水深较大区域,岸坡渗透作用大于浅水变形作用,波高呈现减小趋势;浅水变形剧烈区,浅水变形作用大于岸坡渗透作用,波高呈现增大趋势,最终破碎;孔压随入射波高与波周期的增大而增大,岸坡不同位置处孔压沿深度衰减速率和随波高增长速率均不同;岸坡孔压沿深度衰减速率与入射波周期呈现出正相关关系,与波高并无太大关系。     

Forecasting of tsunami wave heights at the Russian coast of the Black Sea

Forecasting of tsunami wave heights at the Russian coast of the Black Sea is discussed. Prognostic numerical calculations of tsunamis were carried out for the tsunami sources uniformly distributed in the Black Sea basin (a total of 55 events). Their results are compared with the results of numerical modeling of the historical events (in 1939 and 1966) and the data of not numerous measurements. A preliminary forecast is made on this basis for the tsunami wave heights along the Russian coast of the Black Sea.     

浅化波浪层流边界层流速分布特性的数值分析

建立了同时考虑波致雷诺应力和时均水平压强梯度影响的二阶波浪边界层数学模型,模型计算得到的浅化波浪层流边界层内瞬时流速剖面、振荡速度幅值和时均流速剖面均与水槽实验数据吻合较好,在此基础上探讨了浅化波浪边界层流速分布特性及其影响机制。随着波浪的浅化变形,边界层内时均流速剖面"底部向岸、上部离岸"的变化特征越来越明显。这是二阶对流项引起的波致雷诺应力和离岸回流引起的时均水平压强梯度共同作用的结果,在床面附近由波致雷诺应力占主导作用并趋于引起向岸流动,在上部区域由时均水平压强梯度占主导作用并趋于引起离岸流动。