基于射线理论的海脊俘获波机制

虽然众多现场实测资料和数值模拟均表明海脊可以俘获海啸波并引导其传播至远场地区，带来严重的灾害，但少有研究阐述其产生机理。本文基于射线理论，推导了指数型海脊上波浪传播轨迹的理论解，并提出了震源位于海脊顶部的海啸被海脊完全俘获的条件。基于该俘获条件进一步给出了海脊对海啸俘获效率的表达式，用以评估海啸中被海脊俘获影响至远场的能量占海啸总能量的比例。     

双曲余弦海脊上海啸俘获波的解析与数值研究

海啸能被大洋海脊引导以俘获波的形式沿其传播上万千米，且因其特殊的运动方式，携带巨大能量影响远场地区的港口，严重威胁海岸安全。本文首先基于线性浅水方程，推导了双曲余弦平方海脊上俘获波的波面解，其为μ阶ν次的连带勒让德函数的第一类解和第二类解的组合。进一步推导出其对应的频散关系，其中对于确定的频率ω，存在无穷多个波数k_y与之对应。采用MIKE21-BW模型，模拟了产生于海脊脊顶处的海啸在理想双曲余弦平方海脊上的传播变形过程。结果表明，小部分能量以自由先驱波进行传播，海啸波的波能大部分被海脊俘获。海脊俘获波沿着海脊方向为行进波，随着海啸波传播时间的增加，波浪在沿着海脊方向的延展范围也逐渐增大，波高逐渐减小、波的个数逐渐增加。俘获波能量主要由不同频率以相同速度传播的具有孤立波特性的波浪成分和能量主要集中在特定频率范围内的波浪成分组成。     

海啸俘获波在弯曲海脊上的传播规律

越洋海啸会受大洋海脊的引导以俘获波的形式沿其传播上万千米,其携带的巨大能量会严重影响远场地区、威胁海岸地区的安全。本文基于MIKE21-BW模型,分别模拟0°(直海脊)至90°(直角弯曲海脊)不同弯曲角度海脊上俘获波的传播变形过程,并定量比较其能量分配。结果表明,海脊俘获波传至海脊转弯处,少部分能量会泄露出海脊重新以自由波的形式扩散至整个海域;部分能量会被反射回来形成与初始海啸波相反方向的俘获波沿海脊传播,反射的能量会随着海脊弯曲角度的增加而增加;还有一部分能量继续沿着弯曲的海脊向前传播,其随着海脊弯曲的角度增加而减小。     

台阶型海脊俘获波的实验研究

基于物理模型实验研究瞬态冲击波在台阶地形上传播过程,揭示由于反射而在海脊上出现的波浪俘获现象。结果表明:在瞬态波产生区域附近,海脊上所测到的先导波即为最大波,其由泄漏至海脊外的深水波绕射至海脊所致。随着传播距离的增加,由于频散效应的影响,先导波逐渐减小,沿台阶近似直线传播的海脊俘获波和在台阶上曲折传播的海脊俘获波逐渐显现。在距离波浪产生较远区域所测的最大波晚于先导波出现,且这些由俘获波所叠加而成的最大波随着传播距离的增加而呈现出更加复杂的波面过程。     

Wave characteristic and morphologic effects on the onshore hydrodynamic response of tsunamis

While the destruction caused by a tsunami can vary significantly owing to near- and onshore controls, we have only a limited quantitative understanding of how different local parameters influence the onshore response of tsunamis. Here, a numerical model based on the non-linear shallow water equations is first shown to agree well with analytical expressions developed for periodic long waves inundating over planar slopes. More than 13,000 simulations are then conducted to examine the effects variations in the wave characteristics, bed slopes, and bottom roughness have on maximum tsunami run-up and water velocity at the still water shoreline. While deviations from periodic waves and planar slopes affect the onshore dynamics, the details of these effects depend on a combination of factors. In general, the effects differ for breaking and non-breaking waves, and are related to the relative shift of the waves along the breaking–non-breaking wave continuum. Variations that shift waves toward increased breaking, such as steeper wave fronts, tend to increase the onshore impact of non-breaking waves, but decrease the impact of already breaking waves. The onshore impact of a tsunami composed of multiple waves can be different from that of a single wave tsunami, with the largest difference occurring on long, shallow onshore topographies. These results demonstrate that the onshore response of a tsunami is complex, and that using analytical expressions derived from simplified conditions may not always be appropriate.     

Numerical simulation of fluid–structure interaction using a combined volume of fluid and immersed boundary method

In this work, a combined immersed boundary (IB) and volume of fluid (VOF) methodology is developed to simulate the interactions of free-surface waves and submerged solid bodies. The IB method is used to account for the no-slip boundary condition at solid interfaces and the VOF method, utilizing a piecewise linear interface calculation, is employed to track free surfaces. The combined model is applied in several case studies, including the propagation of small-amplitude progressive waves over a submerged trapezoidal dike, a solitary wave traveling over a submerged rectangular object, and wave generation induced by a moving bed. Numerical results depicting the free-surface evolutions and velocity fields are in good agreement with either experimental data or numerical results obtained by other researchers. In addition, the simplification of the initial free-surface deformation used in most tsunami earthquake source study is justified by the present model application. The methodology presented in the paper serves as a good tool for solving many practical problems involving free surfaces and complex boundaries.     

Revisiting the February 6th 1783 Scilla (Calabria, Italy) landslide and tsunami by numerical simulation

On February 6th, 1783, a landslide of about 5 × 10⁶ m³ triggered by a 5.8 M earthquake occurred near the village of Scilla (Southern Calabria, Italy). The rock mass fell into the sea as a rock avalanche, producing a tsunami with a run-up as high as 16 m. The tsunami killed about 1,500 people, making it one of the most catastrophic tsunamis in Italian history. A combined landslide-tsunami simulation is proposed in this paper. It is based on an already performed reconstruction of the landslide, derived from subaerial and submarine investigation by means of geomorphological, geological and geomechanical surveys. The DAN3D model is used to simulate the landslide propagation both in the subaerial and in the submerged parts of the slope, while a simple linear shallow water model is applied for both tsunami generation and propagation. A satisfying back-analysis of the landslide propagation has been achieved in terms of run-out, areal distribution and thickness of the final deposit. Moreover, landslide velocities comparable to similar events reported in the literature are achieved. Output data from numerical simulation of the landslide are used as input parameters for tsunami modelling. It is worth noting that locations affected by recordable waves according to the simulation correspond to those ones recorded by historical documents. With regard to run-up heights a good agreement is achieved at some locations (Messina, Catona, Punta del Faro) between computed and real values, while in other places modelled heights are overestimated. The discrepancies, which were most significant at locations characterized by a very low slope gradient in the vicinity of the landslide, were probably caused by effects such as wave breaking, for which the adopted tsunami model does not account, as well as by uncertainties in the historical data.     

Impacts of the 26 December 2004 tsunami in Eastern Africa

The tsunami of 26 December 2004 was the largest ever recorded in the Indian Ocean, triggered by the 3rd largest earthquake in 100 years measuring 9.2 moment magnitude. The epicenter of the earthquake was off Banda Aceh on the Indian Ocean coast of the island of Sumatra in Indonesia, centered at 3.316°N, 95.854°E. A sudden upward movement of the seafloor that averaged ∼6 m occurred along almost 1300 km of the north-east Indian Ocean plate at 0059 Coordinated Universal Time (UTC) and lasted 8 min. Because of the lack of preparedness and absence of warning systems in the Indian Ocean the tsunami spread silently across the ocean over a span of 8 h causing massive destruction including the deaths of over 250,000 people, with maximum damages occurring in Indonesia, Thailand, Sri Lanka, India and the Maldives. Moderate to low damages were recorded in the Seychelles, Socotra (Yemen) and Somalia, though in the latter a highly vulnerable town was impacted resulting in over 300 deaths. Most of eastern Africa was spared massive damages from the waves due to (a) distance from the epicenter (>6000 km), (b) the dissipation of energy of the tsunami by shallow banks in the middle of the Indian Ocean (the Seychelles banks, Saya de Malha and Cargados Carajos Shoals) and (c) at least for Kenya and Tanzania, the first and largest waves hit at low tide. In Kenya and Tanzania these factors resulted in the waves being experienced as tidal surges of 1–1.5 m amplitude lasting 5–10 min. Damages recorded for eastern Africa include 11 deaths in Tanzania and 1 in Kenya, of people walking and swimming over shallow intertidal flats being trapped by the advancing and receding tidal surges, damage to boats anchored in shallow water and inundation in Mauritius and Rodrigues. Official information, warning and response networks were nonexistent, and even when an official response was generated in Kenya the public demonstrated no faith or willingness to act on warnings from officials such as the police. Importantly, information on the tsunami and the generation of an official response was dependent on two technologies, satellite television and mobile telephony, and these should be built into future warning systems as key mechanisms and backups to official information and warning networks.     

基于类海啸波型的岛礁水动力特性数值模拟研究

基于非静压单相流模型NHWAVE建立了高精度二维数值波浪水槽,采用日本2011年实测真实海啸波型系统研究了海啸波在岛礁上传播变形的规律,并且分析了波高、礁坪淹没水深和礁前斜坡坡度等因素对孤立波和真实海啸传播变形的影响。结果表明,相比孤立波,类海啸波的波长明显大于孤立波波长,在测点处引起的水面变化持续时间更长,同等波高情况下真实海啸波型比孤立波能够携带更多的能量,与岛礁的相互作用也更为复杂,在礁坪上形成的淹没水深约为孤立波的两倍。礁前斜坡坡度和礁坪淹没水深均对类海啸波的反射和透射系数有显著影响。随着礁前斜坡坡度的增加,反射系数和透射系数均逐渐增加。随着礁坪淹没水深的增加,反射系数逐渐减小,而透射系数逐渐增大。但是,反射系数和透射系数均随着入射波高的增加而逐渐减小。     

Numerical investigation of tsunami-like wave hydrodynamic characteristics and its comparison with solitary wave

Solitary waves have been commonly used as an initial condition in the experimental and numerical modelling of tsunamis for decades. However, the main component of a tsunami waves acts at completely different spatial and temporal scales than solitary waves. Thus, use of solitary waves as approximation of a tsunami wave may not yield realistic model results, especially in the coastal region where the shoaling effect restrains the development of the tsunami wave. Alternatively, N-shaped waves may be used to give a more realistic approximation of the tsunami wave profile. Based on the superposition of the sech²(*) waves, the observed tsunami wave profile could be approximated with the N-shaped wave method, and this paper presents numerical simulation results based on the tsunami-like wave generated based on the observed tsunami wave profile measured in the Tohoku tsunami. This tsunami-like wave was numerically generated with an internal wave source method based on the two-phase incompressible flow model with a Volume of Fluid (VOF) method to capture the free surface, and a finite volume scheme was used to solve all the governing equations. The model is first validated for the case of a solitary wave propagating within a straight channel, by comparing its analytical solutions to model results. Further, model comparisons between the solitary and tsunami-like wave are then made for (a) the simulation of wave run-up on shore and (b) wave transport over breakwater. Comparisons show that use of these largely different waveform shapes as inputs produces significant differences in overall wave evolution, hydrodynamic load characteristics as well as velocity and vortex fields. Further, it was found that the solitary wave uses underestimated the total energy and hence underestimated the run-up distance.     

The role of bottom friction in models of nonbreaking tsunami wave runup on the shore

The role of bottom friction in the runup of nonbreaking long waves on the shore is analyzed. The case of the normal incidence of monochromatic waves is considered. The relief of the model region consists of an even horizontal bottom area conjugated with a flat slope. The energy dissipation is estimated as the work of bottom friction forces over the wave field obtained using the known analytical solution based on the Carrier-Greenspan transforms. Estimates of energy losses for waves whose periods are typical for tsunami waves have been obtained. The energy dissipation is shown to be not concentrated in the shore line area as a rule. The question about the practicability of using partially reflecting boundary conditions on the coast to take into account the bottom friction in large-scale models of tsunami propagation is considered.     

Calculation of the initial elevation at the tsunami source using analytical solutions

We have obtained an analytical solution to the problem of determining the initial elevation at the tsunami source, which was formed by small residual deformations of a flat sloping bottom. This solution, which is newly derived, is compared with the known analytical solution of an equivalent problem over a horizontal bottom. It is shown that applying an analytical solution over a horizontal bottom for calculating the initial perturbations in the sources of realistic tsunami provides sufficient accuracy.     

Sediment grains moved by passing tsunami waves: Tsunami deposits in deep water

Tsunamis propagating in the open ocean have associated horizontal particle velocities that do not change with depth — yet the limiting water depth where a tsunami of given characteristics will initiate sediment motion remains unknown. Based upon linear wave theory and a parametrization of the Shields curve, equations are derived and solved, using an iterative scheme, to address the topic of grain movement by tsunami waves as a function of water depth and wave amplitude. The focus is on waves in deep water where tsunami waves behave linearly and on non-cohesive sediment grains. Furthermore, the question is addressed of which grain sizes are picked up on a sloping beach as the wave shoals. According to the results, even the Boxing Day tsunami in 2004 was incapable of moving fine sand in water deeper than 985 m in the Bay of Bengal and 335 m in the Indian and Pacific oceans. The results suggest that tectonic tsunamis of size equal to or smaller than the Boxing Day tsunami cannot initiate motion of deep-water cohesionless sediments that can be correlated on an oceanic basin-wide scale.     

Profile Evolution and Energy Dissipation for Internal Soliton Transmitting over Different Submarine Ridges

1 .IntroductionWhile surface solitary waves arefoundin many physical phenomena (Chouand Shih,1996 ;Chouand Quyang,1999 ;Chouet al .,2003 ; Chenet al .,2004 ; Wang,2004 ;Tsenget al .,2005) ,internal solitary waves (ISWs) have been observed since the beginning of the 20th century.In fact ,some internal waves have alarge enoughamplitudeto cause consequence onthe surface .Hence obser-vation of the oceansurface may helpto detect the activities of internal waves . We require observationsthrough…     

Generation of internal waves by barotropic tidal flow over a steep ridge

A three-dimensional nonhydrostatic numerical model is used to study the generation of internal waves by the barotropic tidal flow over a steep two-dimensional ridge in an ocean with strong upper-ocean stratification. The process is examined by varying topographic width, amplitude of the barotropic tide, and stratification at three ridge heights. The results show that a large amount of energy is converted from the barotropic tide to the baroclinic wave when the slope parameter, defined as the ratio of the maximum ridge slope to the maximum wave slope, is greater than 1. The energy flux of internal waves can be normalized by the vertical integral of the buoyancy frequency over the ridge depths and the kinetic energy of the barotropic tides in the water column. A relationship between the normalized energy flux and the slope parameter is derived. The normalized energy flux reaches a constant value independent of the slope parameter when the slope parameter is greater than 1.5. It is inferred that internal wave generation is most efficient at the presence of strong upper-ocean stratification over a steep, tall ridge. In the Luzon Strait, the strength of the shallow thermocline and the location of the Kuroshio front could affect generation of internal solitary waves in the northern South China Sea.     

基于震级上限估计的渤海海啸危险性与共振特征研究

根据渤海区域地质断层特征和历史地震活动规律,分析得出渤海内潜在最大震级上限为8.1级,并对该海啸源可能的两组震源机制分别进行了数值模拟。模拟结果显示：渤海局部区域海啸波幅最大可达 1.5 m,最大流速可达2.8~3.0 m/s,具备造成灾害损失的风险。在该海啸源情景下,渤海海盆内易激发长期的水位自由振荡,部分区域水位振荡可持续 20 h以上,振荡波幅的大小与海啸首波波幅相当或更大。基于快速傅里叶变换方法对海啸波进行频谱分析,部分长周期频谱成分满足区域固有共振特征。因此,渤海内一旦发生海啸,不仅要关注海啸首波可能造成的灾害性影响,还要密切关注海啸首波到达后,可能产生的长时间、长周期的海啸波共振以及往复式海啸流造成的影响。     

On waves propagating over a submerged poro-elastic structure

In this paper, the problem of incident waves propagating over a submerged poro-elastic structure is studied theoretically. A linear wave theory is used to describe the wave motion. The submerged poro-elastic structure is modeled based on Biot's theory, in which the fluid motion is described using the potential wave theory of Sollitt and Cross (1972). In the present approach, the problem domain is divided into four subregions. Using general solutions for each region and matching dynamic and kinematic conditions for neighboring regions, analytic solutions are derived for the wave fields and poro-elastic structure. The present analytic solutions compare very well with simplified cases of impermeable, rigid structures, and with those of porous structures. Using the present analytic solution, the effects of a poro-elastic submerged structure on waves are studied. The results show that softer poro-elastic structures can induce higher reflection and lower transmission from incident waves. For low permeability conditions, the elasticity of the structure can induce resonance, while higher permeability can depress the resonant effects.     

Numerical simulation of interaction between internal solitary waves and submerged ridges

Direct numerical simulations are performed to study the transformation of internal solitary waves (ISWs) of depression type propagating over an underwater ridge in a two-layer fluid system. Bottom ridges with relatively smooth vertex are employed to represent sills in natural lakes and oceans. Consistent with previous experiments, three interaction types (weak, moderate and strong) are observed to be based on the energy loss. In addition, the moderate interaction are found to be categorized into transmitted and reflected type according to their distinct transformation process. General flow characteristics for ISW–ridge interaction in the benthic boundary layer and in the pycnocline is monitored and analysed. A modified degree of blocking B_m considering both the nonlinear effect of incident ISWs and the blockage effect of the submerged ridge is proposed. Different ISW–ridge interactions are discovered to be linked with B_m. Maximum wave-induced velocities, wave energy losses, reflected and transmitted wave amplitudes are found to have a self-similar feature with B_m. The maximum energy loss is up to 35% and the maximum wave-induced velocity can reach 1.8 times of the phase speed of the incident ISW. Empirical equations are obtained based on the data fitting to predict some useful physical parameters during ISW–ridge interaction.     

Wave interaction with cylindrical porous piles

The interaction of waves with arrays of porous circular cylinders is studied theoretically and, under the assumption of potential flow and linear wave theory, an analytical solution is derived. The solution is valid for either submerged or emerged structures. The extension to the cases of unidirectional and multidirectional waves is obtained by means of a transfer function. For specific conditions the model gives the same solution as those previously presented by other authors. Numerical results are presented which exemplify diverse wave and mechanical parameters on the wave transformation due to the presence of a system of circular cylinders.     

2010 年智利和2011 年日本地震海啸在我国东南沿岸诱导的波流特征及危险性分析

本文基于有限断层模型和OKADA 位错模型计算海表变形场作为初始条件，利用MOST 海啸数值模型模拟分析了2010年智利和2011 年日本地震海啸在我国东南沿海地区的海啸传播特征，海啸波模拟结果与观测数据吻合较好。重点研究分析了沈家门港口海域的海啸波流特征及其诱导的涡旋结构。研究结果表明：尽管两次事件的海啸源位置及破裂特征完全不同，但海啸波流在我国东南沿岸的分布特征大致相似；另外相对于海啸波幅而言，港湾中海啸流具有更强的空间差异性，港口入口、岬角地形处和岛屿间水道中往往会有强流存在。尽管这两次越洋海啸均未能在我国东南沿海引发淹没情形，但通过数值计算发现局部均存在超过3 m/s 以上的强流，因此进行海啸预警及风险管理时应综合考虑海啸波流的影响。