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。     

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。     

抛物型对称海脊引导波完整解析理论

越洋海啸能够被大洋海脊引导并沿海脊传播至远场地区,虽然传播速度较慢,但携带较大的能量,会对远场地区造成灾害影响,相关研究对于提高海啸传播特性本质的认识具有重要意义。本文基于线性长波方程,推导出了抛物型对称海脊引导波完整解析理论。研究表明对称型海脊同时存在对称与反对称引导波,其自由水面波动可以表示为虚宗量Bessel函数形式。利用海脊中心对称条件给出了描述其频率与波数的频散关系。基于所提理论进一步分析讨论了引导波的运动特性,包括频散关系、波速度、能量传播速度与波面空间分布等。本研究为揭示地形坡度由脊顶至两侧逐渐增加的海脊引导波运动特征,预测实际越洋海啸中最具威胁性海啸波的到达时间提供了理论依据。     

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。     

单一海脊地形对海洋内波生成与传播影响的分析

在海洋内波多发区,海底地形变化是影响海洋内波生成、传播和演化的重要因素。本文基于不可压缩原始N-S方程,在非静压近似条件下,通过建立适应于非线性海洋内波研究的非静压海洋动力学模型,并将其应用于正压潮驱动下的内孤立波生成和传播的数值模拟研究。根据模拟结果,研究了一类单海脊地形拓扑结构变化对内孤立波生成和传播的影响;分析并讨论了地形拓扑结构参数变化与生成的内孤立波传播至特定位置的抵达时间、强度等特征参数之间的变化关系;提出内孤立波生成之前在海脊一侧形成"L-下陷"结构的观点,并揭示了与该观点相合的能量"积聚"和"释放"机制。     

吕宋海峡夏季内潮数值模拟

利用三维海洋环流模式MITgcm,对吕宋海峡夏季内潮的生成与传播进行了分析。结果表明,在八分潮驱动的情况下,吕宋海峡夏季生成的内潮能量有4.7GW传入西太平洋,7.7GW传入南海,其中M2分潮最强,K1分潮次之。半日分潮主要在恒春海脊中部和巴坦群岛附近生成,并在传播过程中衰减迅速;全日分潮主要在巴布延群岛西北处及兰屿海脊北部生成,在传播过程中衰减较慢。西传M2和K1内潮主要在兰屿海脊南部生成,且西传M2内潮在恒春海脊北部得到增强,在恒春海脊中部则被削弱。在恒春海脊北部生成的东传M2和K1内潮在经过兰屿海脊时被削弱。恒春海脊使得部分源于兰屿海脊的西北向全日内潮转向西南,形成向南海海盆的内潮分支。     

有限断层模型在2015年9月16日智利Mw8.3级地震海啸数值模拟中的应用与评估

2015年9月16日22时54分（当地时间）智利中部近岸发生M_w8.3级地震,震源深度25 km。同时,强震的破裂区长200 km,宽100 km,随之产生了中等强度的越洋海啸。海啸影响了智利沿岸近700 km的区域,局部地区监测到近5 m的海啸波幅和超过13 m的海啸爬坡高度。太平洋区域的40多个海啸浮标及200多个近岸潮位观测站详细记录了此次海啸的越洋传播过程,为详细研究此次海啸近场及远场传播及演化规律提供了珍贵的数据。本文选择有限断层模型和自适应网格海啸数值模型建立了既可以兼顾越洋海啸的计算效率又可以实现近场海啸精细化模拟的高分辨率海啸模型。模拟对比分析了海啸的越洋传播特征,结果表明采用所建立的模型可以较好地再现远场及近场海啸特征,特别是对近场海啸的模拟结果非常理想。表明有限断层可以较好地约束近场、特别是局部区域的破裂特征,可为海啸预警提供更加精确的震源信息,结合高分辨率的海啸数值预报模式实现海啸传播特征的精细化预报。本文结合观测数据与数值模拟结果初步分析了海啸波的频散特征及其对模型结果的影响。同时对观测中典型的海啸波特征进行的简要的总结。谱分析结果表明海啸波的能量主要分布在10~50 min周期域内。这些波特征提取是现行海啸预警信息中未涉及,但又十分重要的预警参数。进一步对这些波动特征的详细研究将为海啸预警信息及预警产品的完善提供技术支撑。     

珊瑚岛礁海岸多尺度波流运动特性研究新进展

珊瑚岛礁海岸波流动力复杂、地貌形态特殊、工程响应未知, 波浪传播变形和波生环流对建筑物安全、地形地貌演变、防灾减灾和生态环境保护都有重要影响。本文从大范围大洋海脊导波与岛礁波浪俘获、中等尺度的礁坪-潟湖-裂口系统波流特性、建筑物前沿的局部波流特性及工程响应等三种不同空间尺度上综述了波流运动特性研究的新进展, 主要包括深水大范围的海脊波浪引导与岛礁波浪俘获的理论解析、礁坪-潟湖-裂口系统整体物理模型实验、基于大水槽实验的建筑物影响下波流演化过程及越浪量和波浪力计算方法, 并提出亟需深入研究的重点内容。     

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。     

2017年9月8日墨西哥沿岸Mw8.2级地震海啸观测数据分析与模拟

2017年9月8日4时49分（UTC），墨西哥瓦哈卡州沿岸海域（15.21°N，93.64°W）发生M_w8.2级地震，震源深度30 km。强震在该海域引发海啸，海啸对震源附近数百千米范围内造成了严重影响。位于太平洋上的多个海啸监测网络捕捉到了海啸信号并详细记录了此次海啸的传播过程。本文选用了近场2个DART浮标和6个验潮站的水位数据，通过潮汐调和分析和滤波分离出海啸信号，对近场海啸特征值进行了统计分析，并采用小波变换分析方法进一步分析了海啸的波频特征。基于Okada弹性位错理论断层模型计算得到了强震引发的海底形变分布，并采用MOST海啸模式对本次海啸事件近场传播特征进行了模拟，模拟结果与观测吻合较好。最后，基于实测和模拟结果，详细分析了此次地震海啸的近场分布特征，发现除受海啸源的强度和几何分布特征影响外，近岸海啸波还主要受地形特征控制，在与特定地形相互作用后波幅产生放大效应，会进一步加剧海啸造成的灾害。     

Trapping mechanism of submerged ridge on trans-oceanic tsunami propagation

Based on the linear shallow water equations,an analytic solution of trapped waves over a symmetric parabolicprofile submerged ridge is derived.The trapped waves act as propagating waves along the ridge and as standing waves across the ridge.The amplitude gets the maximum at the ridge top and decays gradually towards both sides.The decaying rate gets more gently with higher modes.Besides,an explicit first-order approximate dispersion relation is derived to simplify transcendental functions in the exact solution,which is useful to describe trapped waves over shallowly submerged ridges in reality.Furthermore,the trapping mechanism of the submerged ridge waveguides on the trans-oceanic tsunami propagation can be explained by the ray theory.A critical incident angle exists as a criterion to determine whether the wave is trapped.Besides,a trapped parameter γ is proposed to estimate the ratio of the energy trapped by the oceanic ridge if a tsunami is generated at its top.     

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.     

The role of horizontal impulses of the faulting continental slope in generating the 26 December 2004 tsunami

For a long time, people have believed that the vertical displacement of seafloor due to undersea earthquakes is the primary cause of tsunami genesis. However, seismically-inverted seafloor deformation of the 2004 Sumatra–Andaman earthquake shows that the total vertical displacement is not enough to have generated the powerful Indian Ocean tsunami. Based on the seismically-inverted data and a three-dimensional ocean general circulation model (OGCM), we show that the momentum force, transferred by the horizontal impulses of the faulting continental slope in that earthquake, has accounted for two thirds of the satellite-observed tsunami height and generated kinetic energy 5 times larger than the potential energy due to the vertical displacement. The asymmetric tsunami pattern, recorded by tide-gauges showing leading-elevation waves toward Sri Lanka and leading-depression waves toward Thailand, is best explained by the horizontally-forced mechanism. The same mechanism has also explained the March 2005 Nias earthquake and tsunami data, suggesting that the horizontal motions of faulting have played more important roles in tsunami genesis than previously thought.     

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.     

Tsunami Wave Interaction with Data Buoys

To plan for proper mitigation measures, one should have an advanced knowledge of the phenomenon of tsunami propagation from the deep ocean to coastal waters. There are a few methods to predict tsunamis in the ocean waters; one method is the effective use of data buoy measurements. Although data buoys have been used along the Indian waters there has been a tremendous growth in the number of buoy deployment recently. Under the National Data Buoy Programme (NDBP) of India, the 2.2 m diameter discus data buoys were deployed along the east and west coasts of India for measuring meteorological and ocean parameters. It would be advantageous if these buoys could be efficiently used to measure rare events such as tsunamis. Understanding the dynamic behavior of the buoy is of prime importance if a tsunami warning system is to be successful. This may be accomplished through experimental or numerical studies. A comprehensive experimental study has been conducted to understand the dynamic behavior of a wave rider buoy exposed to a variety of waves. It is common that tsunami waves are represented in terms of shallow water waves, namely solitary and cnoidal waves. Hence, in the present study, the discus type data buoy is scale modeled and tested under the action of solitary and cnoidal waves in the laboratory. The time histories of wave elevations, as well as heave and pitch motions of the buoy model, were analyzed through a spectral approach as well as through wavelet transformations. The wavelet approach gives more detailed insight into the spectral characteristics of the buoy motion in the time scale. The harmonic analyses were performed for the cnoidal wave elevations and subsequent motion characteristics that give an insight into the energy variations. The details of the model, instrumentation, testing conditions and the results are presented in this paper.     

波群与单频率波的波向线的比较

本文根据普遍几何群速的概念和Fermat原理导出的波群的波向线方程,数值计算在理想底形海域中波群与单频率波的波向线,并加以比较,指出两者的异同。同时还检验了前人的一些结论。     

Outer wave number spectrum and statistical distribution of apparent wave number vector

Based on the ray theory and Longuet-Higgins’s linear model of sea waves, the joint distribution of wave envelope and apparent wave number vector is established. From the joint distribution, we define a new concept, namely the outer wave number spectrum, to describe the outer characteristics of ocean waves. The analytical form of the outer wave number spectrum, the probability distributions of the apparent wave number vector and its components are then derived. The outer wave number spectrum is compared with the inner wave number spectrum for the average status of wind-wave development corresponding to a peakness factor P = 3. Discussions on the similarity and difference between the outer wave number spectrum and inner one are also presented in the paper.     

Hindcasting wave spectra in finite‐depth waters

A model is described for hindcasting or forecasting waves in finite‐depth waters. The model is particularly applicable to coastal sites where the water is depth‐limited. The wave energy density spectrum is modelled in the frequency‐directional domain. For each spectral component a ray is defined along which wave energy propagates to reach the site. For sites exposed to the open ocean a background spectral wave model is required to provide input to the ray endpoints. Further growth and dissipation is then effected along the rays according to the local wind and water depth. The model was used to hindcast wave spectra over a period of 9 months for a site in the Canterbury Bight, New Zealand. The results were compared with measurements from a Waveridcr buoy at the site. The model succeeds in explaining about 40% of the variance in measured significant wave heights. However, the present application is handicapped by errors inherent in the background spectral model and in specifying the local wind.