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。     

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。     

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。     

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。     

南海北部a波和b波的生成与传播特征的数值研究

本文基于真实地形、潮汐的高分辨率三维MITgcm海洋环流模式,对南海北部a波（大振幅波列形式）和b波（孤立子形式）的生成与传播特征进行了数值研究。首先,我们总结和分析了这些波动的生成与传播特征。然后我们计算了吕宋海峡的能量收支。能量的生成在一天内有三个极大值,其中最大值对应a波的生成。吕宋海峡西边界的能通量一天内有两个极大值,较大的那个对应a波的生成而另一个对应b波的生成。我们设计了敏感性试验来探究吕宋海峡东西海脊对a、b波的生成和传播造成的影响。通过对比敏感性实验和标准试验的结果,发现对于a波的生成东海脊必不可少,但西海脊几乎没有影响。西海脊削弱了a波的振幅但未对a波波速造成明显的影响。b波来自于从东海脊生成的扰动信号。西海脊加强了这个扰动信号但减慢了它的传播速度。     

内潮致拉格朗日余流的数值研究

利用MITgcm数值模式,研究了单海脊地形下的内潮致拉格朗日余流,发现余流结构与内潮结构相对应,从海脊附近沿波射线分布,向东、西两方向流动。与欧拉余流相比,拉格朗日余流在海脊附近呈现辐散的特征,欧拉余流则表现为辐聚的特征。改变地形、正压潮流速等参数,拉格朗日余流结构随之变化。当海脊变宽时,余流随波射线的消失而变得很小且混乱;当海脊变高时,海脊附近逐渐产生向海底方向的流动,与海面反射的余流形成平行的射线,余流整体增强,海脊附近的余流在向外流动过程中增幅减小;当正压潮流速增大时,余流结构基本不变,但在高窄海脊地形下海脊附近的平行射线会逐渐合为一支从海脊顶部产生的流动。     

一次北印度洋海啸的数值模拟研究

对2012年4月11日(世界时)发生在北印度洋的一次地震海啸进行了模拟研究,给出了海啸模拟所需地震参数的获取途径,以及海啸波初始场的建立方法,分析了该海啸过程最大波幅分布和海啸波传播波时分布,并与测站实测值进行了对比。结果表明,海啸波的能量传播方向存在不均匀性,能量传播集中方向的波幅较大,具有更强的危害性。     

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。     

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。     

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.     

Transmission and reflection of the Rossby waves in a stratified ocean with bottom topography

Transmission and reflection coefficients are calculated for Rossby waves incident on a bottom topography with constant slope in a continuously stratified ocean. The characteristics of the coefficients are interpreted in terms of the quasigeostrophic waves on the slope. In the parameter range where only the barotropic Rossby waves can propagate in the region outside the slope, the bottom trapped wave plays the same role as the topographic Rossby wave in a homogeneous ocean, and hence the transmission is weak unless phase matching takes place. When both of the barotropic and baroclinic Rossby waves can propagate outside the slope, the total transmission can be strong. The bottom trapped wave affects the transmission and reflection, and it leads to the possibility that the Rossby wave is transmitted as a mode different from the incident mode. When the number of the wavy modes on the slope is smaller than that of the Rossby wave modes outside the slope, strong reflection occurs.The results for an ocean with linear distribution of the squared Brunt-Väisälä frequency are compared to those in a uniformly stratified ocean. The weakening of the stratification near the bottom is almost equivalent to reducing the effect of the slope.     

Ocean swell variability along the northern coast of the Gulf of Guinea

This study analyses a 4.5 year (September 2009–March 2014) time-series of remotely-sensed data of altimeter significant wave heights to describe the temporal and spatial variability of ocean swells along the northern coast of the Gulf of Guinea. The NOAA WAVEWATCH III (NWW3) wave model data were used with altimeter data to determine the origin of the swells that occur along the coast of Côte d'Ivoire in West Africa. We show that the ocean swells along the northern coast of the Gulf of Guinea are generated in the Southern Ocean and then propagate from south to north in the South Atlantic Ocean, before turning south-west to north-east close to the coast. This finding corroborates previous studies in this area. The remotely-sensed and NWW3 significant wave height data captured the strong swells observed along the coast of Côte d'Ivoire from the period 28 August–3 September 2011, which were responsible for an extreme erosion event of more than 12?m along that country's coastline. This extreme event was triggered by a strong storm in the region between 40° and 60° S that occurred eight days previously in the South Atlantic. The waves propagated as swells at a speed of about 875?km day–¹ before reaching the northern African coast.     

Propagation of topographically trapped waves on aβ-plane

Topographically trapped (subinertia) waves that propagate along a coast lying in an arbitrary direction on aβ-plane are studied. It is found that the waves also propagate in the direction normal to the coast within an envelope due to theβ-effect. The dispersion relation is hardly affected by theβ-effect except in a long wavelength or long period range in which generalized Haurwitz waves (Takeda, 1984b) exist. In the long wavelength or long period range, two types of waves exist: topographically trapped type waves and generalized Haurwitz type waves.     

Generation of internal waves by a semidiurnal barotropic tide in the Mid-Atlantic ridge area

Internal waves occurring in the specific Mid-Atlantic ridge area as a result of the impinging of a barotropic tide are studied in the terms of the linear theory for surface waves. The ocean is assumed to be double-layered, with a tidal wave running onto it at an arbitrary angle. The dependences of the wave amplitudes and horizontal velocities on the angle of run-on of a tidal wave are derived. Similar studies for the model bottom topography have been reported in refs 1–3. Translated by Vladimir A. Puchkin.     

西风爆发、次表层暖水东移与厄尔尼诺现象

利用最近20 a的大气海洋资料,分析了厄尔尼诺事件与赤道太平洋西风异常以及赤道太平洋次表层海温之间的关系.结果表明,赤道西太平洋(5°S～5°N,120°～160°E)和赤道中东太平洋(5°S～5°N,160°E～160°W)西风异常都存在着与厄尔尼诺周期一致的年际变化,但前者还包含有显著的2～3个月季节内振荡.赤道西太平洋次表层冷暖水东移也呈现年和年际时间尺度的振荡周期.在厄尔尼诺发生前,赤道西太平洋次表层海水出现持续性增暖,赤道西太平洋西风异常频率加快,强度增强.随后赤道中太平洋(160°E～160°W)出现持续性(3个月以上)强西风异常(即西风爆发),并进一步向东扩展,同时次表层暖水沿着赤道波导东移到赤道东太平洋混合层,导致赤道东太平洋海表大面积异常增暖,形成一次厄尔尼诺现象.最后,模式模拟了1980～1984年赤道太平洋海温的变化,进一步证实了赤道纬向西风异常对暖水东移起着重要的作用.     

The effect of currents on the generation of internal waves by a barotropic tide near an underwater ridge

In the frame of the linear theory for long waves, the paper studies long waves generated by a barotropic tide running at an arbitrary angle over a bottom ridge. The ocean is assumed to be two-layered. In the area of a ridge with a rectangular cross section, geostrophic flows are considered, coupled with the inclinations of the free surface and interface. Wave amplitudes are shown to depend on the angle of an onrunning tide and this allows us to reach a conclusion about the influence of a geostrophic current on the generation of internal waves. Translated by Vladimir A. Puchkin.