A numerical study of the generation and propagation of internal solitary waves in the Luzon Strait

A new composite model, which consists of a generation model of the internal tides and a regularized long wave propagation model, is presented to study the generation and evolution of internal solitary waves in the sill strait. Internal bores in the sill strait are first simulated by the generation model, and then the internal tidal field outside of the sill region is given as input for the propagation model. Numerical experiments are carried out to study the imposing tide, depth profile, channel width and shoaling effect, etc., on the generation and evolution of internal solitary waves. It is shown that only when the amplitude of internal tide at the forcing boundary of the propagation model is large enough that a train of internal solitary waves would be induced. The amplitude of the imposing tide in the generation model, shoaling effect, asymmetry of the depth profile and channel width have some effects on the amplitude of the induced internal solitary wave. The imposing tidal flow superimposed on a constant mean background flow has a great damping effect on the induced internal waves, especially on those propagate against the background flow direction. The generation and propagation of internal solitary waves in three possible straits among the Luzon Strait are simulated, and the reasons for the asymmetry of their propagation are also explained.     

潜堤后高阶自由谐波的研究

基于高阶边界元方法的完全非线性数值水槽模型模拟潜堤地形上波浪的传播变形,通过与实验值进行比较,考察数学模型的正确性.采用两点法分离得到堤后高倍频自由波来研究入射波参数、水深对堤后高倍频自由波的影响.研究发现:基频波、二阶和三阶自由波幅值分别与入射波波幅成线性、二次和三次函数关系,基频波幅值基本不随波浪周期变化,而二阶和...     

Numerical Wave Channel with Absorbing Wave-Maker

The numerical wave channel has been developed based on the volume of fluid method (VOF) in conjunction with the Navier-Stokes equations. The absorbing wave-maker boundary on the left side of the channel is presented by prescribing velocity reference to linear wave-maker theory. The principle of which is that the numerical wave-maker is designed to move in a way that generates the required incident wave and cancels out any reflected wave that reach it at the same time. On the right side of the channel, the open boundary is set to permit incident waves to be transmitted freely. The parametric studies have been carried out at a range of ratios of water depth to wave length d/ L from 0.124 to 0.219, with wave height in the front of paddle/water depth ratio (H0 / d) from 0.1 to 0.3. Wave height, wave pressure distribution along the channel and velocity field are obtained for both open boundary condition and reflective boundary condition at the other end of the channel. For a reflective case, it is shown that     

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.     

Numerical Analysis on the Effects of Submerged Depth of the Grid and Direction of Incident Wave on Gravity Cage

In this paper,the numerical model of the net cage with the grid mooring system in waves is set up by the lumped mass method and rigid kinematics theory,and then the motion equations of floating system,net system,mooring system,and floaters are solved by the Runge-Kutta fifth-order method.For the verification of the numerical model,a series of physical model tests have been carried out.According to the comparisons between the simulated and experimental results,it can be found that the simulated and experimental results agree well in each condition.Then,the effects of submerged depth of grid and direction of incident wave propagation on hydrodynamic behaviors of the net cage are analyzed.According to the simulated results,it can be found that with the increase of submerged depth of grid,the forces acting on mooring lines and bridle lines increase,while the forces on grid lines decrease;the horizontal motion amplitudes of floating collar decrease obviously,while the vertical motion amplitudes of floating collar change little.When the direction of incident wave propagation changes,forces on mooting lines and motion of net cage also change accordingly.When the propagation direction of incident wave changes from 0° to 45°,forces on the main ropes and bridle ropes increase,while the forces on the grid ropes decrease.With the increasing propagation direction of incident wave,the horizontal amplitude of the forces collar decreases,while the vertical amplitude of the floating collar has little variation.     

Stokes' expansion of internal deep water waves to the fifth order

Stokes' expansion is applied to the internal waves of finite amplitude, which propagate on the interface between two layers of infinite thickness. Stream function, wave profile, phase velocity and mass transport velocity are given in the fifth order approximation. It is shown that (a) phase velocity increases with increase of wave steepness, (b) mass transport appears in the direction of the wave propagation in both layers as in the case of the surface waves, and (c) when the density difference is very small, the wave profile is flattened not only at the troughs but also at the crests.     

波浪在三维圆形岛地形上的绕射研究

波浪在传播过程中遇到岛屿就会发生绕射。本文使用混合元方法对修正型缓坡方程进行了数值求解,并与KUO et al的解析解进行了比较验证。在此基础上研究了工程尺度背景下,波浪在三维圆形岛地形上的绕射,计算了不同入射波浪周期、浅滩形状参数和岛屿尺寸情况下,沿波浪传播方向断面上和岛屿岸线上的相对波高大小。计算结果表明：随着入射波周期的减小、浅滩形状参数的增大和岛屿尺寸的减小,圆形岛迎浪侧的相对波高振荡幅度、圆形岛背浪侧的相对波高大小以及岛屿岸线上的相对波高振幅和大小均随之增大。不同情况下,岛屿岸线上的相对波高最大值大多数发生在迎浪点,个别发生在迎浪点两侧20°~25°处;最小值发生在背浪点两侧30°附近。     

Wave Transformation and Breaking in Diagonal Opposing Current

- When waves propagate into diagonal opposing current from non-current area, not only the wave parameters but also the direction of wave propagation will change, that is, wave refraction will occur. The authors have calculated the changes of wave parameters, including wave refraction, by Linear Wave Theory, and have also done systematic study on wave transformation and breaking in opposing current by means of experimental analysis and theoretical calculation. In order to know the effect of wave refraction, computation is done in this paper about wave transformation and breaking on gentle slopes in diagonal opposing current.     

Generalized boussinesq model for periodic non-linear shallow-water waves

This paper presents the development of a generalized Boussinesq (gB) model for the periodic non-linear shallow-water waves. An incident cnoidal wave solution for the gB model is derived and applied to the wave simulation. A set of radiation boundary conditions is also established to transmit effectively the cnoidal waves out of the computational domain. The classical solutions of the second-order cnoidal waves are discussed within the content of the KdV equation and the generalized Boussinesq equations. An Euler's predictor-corrector finite-difference algorithm is used for numerical computation. The propagation of normally incident cnoidal waves in a channel is studied. The simulated wave profiles agree well with the analytical results. The temporal and spatial evolution of an obliquely incident cnoidal wave is also modelled. The phenomenon of Mach reflection is discussed.     

Wave kinematics of partial reflection from a vertical wall

A third-order perturbation approximation for the partial reflection from a vertical wall is presented in this paper. The wave parameters are expressed in terms of the amplitude of incident waves. The reflection coefficient is defined as the ratio of the height of reflected waves to incident waves. The numerical results demonstrate the significant influences of reflected coefficient on the wave profile and wave frequency bifurcation. For example, the critical angle of wave frequency bifurcation with partial reflection is about 7.5 degrees, not 21 degrees as reported previously for fully reflection.     

涌浪作用下港内波况试验研究

基于秘鲁钱凯港的防波堤三维整体模型试验结果,研究了涌浪绕射、透射联合作用对港内波况的影响。分析了不同波向、不同谱峰周期的入射波条件下港内不同功能区的波况分布规律,并对比分析了具有不同周期的入射波对港内不同区域波高的影响,兼顾分析了波向的影响。结果表明,在涌浪作用下,受透射、绕射影响,不同入射波条件下港内比波高分布规律相关性较好,距离口门越近、入射波波长越长,港内比波高越大;入射波周期对港内波况影响的差异和对波向的敏感性因港内不同区域而不同;防波堤阻挡效果好的波向,其入射波对港内的影响较小;对于受防波堤掩护性较好的内侧泊位,应重点关注泊位处的低频波浪对系泊的影响。     

边缘波研究进展

由于折射作用,在波浪近岸传播过程中会出现一种特殊的、沿着岸线传播的波浪,这种波浪被称为边缘波。边缘波平行于岸线传播,其振幅在岸线处最大,在远离岸线的方向,其振幅呈指数型减小,它们的能量基本被限制在离海岸一波长的距离之内,因此边缘波对近岸地区工程、地貌等有着重要影响。本文对边缘波的研究历史、研究进展进行了阐述,主要介绍了以下几个方面:（1）基于不同控制方程、不同地形上的边缘波理论;（2）实际观测到的边缘波特性;（3）物理模型试验中边缘波的造波方式以及观测到的边缘波特性;（4）数值模拟方法在边缘波研究中的应用。最后,展望了边缘波在未来的研究趋势。     

南海北部内孤立波数学模型

在二层内潮数学模型的基础上,考虑非静力平衡扰动压力的影响,导出潮频内孤立波产生、传播的数学模型。该模型不受小地形假设的限制,并适用于南海。应用该模型能解释说明产生以下现象的物理机制：潮流流过巴坦-萨布坦海脊时,在一定海洋环境条件下,通过潮流与起伏的底地形相互作用可激发产生潮频内孤立波,并西传至东沙群岛附近的海域。     

Application of desingularized approach to water wave propagation over three-dimensional topography

A numerical approach based on desingularized boundary element method and mixed Eulerian–Lagrangian formulation [Zhang et al., 2006. Wave propagation in a fully nonlinear numerical wave tank: a desingularized method. Ocean Engineering 33, 2310–2331] is extended to solve the water wave propagation over arbitrary topography in a three-dimensional wave tank. A robust damping layer applicable for regular and irregular incident waves is employed to minimize the outgoing wave reflection back into the wave tank. Numerical results on the propagation of regular and irregular incident waves over the flat bottom and linear incident waves over an elliptical shoal show good concurrence with the corresponding analytical solutions and experimental data.     

Shear Flow Dispersion Under Wave and Current

The longitudinal dispersion of solute in open channel flow with short period progressive waves is investigated. The waves induce second order drift velocity in the direction of propagation and enhance the mixing process in concurrent direction. The 1-D wave-period-averaged dispersion equation is derived and an expression for the wave-current induced longitudinal dispersion coefficient (WCLDC) is proposed based on Fischer's expression (1979) for dispersion in unidirectional flow. The result shows that the effect of waves on dispersion is mainly due to the cross-sectional variation of the drift velocity. Furthermore, to obtain a more practical expression of the WCLDC, the longitudinal dispersion coefficient due to Seo and Cheong (1998) is modified to incluee the effect of drift velocity. Laboratory experiments have been conducted to verify the proposed expression. The experimental results, together with dimensional analysis, show that the wave effect can be reflected by the ratio between the wave amplitude and wave period. A comparative study between the cases with and without waves demonstrates that the magnitude of the longitudinal dispersion coefficient is increased under the presence of waves.     

波浪作用下斜坡上单桩周围海床孔隙水压力响应特性试验研究

单桩基础周围斜坡海床中的波致孔隙水压力响应与纯斜坡海床存在较大差异。为了解不同波高、波周期条件下,单桩基础周围波浪传播变形及其对斜坡海床孔压振荡响应的影响,在波浪水槽末端铺设了长6 m、坡度1∶16的斜坡砂床进行试验。通过改变桩身位置和波浪参数,测量斜坡段各处波面形态,采集单桩周围孔隙水压力,分析了桩身位置及波浪参数对斜坡海床孔压响应的影响。结果表明：相同入射波条件下,随距坡脚水平距离增加,波高、近底流速和桩周孔隙水压力幅值都随之增大;桩周孔隙水压力幅值分布规律为：桩前孔压幅值明显大于桩侧与桩后孔压幅值。当Keulegan-Carpenter数大于6时,随着波高和波周期增大,马蹄涡产生的负压区使得桩侧海床孔隙水压力与纯斜坡海床孔隙水压力差值迅速增加。     

Numerical study of pollutant movement in waves and wave-induced long-shore currents in surf zone

Water waves, wave-induced long-shore currents and movement of pollutants in waves and currents have been numerically studied based on the hyperbolic mild-slope equation, the shallow water equation , as well as the pollutant movement equation, and the numerical results have also been validated by experimental data. It is shown that the long-shore current velocity and wave set-up increase with the increasing incident wave amplitude and slope steepness of the shore plane ; the wave set-up increases with the in- creasing incident wave period;and the pollutant morement proceeds more quiekly with the increasing incident wave amplitude and slope steepness of the shore palane. In surf zones, the long-shore currents induced by the inclined incident waves have effectively affected the pollutant movement.     

A Three-Point Method for Separating Incident and Reflected Waves over A Sloping Bed

This study presents a three-point method for separating incident and reflected waves to explain normally incident waves' propagating over a sloping bed. Linear wave shoaling is used to determine changes in wave amplitude and phase in response to variations of bathymetry. The wave reflection coefficient and incident amplitude are estimated from wave heights measured at three fixed wave gauges with unequal spacing. Sensitivity analysis demonstrates that the proposed method can predict the reflection and amplitude of waves over a sloping bed more accurately than the two-point method.     

A Calculation Method for Incidence and Reflection of Irregular Waves Along Seawalls

Some researches have been made in this aspect.In the method by Walton Jr.(1992),incidentwaves are supposed to be the overlapping result of M component waves with different frequencies whichmay take different directions,the direction of incident waves should be available in advance,but in fact thedirection of incident waves is not available.In our study,incident waves are supposed to be composed ofM overlapping component waves with different frequencies,and different frequencies have different direc-tions.Based on the irregular wave reflection theory,the calculation formulas of wave direction,complexamplitude of incident waves,and complex amplitude of reflected waves in surface which are composed ofcomponent waves are derived by means of discrete Fourier transform.Then,the frequency spectra of inci-dent waves and reflected waves and the reflection coefficient of waves with corresponding frequencies areobtained.Verification of the method and the calculation results from in-situ measured data indicate thatt     

珠江“伶仃洋河口湾-虎门-潮汐通道”的潮波传播特征*

珠江“伶仃洋河口湾-虎门-潮汐通道”是珠江河口“网-湾”系统中的特殊地貌结构, 属潮优型河口, 潮波传播受河口湾地形辐聚效应、口门转换效应、潮汐通道辐散效应和底床摩擦等显著影响, 其时空变化复杂。本文根据珠江“伶仃洋河口湾-虎门-潮汐通道”的代表潮位站(赤湾、泗盛围和黄埔)1990—2016年逐日高、低潮位资料, 采用经典调和分析方法提取出主要天文分潮的调和常数, 通过计算获得了分潮振幅梯度及传播速度, 并在此基础上分析了伶仃洋河口湾(赤湾-泗盛围)、潮汐通道(泗盛围-黄埔)和总程(赤湾-泗盛围-黄埔)的潮波传播时空特征。结果表明: 全日分潮的振幅梯度和传播速度年均变化率均比半日分潮大, 其中K₁和O₁分潮的振幅梯度平均每年分别增加9%和18%, 传播速度每年均增加1.4%; M₂和S₂分潮的振幅梯度平均每年分别增加3%和6%, 传播速度每年均增加1%。人类活动导致地形异变, 进而驱动潮波亦发生突变, 伶仃洋河口湾和潮汐通道的M₂分潮传播速度突变年份不同, 分别为2009年和2000年。潮波传播速度突变后, 伶仃洋河口湾、潮汐通道两区段的传播速度和振幅梯度的关系也发生了变化。