Homotopy-based analytical approximation to nonlinear short-crested waves in a fluid of finite depth

A nonlinear short-crested wave system, consisting of two progressive waves propagating at an oblique angle to each other in a fluid of finite depth, is investigated by means of an analytical approach named the homotopy analysis method(HAM). Highly convergent series solutions are explicitly derived for the velocity potential and the surface wave elevation. We find that, at every value of water depth, there is little difference between the kinetic energy and the potential energy for nonlinear waves. The nonlinear short-crested waves with a larger angle of incidence always contain the more potential wave energy. With the aid of the HAM, we obtain the dispersion relation for nonlinear short-crested waves. Furthermore, it is shown that the wave elevation tends to be smoothened at the crest and be sharpened at the trough as the water depth increases, and the wave pressure crests and troughs become steeper with increasing incident wave steepness.     

REFLECTION OF OBLIQUE INCIDENT WAVES BY PERFORATED CAISSONS WITH TRAVERSE WALL

The interaction of oblique incident waves with infinite number of perforated caissons is investigated. The fluid domain is divided into infinite sub-domains by the caissons, and eigen-function expansion is applied to expand velocity potentials in each domain. A phase relation is introduced for wave oscillation in each caisson, and the structure geometry is considered in constructing the models of reflection waves. The reflected waves with the present analysis include all of the waves traveling in different directions when incident wave period is short. Numerical examinations show that velocities at the inner and outer sides of the front walls of caissons are close to each other, and reflection coefficients satisfy the energy conservation relation very well when porous effect parameter is infinite. Numerical results show that the reflection coefficients of oblique incident waves are smaller for shorter caissons at low frequency, and decrease with the increase of wave incident angle.     

Numerical study of edge waves using extended Boussinesq equations

An edge wave numerical model was developed based on extended Boussinesq equations with the internal wave-generation method. The form of edge waves near a seawall was chosen as the input signal in order to avoid treatment of the moving shoreline on a sloping beach. As there was an energy transfer between different edge wave modes, not only the target mode but also other modes appeared in the simulations. Due to the nonlinear effect, the simulation results for mode-0 edge waves were slightly modulated by mode-1 and mode-2 waves. As the magnitudes of these higher-mode waves are not significantly related to those of the target mode, the internal wave-generation method in Boussinesq equations can produce high-quality edge waves. The numerical model was used to investigate the nonlinear properties of standing edge waves, and the numerical results were in strong agreement with theory.     

An experimental study on runup of two solitary waves on plane beaches

Experiments of the runup of two solitary waves on a plane beach are carried out in a wave flume. The two solitary waves with the same amplitude and the crest separating distances are generated by using an improved wave generation method. It is found that, with regard to the two solitary waves with same wave amplitude, the runup amplification of the second wave is less than that of the first wave if the relative crest separating distance is reduced to a certain threshold value. The rundown of the first solitary wave depresses the maximum runup of the second wave. If the leading solitary wave is of relatively smaller amplitude for the two solitary waves, the runup amplification is affected by the overtaking process of two solitary waves. It turns out that the runup amplification of the second wave is larger than that of the first wave if the similarity factor is approximately larger than 15, which means the larger wave overtakes the smaller one before the waves runup on a beach.     

AN IMPROVED NUMERICAL METHOD FOR CALCULATIONS IN WAVE KINEMATICS

The prediction of wave kinematics is a necessary basis for ocean engineering design. In this article, an improved method to calculate the wave kinematics especially in the crest region is presented. This method is based on the local approximation method. According to one measured wave surface, the proposed solution focuses on a Fourier series expansion in a somewhat larger segment of the wave surface record. The horizontal and vertical kinematics under the wave crest can be directly predicted. Good agreement between the numerical results and the theoretical Stokes waves verifies the validity of the numerical model. The effectiveness of the numerical method is also proved by the calculation of the wave kinematics of the laboratory focused wave groups.     

EXPERIMENTAL INVESTIGATION ON WAVE RUN-UP CHARACTERISTICS ALONG COLUMNS AND AIR GAP RESPONSE OF SEMI-SUBMERSIBLE PLATFORM

This article mainly concentrates on a large-volume drilling semi-submersible platform,aiming to reveal wave run-up characteristics along square columns and give the relationship between air gap distributions and wave parameters.The tests with fixed model were conducted firstly on its encountering a series of monochromatic waves.A wide range of wave slope (H /L) were selected to investigate the air gap response in detail.As can be seen,larger wave steepness will generally cause smaller air gap in the same wave period,which indicates nonlinear effects of incoming wave can amplify wave elevation.Model tests with mooring condition were also conducted in the same wave conditions.As was expected,the maximum relative wave elevation reduces obviously compared with the fixed one.However,wave shape close to columns show higher harmonic characteristics due to interaction between waves and the columns of semi-submersible platform.Meaningful conclusions from the model tests are drawn in this article,which is helpful in air gap design of floating offshore platform to a certain extent.In addition,the experimental results will provide an important reference for further research on validation and update of theoretical models of air gap.     

A PRACTICAL MODEL FOR THE DECAY OF RANDOM WAVES ON MUDDY BEACHES

A practical model has been developed for the propagation and decay of random waves on muddy beaches. In the model, an irregular wave train is characterized by its root-mean-squared wave height, mean wave frequency and mean wave direction. It is also assumed that the wave spectrum is narrow-banded in terms of both frequency and direction. Transformation of root-mean-squared wave height is derived from the conservation of energy flux for individual wave components. Energy dissipation is considered due to both wave breaking and the dynamics response of muddy seabed. The model is applied to waves on the muddy beach at Hangzhou Bay, and the numerical results obtained are shown to be acceptably accurate as comparing with available field data.     

中心管管径变化对浮标波能转换性能的影响分析

为了探究中心管管径变化对振荡水柱式波能发电装置能量转化性能的影响,从提高波力发电装置的能量转换效率方面,设计了一种中心管结构,对其上下部分管径取3组比值,采用流体力学仿真软件和网格划分软件对三组模型进行数值模拟计算并在造波水池中进行能量转换效率误差分析。结果表明,直管型中心管能量俘获宽度比仿真结果和实验数据最高值分别为10. 6%、9. 8%,虽然俘获宽度比出现了双峰值,但波峰不高且波谷较低;管径比为5/7和3/7的阶梯型中心管能量俘获宽度比仿真值和试验值分别为15. 7%、15. 2%和17. 6%、16. 4%,阶梯型中心管能量转换效率优于直管型中心管,且都出现了双峰值和较高的波谷。在实际运行中,采用阶梯型中心管可有效提升波能发电装置的能量转化效率,且中心管管径比r_2/r_1越小,其效率提升越明显。考虑到装置的结构合理性,中心管具体尺寸应视实际情况取值。研究成果能够为新型波浪浮标的设计提供理论依据。     

珊瑚岛礁护岸对礁坪上极端波浪传播特性的影响

极端波浪要素是珊瑚岛礁护岸工程设计的重要参数。利用大比尺波浪水槽,采用1: 15的模型比尺开展试验,从波浪形态、增水、波速、波谱等方面研究了珊瑚岛礁护岸对礁坪上极端波浪传播特性的影响规律。护岸工程产生了明显的阻水效应:对于波浪形态,反射波的影响使得波浪在礁缘破碎更为剧烈; 显著增加了礁坪增水,最大增水值是自然地形下的4倍,影响在波周期较短时更为显著; 减小了波速约20%~35%,其影响随波周期的减小而增强; 对于波谱,护岸的存在使得波浪的非线性相互作用更加复杂,降低了波浪在礁缘处的主频能量,但同时增大了礁坪上的主频及高频能量; 护岸距礁缘距离对堤前水位具有重要影响,随该距离的增加,堤前时均水位先增加后降低。     

THE ANALYSIS OF INTRASEASONAL LONG ROSSBY WAVE SPEED IN THE SUBTROPICAL PACIFIC OCEAN

1. INTRODUCTIONLong Rossby waves are the main mechanis mwherebyinformation about one part of the oceanistransferred to another part and a nonequilibriumo-cean state adjusts to an equilibriumone . The studyon the beta views of long Rossby waves is an i m-portant aspect of ocean circulation. In a recentstudy , Chelton and Schlax[1]conducted a thoroughanalysis of the satellite alti meter data from thefirst 3 years TOPEX/POSEIDON mission. Theyfound two interesting properties of long Ro…     

NUMERICAL STUDY OF SOLITARY WAVE FISSION OVER AN UNDERWATER STEP

Solitary wave fission over an underwater step is numerically investigated. The numerical model is based on the enhanced Boussinesq equations, which appropriately represent both the nonlinearity and dispersivity of surface water waves. The finite difference method defined on the staggered grid in space with an implicit scheme for time stepping is employed for the numerical solution of the governing equations. It is demonstrated that Boussinesq type equations, though they are vertically integrated, can describe the details of the solitary wave fission process with very good accuracy. Numerical results of the reflected and transmitting wave heights, the number of solitons emitted from the transmitting wave and their amplitudes all agree very well with the analytical solution derived from KdV equation by virtue of a linear long wave approximation in the vicinity of the underwater step.     

PROPAGATION AND BREAKING OF WAVES ON SLOPING BEACH

In this paper the propagation and breaking of the solitary wave,the sinusoidalwave and the second Stokes wave on a slope of 1/30 are discussed based upon the TUMMACmethod,and the velocity fields of breaking waves on the slope are obtained by using the tracingmethod.The.numerical results for wave deformation are in good agreement with experimentaldata,and the breaker indexes depending on the kinetic criterion agree approximately with previ-ous results.Furthermore,compared with the experimental results measured by Iwagaki and bythe authors,the tendency of velocity distribution of breaking waves computed by this numericalmethod is also satisfactory.     

NUMERICAL SIMULATION OF EXTREME WAVE GENERATION USING VOF METHOD

Numerical simulations of extreme wave generation are carried out by using the Volume Of Fluid (VOF) method. Extreme waves are generated based on wave focusing in a 2-D numerical model. To validate the capability of the VOF-based model described in this article, the propagation of regular waves is computed and compared with the theoretical results. By adjusting the phases of wave components, extreme waves are formed at given time and given position in the computation. The numerical results are compared with theoretical solutions and experimental data. It is concluded that the present model based on the VOF technique can provide acceptably accurate numerical results to serve practical purposes.     

窄深河谷近坝库岸滑坡涌浪特性及传播规律

大比尺水工模型试验可获得更接近原型的相似现象,对窄深河谷近坝库区可能发生的整体大体积滑坡工况进行试验研究,结合三维数值模型分析滑坡次生涌浪的产生、传播和消散特性。研究结果表明:数值模型计算的浪高、相位与试验结果基本一致,库区涌浪类型属于有限水深波,波能沿水深方向均有分布;涌浪产生区附近非线性较强,受窄深地形影响,波高在传播过程中快速衰减,坝肩处涌浪叠加出现瞬时越浪;试验中涌浪近场波形只观测到弱非线性振荡波;试验范围内块体模型冲击动能转化率为2%~19%,滑块动能转化率与相对体积、相对厚度呈正相关,与滑块入水弗劳德数呈负相关;低频波受地形影响较大,在岸坡浅水区域出现波能的暂时集中,谱峰值增大,随时间推移库区水域高频波增多。对于窄深河谷中的大体积滑坡次生涌浪,尽管首浪波能受高陡边坡影响,传播至坝前时波高已明显削减,但坝前最大浪高往往由涌浪反射叠加形成,在首浪到达之后仍存在翻坝风险。     

无反射造波数值波浪水槽

本文应用ＶＯＦ方法建立了二维数值波浪水槽模型。基于线性造波机理论在水槽左端设置了可吸收式造波机数值边界条件。即造波板的运动除了产生行进波外，同时还产生一个抵消反射波的局部波动。水槽右端除了通常的可滑移与无滑移直墙边界条件外，依据线性辐射条件建立了开边界条件。通过水槽右端为直墙时的全反射情形，比较了可吸收造波机与普通造波机的速度变化与波面变化。文中在Ｈ０／ｄ＝０．１￣０．３，ｄ／Ｌ＝０．１２４￣０．     

倾斜底坡上波浪的传播与破碎

本文根据TUMMAC方法探讨了孤立波、微幅波和二阶Stokes波在1/30底坡上的传播与破碎,并采用示踪法测得了相同底坡上濒临破碎波的速度场。与前人的实验结果相比较表明,计算所得的波浪外形变化是一致的,依据运动学标准所得的各项破碎指标也大致相同;与岩垣及本文实验结果比较表明,速度的分布趋势也是一致的。     

孤立波作用下组合型港池共振响应的数值研究

港池受到孤立波入射时会在港池内激发多种模态的共振响应。为进一步研究不同平面布置形式港池的响应特性和共振规律,建立不同内外港池长度和连接位置的组合型港池,采用基于Boussinesq方程的波浪数值模型MIKE 21-BW模拟了孤立波作用下组合型港池的共振响应,对数值模拟的结果进行频谱分析和波幅分布测定并与现有理论值比较。结果表明,孤立波正向入射组合型港池激发的主要响应模态的频率和与其长度相等的细长港池的理论固有频率接近,各主要共振模态的振幅与内外港池的长度和两港池口门的距离有密切关系;波浪入射方向和港池内边界反射条件的改变对狭长组合型港池中形成的各共振模态的形状影响不大,但是增大港池宽度会使港池内激发明显的横向共振。最后提出了消减港湾共振的平面布置形式,可为实际工程设计提供指导。     

NUMERICAL SIMULATION OF PROPAGATION AND BREAKING PROCESSES OF A FOCUSED WAVES GROUP

A two-dimensional numerical wave flume is developed to study the focused waves group propagation and the consequent breaking processes. The numerical model is based on the Reynolds-Averaged Navier-Stokes (RANS) equations, with the standard k-ε turbulence model to simulate the turbulence effects. To track the complicated and broken free-surface, the Volume Of Fluid (VOF) method is employed. The numerical model combines the "Partial Cell Treatment (PCT)" method with the "Locally Relative Stationary (LRS)" concept to treat the moving wave paddle so that various waves can be generated directly in a fixed Cartesian grid system. The theoretical results of the linear and nonlinear waves are used to validate the numerical wave flume firstly, and then a plunging breaking wave created by a focused waves group is simulated. The numerical results are compared to the experimental data and other simulation results, with very good agreements. The turbulence intensity, the flow field and the energy dissipation in the breaking processes are analyzed based on the numerical results. It is shown that the present numerical model is efficient and accurate for studying the waves group generation, the waves packet propagation, and the wave breaking processes.     

DISTRIBUTION OF WAVE-INDUCED EXCESS MOMENTUM FLUXES OVER DEPTH AND APPLICATION TO THREE-DIMENSIONAL NUMERICAL MODELING OF WAVE-CURRENT INTERACTIONS

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多模式瑞雷波波场特征及能量分布特性研究

针对实际工程勘察中3种常见的典型地质结构，利用高阶有限差分正演模拟技术，深入研究了多模式瑞雷波波场特征及能量分布特性。研究结果表明：对于递增型地质结构，基阶波在整个频带波场特征十分明显，基阶波能量占整个波场的主导地位，此时反演分析时可仅利用基阶波信息；而对于含低速软弱夹层或高速硬夹层等复杂地质结构，高模式波波场特征在高频段或中频段十分显著，基阶波能量则在这些频段处于次要地位，此时反演分析时应充分利用多模式瑞雷波信息，以提高复杂地质结构反演解释精度和可靠性。