A higher-order σ-coordinate non-hydrostatic model for nonlinear surface waves

A higher-order non-hydrostatic model in a σ-coordinate system is developed. The model uses an implicit finite difference scheme on a staggered grid to simultaneously solve the unsteady Navier-Stokes equations (NSE) with the free-surface boundary conditions. An integral method is applied to resolve the top-layer non-hydrostatic pressure, allowing for accurately resolving free-surface wave propagation. In contrast to the previous work, a higher-order spatial discretization is utilized to approximate the large horizontal pressure gradient due to steep surface waves or rapidly varying topographies. An efficient direct solver is developed to solve the resulting block hepta-diagonal matrix system. Accuracy of the new model is validated by linear and nonlinear standing waves and progressive waves. The model is then used to examine freak (extreme) waves. Features of downshifting focusing location and wave asymmetry characteristics are predicted on the temporal and spatial domains of a freak wave.     

Bragg resonant reflection of carrier waves composing wave groups

Numerical analyses for the Bragg resonant reflection of carrier waves associated long waves due to sinusoidally varying seabeds are performed by using a set of coupled ordinary differential equations derived from the Boussinesq equations. The Boussinesq equations are firstly approximated with the Fourier decomposition. The coupled governing equations are then derived and used to simulate evolution of both short and long wave components. It is also found that wave groups are generated by two carrier waves with slightly different frequencies. The wave energy of the initial wave components is transferred to other harmonic components during propagation over a long distance. Evolution and reflection of both short and long waves were largely affected by nonlinearity.     

Wave Reflection Caused by Wave Overtopping and Sloping Top of Spructure

In this paper, the theoretical analysis and experimental studies are employed to investigate the reflection characteris-tics of partial standing waves caused by wave overtopping and sloping top of structures. Based on the principle of conser-vation of wave energy flux, the third-order Stokes wave theory is used to formulate the reflection coefficient at wave overtopping; the calculation results are regressed into an applied expression. A series of experiments of wave reflection for a vertical-wall structure with chamfered and overhanging upper sections are carried out to investigate the influence of top slope on wave reflection. The regularity of variation of wave reflection in this case is analysed based on the experimental results.     

Hilbert Transferin Applied to Separation of Waves

The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is ap-plicable to both regular and irregular trains of waves. The wave data series measured with two wave gauges in the experi-ments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily ob-tained. The arrival of reflected waves can also be detected for improveraent of the accuracy of the reflection coefficient. The reflection performance of the physical model can be estimated exactly without calculation of wave height and phase difference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conduct-ed and compared with Goda s method and satisfactory results are obtained.     

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.     

Ocean Waves: Half-a-Century of Discovery

While the nature of most ocean waves has long been known and their basic physics understood since the nineteenth century, intense study of ocean waves during the second half of the twentieth century has taken the subject from the realm of mathematical exercises to that of practical engineering. Modern understanding of the generation, propagation and interactions of ocean waves with each other and with oceanic features has advanced to a quantitative level offering predictive capacity. This paper presents a brief qualitative review of advances in knowledge of sound waves, wind waves, tsunamis, tides, internal waves and long-period vorticity waves. The review is aimed at non-specialists who may benefit from an overview of the current state of the subject and access to a bibliography of general-interest references. This revised version was published online in August 2006 with corrections to the Cover Date.     

环台湾岛海域半日潮波特征的三维模拟

用1997版POM海洋模式,首次应用于环台湾岛海域的潮波数值研究.得到该海域的半日潮波主要为23°N以南西太平洋传来的胁振潮.影响台湾海峡的半日潮波分别由海峡南北口传入的两支潮波,且北支强于南支.福建沿岸湄州湾-兴化湾为最强潮区,其M₂分潮最大振幅可达240cm.最强潮流区位于澎湖水道,M₂分潮最大潮流达196cm/s.环台湾岛海域潮波潮流水平结构上除海峡北部原有一个圆流点外,还发现另外存在4个新的圆流点.潮流垂直结构上主要为右偏,接近底层处为左偏.     

9914号(Dan)台风浪的后报试验研究

利用WAM第三代海浪模式的第四版本(WAMC4)对40a来造成福建沿海灾害最严重的9914号台风海浪过程进行了后报试验，并与近岸常规观测和卫星高度计有效波高资料进行了比较。与常规观测站的比较结果表明，WAMC4能较好地再现海浪的发展过程。后报结果与TOPEX/POSEIDON和ERS-2卫星观测资料的对比研究表明，风速的后报结果与卫星观测有较好的一致性，但海浪的后报比卫星高度计反演的有效波高整体略偏低。     

Reflection of waves from the boundary of a random elastic semi-infinite medium

In this paper the smooth perturbation technique is employed to investigate the problem of reflection of waves incident on the plane boundary of a semi-infinite elastic medium with randomly varying inhomogeneities. Amplitude ratios have been obtained for various types of incident and reflected waves. It has been shown that an incidentSH orSV type of wave gives rise to reflectedSH, P andSV waves, the main components beingSH andP, SV in the respective cases. The reflected amplitudes have been calculated depending upon the randomness of the medium to the square of the small quantity , where measures the deviation of the medium from homogeneity. An incidentP-type wave produces mainly aP component and also a weakSH component to the order of ². The reflected amplitudes obtainable for elastic media are also altered by terms of the same order. The direction of the reflected wave is influenced by randomness in some cases.     

Hybrid seismic modeling based on discrete-wave number and finite-difference methods

Any calculation of seismic wave propagation comprising the seismic source, the travel path, and the receiver site in a single finite-difference (FD) model requires a considerable amount of computer time and memory. Moreover, the methods currently available for including point sources in the 2D FD calculations are far-field approximations only. Therefore we have developed a new hybrid method for treating the seismic wave fields at localized 2D near-surface structures embedded in a 1D background medium, and excited by a point source. The source radiation and propagation in the background model is solved by the discrete-wave number (DW) method, while the propagation in the local 2D structure is calculated by the FD method. The coupling between the two sets of calculations is performed on a rectangular excitation box surrounding the local structure. We show the usefulness of the method in ground-motion studies where both near-field source effects and local site effects are important. Technical problems connected with the inconsistency between the 3D source radiation and the 2D FD calculation are minor for the relatively distant in-plane point explosive sources, but are more serious for the in-plane dislocation sources.