Focusing phenomenon and near-trapped modes of SH waves

In this study, the null-field boundary integral equation method （BIEM） and the image method are used to solve the SH wave scattering problem containing semi-circular canyons and circular tunnels. To fully utilize the analytical property of Circular geometry, the polar coordinates are used to expand the closed-form fundamental solution to the degenerate kernel, and the Fourier series is also introduced to represent the boundary density. By collocating boundary points to match boundary condition on the boundary, a linear algebraic system is constructed. The unknown coefficients in the algebraic system can be easily determined. In this way, a semi-analytical approach is developed. Following the experience of near-trapped modes in water wave problems of the full plane, the focusing phenomenon and near-trapped modes for the SH wave problem of the half-plane are solved, since the two problems obey the same mathematical model. In this study, it is found that the SH wave problem containing two semi-circular canyons and a circular tunnel has the near-trapped mode and the focusing phenomenon for a special incident angle and wavenumber. In this situation, the amplification factor for the amplitude of displacement is over 300.

A Single Mooring System with Sag-Extensibility and Flexural Rigidity Applied to Offshore Platform

Floating platform system has been extensively used in ocean exploitation, particularly for a tension-leg platform （TLP） system in deep water. Most of the TLPs are multi-mooring systems, where multi-joints are connected to the tension-legs so that the platform is not allowed to twist freely and may subject to enormous force induced by large incident waves in the weak-direction of the structure. This study aims to exploit a single moored offshore platform system that may attract less force and can be operated with less effort. In our analysis, in addition to mechanical properties of the tether, two important properties are also taken into consideration for the single mooring tether with expanded cross sectional dimension and utilization of stronger material, namely, the sag-extensibility and the flexural rigidity. Finally, the dynamic structural behavior produced by the mechanical effects on the new system is investigated and compared with that of traditional design while the wave-structure interactions of large body are also accounted for. Our study finds that the neglect of sag-extensibility or the flexural rigidity of large, strong mooring cable may result in a conservative but not necessarily safe design.

Computation of Long-Term Statistical Properties of Wave Agitation in Harbors

In this paper, the long-term statistical properties of wave height in an idealized square harbor with a partial opening are studied. The incident waves are propagated into the harbor numerically by the finite/infinite element method using three different wave models: (1) monochromatic wave train, (2) long-crested random wave train, and (3) short-crested random wave train. This study shows that for a given incident wave, the wave height in the harbor is affected by the wave model used. For long-term estimation of wave height exceedance probability, it is recommended that the waves be propagated into the harbor using the random wave model, and that wave heights be computed by use of the Rayleigh probability distribution.

Analysis of Responses of Floating Dual Pontoon Structure

A numerical model is developed by use of the boundary integral equation method to investigate the responses of a two-dimensional floating structure. The structure under consideration consisting of two pontoons, is connected by a rigid framework, and linked to the sea floor by a mooring system. The theoretical conception is based on potential theory with hnear external forces, and applied to an arbitrarily shaped body and water depth. The discussion includes the influence of draft and space between pontoons on the responses of the floating structure. Finally, the validity of the method is adequately verified by experimental results.

The Reflection of Normal Incident Waves by Absorbing-Type Breakwaters

This paper investigates the reflection of normal incident waves produced by absorbing-type breakwaters. The absorbing-type breakwaters in this study consist of a vertical porous plate, a submerged permeable caisson, and an impermeable back wall. The flow field is divided into four regions： a porous caisson region, and three pure water regions. Under the assumptions of linear wave theory, Darcy＇s law in the perforated wall, and the pore velocity potential theory of Sollitt and Cross （1972） in the porons caisson region, this study creates a 2-D BEM model to calculate the reflection coefficients of water waves using several breakwater properties. This numerical model is calibrated by previous numerical studies and limiting cases for a partially perforated-wall caisson breakwater and a vertical porous breakwater with an impermeable back wall. Generally speaking, the wave dissipation in absorbing-type breakwaters is bigger than that for a partially perforatedwall caisson breakwater. The reflection coefficient values imply the performance of wave absorbers in this study. Therefore, we examine the major factors that affect the reflection coefficient.

Experimental Investigation of Wave Heights in A Directional Wave Field Through Image Sequences

Measurements of wave heights with image sequences from a Charged Coupled Device(CCD) camera were made. Sinusoidal, as well as unidirectional and directional, waves were used for the experiments. A transfer function was obtained by calibration of the magnitudes of the gray values of the images against the results of wave gauge measurements for directional waves. With this transfer function, wave heights for regular waves were deduced. It is shown that the average relative errors are smaller than 16% for both unidirectional and directional waves.

A Note on the Derivation of Wave Action Balance Equation in Frequency Space

In this paper the wave action balance equation in terms of frequency-direction spectrum is derived. A theoretical formulation is presented to generate an invariant frequency space to replace the varying wavenumber space through a Jacobian transformation in the wave action balance equation. The physical properties of the Jacobian incorporating the effects of water depths are discussed. The results provide a theoretical basis of wave action balance equations and ensure that the wave balance equations used in the SWAN or other numerical models are correct. It should be noted that the Jacobian is omitted in the wave action balance equations which are identical to a conventional action balance equation.

Dynamic Behaviors of a Moored Floating Structure with Flexible Skirts

A numerical model was developed by using the dual boundary element method to investigate the dynamic behavior of a moored floating structure with a pair of vertical and flexible skirts attached at its bottom in the linear wave field. Theoretical conception is based on potential theory with linear external forces. The motions of the structure were assumed to be small and linear. The flexible skirts mounted beneath the structure were assumed uniform flexural rigidity and the thickness of the skirts was negligible. Comparison between the present model and Gesraha＇s solution was made to verify the results for a moored floating structure with or without rigid skirts. The influence of the skirt rigidity on the moored floating structure, moored lines and waves is investigated in this study. The results show that, the natural frequencies of structure＇s oscillation, moored force, wave reflection and transmission tend to the region of short-period waves when the flexible rigidity gradually decreases. Positive correlation exists between the aft mooring force and the pitch motion of the floating structure.

A Novel Spacetime Collocation Meshless Method for Solving Two- Dimensional Backward Heat Conduction Problems

In this article,a meshless method using the spacetime collocation for solving the two-dimensional backward heat conduction problem(BHCP)is proposed.The spacetime collocation meshless method(SCMM)is to derive the general solutions as the basis functions for the two-dimensional transient heat equation using the separation of variables.Numerical solutions of the heat conduction problem are expressed as a series using the addition theorem.Because the basis functions are the general solutions of the governing equation,the boundary points may be collocated on the spacetime boundary of the domain.The proposed method is verified by conducting several heat conduction problems.We also carry out numerical applications to compare the SCMM with other meshless methods.The results show that the SCMM is accurate and efficient.Furthermore,it is found that the recovered boundary data on inaccessible boundary can be obtained with high accuracy even though the over specified data are provided only at a 1/6 portion of the spacetime boundary.

Numerical Study on Breaking Criteria for Solitary Waves

Studies of the breaking criteria for solitary waves on a slope are presented in this paper. The boundary element method is used to model the processes of shoaling and breaking of solitary waves on various slopes. Empirical formulae that can be used to characterize the breaking of solitary waves are presented. These include the breaking index, the wave height, the water depth, and the maximum particle velocity at the point of breaking. Comparisons with the results of other researches are given.

结合微孔隙水压力计改良型GR试验系统分析研究(英文)

本研究针对结合微孔隙水压力计改良型GR试验系统与一般GR试验系统进行了一系列的试验分析比较,研究中所使用的试验材料包含4种不同针轧不织布及5种不同比例渥太华砂与风化泥岩混合土壤。试验结果发现,由改良型GR试验系统所得的GR试验值都高于一般GR试验系统所得结果,同时也验证了微孔隙水压力计在GR试验系统中可提供较好的孔隙水压力量测与抗阻塞潜势评估。

An Experi mental Study on Wave-Induced Dynamic Stresses in Seabed

A series of hydraulic model tests with horizontal movable seabed under regular wave actions have been carried out to investigate the dynamic interactions between water waves and seabed soil. Seabed dynamic stresses from experiments are, tound to differ from theoretical resuhs. The response of p0 in permeable seabed has a small decay and phase shift to the nonlinear wave actions, and the dynamic stresses, σs/p0, σh/p0 and u/p0, contain different phase shift characteristics. Such phenomena will strongly affect the dynamic stress path in seabed. If the phase shifts of σs. and σh are neglected, the stress path will become a straight line; otherwise, it will become an elliptical curve. In phase shift cases, the long axis of the p - q diagram will be shortened when the depth increases, and the short axis will become longer when the phase shift increases. For the p＇ - q＇ diagram, the larger the phase lag of u, the longer the short axis. Relative results offer useful information for the analysis of seabed stability.

A Comparative Study on Polynomial Expansion Method and Polynomial Method of Particular Solutions

In this study,the polynomial expansion method(PEM)and the polynomial method of particular solutions(PMPS)are applied to solve a class of linear elliptic partial differential equations(PDEs)in two dimensions with constant coefficients.In the solution procedure,the sought solution is approximated by the Pascal polynomials and their particular solutions for the PEM and PMPS,respectively.The multiple-scale technique is applied to improve the conditioning of the resulted linear equations and the accuracy of numerical results for both of the PEM and PMPS.Some mathematical statements are provided to demonstrate the equivalence of the PEM and PMPS bases as they are both bases of a certain polynomial vector space.Then,some numerical experiments were conducted to validate the implementation of the PEM and PMPS.Numerical results demonstrated that the PEM is more accurate and well-conditioned than the PMPS and the multiple-scale technique is essential in these polynomial methods.