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 harborwith a partial opening are studied.The incident waves are propagated into the harbor numerically by the fi-nite/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 giv-en incident wave,the wave height in the harbor is affected by the wave model used.For long-term estima-tion of wave height exceedance probability,it is recommended that the waves be propagated into the har-bor using the random wave model,and that wave heights be computed by use of the Rayleigh probabilitydistribution.     

An Efficient Model for Transient Surface Waves in Both Finite and Infinite Water Depth

A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Eulerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The boundary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.     

Numerical study of nonlinear freak wave impact underneath a fixed horizontal deck in 2-D space

Freak waves are extreme and unexpected surface waves with huge wave heights that may lead to severe damage to ships and offshore structures. However, few researches have been conducted to investigate the impact underneath fixed horizontal decks caused by freak waves. To study these phenomena, a 2-D numerical wave tank is built in which nonlinear freak waves based on the Peregrine breather solution are generated. As a validation, a regular-wave-induced underneath impact is simulated and compared to the existing experimental measurements. Then the nonlinear freak-wave-induced impact is investigate with different values of deck clearance above the mean free surface. In addition, a comparative simulation of a “large” regular wave based on the 2nd-order Stokes wave theory with the same crest height and wave length of the nonlinear freak wave is carried out to reveal the unique features of the nonlinear freak-wave-induced impact. By applying a fluid–structure interaction (FSI) algorithm in which the bottom deck and front side wall are simplified as Euler beams in 2-D and discretized by the finite element method (FEM), the hydroelastic effects are considered during the impact event. The vertical force acting underneath the bottom deck, the transversal force acting on the front side wall, the structural displacements of the elastic deck and wall are analyzed and discussed respectively, from which meaningful conclusions are drawn.     

A composite numerical model for wave diffraction in a harbor with varying water depth

A composite numerical model is presented for computing the wave field in a harbor. The mild slope equation is discretized by a finite element method in the domain concerned. Out of the computational domain, the water depth is assumed to be constant. The boundary element method is applied to the outer boundary for dealing with the infinite boundary condition. Because the model satisfies strictly the infinite boundary condition, more accurate results can be obtained. The model is firstly applied to compute the wave diffraction in a narrow rectangular bay and the wave diffraction from a porous cylinder. The numerical results are compared with the analytical solution, experimental data and other numerical results. Good agreements are obtained. Then the model is applied to computing the wave diffraction in a square harbor with varying water depth. The effects of the water depth in the harbor and the incoming wave direction on the wave height distribution are discussed.     

Response of skirted suction caissons to monotonic lateral loading in saturated medium sand

Monotonic lateral load model tests were carried out on steel skirted suction caissons embedded in the saturated medium sand to study the bearing capacity. A three-dimensional continuum finite element model was developed with Z_SOIL software. The numerical model was calibrated against experimental results. Soil deformation and earth pressures on skirted caissons were investigated by using the finite element model to extend the model tests. It shows that the ＂skirted＂ structure can significantly increase the lateral capacity and limit the deflection, especially suitable for offshore wind turbines, compared with regular suction caissons without the ＂skirted＂ at the same load level. In addition, appropriate determination of rotation centers plays a crucial role in calculating the lateral capacity by using the analytical method. It was also found that the rotation center is related to dimensions of skirted suction caissons and loading process, i.e. the rotation center moves upwards with the increase of the ＂skirted＂ width and length; moreover, the rotation center moves downwards with the increase of loading and keeps constant when all the sand along the caisson＇s wall yields. It is so complex that we cannot simply determine its position like the regular suction caisson commonly with a specified position to the length ratio of the caisson.     

A composite numerical model for wave diffraction in a harbor with varying water depth

A composite numerical model is presented for computing the wave field in a harbor. The mild slope equation is discretized by a finite element method in the domain concerned. Out of the computational domain, the water depth is assumed to be constant. The boundary element method is applied to the outer boundary for dealing with the infinite boundary condition. Because the model satisfies strictly the infinite boundary condition, more accurate results can be obtained. The model is firstly applied to compute the wave diffraction in a narrow rectangular bay and the wave diffraction from a porous cylinder. The numerical results are compared with the analytical solution, experimental data and other numerical results. Good agreements are obtained. Then the model is applied to computing the wave diffraction in a square harbor with varying water depth. The effects of the water depth in the harbor and the incoming wave direction on the wave height distribution are discussed.     

The dynamic response of a three-leg articulated tower

Articulated towers are a compliant type of platform particularly suited for deep water applications. In the design of articulated towers, it is very important that the motion characteristics include sufficient stability, less acceleration in the deck and the smallest possible loading on the articulated joint. The mass distribution along the tower also plays an important role in the motion characteristics of the tower. Multi-leg articulated towers with three or more towers (legs or shafts), which have been developed from the conventional single tower have reduced horizontal movements and have more deck area compared to the single-leg articulated towers. The experimental and analytical investigations on such towers are not available in the published literature. In this paper, both analytical treatment and an experimental program for a three-leg articulated tower model have been reported. The effect of mass distributions on the variations of the bending moment and the deck accelerations are also presented. The model has been tested in a 2 m wave flume for various wave frequencies and wave heights of regular waves. The model is also analysed using a computer program developed, and the comparison of theoretical results with the experimental results is presented.     

A model for obliquely incident wave interacting with a multi-layered object

This paper presents an analytical solution for scattering of oblique incident, small amplitude, monochromatic wave trains by a stationary rigid multi-layered objects with rectangular cross-section. The object is infinite long and consists of multilayers, which can be either solid or permeable. This paper extends the previous work by Hu and Liu [1] from normal incident wave condition with a special object configuration to oblique incident waves with multi-layered object. The present model is validated with several existing solutions for normal/oblique waves interacting with a single object; excellent agreement is observed. New numerical results are presented to investigate the effects of incidence angle on reflection, transmission and energy loss coefficients for a combined floating and bottom-mounted permeable breakwater. A new floating board-cage breakwater is developed from the present model and its solutions are discussed in detail. A computer program, AWAS-P, has been updated so that it is applicable for both oblique and normal incident waves, while the object is multi-layered.     

An Efficient Model for Transient Surface Waves in Both Finite and Infinite Water Depths

A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Eulerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The boundary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropr...     

Extension of the Frequency-Domain pFFT Method for Wave Structure Interaction in Finite Depth

To analyze wave interaction with a large scale body in the frequency domain, a precorrected Fast Fourier Transform (pFFT) method has been proposed for infinite depth problems with the deep water Green function, as it can form a matrix with Toeplitz and Hankel properties. In this paper, a method is proposed to decompose the finite depth Green function into two terms, which can form matrices with the Toeplitz and a Hankel properties respectively. Then, a pFFT method for finite depth problems is developed. Based on the pFFT method, a numerical code pFFT-HOBEM is developed with the discretization of high order elements. The model is validated, and examinations on the computing efficiency and memory requirement of the new method have also been carried out. It shows that the new method has the same advantages as that for infinite depth.     

Dynamics of Submersible Mussel Rafts in Waves and Current

To investigate the dynamics of submersible mussel rafts, the finite element program Aqua-FE?, developed by the University of New Hampshire (UNH), was applied to rafts moored at the surface and submerged. The submerged configuration is used to reduce wave forcing and to avoid contact with floating ice during winters in northern waters. Each raft consists of three pontoons connected by a grid framework. Rafts are intended to support densely spaced mussel ropes hung from the framework. When submerged, the pontoons are flooded, and the raft is held vertically by floats attached by lines. The computer models were developed in Aqua-FE? to simulate the effects of waves and current. They were validated by comparison with wave tank results by use of a 1/10 scale raft physical model. Comparisons showed good agreement for the important heave (vertical) and pitch (rotational) motions, though there was a tendency towards conservative results for wave and current drag. Full-scale simulations of surface and submerged single raft and two rafts connected in tandem were performed. Submerged raft wave response was found to be reduced relative to that at the surface for both the single and two-raft configurations. In particular, the vertical motion of mussel rope connection points was significantly reduced by submergence, resulting in reduced potential for mussel drop-off. For example, the maximum vertical velocities of mussel rope attachment points in the submerged two raft case were 7%?20% of the corresponding velocities when at the surface.     

Breaking wave prediction with boundary elements and finite volumes for use with small boat capsize studies: Convergence and resource requirements

The prediction of extreme breaking waves forms the foundation of many fields of research. The authors have recently completed a study in the capsize and re-righting of sailing yachts using breaking wave prediction to enhance experimental results. As breaking wave prediction is only the beginning of any research program a prediction method is required to be both accurate and computationally inexpensive. This paper describes the investigation of two methods varying in computational demand. It has been concluded that a non-linear free surface boundary element method is immediately realisable with application to a research program requiring a large number of predicted waves. A finite volume approach is realisable, but its engineering application across numerous waves is difficult.     

波浪与带窄缝方箱作用共振现象的数值模拟

By introducing a source term into the Laplace equation, a two-dimensional fully nonlinear time-domain numerical wave flume (NWF) is developed to investigate the resonance induced by the interaction bet...     

利用有限元方法求解双曲型缓坡方程

本文提出了一种双曲型缓坡方程的有限元计算方法 ,在建立有限元积分方程时通过在造波线处加入脉动源项来实现内部造波 ,并在开边界处利用阻尼层吸波 ,减少了在边界处由于数值处理引起的误差。数值计算结果与实测值吻合良好。本方法可用于大区域波浪场的计算中     

Applications of A Numerical Model to Wave Propagation on Mild Slopes

Based on the mild slope equation that has heen deeomposed inlo three equations related to wave phase function, wave amplitude and wave approach angle, a refraction-diffraction model is developed. The finite difference method has been selected as the solution method. The model results are compared with experimental results and the model is applied to coastal waters of the Fethiye Bay, whieh is located at the Mediterranean Sea of Turkey.     

修正型缓坡方程的有限元模型

与缓坡方程相比,修正型缓坡方程增加了地形曲率项和坡度平方项,从而提高了数值求解的复杂性。本文将计算域划分为内域和外域,内域为水深变化区域,使用修正型缓坡方程,其中的地形曲率项和坡度平方项可用有限单元各节点的水深信息和单元插值函数表示,外域为水深恒定区,速度势满足Helmholtz方程,通过内外域的边界匹配建立有限元方程,并用高斯消去法求解。进而分别模拟了波浪传过Homma岛和圆形浅滩的变形,其结果与相关的解析解和实验数据吻合良好,证明了本文有限元模型的正确性。同时,通过与实验数据的对比也明显看出,在地形坡度较陡的情况下,修正型缓坡方程较缓坡方程具有更高的计算精度。     

Improving force resultant model for anchors in clays from large deformation finite element analysis

Abstract

This paper presents an improved plasticity force-resultant model for anchors deeply embedded in clays, developed from large deformation finite element analyses. The current available force-resultant models for anchors are mainly developed from small strain finite element analysis while experimental approach has not been used due to technical challenges. The advantage of large deformation finite element analysis is that it provides much more data points to fit the yield surface than small strain finite element analysis, in addition to avoiding excess mesh distortion problems. Furthermore, the flow rule or normality can be effectively checked in the large deformation finite element analysis and further used to improve the fitting quality. After validated against retrospective simulations, the better performance of the developed plasticity force-resultant model is demonstrated by comparing with available experimental observations from centrifuge test.     

Development and validation of a finite element morphological model for shallow water basins

Recognising the importance of understanding sediment dynamics to evaluate the status of a coastal lagoon environment, this work has been focused on the investigation of the hydrodynamic and sediment transport processes occurring in such basins. In order to describe the lagoon system, a modelling approach combining hydrodynamics, waves and sediment dynamics has been developed. The framework of the numerical model consists of a finite element hydrodynamic model, a third generation finite element spectral wave model and a sediment transport and morphodynamic model for both cohesive and non-cohesive sediments. The model adopts the finite element technique for spatial integration, which has the advantage to describe more accurately complicated bathymetry and irregular boundaries for shallow water areas. The developed model has been applied to test cases and to a very shallow tidal lagoon, the Venice Lagoon, Italy. Numerical results show good agreement with water level, waves and turbidity measurements collected in several monitoring stations inside the Lagoon of Venice. Such a model represents an indispensable tool in analysing coastal problems and assessing morphological impacts of human interference.     

Nonlinear response of membranes to ocean waves using boundary and finite elements

The behavior of a highly deformable membrane to ocean waves was studied by coupling a nonlinear boundary element model of the fluid domain to a nonlinear finite element model of the membrane. The hydrodynamic loadings induced by water waves are computed assuming large body hydrodynamics and ideal fluid flow and then solving the transient diffraction/radiation problem. Either linear waves or finite amplitude waves can be assumed in the model and thus the nonlinear kinematic and dynamic free surface boundary conditions are solved iteratively. The nonlinear nature of the boundary condition requires a time domain solution. To implicitly include time in the governing field equation, Volterra's method was used. The approach is the same as the typical boundary element method for a fluid domain where the governing field equation is the starting point. The difference is that in Volterra's method the time derivative of the governing field equation becomes the starting point.The boundary element model was then coupled through an iterative process to a finite element model of membrane structures. The coupled model predicts the nonlinear interaction of nonlinear water waves with highly deformable bodies. To verify the coupled model a large scale test was conducted in the OH Hinsdale wave Research Laboratory at Oregon State University on a 3-ft-diameter fabric cylinder submerged in the wave tank. The model data verified the numerical prediction of the structure displacements and of the changes in the wave field.The boundary element model is an ideal modeling technique for modeling the fluid domain when the governing field equations is the Laplace equation. In this case the nonlinear boundary element model was coupled with a finite element model of membrane structures, but the model could have been coupled with other finite element models of more rigid structures, such as a pontoon floating breakwater.     

The difference between the joint probability distributions of apparent wave heights and periods and individual wave heights and periods

The joint distribution of wave heights and periods of individual waves is usually approximated by the joint distribution of apparent wave heights and periods. However there is difference between them. This difference is addressed and the theoretical joint distributions of apparent wave heights and periods due to Longuet-Higgins and Sun are modified to give more reasonable representations of the joint distribution of wave heights and periods of individual waves. The modification has overcome an inherent drawback of these joint PDFs that the mean wave period is infinite. A comparison is made between the modified formulae and the field data of Goda, which shows that the new formulae consist with the measurement better than their original counterparts.