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1.
The present study considers wave scattering phenomena around a cylindrical island mounted on a general axisymmetric topography or a general submerged truncated axi-symmetric shoal based on the mild-slope equation. The method of separation of variables and Taylor series expansion are invoked to find the approximate solution to the variable water depth region which varies proportionally to an arbitrary power of radial distance. Validations against the solutions for the combined wave refraction and diffraction around a cylindrical island mounted on a paraboloidal shoal of Liu et al. in 2004 and the scattering and trapping of wave energy by a submerged truncated paraboloidal shoal of Lin and Liu in 2007 show excellent agreements as the power of radial distance being equal to two. For the solutions of wave refraction and diffraction around a cylindrical island mounted on a shoal with depth proportionally to an arbitrary power of radial distance, good agreements with Zhai et al.'s(2013) solutions are demonstrated. Since the robustness of the assumption of a general axi-symmetric geometry based on an arbitrary power variability of the radial distance, the present solution can be very conveniently employed to investigate the effects of bottom topography on wave scattering and trapping patterns. 相似文献
2.
In this paper, an exact analytic solution in terms of Taylor series to the explicit modified mild-slope equation (EMMSE) for wave scattering by a general Homma island is constructed and the convergence of the series solution is analyzed. To validate the new analytic solution, comparisons are made against the existing solutions including analytic solutions to both the long-wave equation and Helmholtz equation, approximate analytic solutions to the modified mild-slope equation, numerical solutions to the mild-slope equation and experimental solutions. Because of the use of the governing equation EMMSE together with mass-conserving matching conditions along the toe of the shoal, the present model is valid for not only waves in the whole spectrum from long waves to short waves but also bathymetries with the maximal seabed slope being as high as 4.27:1. Since the general Homma island is an extension of the original Homma island, the present solution can be very conveniently used to study the effects of bottom topography on combined refraction and diffraction. It is found that the larger the shoal size is, the more significant the wave amplification against the cylinder is. 相似文献
3.
多方向不规则波传播变形数值模拟 总被引：2，自引：1，他引：1
在推广的缓坡方程数学模型基础上建立了多方向不规则波数学模型,综合考虑了波浪折射、绕射、反射、底摩擦和风能输入等因素。基于线性波浪理论,将波浪方向谱在频率和方向上按等能量分割法离散后,分别计算各组成波的传播变形,再计算合成波要素。缓坡方程数学模型采用改进的ADI法求解,计算效率高,稳定性好。采用椭圆形浅滩不规则波模型试验结果和单突堤不规则波绕射理论解对数学模型进行了验证,数值模拟结果和试验值及理论解符合良好。利用该模型进行了某港港内波浪折射、绕射和反射的联合数值模拟,给出了合理的港内波高分布。 相似文献
4.
This study investigates how the refraction of water waves is affected by the higher-order bottom effect terms proportional to the square of bottom slope and to the bottom curvature in the extended mild-slope equations. Numerical analyses are performed on two cases of waves propagating over a circular shoal and over a circular hollow. Numerical results are analyzed using the eikonal equation derived from the wave equations and the wave ray tracing technique. It is found that the higher-order bottom effect terms change the wavelength and, in turn, change the refraction of waves over a variable depth. In the case of waves over a circular shoal, the higher-order bottom effects increase the wavelength along the rim of shoal more than near the center of shoal, and intensify the degree of wave refraction. However, the discontinuity of higher-order bottom effects along the rim of shoal disperses the foci of wave rays. As a result, the amplification of wave energy behind the shoal is reduced. Conversely, in the case of waves over a circular hollow, the higher-order bottom effects decrease the wavelength near the center of the hollow in comparison with the case of neglecting higher-order bottom effects. Consequently, the degree of wave refraction is decreased, and the spreading of wave energy behind the hollow is reduced. 相似文献
5.
Based on the extended mild-slope equation, the wind wave model (WWM; Hsu et al., 2005) is modified to account for wave refraction, diffraction and reflection for wind waves propagating over a rapidly varying seabed in the presence of current. The combined effect of the higher-order bottom effect terms is incorporated into the wave action balance equation through the correction of the wavenumber and propagation velocities using a refraction–diffraction correction parameter. The relative importance of additional terms including higher-order bottom components, the wave–bottom interaction source term and wave–current interaction that influence the refraction–diffraction correction parameter is discussed. The applicability of the proposed model to calculate a wave transformation over an elliptic shoal, a series of parallel submerged breakwater induced Bragg scattering and wave–current interaction is evaluated. Numerical results show that the present model provides better predictions of the wave amplitude as compared with the phase-decoupled model of Holthuijsen et al. (2003). 相似文献
6.
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。 相似文献
7.
Jen-Men Lo 《Ocean Engineering》1991,18(5)
A combined wave refraction-diffraction numerical model was developed to predict wave conditions around an arbitrary island. The methodology was based on the mild-slope equation, solved using a finite difference scheme with a marching procedure. The new model reduced the computer's memory demand considerably in comparison with finite-element, parabolic, error vector propagation and other finite difference approaches, and could therefore predict wave conditions for a large coastal area under given offshore boundary-wave conditions. Laboratory data on wave conditions under submerged circular and elliptical shoal conditions were selected to validate the numerical results. Good agreement was observed in all cases. Wave characteristics around an island were predicted using this model with the given deep-water wave condition. The model can predict wave conditions for any island with a mild-slope coastline. 相似文献
8.
《Coastal Engineering》2001,42(2):163-172
Applying the Green's theorem and a moving oscillating source as the Green's function, an integral equation method is developed for predicting wave height over a shoal in a weak current. The integral equation is discretized by a higher order element method and a numerical code is implemented. To validate the numerical code, comparison is made on wave run-up around a vertical cylinder with McCamy and Fuchs' analytic solution in the still water and the results in currents from numerical wave tanks. Computation has also been carried out for the wave diffraction over a parabolic shoal in a current, and numerical results are given at many sections. The numerical results from the calculation can be used for benchmark test for other methods on wave diffraction in current. 相似文献
9.
岛屿岛礁海域海浪能谱模型研究进展 总被引：2，自引：0，他引：2
波浪能谱模型在岛屿岛礁海域的波浪预报研究和海洋工程中应用广泛,但存在模式计算格点无法充分体现岛屿岛礁的复杂地形特征和很难刻画波浪受到岛屿岛礁影响发生变形物理过程等两个关键问题。多重网格嵌套方案、岛屿次网格地形效应计算方案以及非结构网格、无网格、动态自适应四叉树网格等技术在体现岛屿岛礁复杂地形方面取得了较好的效果;将相位解析模型与波浪能谱模型优势互补是提高能谱模型对岛屿近岸波浪变形物理过程计算能力的一个有效方法。开展球坐标系下波作用密度谱方程的自适应四叉树网格求解方法研究,借鉴相位解析模型最新成果完善能谱模式的绕射、反射、底摩擦等物理过程,是提高岛屿岛礁海域海浪精细预报技术水平的前沿性、探索性研究方向。 相似文献
10.
ZHENG Yonghong 《中国海洋工程》2001,(2):185-194
The original hyperbolic mild-slope equation can effectively take into account the combined effects of wave shoaling, refraction, diffraction and reflection, but does not consider the nonlinear effect of waves, and the existing numerical schemes for it show some deficiencies. Based on the original hyperbolic mild-slope equation, a nonlinear dispersion relation is introduced in present paper to effectively take the nonlinear effect of waves into account and a new numerical scheme is proposed. The weakly nonlinear dispersion relation and the improved numerical scheme are applied to the simulation of wave transformation over an elliptic shoal. Numerical tests show that the improvement of the numerical scheme makes efficient the solution to the hyperbolic mild-slope equation. A comparison of numerical results with experimental data indicates that the results obtained by use of the new scheme are satisfactory. 相似文献
11.
In the present paper, by introducing the effective wave elevation, we transform the extended ellip- tic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. (2003), the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. (2007)’s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly vary- ing topography and wave breaking, the present model is applied to study: (1) wave refraction and diffraction over a submerged elliptic shoal on a slope (Berkhoff et al., 1982); (2) Bragg reflection of monochromatic waves from the sinusoidal ripples (Davies and Heathershaw, 1985); (3) wave transformation near a shore attached breakwater (Watanabe and Maruyama, 1986). Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models (REF/DIF model and FUNWAVE model) show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone. 相似文献
12.
水下圆形浅滩附近波浪绕射的计算 总被引：2，自引：0，他引：2
采用波数矢量无旋和波能守恒方程对圆形浅滩附近水域波浪绕射进行了数值计算,计算模型中采用Ｂａｔｔｊｅｓ关系与波数矢量无旋,波能量守恒方程一起联合求解圆形浅滩附近水域波浪折射影响下的波浪要素。本文的数值计算模型对圆形浅滩水域波浪折射绕射现象的验证结果表明,计算所得结果与试验结果是吻合的,数学模型是可靠和合理的,具有实用价值。 相似文献
13.
On the basis of the previous studies, the simplest hyperbolic mild-slope equation has been gained and the linear time-dependent numerical model for the water wave propagation has been established combined with different boundary conditions. Through computing the effective surface displacement and transforming into the real transient wave motion, related wave factors will be calculated. Compared with Lin’s model, analysis shows that calculation stability of the present model is enhanced efficiently, because the truncation errors of this model are only contributed by the dissipation terms, but those of Lin’s model are induced by the convection terms, dissipation terms and source terms. The tests show that the present model succeeds the merit in Lin’s model and the computational program is simpler, the computational time is shorter, and the computational stability is enhanced efficiently. The present model has the capability of simulating transient wave motion by correctly predicting at the speed of wave propagation, which is important for the real-time forecast of the arrival time of surface waves generated in the deep sea. The model is validated against analytical solution for wave diffraction and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope. Good agreements are obtained. The model can be applied to the theory research an d engineering applications about the wave propagation in a biggish area. 相似文献
14.
Sasithorn Aranuvachapun 《Ocean Engineering》1977,4(2):91-99
The computerised model on surface wave refraction by Wilson (1966) is applied to the topographic data of the southern North Sea. A series of wave refraction diagrams has been produced and the refraction coefficients are evaluated from these diagrams. It is found that there is an agreement between these refraction coefficients and the coefficients calculated from wave data obtained at various stations in the same area. Both the model and the data suggest that the area of wave ray convergence is highly coherent with the area of concentrated wave energy in which the higher waves are detected.It is the purpose of this paper to demonstrate the relationship between the theoretically derived model and the real data obtained in the southern North Sea where the bottom topography provides a pronounced refraction effect on surface waves as well as to show some spatial variation of wave height in that area. 相似文献
15.
A numerical wave tank is first established using the Navier–Stokes equations and the VOF method assuming laminar flow. The standard k–ε, realizable k–ε and RNG k–ε turbulent models are then incorporated to the numerical tank. An effective numerical method for wave absorption utilizing the energy-dissipating property of porous media is also included. To validate the accuracy of the proposed models, the propagation of a solitary wave, where analytical solution is available for comparison, is first simulated. This is followed by the simulation of irregular wave runup on a composite seawall, wave propagation over submerged bars and wave refraction and diffraction over an elliptic shoal, where experimental data are available for comparison. All computed results agree well with either the analytical solution or the experimental data. 相似文献
16.
A physical model study of combined refraction and diffraction of waves through a breakwater gap at different incident angles was conducted. Both regular and random waves with narrow and broad frequency and direction spreading were studied. Besides the presence of a mild bottom slope in the lee of the breakwater, the distribution of wave heights across the width of a navigation channel inside the model harbor was also simulated. In addition to contributing to an understanding of the phenomenon of refraction and diffraction of random waves, the relatively complete set of data obtained can serve as a benchmark for testing of numerical models. 相似文献
17.
A two-dimensional hybrid finite element method is developed to study the scattering of water waves by an island and to calculate wave forces and moments on offshore structures. The offshore structure, which could be either semi-submerged or fully extended in the water, is assumed to be stationary. The numerical model is based on the mild-slope equation. It can be applied to both long-wave and short-wave problems. A special treatment for the problem with the semi-submerged structure is introduced. Comparisons are given with existing analytical solutions and other numerical results. The present model is shown to be an efficient and accurate method for the solution of wave refraction and diffraction problems. 相似文献
18.
In this paper, following the procedure outlined by Li (1994. An evolution equation for water waves. Coastal Engineering, 23, 227-242) and Hsu and Wen (2000. A study of using parabolic model to describe wave breaking and wide-angle wave incidence. Journal of the Chinese Institute of Engineers, 23(4), 515–527) and Hsu and Wen (2000) the extended refraction–diffraction equation is recasted into a time-dependent parabolic equation. This model, which includes higher-order bottom effect terms, is extended to account for a rapidly varying topography and wave energy dissipation in the surf zone. The importance of the higher-order bottom effect terms is examined in terms of the relative water depth. The present model was tested for wave reflection in a number of different environments, namely from a plane slope with different inclinations, from a patch of periodic ripples. The model was also tested for wave height distribution around a circular shoal and wave breaking on a barred beach. The comparison of predictions with other numerical models and experimental data show that the validity of the present model for describing wave propagation over a rapidly varying seabed is satisfactory. 相似文献
19.
TAO Jianhua 《中国海洋工程》2001,(2):269-280
The "surface roller" to simulate wave energy dissipation of wave breaking is introduced into the random wave model based on approximate parabolic mild slope equation in this paper to simulate the random wave transportation including diffraction, refraction and breaking in nearshore areas. The roller breaking random wave higher-order approximate parabolic equation model has been verified by the existing experimental data for a plane slope beach and a circular shoal, and the numerical results of random wave breaking model agree with the experimental data very well. This model can be applied to calculate random wave propagation from deep to shallow water in large areas near the shore over natu ral topography. 相似文献
20.
A numerical model for coastal water wave motion that includes an effective method for treatment of non-reflecting boundaries is presented. The second-order one-way wave equation to approximate the non-reflecting boundary condition is found to be excellent and it ensures a very low level of reflection for waves approaching the boundary at a fairly wide range of the incidence angle. If the Newman approximation is adopted, the resulting boundary condition has a unique property to allow the free propagation of wave components along the boundary. The study is also based on a newly derived mild-slope wave equation system that can be easily made compatible to the one-way wave equation. The equation system is theoretically more accurate than the previous equations in terms of the mild-slope assumption. The finite difference method defined on a staggered grid is employed to solve the basic equations and to implement the non-reflecting boundary condition. For verification, the numerical model is then applied to three coastal water wave problems including the classical problem of plane wave diffraction by a vertical circular cylinder, the problem of combined wave diffraction and refraction over a submerged hump in the open sea, and the wave deformation around a detached breakwater. In all cases, the numerical results are demonstrated to agree very well with the relevant analytical solutions or with experimental data. It is thus concluded that the numerical model proposed in this study is effective and advantageous. 相似文献