共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
《Coastal Engineering》2001,44(1):1-12
In order to verify modified mild-slope equation models in a horizontal two-dimensional space, a hydraulic experiment is made for surface wave propagation over a circular shoal on which water depth varies substantially. A horizontal two-dimensional numerical model is also constructed based on the hyperbolic equations that have been developed from the modified mild-slope equation to account for the substantial depth variation. Comparison between experimental measurements and numerical results shows that the modified mild-slope equation model is capable of producing accurate results for wave propagation in a region where water depth varies substantially, while the conventional mild-slope equation model gives large errors as the mild-slope assumption is violated. 相似文献
3.
LI Ruijie WANG Houjie
Dr. Associate Professor Engineering College of Ocean University of Qingdao Qingdao P. R. China
Ph. D. Candidate Engineering College of Ocean University of Qingdao Qingdao P. R. China 《中国海洋工程》1999,(3)
Nonlinear effect is of importance to waves propagating from deep water to shallow water.Thenon-linearity of waves is widely discussed due to its high precision in application.But there are still someproblems in dealing with the nonlinear waves in practice.In this paper,a modified form of mild-slope equa-tion with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation.The modified form of mild-slope equation is convenient to solvenonlinear effect of waves.The model is tested against the laboratory measurement for the case of a submergedelliptical shoal on a slope beach given by Berkhoff et al,The present numerical results are also comparedwith those obtained through linear wave theory.Better agreement is obtained as the modified mild-slope e-quation is employed.And the modified mild-slope equation can reasonably simulate the weakly nonlinear ef-fect of wave propagation from deep water to coast. 相似文献
4.
We develop techniques of numerical wave generation in the time-dependent extended mild-slope equations of Suh et al. [1997. Time-dependent equations for wave propagation on rapidly varying topography. Coastal Engineering 32, 91–117] and Lee et al. [2003. Extended mild-slope equation for random waves. Coastal Engineering 48, 277–287] for random waves using a source function method. Numerical results for both regular and irregular waves in one and two horizontal dimensions show that the wave heights and the frequency spectra are properly reproduced. The waves that pass through the wave generation region do not cause any numerical disturbances, showing usefulness of the source function method in avoiding re-reflection problems at the offshore boundary. 相似文献
5.
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
7.
Two types of analytical solutions for waves propagating over an asymmetric trench are derived. One is a long-wave solution and the other is a mild-slope solution, which is applicable to deeper water. The water depth inside the trench varies in proportion to a power of the distance from the center of the trench (which is the deepest water depth point and the origin of x-coordinate in this study). The mild-slope equation is transformed into a second-order ordinary differential equation with variable coefficients based on the longwave assumption [Hunt's, 1979. Direct solution of wave dispersion equation. Journal of Waterway, Port, Coast. and Ocean Engineering 105, 457–459] as approximate solution for wave dispersion. The analytical solutions are then obtained by using the power series technique. The analytical solutions are compared with the numerical solution of the hyperbolic mild-slope equations. After obtaining the analytical solutions under various conditions, the results are analyzed. 相似文献
8.
A non-linear coupled-mode system of horizontal equations is presented, modelling the evolution of nonlinear water waves in finite depth over a general bottom topography. The vertical structure of the wave field is represented by means of a local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent modes, plus two additional terms, the free-surface mode and the sloping-bottom mode, enabling to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. The present coupled-mode system fully accounts for the effects of non-linearity and dispersion, and the local-mode series exhibits fast convergence. Thus, a small number of modes (up to 5–6) are usually enough for precise numerical solution. In the present work, the coupled-mode system is applied to the numerical investigation of families of steady travelling wave solutions in constant depth, corresponding to a wide range of water depths, ranging from intermediate depth to shallow-water wave conditions, and its results are compared vs. Stokes and cnoidal wave theories, as well as with fully nonlinear Fourier methods. Furthermore, numerical results are presented for waves propagating over variable bathymetry regions and compared with nonlinear methods based on boundary integral formulation and experimental data, showing good agreement. 相似文献
9.
10.
The complementary mild-slope equation (CMSE) is a depth-integrated equation, which models refraction and diffraction of linear time-harmonic water waves. For 2D problems, it was shown to give better agreements with exact linear theory compared to other mild-slope (MS) type equations. However, no reference was given to 3D problems. In contrast to other MS-type models, the CMSE is derived in terms of a stream function vector rather than in terms of a velocity potential. For the 3D case, this complicates the governing equation and creates difficulties in formulating an adequate number of boundary conditions. In this paper, the CMSE is re-derived using Hamilton's principle from the Irrotational Green–Naghdi equations with a correction for the 3D case. A parabolic version of it is presented as well. The additional boundary conditions needed for 3D problems are constructed using the irrotationality condition. The CMSE is compared with an analytical solution and wave tank experiments for 3D problems. The results show very good agreement. 相似文献
11.
N. Booij 《Coastal Engineering》1983,7(3):191-203
The mild-slope equation is a vertically integrated refraction-diffraction equation, used to predict wave propagation in a region with uneven bottom. As its name indicates, it is based on the assumption of a mild bottom slope. The purpose of this paper is to examine the accuracy of this equation as a function of the bottom slope. To this end a number of numerical experiments is carried out comparing solutions of the three-dimensional wave equation with solutions of the mild-slope equation.For waves propagating parallel to the depth contours it turns out that the mild-slope equation produces accurate results even if the bottom slope is of order 1. For waves propagating normal to the depth contours the mild-slope equation is less accurate. The equation can be used for a bottom inclination up to 1:3. 相似文献
12.
A numerical model based on the mild-slope equation is applied to reproduce the propagation of small-amplitude transient waves. The model makes use of the Fourier Transform to convert the time-dependent hyperbolic equation into a set of elliptic equations in the frequency domain. The results of two available experimental studies on tsunamis generated by landslides are used to validate the model, which appears to be able of carefully reproducing the effects of the frequency dispersion. An example application of tsunamis propagating around the Stromboli island is also presented to show the applicability of the present approach to real life scenarios. It is finally discussed how this model could be applied as support to a tsunami early warning system. 相似文献
13.
The transformation of nonlinear water waves over porous beds is studied by applying a numerical model based on Chen's [2006. Fully nonlinear Boussinesq-type equations for waves and currents over porous beds. Journal of Engineering Mechanics, 132:2, 220–230] Boussinesq-type equations for highly nonlinear waves on permeable beds. The numerical model uses a high-order time-marching solution and fourth-order finite-difference schemes for discretization of first-order spatial derivatives to obtain a computational accuracy consistent with the model equations. By forcing the wave celerity and spatial porous-damping rate of the linearized model to match the exact linear theory for horizontal porous bed over a prescribed range of relative depths, the values of the model parameters are optimally determined. Numerical simulations of the damped wave propagation over finite-thickness porous layer demonstrate the accuracy of both the numerical model and governing equations, which have been shown by prior theoretical analyses to be accurate for both nominal and thick porous layers. These simulations also elucidate on the significance of the higher-order porous-damping terms and the influence of the hydraulic parameters. Application of the model to the simulation of the wave field around a laboratory-scale submerged porous mound provides a measure of its capability, as well as useful insight into the scaling of the porous-resistance coefficients. For application to heterogeneous porous beds, the assumption of weak spatial variation of the porous resistance is examined using truncated forms of the governing equations. The results indicate that the complete set of Boussinesq-type equations is applicable to porous beds of nonhomogeneous makeup. 相似文献
14.
This paper presents a technique to generate waves at oblique angles in finite difference numerical models in a rectangular grid system by using internal generation technique [Lee, C., Suh, K.D., 1998. Internal generation of waves for time-dependent mild-slope equations. Coast. Eng. 34, 35–57.] along an arc-shaped line source. Tests were made for four different types of wave generation layouts. Quantitative experiments were conducted under the following conditions: the propagation of waves on a flat bottom, the refraction and shoaling of waves on a planar slope, and the diffraction of waves to a semi-infinite breakwater. Numerical experiments were conducted using the extended mild-slope equations of Suh et al. [Suh, K.D., Lee, C., Park, W.S., 1997. Time-dependent equations for wave propagation on rapidly varying topography. Coast. Eng. 32, 91–117.]. The fourth layout type consisting of two parallel lines connected to a semicircle showed the best solutions, especially for a small grid size. This technique is useful for the numerical simulation of irregular waves with broad-banded directional spectrum using conventional spectral wave models for the reasonable estimation of bottom friction and wave-breaking. 相似文献
15.
Tai-Wen Hsu Shih-Chun Hsiao Shan-Hwei Ou Swun-Kwang Wang Bin-Da Yang Shih-En Chou 《Ocean Engineering》2007,34(5-6):870-883
A numerical model based on the second-order fully nonlinear Boussinesq equations of Wei et al. [1995. Journal of Waterway, Port, Coastal and Ocean Engineering 121 (5), 251-263] is developed to simulate the Bragg reflection of both regular and irregular surface waves scattered by submerged bars. Particularly for incident regular waves, the computed results are observed to agree very well with the existing experimental data as presented by Davies and Heathershaw [1984. Journal of Fluid Mechanics 144, 419-446] and Kirby and Anton [1990. Proceedings of the 22nd International Conference on Coastal Engineering, ASCE, New York, pp. 757–768). In the case of incident irregular waves, the simulated results reveal that the distribution of Bragg reflection from irregular waves becomes more flat than that of regular waves. Due to lack of experimental data, the numerical results for incident irregular waves are compared with those of the evolution equation of the mild-slope equation [Hsu et al., 2002 Proceedings of the 24th Ocean Engineering Conference in Taiwan, pp. 70–77 (in Chinese)]. In addition, several parameters such as the number of bars, the relative height of bars and the spacing of bars affecting Bragg reflection are also discussed. 相似文献
16.
Recent progress in formulating Boussinesq-type equations includes improved features of linear dispersion and higher-order nonlinearity. Nonlinear characteristics of these equations have been previously analysed on the assumption of weak nonlinearity, being therefore limited to moderate wave height. The present work addresses this aspect for an important class of wave problems, namely, regular waves of permanent form on a constant depth. Using a numerical procedure which is valid up to the maximum wave height, permanent-form waves admitted by three sets of advanced Boussinesq-type equations are analysed. Further, the characteristics of each set of the Boussinesq-type equations are discussed in the light of those from the potential theory satisfying the exact free-surface conditions. Phase velocity, amplitude dispersion, harmonic amplitudes (namely, second and third) and skewness of surface profile are shown over a two-parameter space of frequency and wave height. 相似文献
17.
Mild-slope equation for water waves propagating over non-uniform currents and uneven bottoms 总被引：5，自引：0，他引：5
I~IOXThe interaction between surface waves and ambient currents and nearshore topography lies atone of the heat of morphological medelling. Accurate predictions of how wave propagates overcurrents and topography, and of the consequent erosion and dePOSition of sand on a beach or tidalflat are vital when assessing how a coastline may be affected by changing conditions.The mild-slope equation was introduced by Berkhoff (1972) as a way of approximating therefraction-diffraction of linearized s… 相似文献
18.
This study presents an analytical solution for the problem of waves passing a submerged porous structure, using a multi-region method in the solution scheme considering the characteristics of geometry and composing materials of the porous structure. Using the flux and pressure conditions on horizontal boundaries and interfaces, the orthogonal property of wave motion within the porous layers through water depth is derived, and applied in the solution process. The flux and pressure conditions on vertical boundaries and interfaces are integrated to give a set of linear matrix equations, through which the unknown coefficients are solved. Comparisons of the present method with previous studies are preceded in verification, which suggests the validity and practicability of the present study, with a further expectation of extending our work to build a mild-slope equation over multiple-layer porous medium in the future. 相似文献
19.
Validation of the three-wave quasi-kinetic approximation for the spectral evolution in shallow water
This paper aims at validating the three-wave quasi-kinetic approximation for the spectral evolution of weakly nonlinear gravity waves in shallow water. The problem is investigated using a one-dimensional numerical wave propagation model, formulated in the spectral representation. This model includes both a nonlinear triad interactions term and a wave breaking dissipation term. Some numerical tests were carried out in order to show the importance of using the triad nonlinear term in wave propagation spectral models, particularly to describe both behavior of the spectral integral parameters and of the spectral shape evolution in shallow water depth. Furthermore; a comparison against different set of experimental observations was carried out. Comparing the numerical results with the experimental observations made it possible to show the modeling efficiency of the three-wave quasi-kinetic approximation. 相似文献