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1.
A new analytic solution of the mild-slope long wave equation is derived for studying the effects of bottom topography on combined refraction and diffraction. The solution is essentially of a series form involving the Bessel functions of real orders but is found to be singular as the bottom tends to be parabolic. Numerical evaluation of the solution nearby the singularity requires some special considerations. The particular solution under the singular condition is also given. Study on combined refraction and diffraction for waves around a circular island on the top of a shoal, which is radially described by a power function with two independent parameters, indicates that there exist an extremely high wave zone near the top of a hyperparabolic shoal. It is also found that the intensity of wave ray focusing increases significantly as the mean slope decreases. A direct consequence of the wave ray focusing is the concentration of wave energy and an increase of the maximal wave runup height around the island. 相似文献
2.
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
3.
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
4.
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
5.
将适用于近岸较大区域波浪传播变形的三种模型,即基于抛物型缓坡方程的不规则波模型、引入浅水波浪谱 TMA 谱的 SWAN(simulating waves nearshore)模型以及采用默认 JONSWAP 谱的 SWAN模型应用于特拉华大学(University of Delaware)圆形浅滩实验进行比较.结果显示,抛物型缓坡方程和SWAN 的模拟结果与实验所测数据符合都比较好; SWAN 在非线性作用较强的浅滩中心及靠后部效果更佳,而抛物型缓坡方程由于没有考虑非线性作用,模拟得到的最大波高较实测值偏高,且波高变化较为剧烈. 相似文献
6.
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
7.
低频长波对港湾共振、泥沙输运、波浪爬高与越浪等过程有重要影响。采用非静压模型SWASH模拟了不规则波在浅滩上的传播及破碎过程,重点探讨了滩顶短波破碎程度对低频波能演变的影响。模拟结果显示,当滩顶短波处于临界破碎状态时,低频波能流沿浅滩持续增长,浅滩对低频长波的放大效应（滩后与滩前低频波能流之比）显著;当滩顶短波轻微破碎、破波仅发生在外破波区时,低频波能流的沿滩增长率进一步变大;当滩顶短波剧烈破碎、破波延续到内破波区时,低频波能流沿滩先增长而后转为衰减,滩后放大率较临界破碎时明显减小。研究结果表明,浅滩顶部水深改变了短波破碎程度,进而影响低频长波的演化过程,浅滩上长波总体增长率随滩顶水深的减小呈现先增大后减小的规律,在短波轻微破碎时最大。 相似文献
8.
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
9.
Application of desingularized approach to water wave propagation over three-dimensional topography 总被引：1，自引：0，他引：1
A numerical approach based on desingularized boundary element method and mixed Eulerian–Lagrangian formulation [Zhang et al., 2006. Wave propagation in a fully nonlinear numerical wave tank: a desingularized method. Ocean Engineering 33, 2310–2331] is extended to solve the water wave propagation over arbitrary topography in a three-dimensional wave tank. A robust damping layer applicable for regular and irregular incident waves is employed to minimize the outgoing wave reflection back into the wave tank. Numerical results on the propagation of regular and irregular incident waves over the flat bottom and linear incident waves over an elliptical shoal show good concurrence with the corresponding analytical solutions and experimental data. 相似文献
10.
This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory. 相似文献
11.
Recently derived (Webster et al., 2011), simplified higher-level Green–Naghdi equations (GN-3, GN-5 and GN-7) are used in this work to simulate the transformation of two-dimensional, shallow-water wave problems. The spatial derivatives are discretized through a five-point difference scheme. A new algorithm is developed to solve the resulting block-pentadiagonal matrix. These high-level GN equations are then utilized to develop a numerical wave tank. A wave-maker is placed at the forcing boundary of the tank that uses the stream-function theory to generate nonlinear incident waves. The numerical wave tank is used to analyze the effects of large-amplitude waves passing over a submerged bar. A damping zone is placed near the wave-maker (up-wave side) to absorb the reflected waves from the front side of the submerged bar. Another damping zone is placed at the down-wave side of the computational domain to absorb the radiated waves. In the first test case, the front and back slopes of the bar are both mild (Luth et al., 1994). The waves that evolved over the bar are simulated by using the GN-3, GN-5 and GN-7 equations. The GN-3 equations provide time histories that compare well with the experimental data at different wave gauges, except at the ones behind the bar. The results of the GN-5 and GN-7 equations compare very well with all the experimental data considered here. In the second test case, the front and back slopes of the bar are both steep (Ohyama et al., 1995). The GN-5 equations predict the wave elevation well. In the third test case, the front and back slopes of the bar alternate, one of them being mild and the other one being steep (Zou et al., 2010). Again, the predictions of the GN-5 equations agree with the experimental data well. In all the test cases considered in this work, there are some differences between the GN-3 and GN-5 results after the crest of the bar. Numerical results obtained by the GN-5 and GN-7 equations are almost the same along the wave flume, but the GN-7 equations require more computational time. Therefore, the GN-5 results are accepted here as the converged GN theory results. The numerical validations show that the GN-5 equations can simulate the strongly nonlinear and dispersive waves observed behind the submerged bar crest satisfactorily. 相似文献
12.
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
13.
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
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.
The vertically-integrated effect of interaction between waves and wave-induced currents on wave transformation over a submerged elliptic shoal was investigated based on numerical simulations of the Vincent and Briggs experiment [Vincent, C.L., Briggs, M.J., 1989. Refraction- diffraction of irregular waves over a mound. Journal of Waterway, Port, Coastal and Ocean Engineering, 115(2), pp. 269–284.]. The numerical simulations were performed using two numerical wave-current model systems: one, a combination of the wave model SWAN and the current model SHORECIRC, and the other, a combination of the wave model REF/DIF and the same current model. A time-dependent, phase-resolving wave and current model, FUNWAVE, was also utilized to simulate the experiment. In the simulations, the developed wave-induced currents defocused waves behind the shoal and brought on a wave shadow zone that showed relatively low wave height distributions. For the breaking case of monochromatic waves, the wave heights computed using FUNWAVE showed good agreement with the measurements and the resulting wave-induced currents showed a jet-like velocity distribution in transverse direction. And the computed results of the two model combinations agreed better with the measurements than the computed results obtained by neglecting wave-current interaction. However, it was found that for the case in which transverse interference pattern caused by refracted waves was strong, REF/DIF-SHORECIRC did not correctly evaluate radiation stresses, the gradients of which generate wave-induced currents. SWAN-SHORECIRC, which cannot deal with the interference patterns, predicted a jet-like wave-induced current. For breaking random wave cases, the computed results of the two model combinations and FUNWAVE agreed well with the measurements. The agreements indicate that it is necessary to take into account the effect of wave-induced current on wave refraction when wave breaking occurs over a submerged shoal. 相似文献
16.
17.
Hyperbolic Mild Slope Equations with Inclusion of Amplitude Dispersion Effect： Regular Waves 总被引：4，自引：2，他引：2
A new form of hyperbolic mild slope equations is derived with the inclusion of the amphtude dispersion of nonlinear waves. The effects of including the amplitude dispersion effect on the wave propagation are discussed. Wave breaking mechanism is incorporated into the present model to apply the new equations to surf zone. The equations are solved nu- merically for regular wave propagation over a shoal and in surf zone, and a comparison is made against measurements. It is found that the inclusion of the amplitude dispersion can also improve model＇ s performance on prediction of wave heights around breaking point for the wave motions in surf zone. 相似文献
18.
Using a linear statement, the paper studies surface waves occurring due to minor shifts of the bottom sections. A plane case
is considered. An analytical solution to the problem has been derived using Fourier transforms. Asymptotic laws for the degeneration
of waves propagating over finite bottom deformations have been defined. Numerical analysis of the integrals is applied to
study the effect of the horizontal extent of a wave generation area and bottom irregularities on the shape of waves and their
amplitudinal and energetic parameters. Attention is focused on the manifestation of frequency dispersion at the stage of wave
generation as a developed wave process.
Translated by Vladimir A. Puchkin. 相似文献
19.
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
20.
《Coastal Engineering》2006,53(4):311-318
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. Coastal Eng., 32, 91–117] and Lee et al. [Lee, C., Kim, G., Suh, K.D., 2003. Extended mild-slope equation for random waves. Coastal Eng., 48, 277–287] are compared analytically and numerically to determine their applicability to random wave transformation. The geometric optics approach is used to compare the two models analytically. In the model of Suh et al., the wave number of the component wave with a local angular frequency ω is approximated with an accuracy of O(ω − ω¯) at a constant water depth, where ω¯ is the carrier frequency of random waves. In the model of Suh et al., however, the diffraction effects and higher-order bottom effects are considered only for monochromatic waves, and the shoaling coefficient of random waves is not accurately approximated. This inaccuracy arises because the model of Suh et al. was derived for regular waves. In the model of Lee et al., all the parameters of random waves such as wave number, shoaling coefficient, diffraction effects, and higher-order bottom effects are approximated with an accuracy of O(ω − ω¯). This approximation is because the model of Lee et al. was developed using the Taylor series expansion technique for random waves. The result of dispersion relation analysis suggests the use of the peak and weighted-average frequencies as a carrier frequency for Suh et al. and Lee et al. models, respectively. All the analytical results are verified by numerical experiments of shoaling of random waves over a slightly inclined bed and diffraction of random waves through a breakwater gap on a flat bottom. 相似文献