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1.
Based on Green–Naghdi equation this work studies unsteady ship waves in shallow water of varying depth. A moving ship is regarded as a moving pressure disturbance on free surface. The moving pressure is incorporated into the Green–Naghdi equation to formulate forcing of ship waves in shallow water. The frequency dispersion term of the Green–Naghdi equation accounts for the effects of finite water depth on ship waves. A wave equation model and the finite element method (WE/FEM) are adopted to solve the Green–Naghdi equation. The numerical examples of a Series 60 (CB=0.6) ship moving in shallow water are presented. Three-dimensional ship wave profiles and wave resistance are given when the ship moves in shallow water with a bed bump (or a trench). The numerical results indicate that the wave resistance increases first, then decreases, and finally returns to normal value as the ship passes a bed bump. A comparison between the numerical results predicted by the Green–Naghdi equation and the shallow water equations is made. It is found that the wave resistance predicted by the Green–Naghdi equation is larger than that predicted by the shallow water equations in subcritical flow
, and the Green–Naghdi equation and the shallow water equations predict almost the same wave resistance when
, the frequency dispersion can be neglected in supercritical flows. 相似文献
2.
Abstract In this article three main stages of tsunami wave evolution are investigated. At first, the development of disturbances from a given patched elevation of the bottom surface in an incompressible nonviscous fluid of the uniform depth is considered. Then, a tsunami wave diffraction by underwater bottom elevation or cavity is investigated. In this case the shallow water equations are already used, and it is supposed that a cylindrical wave is spread from patched water elevation over the epicentrum. Last, the tsunami propagation and transformation in a shallow water region and its run‐up on a beach are investigated on the basis of the improved shallow water theory, taking into consideration the nonlinear and dispersive terms of higher order. The proposed theory is tested in a problem of collisions of two solutions. Solutions of the first and the second problems are obtained by the method of integral Laplace's transformation with following numerical inversion of transformations. A finite difference method for a solution of the last problem is used. 相似文献
3.
南海文昌地区内波振幅反演研究 总被引：3，自引：2，他引：1
The field experiment is conducted from April 16,2005 to July 20,2005 at Wenchang area east of Hainan Island(19°35'N,112°E) of China.Internal wave packets are observed frequently with thermistor chains during the experiment.Meanwhile,internal waves are also detected from a synthetic aperture radar(SAR) image on June 19,2005 and several other moderate-resolution imaging spectroradiometer(MODIS) images near a mooring position.The distance between the positive and negative peaks induced by the internal wave can be obtained from satellite images.Combined with remote sensing images and in situ data,a new method to inverse the amplitude of the internal wave is proposed based on a corrected nonlinear Schr?dinger(NLS) equation.Two relationships are given between the peak-to-peak distance and the characteristic wavelength of the internal wave for different nonlinear and dispersion coefficients.Based on the satellite images,the amplitude inversion of the internal waves are carried out with the NLS equation as well as the Kd V equation.The calculated amplitudes of the NLS equation are close to the observation amplitude which promise the NLS equation a reliable method. 相似文献
4.
The paper presented is a solution of shallow water wave force, using small amplitude linear wave theory on two-dimensional vertically submerged circular thin plates under three different configurations: (1) a surface-piercing circular thin plate, (2) a submerged circular thin plate, and (3) a bottom-standing circular thin plate. Finally Morison's equation is used for the determination of wave force which is based on the linear wave theory. The plate is submerged in water near the shore on uniformly sloping bottom. The solution method is confined in a finite domain, which contains both the region of different depth of water and the plate. Laplace's equation and boundary value problems are solved in a finite domain, by the method of separation of variables and the small amplitude linear wave theory. The variation of horizontal force by single particle, total horizontal force and moment with respect to the wave amplitude are obtained at different depth of water and at different wave period. It is observed that the force and moment are converging with the increase of wave period and the gradients of force and moment with respect to the wave amplitude are extremely high for lower wave period. 相似文献
5.
Hydraulic Modeling of A Curtain-Walled Dissipater by the Coupling of RANS and Boussinesq Equations 总被引：5，自引：1，他引：5
A hybrid numerical method for the hydraulic modeling of a curtain-walled dissipater of reflected waves from breakwa-ters is presented. In this method, a zonal approach that combines a nonlinear weakly dispersive wave (Boussinesq-type equation) method and a Reynolds-Averaged Navier-Stokes (RANS) method is used. The Boussinesq-type equation is solved in the far field to describe wave transformation in shallow water. The RANS method is used in the near field to re-solve the turbulent boundary layer and vortex flows around the structure. Suitable matching conditions are enforced at the interface between the viscous and the Boussinesq region. The Coupled RANS and Boussinesq method successfully resolves the vortex characteristics of flow in the vicinity of the structure, while unexpected phenomena like wave re-reflection are effectively controlled by lengthening the Boussinesq region. Extensive results on hydraulic performance of a curtain-walled dissipater and the mechanism of dissipation of reflected waves 相似文献
6.
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
7.
Qiu Dahong 《中国海洋工程》1992,(2)
Based on the 1st order cnoidal wave theory, the nonlinear wave diffraction around a circular cylinder in shallow water is studied in this paper. The equation of the wave surface around the cylinder is formulated and by using this formula the wave surface elevation on the cylinder surface can be obtained. In this paper, the formula for calculating the cnoidal wave force on a circular cylinder is also derived. For the wave conditions which are often encountered in practical engineering designs, the ratios of the nonlinear wave forces to the linear wave forces are calculated, and the results are plotted in this paper for design purposes. In order to verify the theoretical results, model tests are conducted. After comparing the test results with the theoretical ones, it is concluded that, in shallow water, for the case of T g / d~(1/2) > 8-10 and H / d > 0.3, the cnoidal wave theory should be used to calculate the wave action on a cylindrical pier. 相似文献
8.
When waves propagate from deep water to shallow water, wave heights and steepness increase and then waves roll back and break. This phenomenon is called surf. Currently, the present statistical calcula... 相似文献
9.
针对目前缓坡方程中势函数假设比较多的问题,本文利用二维浅水方程来描述海浪水质点运动的有势假设,采取WKBJ方法推导缓坡方程在缓变地形下的波包方程,对势函数缓坡方程进行修正,以建立更全面更实用的近岸波浪传播计算模式。同时,文中还采用非势函数型模拟波浪传播。 相似文献
10.
11.
An analytic solution to the mild slope equation is derived for waves propagating over an axi-symmetric pit located in an otherwise constant depth region. The water depth inside the pit decreases in proportion to an integer power of radial distance from the pit center. The mild slope equation in cylindrical coordinates is transformed into ordinary differential equations by using the method of separation of variables, and the coefficients of the equation in radial direction are transformed into explicit forms by using the direct solution for the wave dispersion equation by Hunt (Hunt, J.N., 1979. Direct solution of wave dispersion equation. J. Waterw., Port, Coast., Ocean Div., Proc. ASCE, 105, 457–459). Finally, the Frobenius series is used to obtain the analytic solution. Due to the feature of the Hunt's solution, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth waters. The validity of the analytic solution is demonstrated by comparison with numerical solutions of the hyperbolic mild slope equations. The analytic solution is also used to examine the effects of the pit geometry and relative depth on wave transformation. Finally, wave attenuation in the region over the pit is discussed. 相似文献
12.
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
13.
A comparison of weakly and fully non-linear models of the shoaling of a solitary internal wave 总被引：1，自引：0，他引：1
This study investigates the behaviour of internal solitary waves crossing a continental slope in the presence of a seasonal thermocline. Comparisons are made between a fully non-linear computational fluid dynamics (CFD) model, and weakly non-linear theory. Previous observations suggested that the amplitudes of solitary waves are capped as they pass across the continental slope, which may be due to laminar dynamics, or due to the effect of turbulence. Across the continental slope, CFD and second order variable depth KdV (vEKdV) predictions agree well with observations of a limited change in solitary wave amplitude. First order variable depth KdV theory overpredicts the final amplitude significantly. In terms of the wave shape, the CFD modeled wave changes from a KdV shape in deep water towards an EkdV solution in shallow water, as observations suggest. The phase speed of the CFD and vEKdV waves are similar to that observed in waters of 400–500 m deep, but are slightly lower than observed in 140 m depth. CFD predictions using a standard k, turbulence model showed that turbulence had little effect on the amplitude. These preliminary results indicate that in this situation wave capping is due to laminar, large amplitude solitary wave dynamics and is independent of turbulent mixing. 相似文献
14.
M. Rahman 《Applied Ocean Research》1984,6(2):90-100
An exact second order theory has been formulated in this paper to calculate the wave forces on offshore structures. Lighthill's method for deep water waves has been extended to shallow water waves. Exact expression for linear velocity potential applicable to the circular cylindrical strcutures for shallow water waves have been used in these calculations. These results have been verified with those obtained by direct perturbation technique reported recently by Rahman and Heaps. It is interesting to note that both the methods yield identical results. 相似文献
15.
通过改进二阶全非线性 Boussinesq 波浪方程中的色散项,得到了一组没有改变原方程的数学形式但适用于更大变化水深的新方程,其色散性能和变浅性能都比原方程有了很大改进,所适用的水深范围更大,能更好地描述从深水到近岸浅水处的波浪传播;并基于新方程建立了波浪数值模型,通过模拟波浪从浅水到深水的传播变形来验证新方程的有效性. 相似文献
16.
应用内外解匹配的方法和驻相法推导了柱坐标系下地震引起的水面波动方程的解,即推导了地震海啸波生成与传播的理论方程,并对越洋地震海啸理论方程进行了求解。基于Boussinesq方程出发,建立了二维越洋海啸波传播数学模型,并对越洋海啸进行了数值计算,计算方法采用有限差分方法,差分格式采用交替方向隐格式(Alternating Direction Implicit即ADI方法)。利用越洋海啸计算模式对发生在大洋中的地震海啸进行了模拟,将数值模拟结果与地震海啸波理论方程的计算结果进行了比较,两种计算结果吻合较好。 相似文献
17.
Nonlinear Effect of Wave Propagation in Shallow Water 总被引：5，自引：2，他引：5
LI Ruijie WANG Houjie
Associate Professor Ocean University of Qingdao Qingdao P. R. China.
Graduate Student Ocean University of Qingdao Qingdao P. R. China. 《中国海洋工程》1999,(1)
—In this paper,a nonlinear model is presented to describe wave transformation in shallow wat-er with the zero-vorticity equation of wave-number vector and energy conservation equation.Thenonlinear effect due to an empirical dispersion relation(by Hedges)is compared with that of Dalrymple＇sdispersion relation.The model is tested against the laboratory measurements for the case of a submergedelliptical shoal on a slope beach,where both refraction and diffraction are significant.The computation re-sults,compared with those obtained through linear dispersion relation.show that the nonlinear effect ofwave transformation in shallow water is important.And the empirical dispersion relation is suitable for re-searching the nonlinearity of wave in shallow water. 相似文献
18.
浅海水下地形的SAR遥感仿真研究 总被引：2，自引：0，他引：2
结合连续性方程和布拉格后向散射模型,在准一维简化浅海水下地形情况下,建立了浅海水下地形SAR海面相对后向散射强度仿真模型,将浅海水下地形区域的SAR海面后向散射强度的相对变化与大尺度背景流场、海面风场和雷达系统参数等联系起来.海上实验和研究结果表明,浅海水下地形的SAR成像主要由通过受水下地形影响的海表层流场对海表面风引起的微尺度波的水动力调制而获取浅海水下地形信息,其中潮流与水下地形的相互作用过程改变海表层流场,变化的海表层流与海表面微尺度波之间的相互作用改变海表面波的空间分布,雷达波与海表面波之间的相互作用决定雷达海面后向散射强度.因此SAR图像中浅海水下地形或水深信息量的多少不仅与海表层流场和海面风速有关,而且与雷达工作波段、雷达波束入射角和极化方式也密切相关.认为由水下地形变化引起的缓慢变化的表层流场中海表面定常微尺度波谱能量密度的变化满足波作用量谱平衡方程;而在波数空间中,海表面微尺度波谱的成长过程也可以用波数谱平衡方程描述,在此基础上,得出了海表面波高频谱(毛细-重力波)形式的解析表达式.众所周知,浅海水下地形信息是由于水下地形影响下SAR海面后向散射强度与背景海面后向散射强度的相对差异而在SAR图像上的呈现,从而在建立浅海水下地形SAR海面相对后向散射强度仿真模型的基础上,仿真计算了浅海水下地形SAR海面相对后向散射强度相对于海表层流场、海面风场等海况参数和SAR工作波段、SAR波束入射角、极化方式等雷达系统参数的数值仿真结果,分析得到了有关浅海水下地形SAR海面相对后向散射强度的特征和SAR浅海水下地形遥感的最佳海况参数与最佳雷达系统参数,为研究和开展SAR浅海水下地形遥感研究提供了有价值的参考. 相似文献
19.
曹祖德 《海洋学报(英文版)》1983,2(2):178-189
The effects of wind on wave propagation in shallow water are approached in this paper. The equations for calculating wave elements in shallow water are derived by the law of wave refraction and the equation of wave energy flux. The numerical results calculated by the electronic computer show that under the influence of wind, the wave elements, wave direction angle and the conditions of wave breaker change greatly. Consequently, the effects of wind on the water wave propagating in shallow water need to be considered in practice. 相似文献
20.
基于弱二维的KP方程,并结合南中国海东沙群岛附近内孤立波的观测资料,模拟了内孤立波的波-波相互倌用0数值结果较好的反应了内孤立波的二维特征,同时体现两个内孤立波波-波相互作用的非线性特征,即两波相交处相速随振幅的增大而变大。相比于一维的KdV方程,KP在内孤立波的仿真反演方面具有更大的优势。 相似文献