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1.
Refraction of incoherent random gravity waves with currents and bottom topography results in spatial variations in the spectral characteristics of the free surface. Prediction of such variations based on the radiation transfer equation is in a simple analytic form for the case of one dimensional inhomogeneities in currents and topography. This analytic form is examined in terms of two-dimensional wave number- and polar frequency-direction spectra along the associated dynamic and kinematic constraints relevant to wave breaking and reflection. Results are specialized to the simplest case of horizontal shear currents in deep and shallow water with explicit examples to illustrate the relative and combined effects of currents and topography on free surface spectra. 相似文献
2.
A new set of equations of motion for wave propagation in water with varying depth is derived in this study. The equations expressed by the velocity potentials and the wave surface elevations include first-order non-linearity of waves and have the same dispersion characteristic to the extended Boussinesq equations. Compared to the extended Boussinesq equations, the equations have only two unknown scalars and do not contain spatial derivatives with an order higher than 2. The wave equations are solved by a finite element method. Fourth-order predictor–corrector method is applied in the time integration and a damping layer is applied at the open boundary for absorbing the outgoing waves. The model is applied to several examples of wave propagation in variable water depth. The computational results are compared with experimental data and other numerical results available in literature. The comparison demonstrates that the new form of the equations is capable of calculating wave transformation from relative deep water to shallow water. 相似文献
3.
lt is shown that Maxwell's equations which describe the propagation of electromagnetic radiation are analogous to the kinematic relationships which govern the propagation of long water waves, if the latter equations are described in terms of a vector potential. The analogy between the two phenomena may be used to study, for example, seiching, or long wave resonance, in harbors by means of an equivalent microwave cavity. The plan geometry of the cavity would be geometrically similar to that of the harbor basin so that wave reflections were correctly reproduced, and the refraction caused by depth variations in the harbor would be modeled by varying the dielectric properties of the cavity interior. When supplied with an appropriate source of microwaves, the intensity of the electric field at a given point can be related to wave induced currents at a similar location in the harbor. Such information is an important factor in the siting of berthing and mooring facilties for shipping. It is also shown how the impedance concept can be used to study the transformation of long waves as they traverse a step change in water depth. 相似文献
4.
Based on the Boussinesq assumption,derived are couple equations of free surface elevationand horizontal velocities for horizontal irrotational flow,and analytical expressions of the correspondingpressure and vertical velocity.After the free surface elevation and horizontal velocity at a certain depth areobtained by numerical method,the pressure and vertical velocity distributions can be obtained by simplecalculation.The dispersion at different depths is the same at the O(ε)approximation.The waveamplitude will decrease with increasing time due to viscosity,but it will increase due to the matching ofviscosity and the bed slope.thus,flow is unstable.Numerical or analytical results show that the waveamplitude.velocity and length will increase as the current increases along the wave direction.but theamplitude will increase.and the wave velocity and length will decrease as the water depth decreases. 相似文献
5.
海洋浅层土质剪切波速与深度的关系分析 总被引：1，自引：0，他引：1
剪切波速是工程场地地震安全性评价最重要的参数之一。应用测试的大量海洋浅层土质的剪切波速数据,利用最小二乘法通过三种模型探讨了不同土质类型的剪切波速与深度的关系,给出了不同土质类型的剪切波速与深度拟合最佳的统计公式。并与《构筑物抗震设计规范》的推荐公式在某一海域工程场地的测试结果进行对比分析,结果表明:本文所建立的统计公式对剪切波速的预测效果明显好于规范所推荐的统计公式。所推荐的海洋不同土质类型的剪切波速与深度间的统计公式,可供无波速测试的海洋工程场地使用。 相似文献
6.
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
7.
8.
风作用于水面产生风浪, 其中由于波流紊动产生的动量和能量的交换机制是一个很复杂的过程。风应力一般用来描述这种能量交换, 可以分为3个部分: 水面的剪切力、波生应力以及紊动应力。采用一种有效的非线性波流分离方法——NSFM(Nonlinear Stream Function Method)对波流运动的动量和能量输移进行定性描述。构造能够有效表达非线性波浪的解析流函数, 摄动求解使其满足拉普拉斯方程、动力边界条件和运动边界条件, 结合实验室风浪数据, 分离出波生速度场。通过交叉谱分析, 得到波生雷诺应力在不同风速下对风应力的贡献。结果表明: NSFM对不同工况条件下的风浪的处理具有较高的精度, 模型适应性良好; 且风速越大, 波生应力沿着水深衰减得越快, 且自由面波生应力在动量输移中的比重会逐渐减弱。 相似文献
9.
Unsteady nonlinear wave motions on the free surface in shallow water and over slopes of various geometries are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier–Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. Either linear or Stokes wave theory is employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with various wave periods and sea bottom slopes in surf zone. The results are compared with other existing computational and experimental results. Agreement between the experimental data and the computation results is good. 相似文献
10.
A numerical model is developed by combining a porous flow model and a two-phase flow model to simulate wave transformation in porous structure and hydraulic performances of a composite type low-crest seawall. The structure consists of a wide submerged reef, a porous terrace at the top and an impermeable rear wall. The porous flow model is based on the extended Navier-Stokes equations for wave motion in porous media and k−ε turbulence equations. The two-phase flow model combines the water domain with the air zone of finite thickness above water surface. A unique solution domain is established by satisfying kinematic boundary condition at the interface of air and water. The free surface advection of water wave is modeled by the volume of fluid method with newly developed fluid advection algorithm. Comparison of computed and measured wave properties shows reasonably good agreement. The influence of terrace width and structure porosity is investigated based on numerical results. It is concluded that there exist optimum value of terrace width and porosity that can maximize hydraulic performances. The velocity distributions inside and in front of the structure are also investigated. 相似文献
11.
《Coastal Engineering》1999,38(1):1-24
This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary conditions. It is demonstrated that previous fully dispersive formulations from the literature have used an inconsistent linear relation between the velocity potential and the surface elevation. As a consequence these formulations are accurate only in shallow water, while nonlinear transfer of energy is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement with the measurements, and it is found that the accuracy of e.g., the energy spectrum and of the third-order statistics is considerably improved by the new formulations, particularly outside the shallow-water range. 相似文献
12.
《Coastal Engineering》2006,53(2-3):181-190
Two-dimensional depth-averaged Boussinesq-type equations were presented with the consideration of slowly varying bathymetry and effects of bottom viscous boundary layer. These Boussinesq-type equations were written in terms of the horizontal velocity components evaluated at an arbitrary elevation in the water depth and the free surface displacement. The leading order effects of the bottom boundary layer were represented by a convolution integral in the depth-integrated continuity equation. To test the validity of the theory, a set of laboratory experiments was performed to measure the viscous damping and shoaling of a solitary wave propagating in a wave tank. The time histories of the free surface profiles were measured at several locations along the centerline of the flume. To compare these laboratory data with theoretical results, the two-dimensional Boussinesq-type equations were integrated across the wave tank, resulting in a set of one-dimensional equations, while the side-wall boundary layers were properly considered. The agreement between the experimental data and numerical results was very good. The bottom shear stress formula was also given and its impact on the sediment transport rate was discussed. 相似文献
13.
Using the recently developed expansion formulae for wave structure interaction problems, the scattering of surface water waves by a semi-infinite floating membrane due to abrupt change in bottom topography is analyzed. Both the cases of finite and infinite steps are analyzed. In the present paper, the analysis is based on the linearized theory of water waves and small amplitude membrane response. Combining the linearized kinematic and dynamic surface conditions on the water surface with the dynamic pressure condition on the membrane, a third order differential equation is derived to describe the membrane covered free surface condition. General wave energy relation for wave scattering by floating horizontal membrane is derived by the application of law of conservation of energy flux and alternately by the direct application of Green's second identity. In the floating membrane covered region, the wave energy density is a combination of the kinetic and potential energy density due to the surface gravity waves, and the surface energy density which is due to the existence of the floating membrane on the free surface. Gravity wave transformations due to an abrupt change in bottom topography in the presence of a floating membrane in finite water depth are analyzed based on shallow water approximation. Numerical results are computed and analyzed to understand the wave transformation due to the floating membrane when there is an abrupt change in topography in different cases. 相似文献
14.
To deal with the moving boundary hydrodynamic problems of the tidal flats in shallow water flow models,a new wetting and drying (WD) method is proposed.In the new method,a "predicted water depth" is evaluated explicitly based on the simplified shallow water equations and used to determine the status (wet or dry) together with the direction of flow.Compared with previous WD method,besides the water elevation,more factors,such as the flow velocity and the surface shear stress,are taken into account in the new method to determine the moving boundary.In addition,a formula is deduced to determine the threshold,as critical water depth,which needs to be preset before simulations.The new WD method is tested with five cases including three 1D ones and two 2D ones.The results show that the new WD method can simulate the wetting and drying process,in both typical and practical cases,with smooth manner and achieves effective estimation of the retention volume at shallow water body. 相似文献
15.
The main objective of this study is the simulation of flow dynamics in the deep parts of the Caspian Sea, in which the southern and middle deep regions are surrounded by considerable areas of shallow zones. To simulate spatio-temporal wind induced hydrodynamics in deep waters, a conjunctive numerical model consisting of a 2D depth average model and a 3D pseudo compressible model is proposed. The 2D model is applied to determine time dependent free surface oscillations as well as the surface velocity patterns and is conjunct to the 3D flow solver for computing three-dimensional velocity and pressure fields which coverage to steady state for the top boundary condition. The modified 2D and 3D sets of equations are conjunct considering interface shear stresses. Both sets of 2D and 3D equations are solved on unstructured triangular and tetrahedral meshes using the Galerkin Finite Volume Method. The conjunctive model is utilized to investigate the deep currents affected by wind, Coriolis forces and the river inflow conditions of the Caspian Sea. In this study, the simulation of flow field due to major winds as well as transient winds in the Caspian Sea during a period of 6 hours in the winter season has been conducted and the numerical results for water surface level are then compared to the 2D numerical results. 相似文献
16.
Longitudinal and transverse oscillations within a harbor of constant slope are analyzed. Based on the linear shallow water approximation, longitudinal oscillations are described with Bessel equations. Ignoring friction, oscillations are forced using the period of the incident perpendicular wave field by the method of matched asymptotics. The analytic results show that the varying depth shifts the resonant wave numbers to lower values than those for the same geometric harbor with constant depth. Furthermore, we extend the shallow water equations to a linear, weakly dispersive, Boussinesq-type equation by modifying the offshore velocity component, and then use it to investigate possible existing transverse oscillations in the harbor of constant slope. These oscillations are types of standing edge waves. Their character is quite sensitive to the boundary condition at the backwall of the harbor. 相似文献
17.
Jacobus P. Le Roux Zeki Demirbilek Marysia Brodalka Burghard W. Flemming 《Geo-Marine Letters》2010,30(5):549-560
The generation and growth of waves in deep water is controlled by winds blowing over the sea surface. In fully developed sea
states, where winds and waves are in equilibrium, wave parameters may be calculated directly from the wind velocity. We provide
an Excel spreadsheet to compute the wave period, length, height and celerity, as well as horizontal and vertical particle
velocities for any water depth, bottom slope, and distance below the reference water level. The wave profile and propagation
can also be visualized for any water depth, modeling the sea surface change from sinusoidal to trochoidal and finally cnoidal
profiles into shallow water. Bedload entrainment is estimated under both the wave crest and the trough, using the horizontal
water particle velocity at the top of the boundary layer. The calculations are programmed in an Excel file called WAVECALC,
which is available online to authorized users. Although many of the recently published formulas are based on theoretical arguments,
the values agree well with several existing theories and limited field and laboratory observations. WAVECALC is a user-friendly
program intended for sedimentologists, coastal engineers and oceanographers, as well as marine ecologists and biologists.
It provides a rapid means to calculate many wave characteristics required in coastal and shallow marine studies, and can also
serve as an educational tool. 相似文献
18.
程鹏 《海洋学报(英文版)》2020,42(5):1-2
在受波动影响的近岸浅水区域，运用sigma坐标是计算平均水位附近的余流的有效途径。本项研究在理论上分析了在狭窄潮汐水道中sigma坐标下的余流的物理意义，并运用一系列的理想化数值模型对分析结果进行了验证。对于浅水波，sigma层和水体中的波动面相一致，因而斯托克斯速度及其分量可以用sigma坐标上的速度来表达。一个sigma层上的余流（即sigma余流）是位于这一sigma层平均深度上的欧拉余流和斯托克斯速度垂向分量的和，可以被看做是半拉格朗日余流。因为斯托克斯速度的垂向分量比其水平分量小一个量级，sigma余流可看做为欧拉余流的近似。在sigma层上的物质输运余流是sigma余流和斯托克斯速度水平分量的和，在大小和方向上和拉格朗日余流近似。 相似文献
19.
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
20.
利用一维Boussinesq方程描述了在浅水中的波浪运动以及破碎情况。在方程中引入了表面翻滚的概念，认为翻滚的水体是以波速运动的，翻滚的作用表现在水平速度的垂直分布上，产生了附加迁移动量项。通过对Airy波在浅水中运动以及破碎情况的研究，得出的一些结论与Schaeffer和合田的成果吻合良好。 相似文献