Simulation of Wetting and Drying Processes in A Depth Integrated Shallow Water Flow Model by Slot Method

A particular porosity method named ＂slot method＂ is implemented in a depth-integrated shallow water flow model （DIVAST） to simulate wetting and drying processes. Discussed is the relationship between the shape factors of the ＂slot＂ and the preset depth used in ＂wetting-drying＂ algorithm. Two typical tests are conducted to examine the performance of the method with the effect of the shape factors of the ＂slot＂ being checked in detail in the first test. Numerical results demonstrate that： 1 ） no additional effort to improve the finite difference scheme is needed to implement ＂slot method＂ in DIVAST, and 2） ＂slot method＂ will simulate wetting and diying processes correctly if the shape factors of the ＂slot＂ being selected properly.     

Simulation of nearshore wave processes by a depth-integrated non-hydrostatic finite element model

This paper presents CCHE2D-NHWAVE, a depth-integrated non-hydrostatic finite element model for simulating nearshore wave processes. The governing equations are a depth-integrated vertical momentum equation and the shallow water equations including extra non-hydrostatic pressure terms, which enable the model to simulate relatively short wave motions, where both frequency dispersion and nonlinear effects play important roles. A special type of finite element method, which was previously developed for a well-validated depth-integrated free surface flow model CCHE2D, is used to solve the governing equations on a partially staggered grid using a pressure projection method. To resolve discontinuous flows, involving breaking waves and hydraulic jumps, a momentum conservation advection scheme is developed based on the partially staggered grid. In addition, a simple and efficient wetting and drying algorithm is implemented to deal with the moving shoreline. The model is first verified by analytical solutions, and then validated by a series of laboratory experiments. The comparison shows that the developed wave model without the use of any empirical parameters is capable of accurately simulating a wide range of nearshore wave processes, including propagation, breaking, and run-up of nonlinear dispersive waves and transformation and inundation of tsunami waves.     

Unsteady ship waves in shallow water of varying depth based on Green–Naghdi equation

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 (C_B=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.     

长江口南支潮流的一个数值模拟

为了能够精确地拟合天然水域不规则的水陆边界,并能保持有限差分数值计算在矩形网格中进行,本文利用Thompson的数值网格生成技术,在长江口南支七丫口至横沙河段设计了一个椭圆型边界拟合坐标系,并在这个坐标系下建立了平面二维潮流数学模型。通过数值求解此数学模型,实现了计算区域内现状潮流的一个数值模拟,模拟结果表明,模式的设计是成功的。     

Approach of moving boundary and its application in 3D tidal current simulation of Changjiang (Yangtze) River Estuary based on ECOMSED model

Considering three-dimensional model ECOMSED can not simulate wetting-drying of shoal with its fixed boundary, an approach to represent moving boundary in the model is introduced here. This approach smoothly joints the internal and external mode by making use of wetting and drying technique and is verified by a numerical test which presents a good agreement with the previous test results obtained by other researchers. A three dimensional numerical model is established to simulate the hydrodynamics in spring tide in the Changjiang (Yangtze) River estuary by this modified ECOMSED model which is also validated through the observed field data, the simulation presents a good periodic tidal change. It also successfully simulates the tidal current of computational areas and reproduces the tidal flat intermittent appearance.     

强非线性和色散性Boussinesq方程数值模型检验

采用同位网格有限差分法,建立了强非线性和色散性Boussinesq方程数值计算模型。以稳恒波Fourier近似解给定入射波边界条件,对均匀水深深水和浅水域不同非线性的行进波、缓坡地形上深水至浅水域的浅水变形波、以及缓坡和陡坡地形上的波浪水槽实验进行了数值计算,并将计算结果与解析解、解析数值解以及实验值进行了较为详细的比较,从而检验了模型的色散性、非线性以及不同底坡下非线性波的浅水变形性能。     

Third order contribution to the wave-making resistance of a ship at finite depth of water

This paper presents a potential based boundary element method for solving a nonlinear free surface flow problem for a ship moving with a uniform speed in finite depth of water. The free surface boundary condition is linearized by the systematic method of perturbation in terms of a small parameter up to third order. The surfaces are discretized into flat quadrilateral elements and the influence coefficients are calculated by Morino's analytical formula. Dawson's upstream finite difference operator is used in order to satisfy the radiation condition. The second order solution gives better result than the first or third order solution. So the present method with the second order solution can be adopted as a powerful tool for the hydrodynamic analysis of the thin ship in finite depth of water.     

Conjunction of 2D and 3D modified flow solvers for simulating spatio-temporal wind induced hydrodynamics in the Caspian Sea

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.     

Interactions between nonlinear water waves and non-wall-sided 3D structures

Interactions between water waves and non-wall-sided cylinders are analyzed based on velocity potential theory with fully nonlinear boundary conditions on the free surface and the body surface. The finite element method (FEM) is adopted together with a 3D mesh generated through an extension of a 2D Delaunay grid on a horizontal plane along the depth. The linear matrix equation for the velocity potential is constructed by imposing the governing equation and boundary conditions through the Galerkin method and is solved through an iterative method. By imposing the gradient of the potential equal to the velocity, the Galerkin method is used again to obtain the velocity field in the fluid domain. Simulations are made for bottom mounted and truncated cylinders with flare in a numerical tank. Periodic waves and wave groups are generated by a piston type wave maker mounted on one end of the tank. Results are obtained for forces, wave profiles and wave runups. Further simulations are made for a cylinder with flare subjected to forced motion in otherwise still open water. Results are provided for surge and heave motion in different amplitudes, and for a body moving in a circular path in the horizontal plane. Comparisons are made in several cases with the results obtained from the second order solution in the time domain.     

Filtering inertia-gravity waves from the initial conditions of the linear shallow water equations

A method for filtering inertia-gravity waves from elevation and depth-averaged velocity is described. This filtering scheme is derived from the linear shallow water equations for constant depth and constant Coriolis frequency. The filtered solution is obtained by retaining only the eigenvectors corresponding to the geostrophic equilibrium and by discarding explicitly the eigenvectors corresponding to the fast moving inertia-gravity waves. An alternative formulation is derived using a variational approach. Both filtering methods are tested numerically for a periodic domain with constant depth and the variational approach is implemented for a closed domain with large topographic variations. The filtering methods significantly reduce the amplitudes of the inertia-gravity waves while preserving the mean flow. The variational method is compared to the Incremental Analysis Update technique and the benefits of the variational filter are presented.     

Three-dimensional hydrodynamic model of Xiamen waters

Abstract-A semi-implicit and Eulerian-Lagrangian finite difference method for three-dimensionalshallow flow has been extended to a more complete system of equations incorporating second-momentturbulence closure model and transport equations of salinity and temperature. The simulation for flood-ing and drying of mudflats has been improved. The model is applied to Xiamen waters. Based on exten-sive survey data, water level elevation, temperature and salinity field along the eastern open boundaryand at the Jiulong River inlets and runoffs are analyzed, specified and calibrated. The computed resultsshow good agreement with the measured data, reproduce flooding, emergence of large and complexmudflat region.     

Numerical and experimental study on seakeeping performance of ship in finite water depth

Vessels operating in shallow waters require careful observation of the finite-depth effect. In present study, a Rankine source method that includes the shallow water effect and double body steady flow effect is developed in frequency domain. In order to verify present numerical methods, two experiments were carried out respectively to measure the wave loads and free motions for ship advancing with forward speed in head regular waves. Numerical results are systematically compared with experiments and other solutions using the double body basis flow approach, the Neumann-Kelvin approach with simplified m-terms, and linearized free surface boundary conditions with double-body m-terms. Furthermore, the influence of water depths on added mass and damping coefficients, wave excitation forces, motions and unsteady wave patterns are deeply investigated. It is found that finite-depth effect is important and unsteady wave pattern in shallow water is dependent on both of the Brard number τ and depth Froude number F_h.     

The depth-varying response of coastal circulation and water levels to 2D radiation stress when applied in a coupled wave–tide–surge modelling system during an extreme storm

During storm events wave setup in shallow regions can contribute significantly to the total water elevation, and radiation stress can also generate alongshore drift influencing sediment transport. In low lying coastal regions this generates the potential for flood inundation and morphological change. A coupled tide–surge–wave modelling system is therefore required for accurate forecasting. Liverpool Bay, UK, is taken as a case study because it has a resource of observations and incorporates three estuaries, thus providing conditions to assess the model performance both at the open coast and within estuarine environments. The model covers a region encompassing depths from about 50 m below the mean tidal level to shallow wetting and drying regions, and has previously given good wave and surge hindcasts both for individual storm events and multi-year studies.The present study builds on an already accepted model, to include and assess the spatial influence of 2D radiation stress when implemented in a 3D circulation model. The results show that the method is computationally efficient, so relevant for operational use, and also provides a plausible solution. The varied influence of radiation stress across a coastal domain is demonstrated, with larger impact at an estuary mouth and along the open coast, while having lesser impact within an estuary and further offshore.     

A new form of generalized Boussinesq equations for varying water depth

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.     

胶州湾潮汐潮流动边界数值模拟

基于普林斯顿海洋模式,通过干湿网格判别法引入潮汐潮流的漫滩过程,考虑M₂,S₂,K₁,O₁,M₄和MS₄六个主要分潮,建立了胶州湾潮汐潮流数值模拟和预报模型,研究了该海域潮汐潮流特征,并讨论了漫滩对潮流模拟的影响。与实测资料的对比验证表明,该模式能够对胶州湾的潮汐和潮流做出较为合理的预测。给出了胶州湾潮汐、潮流、余流等分布特征,模拟的潮流场以及余流场涡旋等现象与观测符合良好;计算了潮波能通量,从能量角度探讨了潮波的传播特性;对潮位与潮流场演变规律,以及潮能通量的分析表明,胶州湾内的潮波以驻波为主。通过数值试验发现,漫滩过程的引入对胶州湾潮流速度的模拟至关重要,不考虑漫滩过程的模式会夸大或者低估潮流流速。对于滩涂面积广阔的海域来说,潮流数值模式中考虑漫滩的影响是必要的。     

数值波浪水槽中完全非线性浅水波仿真特性研究

应用基于势流理论的时域高阶边界元方法,建立一个完全非线性的三维数值波浪水槽,通过实时模拟推板造波运动的方式产生波浪。通过混合欧拉-拉格朗日方法和四阶Runge-Kutta方法更新自由水面和造波板的瞬时位置。利用所建模型分别模拟了有限水深波和浅水波,与试验结果、相关文献结果和浅水理论结果吻合较好,且波浪能够稳定传播。系统地讨论造波板的运动圆频率、振幅和水深等对波浪传播和波浪特性的影响,并对波浪的非线性特性进行分析,研究发现造波板运动频率、运动振幅以及水深均将对波浪形态和波浪非线性产生显著影响。结果为真实水槽造波机的运动控制以及波浪生成试验提供了依据,便于实验室设置更合理的参数来准确模拟不同条件下的波浪。     

Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure

A numerical method for non-hydrostatic, free-surface, irrotational flow governed by the nonlinear shallow water equations including the effects of vertical acceleration is presented at the aim of studying surf zone phenomena. A vertical boundary-fitted grid is used with the water depth divided into a number of layers. A compact finite difference scheme is employed for accurate computation of frequency dispersion requiring a limited vertical resolution and hence, capable of predicting the onset of wave breaking. A novel wet–dry algorithm is applied for a proper handling of moving shoreline. Mass and momentum are strictly conserved at discrete level while the method only dissipates energy in the case of wave breaking. The numerical results are verified with a number of tests and show that the proposed model using two layers without ad-hoc assumptions enables to resolve propagating nonlinear shoaling, breaking waves and wave run-up within the surf and swash zones in an efficient manner.     

BOM的动边界改进及其应用

针对河口海岸数值模拟的动边界问题,使用了一个简便的干湿网格法,对BOM(Burgen Ocean Model)模型进行了动边界改进。并将该模型应用于瓯江口海域进行数值模拟计算,计算结果表明实测值与计算值吻合良好,模型能够较好的模拟岸边界随潮位涨落的变动。     

Active exchange of water and nutrients between seawater and shallow pore water in intertidal sandflats

In order to determine the temporal and spatial variations of nutrient profiles in the shallow pore water columns (upper 30 cm depth) of intertidal sandflats, we measured the salinity and nutrient concentrations in pore water and seawater at various coastal environments along the southern coast of Korea. In the intertidal zone, salinity and nutrient concentrations in pore water showed marked vertical changes with depth, owing to the active exchange between the pore water and overlying seawater, while they are temporally more stable and vertically constant in the sublittoral zone. In some cases, the advective flow of fresh groundwater caused strong vertical gradients of salinity and nutrients in the upper 10 cm depth of surface sediments, indicating the active mixing of the fresher groundwater with overlying seawater. Such upper pore water column profiles clearly signified the temporal fluctuation of lower-salinity and higher-Si seawater intrusion into pore water in an intertidal sandflat near the mouth of an estuary. We also observed a semimonthly fluctuation of pore water nutrients due to spring-neap tide associated recirculation of seawater through the upper sediments. Our study shows that the exchange of water and nutrients between shallow pore water and overlying seawater is most active in the upper 20 cm layer of intertidal sandflats, due to physical forces such as tides, wave set-up, and density-thermal gradient.     

Numerical Simulation of Water Exchange Characteristics of the Jiaozhou Bay Based on A Three-Dimensional Lagrangian Model

Based on theory of three-dimensional hydrodynamics,an Euler-Lagrangian particle model is established to study the transport and water exchange capability in the Jiaozhou Bay.The three-dimensional hydrodynamic model,driven by tide and wind,is used to study the effects of wetting and drying of eatuarine intertidal flats by the dry-wet grid technology based on the Estuarine,Coastal and Ocean Model (ECOM).The particle model includes the advection and the diffusion processes,of which the advection process is simulated with a certain method,and the diffusion process is simulated with the random walk method.The effect of the intertidal zone,the turbulent diffusion and the timescales of the water exchange are also discussed.The results show that a moving boundary model can simulate the transport process of the particle in the intertidal zone,where the particles are transported for a longer distance than that of the stationary result.Simulations with and without the turbulent random walk show that the effect of turbulent diffusion is very effective at spreading particles throughout the estuary and speeding up the particle movement.The spatial distribution of residence time is given to quantify the water exchange capability that has very important ramifications to water quality.The effect of wind on the water exchange is also examined and the southeasterly wind in summer tends to block the water exchange near the northeast coast,while the northerly wind in winter speeds up the transport process.These results indicate that the Lagrangian particle model is applicable and has a large potential to help understanding the water exchange capability in estuaries,which can also he useful to simulate the transport process of contaminant.