Internal generation of waves: Delta source function method and source term addition method

In this study, we investigate two internal wave generation methods in numerical modeling of time-dependent equations for water wave propagation, i.e., delta source function method and source term addition method, the latter of which has been called the line source method in literatures. We derive delta source functions for the Boussinesq-type equations and extended mild-slope equations. By applying the fractional step splitting method, we show that the delta source function method is equivalent to the source term addition method employing the energy velocity. This suggests that the energy velocity should be used rather than the phase velocity for the transport of incident wave energy in the source term addition method. Finally, the performance of the delta source function method is verified by accurately generating nonlinear cnoidal waves as well as linear waves for horizontally one-dimensional cases.     

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.     

Modelling of periodic wave transformation in the inner surf zone

In this paper, we analyse the ability of the nonlinear shallow-water (NSW) equations to predict wave distortion and energy dissipation of periodic broken waves in the inner surf zone. This analysis is based on the weak-solution theory for conservative equations. We derive a new one-way model, which applies to the transformation of non-reflective periodic broken waves on gently sloping beaches. This model can be useful to develop breaking-wave parameterizations (in particular broken-wave celerity expression) in both time-averaged wave models and time-dependent Boussinesq-type models. We also derive a new wave set-up equation which provides a simple and explicit relation between wave set-up and energy dissipation. Finally, we compare numerical simulations of both, the NSW model and the simplified one-way model, with spilling wave breaking experiments and we find a good agreement.     

Possible Density Change of the Origin of North Pacific Intermediate Water Due to Double Diffusion in the Mixed Water Region

In this study we test Talley's hypothesis that Oyashio winter mixed-layer water (26.5–26.6σ _θ) increases its density to produce the North Pacific Intermediate Water (NPIW) salinity minimum (26.7– 26.8σ_θ) in the Mixed Water Region, assuming a combination of cabbeling and double diffusion. The possible density change of Oyashio winter mixed-layer water is discussed using an instantaneous ratio of the change of temperature and salinity along any particular intrusion (R _l ). We estimate the range of R _l ^DD required to convert Oyashio winter mixed-layer water to the NPIW salinity minimum due to double diffusion, and then assume double-diffusive intrusions as this conversion mechanism. A double-diffusive intrusion model is used to estimate R _l ^DD in a situation where salt fingering dominates vertical mixing, as well as to determine whether Oyashio winter mixed-layer water can become the NPIW salinity minimum. Possible density changes are estimated from the model R _l ^DD by assuming the amount of density change due to cabbeling. From these results, we conclude that Oyashio winter mixed-layer water contributes to a freshening of the lighter layer of the NPIW salinity minimum (around 26.70σ_θ) in the MWR.     

Three-dimensional Layer-integrated Modelling of Estuarine Flows with Flooding and Drying

Details are given of the refinement and application of a thee-dimensional (3-D) layer-integrated numerical model of tidal circulation, with the aim of simulating severe tidal conditions for practical engineering applications. The mode splitting strategy has been used in the model. A set of depth-integrated 2-D equations are first solved to give the pressure gradient, and the layer-integrated 3-D equations are then solved to obtain the vertical distributions of the flow velocities. Attention has been given to maintaining consistency of the physical quantities derived from the 2-D and 3-D equations. A TWO=layer mixing length turbulence model for the vertical shear stress distribution has been included in the model. Emphasis has been focused on applying the model to a real estuary, which is geometrically complicated and has large tidal ranges giving rise to extensive flooding and drying. The model has been applied to three examples, including: wind-driven flow in a rectangular lake, tidal circulation in a model rectangular harbour, and tidal circulation in a large estuary. Favourable results have been obtained for both the simple and complex flow beds.     

关于波浪Boussinesq方程的研究

对有关波浪 Boussinesq方程的研究成果进行了系统的归纳总结和评述 ,以期对本学科的发展起到一定的引导和促进作用     

Numerical simulation of solitary wave scattering by a circular cylinder array

The interaction of a solitary wave with an array of surface-piercing vertical circular cylinders is investigated numerically. The wave motion is modeled by a set of generalized Boussinesq equations. The governing equations are discretized using a finite element method. The numerical model is validated against the experimental data of solitary wave reflection from a vertical wall and solitary wave scattering by a vertical circular cylinder respectively. The predicted wave surface elevation and the wave forces on the cylinder agree well with the experimental data. The numerical model is then employed to study solitary wave scattering by arrays of two circular cylinders and four circular cylinders respectively. The effect of wave direction on the wave forces and the wave runup on the cylinders is quantified.     

近岸溢油漂移扩散预测方法研究——以胶州湾溢油事件为例

近些年,由于中国经济的高速发展,原油需求逐年增长,同时海上溢油事故发生的风险也在加剧。海上溢油会严重破坏海洋环境,危害我国经济发展,加强溢油漂移扩散预报研究能够为海上溢油应急响应提供技术支撑。因此,国家海洋信息中心研发了海上突发事件应急一体化预测预警系统。该系统基于GIS平台研发,能够在二维电子海图基础上叠加相关的海洋环境动力要素信息,模拟溢油扩散和漂移态势,同时计算剩余油量,估算溢油面积以及岸线吸附程度等。2013年11月22日,山东黄岛发生输油管道爆炸事故,造成大量原油溢入胶州湾。本文利用该系统结合高分辨率大气模型WRF的三重嵌套技术和海流模型SELFE的非结构化网格加密技术,对事故溢油漂移扩散开展了预测工作。预测结果显示,油污受胶州湾内往复流的影响极大,72 h后,胶州湾内外大部分海域都将存在油污,主要集中在黄岛沿岸海域、团岛及浮山湾附近,预测扫海面积为70.32 km2。经海事部门高分辨率卫星观测结果印证,系统模拟的溢油分布较为合理。该系统的业务化应用为相关海上溢油污染应急工作提供了一定理论依据和参考。     

现场海域水平扩散系数的探讨 Ⅱ．黄河三角洲埕北海域的计算

根据Ｔａｙｌｏｒ的湍流扩散理论和Ｈａｙ、Ｐａｓｑｕｉｌｌ提出的拉格朗日流和欧拉流的相关函数的相似性，用黄河三角洲埕北海域的实测资料，按四种不同方案计算出该海域的水平扩散系数和谱密度分布。指出：该海区潮流扩散系数主要受潮流的影响，其分布特征与潮流的分布基本一致，所求的水平扩散系数主要是由周期性的潮运动给予潮流扰动所致。方案４是通过富氏变换滤波消去了周期性潮流扰动，本方案计算的水平扩散系数是由周期为６ｈ以下的小尺度涡提供能量。     

A Compact Explicit Difference Scheme of High Accuracy for Extended Boussinesq Equations

Presented here is a compact explicit difference scheme of high accuracy for solving the extended Boussinesq equations.For time discretization,a three-stage explicit Runge-Kutta method with TVD property is used at predicting stage,a cubic spline function is adopted at correcting stage,which made the time discretization accuracy up to fourth order;For spatial discretization,a three-point explicit compact difference scheme with arbitrary order accuracy is employed.The extended Boussinesq equations derived by Beji and Nadaoka are solved by the proposed scheme.The numerical results agree well with the experimental data.At the same time,the comparisons of the two numerical results between the present scheme and low accuracy difference method are made,which further show the necessity of using high accuracy scheme to solve the extended Boussinesq equations.As a valid sample,the wave propagation on the rectangular step is formulated by the present scheme,the modelled results are in better agreement with the experimental data than those of Kittitanasuan.