Two-dimensional scour simulations based on coupled model of shallow water equations and sediment transport on unstructured meshes

A two-dimensional scour model based on coupled system of shallow water equations (SWEs) and sediment transport on unstructured mesh is developed. The coupled system of hydrodynamic and morphodynamic equations is solved by finite volume method using Godunov scheme. Roe's approximate Riemann solver is used to calculate the inviscid fluxes. The use of unstructured mesh makes the model applicable to complex domains. However, it is difficult to evaluate the eigenvalues and eigenvectors of the Jacobian matrix in the global coordinate. The method proposed herein to deal with this difficulty is to transform the system into the local coordinate with one of the axes in the same direction as the interface outward normal vector. In the local coordinate system, the Jacobian matrix is simplified and the eigenvalues are analyzed using asymptotic method. Regular expansion breaks down when the flow is near critical. Uniformity of the expansion is achieved by changing the scales. Rotational invariance theorem is used to relate the interfacial fluxes in the global and local coordinate systems. Special treatment of the source term on unstructured grid makes the scheme stable and physically balanced (both mass and momentum). The method proposed in this paper for the eigen-system is very efficient comparing to iterative numerical methods. Results from the test cases show good agreement with the experiments.     

Dispersion and stability analyses of the linearized two-dimensional shallow water equations in Cartesian coordinates

In the present study, a Fourier analysis is used to develop expressions for phase and group speeds for both continuous and discretized, linearized two-dimensional shallow water equations, in Cartesian coordinates. The phase and group speeds of the discrete equations, discretized using a three-point scheme of second order, five-point scheme of fourth order and a three-point compact scheme of fourth order in an Arakawa C grid, are calculated and compared with the corresponding values obtained for the continuous system. The three-point second-order scheme is found to be non-dispersive with grid resolutions greater than 30 grids per wavelength, while both the fourth-order schemes are non-dispersive with grid resolutions greater than six grids per wavelength. A von Neumann stability analysis of the two- and three-time-level temporal schemes showed that both schemes are stable. A wave deformation analysis of the two-time-level Crank–Nicolson scheme for one-dimensional and two-dimensional systems of shallow water equations shows that the scheme is non- dispersive, independent of the Courant number and grid resolution used. The phase error or the dispersion of the scheme decreases with a decrease in the time step or an increase in grid resolution.     

浅水分潮对海岸潮致地下水波动特征的影响

基于一维Boussinesq方程,在斜坡海岸边界条件中考虑了半日潮及其浅水分潮的综合作用,应用摄动法得到了方程的二阶解。通过与现场实测资料和数值解的比较,分析了浅水分潮对海岸潮致地下水波动特征的影响。分析结果显示,考虑浅水分潮后,方程数值解能较好地反映实测的潮致地下水波动基本特征;方程各阶摄动解虽与现场实测数据有一定误差,但基本上能反映其波动的趋势性特征。研究结果表明,浅水分潮对海岸潮致地下水波动振幅及其超高值的影响比较显著,也能较好地改善相位上的偏移,因此在对海岸潮致地下水波动特征进行研究分析时,应该考虑浅水分潮的作用。     

Threshold of motion of coarse-grained sediment under waves in shallow water

This paper considers the threshold of motion of sediment in shallow coastal waters under breaking and non-breaking waves. A simple model, representing conditions at the fluid/sediment interface, is developed. The representation of a breaking wave is based on bore theory, and the shear stress at the bed is based on the friction formula of O'Connor and Yoo. A threshold formula is presented based on the use of energy dissipation. The threshold data is also related to the Shields threshold criterion.     

Experimental investigation of free-running ship manoeuvers under extreme shallow water conditions

We present an experimental investigation of a free-running manoeuvring inland waterway ship at extreme shallow water conditions. Physical tests of zig-zag manoeuvres at two different water depths were performed in model scale and investigated with regards to the effects of limited under-keel clearance. Experimental data comprise results from repeatability studies and may serve for validation of manoeuvring simulations.     

多光谱遥感影像的两种浅海水深反演模型对比与分析

利用WorldView-2高分辨率卫星影像,以南海北岛附近海域为研究区,研究了两种水深反演模型——对数变换模型(Stumpf 2003)和双波段线性回归模型(Lyzenga 1985)。分析了不同底质情况下水深与各波段的相关性,并利用L-M(Levenberg-Marquardt)算法求解模型参数,然后对两种模型反演的水深结果的精度进行了对比分析。对于珊瑚底质,Lyzenga 1985模型水深反演的决定系数和均方根误差分别为0.902和1.651,均优于Stumpf 2003模型(0.882,6.421);对于砂质底质,Lyzenga 1985模型水深反演的决定系数和均方根误差分别为0.897和0.529,均优于Stumpf 2003模型(0.779,0.723)。可见,在水体清澈的珊瑚底质和砂质底质区域,Lyzenga 1985模型的水深反演精度均优于Stumpf 2003模型,Lyzenga 1985模型普适性更强,能够呈现出较为稳定的反演效果。     

Accurate representation of geostrophic and hydrostatic balance in unstructured mesh finite element ocean modelling

Accurate representation of geostrophic and hydrostatic balance is an essential requirement for numerical modelling of geophysical flows. Potentially, unstructured mesh numerical methods offer significant benefits over conventional structured meshes, including the ability to conform to arbitrary bounding topography in a natural manner and the ability to apply dynamic mesh adaptivity. However, there is a need to develop robust schemes with accurate representation of physical balance on arbitrary unstructured meshes. We discuss the origin of physical balance errors in a finite element discretisation of the Navier–Stokes equations using the fractional timestep pressure projection method. By considering the Helmholtz decomposition of forcing terms in the momentum equation, it is shown that the components of the buoyancy and Coriolis accelerations that project onto the non-divergent velocity tendency are the small residuals between two terms of comparable magnitude. Hence there is a potential for significant injection of imbalance by a numerical method that does not compute these residuals accurately. This observation is used to motivate a balanced pressure decomposition method whereby an additional “balanced pressure” field, associated with buoyancy and Coriolis accelerations, is solved for at increased accuracy and used to precondition the solution for the dynamical pressure. The utility of this approach is quantified in a fully non-linear system in exact geostrophic balance. The approach is further tested via quantitative comparison of unstructured mesh simulations of the thermally driven rotating annulus against laboratory data. Using a piecewise linear discretisation for velocity and pressure (a stabilised P₁P₁ discretisation), it is demonstrated that the balanced pressure decomposition method is required for a physically realistic representation of the system.     

The wave transformation and breaking phenomena in shallow water

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浅海沉积层声学特性对声传播损失的影响仿真研究

为厘清海底沉积层声学特性信息的水声环境保障需求,构建浅海两层海底环境参数模型,并参考Hamilton海底底质9种分类设置沉积层声速、密度、衰减系数及厚度的参考值及计算采样区间,利用Kraken简振波模型,采用控制变量的方法,研究了浅海沉积层声学特性参数对声传播损失的影响;开展了建模理论推导及数值技术分析,研究了海底沉积层声学特性参数在模型计算过程中调用过程,并从建模计算的角度对仿真计算的结果进行解释,对海底沉积层声学特性调查装备发展及调查重点参数具有一定的参考价值。     

Parameterization and simulation of near bed orbital velocities under irregular waves in shallow water

A set of empirical formulations is derived that describe important wave properties in shallow water as functions of commonly used parameters such as wave height, wave period, local water depth and local bed slope. These wave properties include time varying near-bed orbital velocities and statistical properties such as the distribution of wave height and wave period. Empirical expressions of characteristic wave parameters are derived on the basis of extensive analysis of field data using recently developed evolutionary algorithms. The field data covered a wide range of wave conditions, though there were few conditions with wave periods greater than 15 s. Comparison with field measurements showed good agreement both on a time scale of a single wave period as well as time averaged velocity moments.     

浅水非线性波作用下沙质底床孔隙水压力响应数值分析

近岸水深较浅,波浪具有较强的非线性,海床破坏与波浪作用下孔隙水压力的分布有着密切的关系。波浪场控制方程采用雷诺时均方程和k-ε紊流模型,入射波采用椭圆余弦波,采用PLIC-VOF法追踪自由表面;海床域以Biot动力固结理论为基础,建立了非线性波浪与海床相互作用的弱耦合数学模型,获得椭圆余弦波作用下沙质海床中孔隙水压力响应规律。计算结果表明,与线性波浪相比,浅水非线性波作用下沙质海床中孔隙水压力幅值增大非常显著。     

Combined refraction and diffraction models for sea waves over complicated topography and with currents in shallow water

-Combined refraction and diffraction models in the form of linear parabolic approximation are derived through smallparameter method. More strictly theoretical basis and more accuracy in the models than Lozano's (1980) are obtained. Some theoretical defects in Liu's model (1985) with consideration of current are not only found but also eliminated. More strict and accurate models are, therefore, presented in this paper.The calculation results and analysis in applying the models to actual wave field with consideration of bottom friction will be given in the following paper.     

非结构网格模型在闽东沿海台风浪模拟中的应用

基于加密的非结构三角网格,以Holland模型风场叠加美国国家环境预报中心（NCEP）海面风场构造的合成风场驱动第三代浅水波浪数值模型（SWAN）对2017年影响闽东海域的“纳沙”和“泰利”台风过程进行数值模拟,并运用浮标站的实测数据对模拟结果进行验证.结果表明,模型计算的风速、有效波高与实测值符合较好,合成风场能较好地模拟台风期间的风速变化过程,SWAN模式能够合理地再现闽东沿海台风浪的时空分布特征.由模拟结果可见：台风“纳沙”中心越过台湾岛进入台湾海峡北部海面,受海峡地形的约束,其波浪场呈NE—SW向椭圆状分布,北部海域的浪高大于南部,闽东沿海遍布大范围的巨浪到狂浪;超强台风“泰利”未登陆闽东,当其台风中心与大陆的距离最近时,海面波浪场分布与台风风场结构一致,台风中心附近海域为14 m以上的怒涛区,巨浪遍布于闽东沿海.研究结果可为闽东沿海台风浪灾害预警和应急管理提供技术支撑和参考依据.     

Spectral classification of water masses under the influence of the Amazon River plume

The large amount of dissolved and particulate material discharged by the Amazon River into the Equatorial Atlantic Ocean cause distinct spectral response of its waters as compared to the nearby ocean waters. This paper shows the application of K-means clustering algorithm for classifying water masses in the region under the Amazon River plume influence according to their spectral behavior. Salinity and temperature data from 67 oceanographic stations were related to Sea-viewing Wide Field-of-view Sensor (SeaWiFS) remote sensing reflectances values and the following bio-optical products:(i) chlorophyll-a concentration, (ii) water attenuation coefficient and (iii) absorption coefficient for dissolved and detrital material. Four different water masses were identified such as:(1) oceanic water, (2) intermediate oceanic water, (3) intermediate river plume water and (4) Amazon River plume water. The spectral behavior of these water masses allowed concluding that the main active optical component of the waters in the region is the colored dissolved organic matter originated mostly from the Amazon River.     

The applicability of the shallow water equations for modelling violent wave overtopping

The shallow water equations (SWE) have been used to model a series of experiments examining violent wave overtopping of a near-vertical sloping structure with impacting wave conditions. A finite volume scheme was used to solve the shallow water equations. A monotonic reconstruction method was applied to eliminate spurious oscillations and ensure proper treatment of bed slope terms. Both the numerical results and physical observations of the water surface closely followed the relevant Rayleigh probability distributions. However, the numerical model overestimated the wave heights and suffered from the lack of dispersion within the shallow water equations. Comparisons made on dimensionless parameters for the overtopping discharge and percentage of waves overtopping between the numerical model and the experimental observations indicated that for the lesser impacting waves, the shallow water equations perform satisfactorily and provide a good alternative to computationally more expensive methods.     

浅海聚焦定位中简化地声模型的应用研究

为了提高定位算法的环境宽容性,聚焦法将环境参数纳入了寻优空间。聚焦法虽然降低了对环境测量的要求,但是反演参数的增加也增加了反演的复杂性。基于海底反射特性,用两个参数对海底进行建模。通过标准的反演测试问题对简化地声模型在浅海聚焦定位中的有效性进行了分析。结果表明:基于简化地声模型的聚焦定位是可行的。在获得正确定位结果的同时,随着地声参数个数的减少,匹配场处理的便捷性得到了提高。文中引入的简化地声模型是聚焦问题中参数最少的地声模型,它可以有效减少聚焦定位参数维数以提升反演的便捷性。同时,简化地声模型在参数敏感性和耦合性上有较好的表现,这些优点可以保证定位结果的稳健性。     

The dynamics of wave induced ship motions in shallow water

The analytical method developed by Svendsen (1968) for a forced heave motion is extended to the general problem of wave induced heave, roll and sway motions of a long ship at a depth of water which is only slightly larger than the draught of the ship. This corresponds, for example, to the situation of a fully loaded ship in a harbour area.After linearization of the problem, the water motion is considered for each of the three individual motions and for the wave reflection-transmission problem for a fixed ship. The ensuing results for the forces on the ship are then synthesized to form the equations of motion, which are presented with all coefficients given, including mooring forces.Analytical and numerical results are given for the three components of motion, for the associated resonance frequencies, and for the hydrodynamic masses and moments of inertia. Finally, the assumptions used are analyzed and evaluated by comparison with measurements and with other results for a special case.     

海工结构物浅基础稳定性的可靠度分析

应用可靠度理论对渤海某油田软粘土地基工作的沉垫式基础的稳定性进行了可靠度分析，阐述了各个设计指标的变化对分项系数及可靠度指标的影响规律，并将分析结果与该标准中规定的分项系数进行了比较。     

波浪破碎下油滴粒径分布理论模型研究

海上溢油在波浪破碎的情况下经常会形成油滴,本文讨论了油滴形成的可能机制,根据量纲分析瑞利法建立了油滴卷入率与能量耗散率、卷入深度等破碎统计物理量的关系。基于量纲分析Π定理并根据毛细数、无量纲卷入时间与粘度比的实验关系,导出了油径谱的理论模型。初步结果表明,理论谱斜率-2.29与观测谱斜率-2.3符合良好,剪切率、表面张力、油滴半径、油和水的黏度等因素是影响油滴总数的主要原因。