Application of Two Turbulence Closure Schemes in the Modelling of Tidal Currents and Salinity in the Hooghly Estuary

This paper has two purposes. The first is to study the circulation and salinity in Hooghly Estuary, along the east coast of India and the second is to compare the performance of two turbulence closure schemes by modelling it. A breadth averaged numerical model using a sigma co-ordinate system in the vertical is briefly described. Vertical diffusion of momentum and salt are parameterized by a simple first-order turbulent closure or by a one equation model for turbulent kinetic energy (TKE) which uses a specified mixing length. The results are compared with the available neap and spring tide observations along the estuary for both low and high discharge periods.The computed elevations and currents are in reasonable agreement with the observations showing no major differences in vertical current profiles by both the turbulent schemes. However, there is a slight under-prediction of bottom currents. The salinity profiles predicted by TKE model show better matching with observations. Statistical tests are also conducted to study the comparative performance of the turbulent closure schemes. The maintenance of two layer structure in residual currents and salt variability are also studied by using the model.     

台风浪数值模拟方法比较——以1513号台风“苏迪罗”为例

为减少复杂地形对台风浪数值模拟的干扰,有效优化模拟精度和效果,充分发挥台风浪数值模式在防灾减灾中的作用,文章利用ERA-interim风场驱动模式,以1513号台风"苏迪罗"为例,采用2种方案对其形成的台风浪进行数值模拟,并对二者进行比较。其中,方案(1)为采用WW3模式,方案(2)为采用WW3模式和SWAN模式嵌套。研究结果表明:选取有效波高的模拟值和观测值,根据对散点分布的定性分析以及对相关系数、偏差和均方根误差的定量计算,采用方案(2)的模拟精度更高;通过绘制台风浪场分布图,采用方案(2)对有效波高的动态数值模拟更加明显和准确,尤其对于复杂地形海域的模拟效果更优。因此,在未来的海浪数值模拟中,可参照采用方案(2),即在大区域采用WW3模式,在复杂地形海域嵌套SWAN模式。     

MASNUM-WAM海浪模式集合Kalman滤波同化研究——Ⅱ.集合样本对同化效果的影响

背景误差相关结构的确定是影响海浪同化效果的关键因素之一。集合Kalman滤波是一种较为成熟的同化方法,其可以对背景误差进行实时更新和动态估计,现已广泛应用于海洋和大气领域的研究。本文基于MASNUM-WAM海浪模式,分别采用静态样本集合Kalman滤波和EAKF方法,针对2014年全球海域开展海浪数据同化实验,同化资料为Jason-2卫星高度计数据,利用Saral卫星高度计资料对同化实验结果进行检验。结果表明,两组同化方案均有效提高了海浪模式的模拟水平,EAKF方案在风场变化较大的西风带区域表现显著优于静态样本集合Kalman滤波方案,但总体上两者相差不大。综合考虑计算成本和同化效果,静态样本集合Kalman滤波方案更适用于海浪业务化预报。     

Different approaches to model error formulation in 4D-Var: a study with high-resolution advection schemes

All numerical models are imperfect. Weak constraint variational data assimilation ( VDA ), which provides a treatment of the modelling errors, is studied; building on the approach of Vidard et al. (Tellus, 56 A, pp. 177–188, 2004). The evolution of model error ( ME ) is modelled using ordinary differential equations, which involve a scalar parameter. These approaches were tested using different high-resolution advection schemes. The first set of experiments were constructed to see if it is possible to account for (numerical) discretization error within such a framework. In other set of experiments, a systematic source of modelling error was introduced by deliberately specifying an incorrect value for the Coriolis parameter in the model. Results with observational state at half of the model state resolution, are also presented. We also discuss a method of estimating the scalar parameter in the ME through VDA . In all cases, the inclusion of ME provides reduction in forecasting errors. Also, our experiments indicate that different settings of the model (e.g. using different high-resolution advection schemes) would need different ME formulation. Results presented in this paper could be used to formulate sophisticated ME forms to account for systematic errors in higher dimensional models with complex advection schemes.     

Developments in terrain-following ocean models: intercomparisons of numerical aspects

During the course of developing new numerical algorithms for a terrain-following ocean modeling system (TOMS), different numerical aspects have been evaluated through a comparison between two widely used community ocean models, the Princeton ocean model (POM) and the regional ocean modeling system (ROMS). While both models aim at modeling coastal to basin-scale problems using similar grids, their numerical algorithms, code structure, and parameterization options are very different. Sensitivity studies with an idealized channel flow and a steep seamount configuration demonstrate how different algorithms in the two models may affect numerical errors, the stability of the code and the computational efficiency. For example, new pressure gradient schemes using polynomial fits and new time stepping algorithms may reduce numerical errors and allow using longer time steps than standard schemes do. However, the new schemes may require more careful choices of time steps and the use of higher order advection schemes to maintain numerical stability.     

Meridional heat transport in the model of the general circulation for the North Atlantic

The meridional heat transport obtained from numerical experiments using the general circulation model for the North Atlantic encompassing the equatorial area is analysed. The surface turbulent layer is included in the model, and its realization is based on conservative difference schemes. It is shown that the upper 50 m layer plays a dominant role in the formation of meridional heat transport in the low latitudes.Translated by Mikhail M. Trufanov.     

A finite element cable model and its applications based on the cubic spline curve

For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.     

长兴岛海区波流相互作用数值模拟研究

波和流是近岸海区的主要动力因素。应用二维潮流数学模型和最新第三代近岸海浪模式SWAN,建立了非结构网格下二维情况近岸波流耦合作用数学模型。时间离散采用欧拉向前格式,空间离散采用有限体积法显式格式。通过将波浪场及潮流场进行迭代耦合计算,实现了对波流共同作用下波浪场和潮流场的数值模拟。将模型应用于矩形海湾实验和李孟国数模实验等理想地形以及大连长兴岛海区实际复杂地形算例,并用现场实测资料对计算结果进行验证,结果表明:耦合结果与实测结果吻合良好,并且要优于未耦合的结果。     

格型钢板桩结构数值建模方法研究

针对格型钢板桩结构的三种建模方法(考虑板桩间铰接特性,用壳体单元模拟板桩的有限元模型;不考虑板桩间铰接特性,用壳体单元模拟板桩的有限元模型;将格体看做一个整体,用实体单元模拟板桩的有限元模型)进行分析,对各种建模方法得出的关于稳定性、破坏模式、格体环向应力、格体内外土体压力的相关结论进行比较,得到适合工程应用的建模方法。结果表明:三种有限元模型中,考虑板桩间铰接特性的壳体单元模型,因其考虑因素全面,是最准确的模型。对于重要工程,应采用考虑板桩间铰接特性的壳体单元模型进行计算。对于一般工程结构,在稳定性分析方面,三种有限元模型都很适用,由于壳体单元模型收敛性较差,建议采用比较成熟的实体单元模型进行简化;对于破坏模式和板桩间环向应力,建议采用不考虑板桩间铰接作用的壳体单元模型进行简化;对于结构背浪侧格型钢板桩结构格体外侧土体最大被动土压力和格内土体压力,采用不考虑板桩间铰接特性的壳体单元模型进行估算。结论对工程数值建模运算具有指导意义。     

Diffusion reduction in an arbitrary scale third generation wind wave model

The numerical schemes for the geographic propagation of random, short-crested, wind-generated waves in third-generation wave models are either unconditionally stable or only conditionally stable. Having an unconditionally stable scheme gives greater freedom in choosing the time step (for given space steps). The third-generation wave model SWAN (“Simulated WAves Nearshore”, Booij et al., 1999) has been implemented with this type of scheme. This model uses a first order, upwind, implicit numerical scheme for geographic propagation. The scheme can be employed for both stationary (typically small scale) and nonstationary (i.e. time-stepping) computations. Though robust, this first order scheme is very diffusive. This degrades the accuracy of the model in a number of situations, including most model applications at larger scales. The authors reduce the diffusiveness of the model by replacing the existing numerical scheme with two alternative higher order schemes, a scheme that is intended for stationary, small-scale computations, and a scheme that is most appropriate for nonstationary computations. Examples representative of both large-scale and small-scale applications are presented. The alternative schemes are shown to be much less diffusive than the original scheme while retaining the implicit character of the particular SWAN set-up. The additional computational burden of the stationary alternative scheme is negligible, and the expense of the nonstationary alternative scheme is comparable to those used by other third generation wave models. To further accommodate large-scale applications of SWAN, the model is reformulated in terms of spherical coordinates rather than the original Cartesian coordinates. Thus the modified model can calculate wave energy propagation accurately and efficiently at any scale varying from laboratory dimensions (spatial scale O(10 m) with resolution O(0.1 m)), to near-shore coastal dimension (spatial scale O(10 km) with resolution O(100 m)) to oceanic dimensions (spatial scale O(10 000 km) with resolution O(100 km).     

Characteristics of quadrant and octant advection schemes in wave models

We point out one problem of the grid advection schemes when used in wave models in coastal areas. The deficiency of the schemes is investigated by means of the ‘third' generation WAM wave model, in which the wave energy is advected by a first order upwind scheme. Two similar, alternative modifications of this scheme are analyzed, the second of which is shown to solve most of the problems encountered with advection along the co-ordinate axes.     

不同时空格式在求解污染物对流扩散方程中的应用

为了研究污染物对流扩散方程中不同时空格式的适用性,针对对流扩散方程的一维﹑二维和三维3种情况,分别建立了预报-校正的有限差分数值模型。在时间步进格式上分别采用了Crank-Nicolson格式或混合4阶Adams-Bashforth-Moulton格式,对对流项分别采用2阶精度或4阶精度,对扩散项采用了2阶精度。利用建立的数值模型求解了经典的污染物浓度场对流扩散,通过数值解与解析解的比较讨论了不同时空格式对数值模型计算结果的影响。结果表明:对空间一次导数采用4阶精度可以避免采用2阶精度带来的误差。采用混合4阶Adams-Bashforth-Moulton格式或Crank-Nicolson格式数值计算结果均与解析解吻合程度较好,但对于数组为[40,40,40]的三维对流扩散问题,前者比后者省时20.7%。     

Kalman滤波风暴潮数值预报四维同化模式研究进展

本文首先介绍了Kalman滤波在风暴潮数值预报中的应用，特别介绍了近年来国际上发展的一些在实际中可行的次优化Kalman滤波算法。并通过一个稳态Kalman滤波风暴潮数值预报模式的实例表明，使用资料同化可以明显改进风暴潮后报结果；资料同化能够提供更为合理的预报初始场，对风暴潮的短期预报有较明显的改进。一旦没有资料同化到模式中去，预报结果很快接近确定性模式。     

A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations

A numerical scheme for solving the class of extended Boussinesq equations is presented. Unlike previous schemes, where the governing equations are integrated through time using a fourth-order method, a second-order Godunov-type scheme is used thus saving storage and computational resources. The spatial derivatives are discretised using a combination of finite-volume and finite-difference methods. A fourth-order MUSCL reconstruction technique is used to compute the values at the cell interfaces for use in the local Riemann problems, whilst the bed source and dispersion terms are discretised using centred finite-differences of up to fourth-order accuracy. Numerical results show that the class of extended Boussinesq equations can be accurately solved without the need for a fourth-order time discretisation, thus improving the computational speed of Boussinesq-type numerical models. The numerical scheme has been applied to model a number of standard test cases for the extended Boussinesq equations and comparisons made to physical wave flume experiments.     

Numerical study on residual current and its impact on mass transport in the Hangzhou Bay and the Changjiang Estuary I. A3-D joint model of the Hangzhou Bay and the Changjiang Estuary

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Numerical study on residual current and its impact on mass transport in the Hangzhou Bay and the Changjiang Estuary Ⅰ.A3-D joint model of the Hangzhou Bay and the Changjiang Estuary

A 3-D numerical model is set up in a large domain covering the Hang zhou Bay and the Changjiang Estuary based on the ECOM model in orthogonal curvilinear coordinates.The numerical schemes for baroclinic pressure gradient (BPG) terms and convective terms are improved in the paper according to the characteristics of velocity field and mass transport in the area.The model is validated by the simulations of residual current and salinity transport in the Hangzhou Bay and the Changjiang Estuary.     

钱塘江河口尖山河段整治规划线的方案试验研究

根据实测资料分析和二维数值计算 ,借助实体模型 ,通过定床与动床试验 ,比较分析了两种整治规划线方案。结果表明 ,推荐方案对削弱尖山以上江道的潮势 ,改善萧绍平原的排涝条件 ,效果显著     

水动力与生态耦合的赤潮藻类生长模型研究

针对近岸海域赤潮藻类生长及分布的特点,将简化了的赤潮藻类模型与水动力学中的对流扩散方程相耦合,建立了一个水动力与生态耦合的赤潮藻类生长的深度模型。模型中用一个积分形式的指数函数模拟了藻类生长过程,用一个一阶线性函数近似模拟了藻类的死亡过程,用藻类浓度的一阶导数项模拟藻类的输运过程,用浓度的二阶导数模拟了藻类的扩散过程,并用高精度的三阶迎风格式对模型进行了数值模拟,结果表明,该模型能正确的反映藻类的生长特点,与实际情况吻合良好。     

An efficient shock capturing algorithm to the extended Boussinesq wave equations

A hybrid finite-volume and finite-difference method is proposed for numerically solving the two-dimensional (2D) extended Boussinesq equations. The governing equations are written in such a way that the convective flux is approximated using finite volume (FV) method while the remaining terms are discretized using finite difference (FD) method. Multi-stage (MUSTA) scheme, instead of commonly used HLL or Roe schemes, is adopted to evaluate the convective flux as it has the simplicity of centred scheme and accuracy of upwind scheme. The third order Runge–Kutta method is used for time marching. Wave breaking and wet–dry interface are also treated in the model. In addition to model validation, the emphasis is given to compare the merits and limitations of using MUSTA scheme and HLL scheme in the model. The analytical and experimental data available in the literature have been used for the assessment. Numerical tests demonstrate that the developed model has the advantages of stability preserving, shock-capturing and numerical efficiency when applied in the complex nearshore region. Compared with that using HLL scheme, the proposed model has comparable numerical accuracy, but requires slightly less computation time and is much simpler to code.