一种台风暴潮数值模拟方法

本文提出一种简便的交替方向隐式差分格式求解沿水深平均的二维风暴潮模型。这种差分格式比常用的ＡＤＩ法具有更简单的形式和更高的计算效率。文中的精度分析和稳定性分析表明该差分格式在等步长条件下具有二阶精度、无条件稳定。在采用理想模型验证之后，本文给出了一次台风暴潮过程的计算实例，其中台风气压场和风场的模拟采用藤田气压模式和梯度风公式，并考虑台风移行产生的风场以及梯度风到海面风的订正。数值摸拟结果和实测值符合良好，其精度达到工程应用要求。     

一种渤海风暴潮数值预报模式与试验

通过三维模式导出二维数值模式,采用守恒型空间差分格式对渤海风暴潮进行数值模拟。同时采用由三维模式导出的任意形式的底摩擦表达式,找出适用于渤海风暴潮的底摩擦参数。对曾经发生在渤海的四次较严重的风暴潮进行数值后报并与实测资料相比较,证实预报模式的可行性。     

Boussinesq水波方程新型数值解法

为建立高效的Boussinesq类水波数值模型,提出了一种新型的、基于有限差分和有限体积方法的混合数值格式。针对守恒形式的一维控制方程,在等间距矩形控制体内对其进行积分并离散,采用有限体积方法计算界面数值通量,剩余源项采用有限差分方法计算。其中,采用MUSTA格式并结合高精度状态插值方法计算控制体界面数值通量。时间积分则采用具有TVD性质的三阶龙格-库塔多步积分法进行。除验证模型外,重点对MUSTA格式和广泛使用的HLL格式进行了比较。结果表明,MUSTA格式可用于Boussinesq类水波方程数值求解,综合考虑数值精度、计算效率、程序编制和实际应用这几个方面,其较HLL格式更具有优势。     

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.     

台风风暴潮异模式集合数值预报技术研究及应用

台风风暴潮数值预报的准确性在很大程度上取决于台风路径预报和强度预报的精度以及风暴潮预报模型的计算精度。目前,国际上24/48 h台风路径预报平均误差分别约为120/210 km左右[1],对于走向异常的台风误差更大;更有,根据单一的台风路径和单族的风暴潮数值预报模式并不能保证获得可靠的风暴潮预报结果。考虑多重网格法原理具有在疏密不同的网格层上进行迭代以达到平滑不同频率的误差分量,使得计算快速收敛,精度提高的特性。在前期研究基础上基于业务化高分辨率(结构网格/有限差分算法)和精细化(非结构网格/有限元算法)台风风暴潮集合数值预报模型构建多模型台风风暴潮集合数值预报系统。采用"非同族"模型进行集合预报很大程度上降低了误差相似遗传的可能性。应用该方法对典型台风风暴潮过程进行了试应用,试报结果表明:该方法对风暴潮增、减水预报效果高于单一集合预报,具有一定的应用前景。     

Computations of the almost highest short-crested waves in deep water

The highest short-crested waves have been studied analytically and numerically by several workers, but without a conclusive view. An efficient numerical scheme is proposed in this paper which retains the water-surface elevations in an implicit form in the governing equations, rather than using a series approximation, thus improving the accuracy of the numerical results. Convergence of the numerical scheme is verified. The almost highest short-crested waves in deep water are then evaluated, which are defined for the condition with the largest wave energies. It is found that the critical angle for wave frequency reversal also demarcates the wave characteristics near breaking, for either kinematic or dynamic prominence. The known results available for the limiting two-dimensional cases of standing and progressive waves are compared favourably.     

基于多源数据的台风风暴潮概率预报研究:台风集合的构建

建立了一套用于台风风暴潮集合预报的台风集合构建方案.首先基于中国中央气象台、中国香港天文台、中国台湾中央气象局、美国联合台风预警中心、日本气象厅和韩国气象台6家预报中心的预报数据,构建一个误差更小的24 h、48h和72 h预报时效的台风分析数据;然后基于分析数据构建9个路径样本(1条分析路径+2个概率圆上的8条概率路...     

Numerical analysis of effects of tidal variations on storm surges and waves

This study examines the effects of tides on surges, wave setups and waves, in terms of tidal amplitudes and phases, by using a coupled numerical model of Surge, WAve and Tide (called as SuWAT). The SuWAT model, composed of depth integrated nonlinear shallow water equations and Simulating WAves Nearshore (SWAN) model, is able to simultaneously run with an arbitrary number of nested domains by using the Message Passing Interface. The results for an idealized case indicate that surge and wave setup are increased in the phase of low water and decreased in the high water phase; on the other hand, waves change in a reverse manner. Such changes are enhanced by large tidal variations. The conventional method (e.g., surge plus tide independently) has the possibility of overestimation for the total water level. The hindcast results for Typhoon Ewiniar in 2006 show that the run with tides is more accurate 10% than that without tides in coastal areas of Korea. The nested scheme improves the accuracy up to 40% for the prediction of water levels in the simulations. It is shown that the present coupled model, SuWAT, is capable of predicting both water levels and waves under storm events with reasonable accuracy against the observations.     

Numerical analysis and validation of weakly nonlinear ship motions and structural loads on a modern containership

This paper aims to validate a numerical seakeeping code based on a 3D Rankine panel method by comparing its results with experimental data. Particularly, the motion response and hull-girder loads on a real modern ship, a 6500 TEU containership, are considered in this validation study. The method of solution is a 3D Rankine panel method which adopts B-spline basis function in the time domain. The numerical code is based on the weakly nonlinear scheme which considers nonlinear Froude-Krylov and restoring forces. The main focus of this study is given to investigate the nonlinear characteristics of wave-induced loads, and to validate this present scheme for industrial use in the range of low Froude number. The comparisons show that the nonlinear motions and hull-girder loads, computed by the present numerical code, have good overall agreements with experimental results. It is found that, for the better accuracy of computational results, particularly at extreme waves in oblique seas, the careful treatment of soft-spring (or compatible) system is recommended to the control of non-restoring motions such as surge, sway, and yaw.     

Efficient Numerical Solution of the Modified Mild-Slope Equation

An efficient numerical model for wave refraction,diffraction and reflection is presented in thispaper.In the model,the modified time-dependent mild-slope equation is transformed into an evolutionequation and an improved ADI method involving a relaxation factor is adopted to solve it.The methodhas the advantage of improving the numerical stability and convergence rate by properly determining therelaxation factor.The range of the relaxation factor making the differential scheme unconditionally stableis determined by stability analysis.Several verifications are performed to examine the accuracy of the pres-ent model.The numerical results coincide with the analytic solutions or experimental data very well,andthe computer time is reduced.     

Modeling a neutrally stratified turbulent air flow over a horizontal rough surface

The neutrally stratified boundary layer over a smooth rough surface is consider. The turbulent flow is simulated using a finite-difference eddy-resolving model of the atmospheric boundary layer (ABL). The model includes different turbulence closure schemes and numerical approximations for advection components of the momentum balance equation. We investigate the quality of reproduction of spectral characteristics of the turbulent flow and the model’s capabilities to reproduce the observed profile of mean wind velocity near the rough surface. It is shown that the best result is obtained by coupling a numerical scheme of higher order of accuracy with a mixed closure scheme based on an adaptive estimation of the mixing length for subgrid-scale fluctuations. Here, we are able to reproduce the asymptotics of the fluctuation spectrum of the longitudinal component of wind velocity near the surface and within the boundary layer as well as the logarithmic profile of mean velocity near the surface.     

Fully nonlinear numerical wave tank (NWT) simulations and wave run-up prediction around 3-D structures

A finite-difference scheme and a modified marker-and-cell (MAC) algorithm have been developed to investigate the interactions of fully nonlinear waves with two- or three-dimensional structures of arbitrary shape. The Navier–Stokes (NS) and continuity equations are solved in the computational domain and the boundary values are updated at each time step by the finite-difference time-marching scheme in the framework of a rectangular coordinate system. The fully nonlinear kinematic free-surface condition is implemented by the marker-density function (MDF) technique developed for two fluid layers.To demonstrate the capability and accuracy of the present method, the numerical simulation of backstep flows with free-surface, and the numerical tests of the MDF technique with limit functions are conducted. The 3D program was then applied to nonlinear wave interactions with conical gravity platforms of circular and octagonal cross-sections. The numerical prediction of maximum wave run-up on arctic structures is compared with the prediction of the Shore Protection Manual (SPM) method and those of linear and second-order diffraction analyses based on potential theory and boundary element method (BEM). Through this comparison, the effects of non-linearity and viscosity on wave loading and run-up are discussed.     

非规则三角网格有限差分法地震正演模拟

针对有限差分方法在地震正演模拟中的广泛应用,提出了1种基于三角形网格的地震正演模拟差分算法。相对于矩形网格差分法而言,该方法可以更为精确地描述弯曲的速度界面,可直接用于起伏地表模型的正演模拟计算而无需对模型做特殊处理。由于空间步长可随速度的变化而改变,加之在递推计算中采用了显式差分算法,该方法可视为对传统的规则网格有限差分法的有效改进。数值模拟的结果表明该方法是稳定、精确的且具有较高的计算效率。     

一次登陆湛江台风风暴潮数值预报

本文对2002年8月在湛江附近登陆的0214号强热带风暴(黄蜂)进行了风暴潮实时预报。根据中央气象台预报的热带气旋强度和位置,采用数值模式,在该热带气旋由北上加强到登陆减弱的整个过程中,进行了三次实时预报,分别为18日20时、19日08时和19日 17时。预报结果表明本数值模式具有良好的预报功能,并指出其风暴潮预报时效和精度在很大程度上取决于热带气旋气象预报的时效和精度。     

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.     

覆盖中国沿海地区的精细化台风风暴潮模型的研究及适用

精细化风暴潮预报是目前风暴潮预报重点发展方向之一,本文首次建立起了一个覆盖整个中国沿海地区的精细化台风风暴潮数值模型,克服了以往分区域数值模型的不足,该模型在中国沿海地区的分辨率达到300m左右。模型采用了并行计算,并对2012年和2013年灾害性台风风暴潮过程进行了数值检验,计算精度和计算所用时间都能够满足业务化运行的要求。本文同时还根据中国气象局、美国国家气象局等5家主要台风预报机构给出的24h台风预报,对2013年度灾害性台风风暴潮过程进行了24h数值预报检验,检验结果表明:根据中国气象局台风登陆前24h预报可以得到更准确的风暴潮预报结果,其预报结果优于其他各家预报结果。该结论可以为今后的台风风暴潮预报中台风路径的选取提供重要的参考。     

铁山湾内天文潮对风暴潮水位的影响研究

作为半封闭狭长海湾,铁山湾受风暴潮灾害的影响较为严重。根据多年观测资料和数值模型对铁山湾内的风暴潮水位特征进行了研究。观测资料表明海湾内风暴潮峰值水位受天文潮相位影响较为显著,然后基于ADCIRC风暴潮模型和1409号“威马逊”台风参数,定量评估了天文潮对风暴潮水位的影响。模拟结果表明当考虑天文潮作用时,会显著提高模拟结果精度,然后通过数值实验研究了风暴潮与不同相位天文潮相互作用时的水位变化特征。数值实验结果表明天文潮-风暴潮相互作用引起的非线性水位在涨潮阶段不明显,在高潮位时非线性水位达到负值最大;在落潮时达到正值最大。风暴潮增水峰值由于受到这种非线性效应的影响,在高潮位时数值最小。海湾内非线性作用要远大于外部,非线性效应越强,总水位峰值相对于天文潮高潮位的延迟时间也就越长。     

风暴潮三维数值计算模式的研究及在渤海湾的应用

以实验室二维温带风暴潮数值模型为基础,综合考虑海洋潮波动力与风应力联合作用,建立温带风暴潮三维数值计算模型.模型从推导三维风暴潮基本控制方程出发,并应用交替方向隐格式(ADI)方法对方程进行离散求解.对于浅水动边界,模型采取局部深槽、缩小水域的活动边界处理方法.利用拟三维数值计算方法,并提出了非平面水深等分模式和平面等水深分布模式,应用这两种计算模式分别对渤海湾2009年5月8～10日发生的风暴潮过程进行了数值模拟.将风暴潮位计算结果和增水位计算结果与塘沽验潮站的实际观测数值进行对比验证,结果显示受风应力与潮波联合作用的风暴潮位和增水位与实测数据吻合良好;通过比较得到了平面等水深分布模式的计算成果要比非平面水深等分模式的计算成果更接近观测资料的结论,为风暴潮预报提供了理论依据.     

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.     

Simulation of Storm Surges in the Bay of Bengal Using One-Way Coupling Between NMM-WRF and IITD Storm Surge Model

The storm surge associated with severe tropical cyclones (TCs) in the Bay of Bengal (BoB) is a serious concern along the coastal regions of India, Bangladesh, Myanmar, and Sri Lanka. It is one of the most hazardous elements associated with landfalling TCs other than strong winds and heavy precipitation and about 75% of the casualities in this region are attributed to storm surges. Therefore, it is highly essential to predict the storm surges with greater accuracy at least 2 days in advance for effective evacuation. In the present study, an attempt is made to simulate the storm surges associated with severe TCs in the BoB using one-way coupling of the Non-hydrostatic Mesoscale Model core of Weather Research and Forecasting (NMM-WRF) system with the two-dimensional finite-difference storm surge model developed at the Indian Institute of Technology Delhi (IITD). The NMM-WRF model simulated track, pressure drop, and radius of maximum wind are used to calculate the wind-stress through Jelesnianski wind formulation. The results are compared with the observed/estimated values as provided by the operational/meteorological agencies of India, Bangladesh, and Myanmar. This study suggests that using simulated surface meteorological fields of a high-resolution mesoscale model, the storm surge can be predicted at least 2 days in advance of the actual landfall of TCs with reasonable accuracy. This approach will be helpful in providing disastrous storm warning well in advance in a coastal region, which will help with rapid evacuation from the vulnerable coastal region, relocation as well as protection of valuables, disaster mitigation, and coastal zone management.