大尺度圆柱墩群周围的波流场的数值模拟

本文对波流共同作用下大尺度圆柱墩群周围的波流场进行了数值研究。利用波浪弥散关系的迭代计算求得波向与流向的夹角以及波浪的相对频率。流场通过求解浅水环流方程得到,波浪场通过求解含流的缓坡方程得到,通过二者的迭代计算得到大尺度圆柱墩群周围的波流场的耦合解。用有限元法建立了数值模型,并将本文的计算数据与试验数据以及其他学者计算数据进行了比较,结果较为合理。     

Tide simulation using the mild-slope equation with Coriolis force and bottom friction

Since the mild-slope equation was derived by Berkhoff (1972),the researchers considered various mechanism to simplify and improve the equation,which has been widely used for coastal wave field calculation.Recently,some scholars applied the mild-slope equation in simulating the tidal motion,which proves that the equation is capable to calculate the tide in actual terrain.But in their studies,they made a lot of simplifications,and did not consider the effects of Coriolis force and bottom friction on tidal wave.In this paper,the first-order linear mild-slope equations are deduced from Kirby mild-slope equation including wave and current interaction.Then,referring to the method of wave equations’ modification,the Coriolis force and bottom friction term are considered,and the effects of which have been performed with the radial sand ridges topography.Finally,the results show that the modified mild-slope equation can be used to simulate tidal motion,and the calculations agree well with the measurements,thus the applicability and validity of the mild-slope equation on tidal simulation are further proved.     

结合椭圆型缓坡方程模拟近岸波流场

波浪向近岸传播的过程中,由波浪破碎效应所产生的近岸波流场是近岸海域关键的水动力学因素之一.结合近岸波浪场的椭圆型缓坡方程和近岸波流场数学模型对近岸波浪场及由斜向入射波浪破碎后所形成的近岸波流场进行了数值模拟.计算中考虑到波浪向近岸传播中由于波浪的折射、绕射、反射等效应使局部复杂区域波向不易确定,采用结合椭圆型缓坡方程所给出的波浪辐射应力公式来计算波浪产生的辐射应力,在此基础上耦合椭圆型缓坡方程和近岸波流场数学模型对近岸波流场进行数值模拟,从而使模型综合考虑了波浪的折射、绕射、反射等效应且避免了对波向角的直接求解,可以应用于相对较复杂区域的近岸波流场模拟.     

Comparison between characteristics of mild slope equations and Boussinesq equations

Boussinesq-type equations and mild-slope equations are compared in terms of their basic forms and characteristics. It is concluded that linear mild-slope equations on dispersion relation are better than non-linear Boussinesq equations. In addition, Berkhoffexperiments are computed and compared by the two models, and agreement between model results and available experimental data is found to be quite reasonable, which demonstrates the two models＇ capacity to simulate wave transformation. However they can deal with different physical processes respectively, and they have their own characteristics.     

近岸波浪和波生流环境中泥沙输运的数值模拟

Owing to lack of observational data and accurate definition,it is difficult to distinguish the Kuroshio intrusion water from the Pacific Ocean into the South China Sea(SCS).By using a passive tracer to identify the Kuroshio water based on an observation-validated three-dimensional numerical model MITgcm,the spatio-temporal variation of the Kuroshio intrusion water into the SCS has been investigated.Our result shows the Kuroshio intrusion is of distinct seasonal variation in both horizontal and vertical directions.In winter,the intruding Kuroshio water reaches the farthest,almost occupying the area from 18°N to 23°N and 114°E to 121°E,with a small branch flowing towards the Taiwan Strait.The intrusion region of the Kuroshio water decreases with depth gradually.However,in summer,the Kuroshio water is confined to the east of 118°E without any branch reaching the Taiwan Strait;meanwhile the intrusion region of the Kuroshio water increases from the surface to the depth about 205 m,then it decreases with depth.The estimated annual mean of Kuroshio Intrusion Transport(KIT) via the Luzon Strait is westward to the SCS in an amount of –3.86×106 m3/s,which is larger than the annual mean of Luzon Strait Transport(LST) of –3.15×106 m3/s.The KIT above 250 m accounts for 60%–80% of the LST throughout the entire water column.By analyzing interannual variation of the Kuroshio intrusion from the year 2003 to 2012,we find that the Kuroshio branch flowing into the Taiwan Strait is the weaker in winter of La Ni?a years than those in El Ni?o and normal years,which may be attributed to the wind stress curl off the southeast China then.Furthermore,the KIT correlates the Ni?o 3.4 index from 2003 to 2012 with a correlation coefficient of 0.41,which is lower than that of the LST with the Ni?o 3.4 index,i.e.,0.78.     

缓坡方程与Boussinesq方程特征的分析比较

在对缓坡方程和Boussinesq方程研究的基础上，从方程的基本形式和特征以及频散关系等方面对二者进行了分析和比较，明确了线性缓坡方程在频散性上要好于非线性Boussinesq方程。此外还对Boussinesq型模型与抛物型缓坡方程模型在Berkhoff椭圆地形的计算结果及其精度也进行比较，计算结果与实测数据吻合很好，说明这两种模型都可以用于模拟近岸波浪传播过程所发生的各种变形。但由于各自控制方程对各物理过程的处理不同，因此各有特征。     

抛物型缓坡方程的变分及数值模拟

对线性水波的折射一绕射问题应用变分原理,对非等深、具有缓坡和不连续的底被导出了一种修改的抛物型缓坡方程近似模型,可预测三维地形上波浪的折射一绕射。同抛物型缓坡方程的线性方程进行了对比。通过数值模拟方法进行数值求解,表明本方法可用于地形条件下的波浪折射一绕射问题。     

A Modified Form of Mild-Slope Equation with Weakly Nonlinear Effect

Nonlinear effect is of importance to waves propagating from deep water to shallow water.Thenon-linearity of waves is widely discussed due to its high precision in application.But there are still someproblems in dealing with the nonlinear waves in practice.In this paper,a modified form of mild-slope equa-tion with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation.The modified form of mild-slope equation is convenient to solvenonlinear effect of waves.The model is tested against the laboratory measurement for the case of a submergedelliptical shoal on a slope beach given by Berkhoff et al,The present numerical results are also comparedwith those obtained through linear wave theory.Better agreement is obtained as the modified mild-slope e-quation is employed.And the modified mild-slope equation can reasonably simulate the weakly nonlinear ef-fect of wave propagation from deep water to coast.     

中国海域浮游硅藻钟形中鼓藻Bellerochea orologicalis Stosch初步研究

我国迄今已记录的中鼓藻属中只有一种——锤状中鼓藻Bellerochea malleus(Bright- well)Van Heurck有详细报导,作者在中国海域进行浮游生物取样时采到本属的另一种钟形中鼓藻Bellerochea horologicalis Stosch,1977.对本种与锤状中鼓藻的重要区别,以及本种的细胞形态、结构、生态习性与分布进行了描述。     

综合考虑多种变形因素的近岸规则波传播数学模型Ⅰ. 基本方程的导出

推广了Kirby的有环境水流影响的缓坡方程,得到了综合考虑环境水流(水流因子)、非线性弥散影响(非线性因子)、底摩擦波能损失(底摩擦因子)、非缓坡地形影响(地形因子)、折射、绕射、波浪破碎多种变形因素的波浪传播控制方程,并给出了非线性因子、地形因子、底摩擦因子、水流因子的确定方法。基于导出的方程做进一步推导,得到了波高和波向为变量的综合考虑多种变形因素的波浪传播基本方程,该方程有许多优点:1)其绕开了求解波势函数的困难,将椭圆型方程的边值问题化为初值问题;2)直接求解波高和波向;3)可采用有限差分法离散求解,对空间步长没有限制,适合大面积海区波场计算;4)综合考虑了多种波浪变形因素,方程更为合理,5)容易处理波浪破碎问题。     

近岸沿岸流及污染物运动的数值模拟

基于双曲型缓坡方程和近岸浅水方程对近岸波浪斜向入射破碎所生成的沿岸流及污染物在沿岸波流作用下的运动进行了数值模拟,并对数值模拟结果进行了验证分析。数值模拟结果表明,在相近工况参数下,随着入射波高的增大,沿岸流流速和平均水面升高值均明显增大;随着岸坡坡度的增加,沿岸流流速和平均水面升高值明显增大;随着入射波浪周期的增大,平均水面升高值明显增大。在沿岸缓坡区域,由斜向入射波浪破碎所产生的沿岸流对污染物的运动起着不可忽略的影响。     

对近岸海浪非势函数、势函数型缓坡方程的初步探讨

针对目前缓坡方程中势函数假设比较多的问题,本文利用二维浅水方程来描述海浪水质点运动的有势假设,采取WKBJ方法推导缓坡方程在缓变地形下的波包方程,对势函数缓坡方程进行修正,以建立更全面更实用的近岸波浪传播计算模式。同时,文中还采用非势函数型模拟波浪传播。     

波浪作用下近岸区污染物输移扩散的数学模型及其实验验证

在近岸缓坡浅水海岸,波浪破碎产生沿岸流是近岸海域流场的重要组成部分,它对污染物输移扩散规律的影响重大,在高阶近似抛物化缓坡方程求解大面积波浪场基础上,建立了波浪作用下污染物输移扩散数学模型.计算结果与不同坡度均匀斜坡地形上具有不同波高、周期的规则波及不规则波浪作用下污染物输移扩散实验结果进行了比较,分析了各种因素对波浪作用下沿岸流分布规律影响,所得结论认为地形坡度及入射波高对污染物输移扩散的影响较大,波浪作用将使缓坡海滩上污染物的输移扩散平行岸线方向.     

Numerical Modeling of Wave Diffraction-Refraction in Water of Varying Current and Topography

—A numerical model for wave diffraction-refraction in water of varying current and topogra-phy is proposed,and time-dependent wave mild-slope equation with a dissipation term and correspondingequivalent governing equations are presented.Two different expressions of parabolic approximations forthe case of the absence of current are also given and analyzed.The influence of current on the results ofsimulation of waves is discussed.Some examples show that the present model is better than others in simu-lating wave transformation in large water areas.And they also show that the influence of current shouldbe taken into account,on numerical modeling of wave propagation in water of strong current and coastalareas,otherwise the modeling results will be largely distorted.     

考虑风能输入的抛物型缓坡方程

在Radder和Kirby发展的波浪折射绕射缓坡方程抛物型模型基础上,对这种模型进行了改进,改进后的模型除可以考虑波浪传播过程中的底摩阻损耗、非线性作用外,加入了风能输入对波浪传播的影响。基于风能输入项的波浪模型数值计算结果表明,在纯风浪情况下的计算结果与传统的风浪计算方法结果一致,在波浪传播过程中由于风的作用,将导致波高比无风作用下计算的波高大。     

利用网格划分软件和缓坡方程计算港内波浪场

提出了一套可方便应用于波浪场计算的方法。该方法包含了准确的边界输入输出技术,简便的地形输入技术,高质量的计算网格生成以及加速查寻、排序的数据结构。应用双曲型缓坡方程计算了港湾内的波浪场,数值计算时提出了处理建筑物表面部分反射边界条件的方法。将计算结果与边界元方法的结果和实验值进行了比较,证明该方法应用于波浪场可得到较理想的结果。对大连港区内的波浪折射绕射进行了计算,表明本方法可以应用于实际港口的波浪场计算中。     

New Numerical Scheme for Simulation of Hyperbolic Mild-Slope Equation

The original hyperbolic mild-slope equation can effectively take into account the combined effects of wave shoaling, refraction, diffraction and reflection, but does not consider the nonlinear effect of waves, and the existing numerical schemes for it show some deficiencies. Based on the original hyperbolic mild-slope equation, a nonlinear dispersion relation is introduced in present paper to effectively take the nonlinear effect of waves into account and a new numerical scheme is proposed. The weakly nonlinear dispersion relation and the improved numerical scheme are applied to the simulation of wave transformation over an elliptic shoal. Numerical tests show that the improvement of the numerical scheme makes efficient the solution to the hyperbolic mild-slope equation. A comparison of numerical results with experimental data indicates that the results obtained by use of the new scheme are satisfactory.     

Linear wave reflection by trench with various shapes

Two types of analytical solutions for waves propagating over an asymmetric trench are derived. One is a long-wave solution and the other is a mild-slope solution, which is applicable to deeper water. The water depth inside the trench varies in proportion to a power of the distance from the center of the trench (which is the deepest water depth point and the origin of x-coordinate in this study). The mild-slope equation is transformed into a second-order ordinary differential equation with variable coefficients based on the longwave assumption [Hunt's, 1979. Direct solution of wave dispersion equation. Journal of Waterway, Port, Coast. and Ocean Engineering 105, 457–459] as approximate solution for wave dispersion. The analytical solutions are then obtained by using the power series technique. The analytical solutions are compared with the numerical solution of the hyperbolic mild-slope equations. After obtaining the analytical solutions under various conditions, the results are analyzed.     

A coupled-mode model for water wave scattering by horizontal, non-homogeneous current in general bottom topography

A coupled-mode model is developed for treating the wave–current–seabed interaction problem, with application to wave scattering by non-homogeneous, steady current over general bottom topography. The vertical distribution of the scattered wave potential is represented by a series of local vertical modes containing the propagating mode and all evanescent modes, plus additional terms accounting for the satisfaction of the free-surface and bottom boundary conditions. Using the above representation, in conjunction with unconstrained variational principle, an improved coupled system of differential equations on the horizontal plane, with respect to the modal amplitudes, is derived. In the case of small-amplitude waves, a linearised version of the above coupled-mode system is obtained, generalizing previous results by Athanassoulis and Belibassakis [J Fluid Mech 1999;389:275–301] for the propagation of small-amplitude water waves over variable bathymetry regions. Keeping only the propagating mode in the vertical expansion of the wave potential, the present system reduces to an one-equation model, that is shown to be compatible with mild-slope model concerning wave–current interaction over slowly varying topography, and in the case of no current it exactly reduces to the modified mild-slope equation. The present coupled-mode system is discretized on the horizontal plane by using second-order finite differences and numerically solved by iterations. Results are presented for various representative test cases demonstrating the usefulness of the model, as well as the importance of the first evanescent modes and the additional sloping-bottom mode when the bottom slope is not negligible. The analytical structure of the present model facilitates its extension to fully non-linear waves, and to wave scattering by currents with more general structure.     

Experimental verification of horizontal two-dimensional modified mild-slope equation model

In order to verify modified mild-slope equation models in a horizontal two-dimensional space, a hydraulic experiment is made for surface wave propagation over a circular shoal on which water depth varies substantially. A horizontal two-dimensional numerical model is also constructed based on the hyperbolic equations that have been developed from the modified mild-slope equation to account for the substantial depth variation. Comparison between experimental measurements and numerical results shows that the modified mild-slope equation model is capable of producing accurate results for wave propagation in a region where water depth varies substantially, while the conventional mild-slope equation model gives large errors as the mild-slope assumption is violated.