应用Boussinesq方程对Genus—2波系的理论研究

本文应用Ｂｏｕｓｓｉｎｅｓｑ方程，对由直立防波堤反射而形成Ｇｅｎｕｓ－２波系进行了理论研究。通过对Ｂｏｕｓｓｉｎｅｓｑ方程二阶非线性波求解得到了４个不同传播方向的高阶波解。由一阶线性入射波与二阶非线性波的叠加在形成了具有双周期结构的Ｇｅｎｕｓ－２波系结构菱形波面图。通过物模实验，这种Ｇｅｎｕｓ－２波系的菱形波面得以呈现于物模港池中。物模实验与所做的数值结果比较可看出，数值结果与物模实验之值有着较好     

直立摇板简谐摇荡造二维波时所受水动力矩的频域二阶解和时域线性解

本文给出直立摇板简谐摇荡造二维波时所受水动力矩的频域二阶解和时域线性解的解析表达式,可供估算摇板式造波机设计功率时使用,也可为摇板所受水动力矩时域非线性数值计算提供比较的依据。     

沙坝海岸上裂流的数值模拟

建立了基于二阶完全非线性Boussinesq水波方程的二维波浪破碎数值模型,对沙坝海岸上产生的裂流进行了数值模拟研究。首先将文献[1]中给出的一组二阶完全非线性Boussinesq方程进行扩展,在动量方程中引入紊动粘性项模拟波浪破碎引起的能量耗散,采用窄逢法处理海岸动边界问题,并考虑了混合子网格效应以及水底摩擦。然后,在矩形网格上离散控制方程,采用有限差分方法和混合四阶Adams-Bashforth-Moulton预报矫正格式建立了数值模型。应用所建立模型对一带沟槽沙坝海岸上产生裂流的实验进行数值模拟,将计算的波高、增减水、时均流速、时均流场等与实验数据进行了比较。数值结果与实验结果吻合较好,这说明建立的数值模型是准确有效的,为下一步应用该模型模拟实际海岸上的裂流提供了研究基础。     

水面波动问题频域三阶解的一个实例(之二):三阶波形和水动力的求解

针对定深水域中一块直立推板简谐运动引起水面二维波动的问题,在论文[1]已给出速度势三阶解表达式的基础上,本文进一步求取波形和推板所受水动力的三阶解.通过与二阶解及完全非线性解的比较,分析了三阶解在非线性解中的地位和作用.     

SECOND-ORDER TRANSIENT STANDING WAVES IN A RECTANGULAR TANK

ＳＥＣＯＮＤ－ＯＲＤＥＲＴＲＡＮＳＩＥＮＴＳＴＡＮＤＩＮＧＷＡＶＥＳＩＮＡＲＥＣＴＡＮＧＵＬＡＲＴＡＮＫＷｕＧ．Ｘ．（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｃｈａｎｉｃａｌＥｎｇｉｎｅｅｒｉｎｇ，ＵｎｉｅｒｓｉｔｙＣｏｌｌｅｇｅＬｏｎｄｏｎ，Ｔｏｒｒｉｎｇｔｏ...     

应用Boussinesq方程对非线性波与流相互作用的理论研究

本文应用了Ｂｏｕｓｓｉｎｅｓｑ方程，对潮汐势流与规则波和不规则波共存时的非线性二阶波一流相互作用现象进行了理论分析，得到了在等水深条件下非线性相互作用二阶波流计算公式。应用此一公式可分析发现波受水流的非线性作用，不同于波受地形等水深变化的影响，其二阶波流频率不变，仍保持一阶线性入射波频率。本文最后采用所推导得到的二阶波流计算公式，对不规则波与势流相互作用等现象进行工程验算。得到了与物模实验较为一致的计算结果。应用本文的计算公式可以对现有工程规范中波与流计算公式进行修正和补充。由于其简便易行，势必会被工程界人士所接受     

THE SECOND-ORDER HYDROELASTIC ANALYSIS OF A SWATH SHIP MOVING IN LARGE-AMPLITUDE WAVES

1. INTRODUCTION During the last two decades, the linear three-dimensional hydroelasticity theory[1,2] has been extensively applied to a wide range of fluid-structure interaction problems in the field of naval architecture and marine engineering[3-5]. Thes…     

风对二维极值波作用的数值研究

实际海域中风浪往往共存,当极值波浪出现时,风会对其特性产生很大影响。为了研究风对极值波浪特性的影响规律,该文基于势流理论建立自由水面满足完全非线性边界条件的风浪混合作用数值水槽模型,通过实时模拟造波板运动产生入射波,并基于波群聚焦原理定点产生极值波浪,利用改进的杰弗里斯遮蔽原理(Jeffreys'sheltering mechanism)将风压引入到自由水面动力边界条件中。在时域模拟中,采用混合欧拉-拉格朗日方法追踪瞬时水面,利用格林第二定理建立了边界积分方程,采用高阶边界元方法进行离散求解。通过与已发表实验结果对比验证模型的准确性,进而开展数值实验研究风对极值波浪水动力特性的影响,包括聚焦幅值、聚焦位置和极值波高随风速的变化以及波群聚焦和解焦过程波浪演变特性等。     

结构可靠度分析的一种实用方法及其时变预测

一次二阶矩方法是传统的可靠度方法，其精度受到验算点处极限状态方程非线形程度影响，将功能函数泰勒展开至二次项，形成二次二阶矩方法可提高可靠度精度，考虑验算点法在计算时要求进行不断迭代，为此在满足设计精度要求的前提下，提出不需迭代的一次性设计点直接进行可靠度计算，从而大大减少计算工作量，对结构在整个使用期内可靠度风险性随机预测，基于灰色理论，建立GM优化模型，求出结构时变可靠度。     

基于耗散结构理论的黄河健康生命内涵分析

应用基于热力学第二定律发展起来的耗散结构理论，对黄河健康生命的内涵进行了分析，认为：黄河是一个复杂的开放系统，具有非平衡有序结构、内部子系统之间存在非线性作用、通过结构与功能之间的涨落可达到有序和谐，因而满足耗散结构的4个条件。增大负熵流是维持黄河健康生命的根本途径，应根据不同子系统的特点采取相应措施，确保黄河向有序的方向发展，成为一种自组织的时间、空间和功能的有序耗散结构。     

Nonlinear motions in head waves with a RANS and a potential code

In the last years, the employment of RANS codes for a wide range of naval architecture problems is grown, since this methodology is capable of reproducing physical behaviors that are generally neglected by other models. The paper presents the results of a set of numerical tests performed employing this methodology with the aim of verifying its capability in the solution of seakeeping problem. Several condition are analyzed varying the frequency of the incident wave and its amplitude, in order to catch nonlinear effects. The results are compared with the ones achieved by a weakly nonlinear procedure based on potential theory.

     

Finite element analysis of second order wave radiation by a group of cylinders in the time domain

A finite element based numerical method is employed to analyze the wave radiation by multiple or a group of cylinders in the time domain. The nonlinear free surface and body surface boundary conditions are satisfied based on the perturbation method up to the second order. The first- and second-order velocity potential problems at each time step are solved through a Finite Element Method (FEM). The matrix equation of the FEM is solved through iteration and the initial solution is obtained from the result at the previous time step. The three-dimensional (3-D) mesh required is generated based on a two-dimensional (2-D) hybrid mesh on a horizontal plane and its extension in the vertical direction. The hybrid mesh is generated by combining an unstructured grid away from cylinders and two structured grids near the cylinder and the artificial boundary. The fluid velocity on the free surface and the cylinder surface are calculated by using a differential method. Results for various configurations including the cases of two cylinders and four cylinders and a group of eighteen cylinders are obtained to show the joint influences of cylinders on the first- and second-order waves and forces, including the effects of spacing ratios and wave frequency on the second order waves and the mean force, in particular.     

High-order finite difference solution for 3D nonlinear wave-structure interaction

This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme OceanWave3D presented in [1, 2]. A nonlinear decomposition of the solution into incident and scattered fields is used to increase the efficiency of the wave-structure interaction problem resolution. Application of the method to the diffraction of nonlinear waves around a fixed, bottom mounted circular cylinder are presented and compared to the fully nonlinear potential code XWAVE as well as to experiments.

     

一般密度分布的分层流体中内孤立波三阶理论

在浅水假定下,可以用KdV方程描述一阶内孤立波演化,其单个孤立波解有熟知的“Sech”波形,波速与波幅呈线性关系,波长与波幅的平方根成反比。本文借助计算机代数软件一MATHEMATICA,这种理论推广到三阶,得知高阶项满足线性化非齐次KdV方程,并得到波形和波速的三阶修正以及波长的二阶修正。在Boussinesq近似下讨论了有线性基本剪切流动与不变的Brunt-Vaeisalae频率这一特殊情形。     

造波板运动造波的实时模拟

基于势流理论和时域高阶边界元方法,建立了完全非线性数值波浪水槽模型,通过实时模拟造波板运动来产生波浪.采用混合欧拉-拉格朗日方法追踪流体瞬时水面,运用四阶Runga-Kutta方法更新下一时间步的波面和速度势,同时应用镜像格林函数消除了水槽两个侧面和底面上的积分,在水槽末端布置人工阻尼层消除反射波浪,通过加速势的方法准确计算速度势的时间导数.利用所建模型分别对规则波和不规则波进行了模拟研究,得到了稳定的波形,与试验结果、理论结果和已发表结果均吻合良好,同时计算了造波板做单一频率运动产生的非线性波浪力.     

A two steps solution approach to solving large nonlinear models: application to a problem of conjunctive use

This article describes a solution method of solving large nonlinear problems in two steps. The two steps solution approach takes advantage of handling smaller and simpler models and having better starting points to improve solution efficiency. The set of nonlinear constraints (named as complicating constraints) which makes the solution of the model rather complex and time consuming is eliminated from step one. The complicating constraints are added only in the second step so that a solution of the complete model is then found. The solution method is applied to a large-scale problem of conjunctive use of surface water and groundwater resources. The results obtained are compared with solutions determined with the direct solve of the complete model in one single step. In all examples the two steps solution approach allowed a significant reduction of the computation time. This potential gain of efficiency of the two steps solution approach can be extremely important for work in progress and it can be particularly useful for cases where the computation time would be a critical factor for having an optimized solution in due time.     

海堤龙口水力计算方法探讨

针对深厚淤泥软土滩涂的海堤龙口抗水流冲刷能力较差的问题,对海堤龙口水力学特性进行了研究分析,依据水力学理论及水量平衡原理建立了海堤龙口水力计算基本方程,该方程为非线性常微分方程,一般情况下难以给出精确解析解,依据数值分析理论利用经典四阶Runge-Kutta法结合MATLAB数值计算软件编程可给出数值解;另外,利用正弦函数拟合外海潮位周期变化特性,利用二次函数拟合围区库容-水位关系曲线,结合相关数值等效分析法及海堤龙口计算经验,给出了海堤龙口最大水位差与龙口宽度之间的近似解析计算方法;最后通过工程案例,利用MATLAB数值分析软件计算对比分析,认为本算法能满足工程实际应用要求。     

混凝土短期荷载下变形的一个本构模型

提出了一个混凝土一般应力状态下的变形模型。它建立在应变功硬化塑性增量流动理论的基础上，使用一个完整的二次型载荷函数，包含３个应力不变量，以模拟材料在拉、压应力偏量作用下的性质差异。为应用方便，文中详细列出数值计算步骤。     

浮体的非线性辐射效应

本文在空间上应用面源法，在时间域上应用步进法，研究了浮体的非线性辐射效应，本文探讨了：（1）不同形式的辐射条件对非线性辐射问题解的影响；（2）不同距离的辐射面对开边界条件的使用所产生的影响；（3）大振幅的浮体受近运动所产和的非线性效应。     

WAVES GENERATED BY A SUBMERGED BODY MOVING IN STRATIFIED FLUIDS AND VERTICAL STRUCTURES OF INTERNAL WAVES

This dissertation deals with the internal waves generated by a submerged moving body in stratified fluids by combining theoretical and experimental methods. Our purpose is to provide some scientific evidences for non-acoustic detection of underwater moving bodies based on the principles of dynamics of the internal waves. An approach to velocity potentials obtained by superposing Green‘s functions of sources and sinks was proposed for Kelvin waves at the free surface or interface in a two-layer fluid. The effects of interacting surface and internal wave modes induced by a dipole on the surface divergence field were investigated. A new theoretical model formulating the interaction of a two dimensional submerged moving body with the conjugate flow in a three-layer fluid was established. An exact solution satisfying the two dimensional Benjamin Ono equation was obtained and the vertically propagating properties of the weakly nonlinear long waves were studied hy means of the ray theory and WKB method. The above theoretical results are qualitatively consistent with those obtained in the experiments conducted by the author.