促进其线性频散特征另一种形式的Bousinesq方程

Ｂｏｕｓｉｎｅｓｑ方程能够用于模拟表面重力波传播过程中的折射、绕射、反射以及浅化，非线性作用等现象．用不同垂直积分方法所得到的二维Ｂｏｕｓｓｉｎｅｓｑ方程形式具有不同的线性频散特征．采用两个不同的水深层的水平速度变量组合，推导出一个新形式的Ｂｏｕｓｉｎｅｓｑ方程．通过对其参数的设置可得到精确的线性频散解Ｐａｄｅ近似４阶精度．其适用范围已由原来的浅水，向深水拓进．相速误差小于２％，其拓展适用范围可达到０８个波长水深．应用所得到的新型Ｂｏｕｓｉｎｅｓｑ方程，采用有限差分法，对经典工况进行了数值模拟，其计算结果表明，计算值与物模实验值吻合较好．这说明本文新形式的Ｂｏｕｓｓｉｎｅｓｑ方程对变水深非线性效应所产生的能量频散有着较为精确的描述     

Boussinesq方程的发展形式与Airy波理论差异性研究

应用势流理论，采用递推函数方法推导出一个新形式的Ｂｏｕｓｉｎｅｓｑ方程。通过对新方程的参数设置，可以讨论出Ｂｏｕｓｓｉｎｅｓｑ方程发展趋势和不同的发展形式。对浅水波动的描述方程，Ｂｏｕｓｓｉｎｅｓｑ方程的发展趋势为适用水深范围的拓展。拓展应用范围的大小则由其方程频散特征向Ａｉｒｙ波频散解逼近程度来决定。而Ｂｏｕｓｉｎｅｑ方程又不同于Ａｉｒｙ波，主要原因是Ｂｏｕｓｓｉｎｅｓｑ方程中含有线性频散项，Ａｉｒｙ波则只是长波首项近似，无线性频散项。其频散特征为精确的线性频散解。对实际水波传播而言，Ａｉｒｙ波理论的局限性是不言而喻的。     

一阶非线性项、四阶色散项的Boussinesq类方程

推导了由一阶色散项Ｏ（β２）表示的Ｂｏｕｓｉｎｅｓｑ类方程，方程中保留了一阶非线性项Ｏ（α）及四阶色散项Ｏ（β８），其中α＝Ａ／ｈ０，β＝ｈ０／Ｌ，Ａ为特征波高，Ｌ为特征波长，ｈ０为特征水深从理论上证明了Ｂｏｕｓｉｎｅｓｑ改善型方程对色散性精度的提高，阐明了此类方程对色散项所保留的精度为Ｏ（β８），而并非是此类方程推导之初的假设为Ｏ（β２）这一点，将改变人们传统的认识     

一类偏微分方程的Hamilton正则表示

主要给出一系列关于力学中的偏微分方程的无穷维Ｈａｍｉｌｔｏｎ正则表示．其中包括变系数线性偏微分方程,ＫｄＶ方程,ＭＫｄＶ方程,ＫＰ方程,Ｂｏｕｓｉｎｅｓｑ方程等的无穷维Ｈａｍｉｌｔｏｎ正则表示．     

非线性湍流模式研究及进展

现代湍流模式研究已经超出了经典的Ｂｏｕｓｓｉｎｅｓｑ涡粘性概念和线性的雷诺应力输运范畴,湍流运动过程中的非线性本质已成为模式研究人员所关心的中心问题。其目的在于使湍流模式能更加真实地再现湍流运动的复杂性,提高模式的适用范围,使复杂湍流能够得到合理的模拟,非线性湍流模式在解决复杂湍流运动的计算中已经取得可喜进展,正逐步应用于工程湍流的计算。同时,工程中的湍流问题计算也已走出了简单剪切流动类型及传统的ｋ－ε（及其它形式的）二方程模式框架,二阶矩封闭模式在先进的工程计算中已被用来解决诸如可压缩的空气动力学、发动机气缸及三维复杂几何场内等具有重要应用背景的流动问题,并逐步进入计算流体力学商业软件包。      

变分原理与非线性水波的Hamilton描述

本文用全变分方法导出水波动力学问题的基本方程组，再用平均势函数Ｆ（Ｘ，ｔ）渐近表示速度势函数（Ｘ，ｙ，ｔ）和Ｌａｇｒａｎｇｅ函数Ｌ（Ｘ，ｙ，ｔ），导出具有Ｂｏｕｓｉｎｅｓｑ形式的方程．研究了Ｈａｍｉｌｔｏｎ正则方程的简单推导问题．     

集中力拉伸作用下的不可压缩橡胶类锥体

分析了受集中力拉伸作用下不可压缩橡胶类锥体尖端附近的应力分布及形变行为。给出了锥体尖端应力场的渐近解，当锥角为１８０°时，即为非线性的Ｂｏｕｓｓｉｎｅｓｑ问题的解。     

孤立波与多孔介质结构物的非线性相互作用

基于精确至Ｏ（εμ＾２,μ＾４）的多孔介质无压渗流模型方程和均匀流体质波动的Ｂｏｕｓｓｉｎｅｓｑ方程,本文对孤立波与多孔介质结构物的相互作用了较系统的数值实验。控制方程采用基于有限差分方程离散,在时域上采用了预估－校正方法进行了时间积分。在求解演化方程的过程中,引入“内迭代”过程实现流体域和多孔介质交界面的连接条件。结果表明孤立波在多孔介质上的反射与在不可渗透的界面上的反射类似,形成反向的孤立波但     

管内湍流旋流的数值计算

本文用有限差分法对直管内的湍流旋流进行了数值模拟。计算中采用Ｂｏｕｓｓｉｎｅｓｑ湍流涡粘性假设的基本思想和Ｋ－ε双方程模型来求解雷诺应力各分量。为了反映旋流中湍流转输的非均匀性和各向异性特征，对雷诺应力各分量及与之相主尖的各湍流粘性系数分别进行计算。计算结果表明该模型能较好地反映直管内湍流旋流的流动结构。     

具有精确色散性的非线性波浪数学模型

以完全非线性的自由表面边界条件为基础,以波面升高\eta和自由表面速度势\phi _\eta为待求变量,建立了新的波浪方程．方程在色散性上是完全精确的,非线性近似至三阶．与缓坡方程相比较,两者都具有精确的色散性,但该方程属于非线性模型,可模拟波浪的非线性效应,且适用于不规则波．方程的特点是属于微分-积分方程,对如何处理方程中积分项进行了讨论,并数值模拟了不同周期的线性波和二阶Stokes波,也模拟了波群的非线性演化,以对模型进行验证．      

A Boussinesq model with alleviated nonlinearity and dispersion

The classical Boussinesq equation is a weakly nonlinear and weakly dispersive equation, which has been widely applied to simulate wave propagation in off-coast shallow waters. A new form of the Boussinesq model for an uneven bottoms is derived in this paper. In the new model, nonlinearity is reduced without increasing the order of the highest derivative in the differential equations. Dispersion relationship of the model is improved to the order of Pade （2,2） by adjusting a parameter in the model based on the long wave approximation. Analysis of the linear dispersion, linear shoaling and nonlinearity of the present model shows that the performances in terms of nonlinearity, dispersion and shoaling of this model are improved. Numerical results obtained with the present model are in agreement with experimental data.     

海沟内海底地震激发的表面波动

通过底面运动学边界条件引入底面运动影响,采用高阶Boussinesq方程计算了光滑海底变形引起的表面波动形态.对于线性问题,与线性势流波浪理论进行了比较,二者结果符合良好.运用高阶Boussinesq波浪模型,针对冲绳海沟的实际地形,模拟海沟内不同震级的海底地震激发的海啸,分析了不同强度地震引起的表面波扰动形态及其非线性和色散效应.     

基于Boussinesq方程的波浪模型

从欧拉方程出发，提供了另一种推导完全非线性Boussinesq方程的方法，并对方程的 线性色散关系和线性变浅率进行了改进. 改进后方程的线性色散关系达到了一阶Stokes波 色散关系的Pad\'{e}[4,4]近似，在相对水深达1.0的强色散波浪时仍保持较高的准确性，并且方程的非线性和线性 变浅率都得到了不同程度的改善. 方程的水平一维形式用预估-校正的有限差分格式求解， 建立了一个适合较强非线性波浪的Boussinesq波浪数值模型. 作为验证，模拟了波浪在潜 堤上的传播变形，计算结果和实验数据的比较发现两者符合良好.     

Internal waves in a two‐layer system using fully nonlinear internal‐wave equations

In order to understand the nonlinear effect in a two‐layer system, fully nonlinear strongly dispersive internal‐wave equations, based on a variational principle, were proposed in this study. A simple iteration method was used to solve the internal‐wave equations in order to solve the equations stably. The applicability of the proposed numerical computation scheme was confirmed to agree with linear dispersion relation theoretically obtained from variational principle. The proposed computational scheme was also shown to reproduce internal waves including higher‐order nonlinear effect from the analysis of internal solitary waves in a two‐layer system. Furthermore, for the second‐order numerical analysis, the balance of nonlinearity and dispersion was found to be similar to the balance assumed in the KdV theory and the Boussinesq‐type equations. Copyright © 2009 John Wiley & Sons, Ltd.     

Solitary waves in longitudinally wrinkled and creased helicoids

Elastic ribbons subjected to twist and stretch handle multiple morphological instabilities, amongst others, the longitudinally wrinkled and creased helicoids are investigated in the present paper as promising periodic nonlinear waveguides. Modeling the ribbon by isogeometric Kirchhoff–Love shells, the first longitudinal buckling mode is recovered numerically and used into the Bloch–Floquet method to obtain dispersion curves. After analyzing the effects of the buckling pattern on the different wavemodes, it is shown that classical linear axial waves interact with bending ones and become dispersive. Additionally, as buckling involves geometrical nonlinearities, the structure is expected to host stable nonlinear waves. Indeed, clear supersonic rarefaction trains are observed experimentally and their characteristics are found in agreement with the weakly nonlinear Boussinesq model.     

On uniformly accurate high‐order Boussinesq difference equations for water waves

A new accurate finite‐difference (AFD) numerical method is developed specifically for solving high‐order Boussinesq (HOB) equations. The method solves the water‐wave flow with much higher accuracy compared to the standard finite‐difference (SFD) method for the same computer resources. It is first developed for linear water waves and then for the nonlinear problem. It is presented for a horizontal bottom, but can be used for variable depth as well. The method can be developed for other equations as long as they use Padé approximation, for example extensions of the parabolic equation for acoustic wave problems. Finally, the results of the new method and the SFD method are compared with the accurate solution for nonlinear progressive waves over a horizontal bottom that is found using the stream function theory. The agreement of the AFD to the accurate solution is found to be excellent compared to the SFD solution. Copyright © 2005 John Wiley & Sons, Ltd.     

海岸波浪场模型研究进展

从建模原理、波浪在近岸区域传播的众多机制、模型的类别、优势、局限性以及模型在未来的发展趋势等方面,综述了在海岸工程实践中广泛运用的以下两大类海岸波浪场预测模型的最新研究进展:(1)能量平衡模型.它一般用来预测海洋深水波候,已发展到相当完善的阶段,例如,最为著名的WAM3G模型.这种模型在海岸工程中的作用就在于可以模拟施加在波浪上的随时间变化的风场效应.(2)质量、动量守恒模型.它在海岸工程中应用最为普遍,并且内容丰富,数值技巧多样.目前包含了以下代表性的模型:缓坡方程、抛物型方程、非线性浅水方程、高阶Boussinesq型方程、Green-Naghdi理论.      

Concerning the description of long nonlinear waves in channels

A method of deriving the equations that describe long nonlinear waves in channels of arbitrary cross section, taking the transverse acceleration of fluid particles into account (the Boussinesq approximation), is proposed. For channels of certain cross sections the equations are written in explicit form. In the case of narrow channels the Boussinesq equations and those of the next approximation are written in explicit form for arbitrary cross sections.     

Boussinesq cut‐cell model for non‐linear wave interaction with coastal structures

Boussinesq models describe the phase‐resolved hydrodynamics of unbroken waves and wave‐induced currents in shallow coastal waters. Many enhanced versions of the Boussinesq equations are available in the literature, aiming to improve the representation of linear dispersion and non‐linearity. This paper describes the numerical solution of the extended Boussinesq equations derived by Madsen and Sørensen (Coastal Eng. 1992; 15 :371–388) on Cartesian cut‐cell grids, the aim being to model non‐linear wave interaction with coastal structures. An explicit second‐order MUSCL‐Hancock Godunov‐type finite volume scheme is used to solve the non‐linear and weakly dispersive Boussinesq‐type equations. Interface fluxes are evaluated using an HLLC approximate Riemann solver. A ghost‐cell immersed boundary method is used to update flow information in the smallest cut cells and overcome the time step restriction that would otherwise apply. The model is validated for solitary wave reflection from a vertical wall, diffraction of a solitary wave by a truncated barrier, and solitary wave scattering and diffraction from a vertical circular cylinder. In all cases, the model gives satisfactory predictions in comparison with the published analytical solutions and experimental measurements. Copyright © 2007 John Wiley & Sons, Ltd.