含强水流高阶Boussinesq水波方程

采用摄动法并利用已建立的纯波情况下高阶Boussinesq方程,建立了可以考虑强水流与波浪相互作用的高阶Boussinesq方程.水流速度与波浪群速具有相同量级,且随时间和空间的变化尺度远大于波浪周期和波长.方程色散性近似到[4/4]阶Pade展开,对浅水情况方程可以是完全非线性的,可适用于波流相互作用的强非线性问题.通过将水流存在时波长和波幅的结果与一阶斯托克斯波结果对比,讨论了具有不同近似程度的3种含波流相互作用的Boussinesq方程的适用性.     

海岸带边坡防浪林消浪理论与实验研究

在海岸边坡上种植防浪林是一种新的护岸形式,应用理论分析和模型实验对其进行了初步研究.建立波浪在斜坡上传播的控制方程及边界条件,应用摄动理论求解非线性解,得到了一阶精确解和二阶近似解.在模型实验中,确定几何比尺为 1∶10,选取桧柏树枝作为防浪林模型,根据量纲分析,确定的主要影响因素是海岸边坡坡度、波高、波周期、水深与防浪林树宽.实验结果表明,防浪林宽度与岸坡坡度对消浪效果影响较大.     

Boussinesq 方程组的一个精确解

浅水波的Boussinesq方程组是弱频散的、非线性的,它与Kdv方程有一定联系,但并不等价。本文给出这个方程组的一个孤立波精确解。它含有两个方向传播的孤立波,其一阶近似包括了Kdv方程的精确解,而零阶近似则为波峰处导数不连续的奇异解。     

非线性三维波波要素的计算方法

本文根据作者以前提出的重力表面波非线性相互作用理论解,系统地探讨非线性三维波波要素四阶近似理论关系式的计算方法,其中包括二维行进波和立波,也适用于斜向波与直墙相互作用(全反射和部分反射)。给出二种主要计算情况的计算方法,其中包括利用拟牛顿法求解非线性波要素方程组,卡尔丹法、迭代法和级数近似解析式,分析比较表明,本文提供的计算方法较为精确、有效,可应用于计算波浪及其与建筑物相互作用。     

非线性随机波的数值模拟

本文根据作者提出的非线性不规则波四阶近似理论解,首先导出二阶非线性谱和线性谱的关系式,并应用非线性有约束最优化方法建立了从靶谱分解线性谱和二阶非线性谱的数学模式,进而建立非线性随机波数值模拟的数学模型及其快速傅里叶交换算式,从而大大地缩短计算机时。由于采用从靶谱分解出的线性谱,模拟的非线性随机波现实谱和靶谱符合一致。最后通过算例,对模拟的非线性及线性随机波的谱估计及波面统计特性进行初步分析,本方法为浅水不规则波与水流及建筑物相互作用的研究提供随机模拟基础。     

作用于直立堤上的波总压力概率分布

长期以来,海浪与直立堤的相互作用问题一直是海岸工程研究中为人们所重视的课题之一.至今,在工程设计计算中,关于海浪对直立堤作用的波压力计算方法,大都仍采用规则波的研究结果.几十年来,通过实验室和液体波动理论进行了大量的规则波与直立堤相互作用的研究,提出了相当数量的试验与理论成果,其中目前较为广泛采用的有森佛罗(Sainflou)、米许(Miche)-贝塞尔(Biesel)等一阶及二阶近似立波压力方法.     

双曲余弦海脊上海啸俘获波的解析与数值研究

海啸能被大洋海脊引导以俘获波的形式沿其传播上万千米,且因其特殊的运动方式,携带巨大能量影响远场地区的港口,严重威胁海岸安全。本文首先基于线性浅水方程,推导了双曲余弦平方海脊上俘获波的波面解,其为μ阶ν次的连带勒让德函数的第一类解和第二类解的组合。进一步推导出其对应的频散关系,其中对于确定的频率ω,存在无穷多个波数k_y与之对应。采用MIKE21-BW模型,模拟了产生于海脊脊顶处的海啸在理想双曲余弦平方海脊上的传播变形过程。结果表明,小部分能量以自由先驱波进行传播,海啸波的波能大部分被海脊俘获。海脊俘获波沿着海脊方向为行进波,随着海啸波传播时间的增加,波浪在沿着海脊方向的延展范围也逐渐增大,波高逐渐减小、波的个数逐渐增加。俘获波能量主要由不同频率以相同速度传播的具有孤立波特性的波浪成分和能量主要集中在特定频率范围内的波浪成分组成。     

均匀倾斜水底上非线性波浪的传播与变形Ⅰ——非线性波动

本文以倾斜水底为边界条件,用摄动法求解二维非线性流体力学方程组,得到一种非线性波动群,其一阶近似与Biesel提出的势函数相同,文中对二阶近似进行了数值计算并就此解讨论了波浪破碎前的波动特性,特别包括了平均水位的下降,将所得结果与实验资料以及其他理论在其各自实用的有效范围内作了比较,结果表明,就波浪自深水至浅水传播的整个过程来说,本文提出的理论有更广泛的有效应用范围。     

非线性海浪波面斜率的概率分布和白浪覆盖率的计算

依二维非线性海浪模型,在三阶近似下,利用特征函数展开技术和直接求矩的方法,导出了波面斜率的概率分布。据此分布,利用极限表面斜率判据,给出了白浪覆盖率的一个解析模式。该模式依赖于3个参量,这3个参量可由线性意义下的海浪波数谱及三类波-波相互作用所确定。     

深水有限振幅重力波的一种解法

采用变量代换的方法,处理水波的自由边界,获得了新的水波控制方程和边界条件。以摄动法解非线性偏微分方程的近似解析解,求得了与三阶斯托克斯波略有差别的非线性波面和包含振幅的非线性水波色散关系,并且得出了二阶以上的波动势函数在深水情况下不为零的结论。     

A second order random wave model for predicting the power performances of a wave energy converter

The power performances of a point absorber wave energy converter(WEC) operating in a nonlinear multidirectional random sea are rigorously investigated. The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter. This is a new approach, and, as the second order random wave model can be utilized to accurately simulate the nonlinear waves in an irregular sea, avoids the inaccuracies resulting from using a first order linear wave model in the simulation process. The predicted results have been systematically analyzed and compared, and the advantages of using this new approach have been convincingly substantiated.     

Nonlinear wave effect on the slow drift motion of a floating body

The slow drift motion of a floating body in a two-dimensional wave field has been investigated using a time-domain, fully nonlinear numerical model with non-reflective open boundaries. Preliminary computations were conducted for incident bichromatic waves, in which wave theories with different orders were applied in generating the waves required. The results show that the use of low-order theories generates undesirable free waves, and that fourth-order terms contribute markedly to low-frequency input. The motion of a rectangular floating body in response to nonlinear bichromatic waves was computed. The numerical results for small-amplitude incident waves agree reasonably well with the second-order approximation for both the steady and difference-frequency (Δσ) components in the body's motion. For relatively large waves, however, the 2Δσ component becomes predominant compared with the Δσ component. The motion of the body in irregular waves with different wave parameters has also been presented in order to discuss the validity range of a second-order approximation.     

NONLINEAR INTERACTIONS AMONG GRAVITY SURFACE WAVES

Based on the perturbation method, a fourth order theory for nonlinear interactions among three dimensional gravity waves in water of any uniform depth is presented in this paper. Two cases are considered: ( i ) wave number vectors fixed, frequencies perturbed, and ( ii ) wave number vectors and frequencies both fixed. According to this solution, expressions of thesame order for progressive waves, short-crested waves and nonlinear interaction between wave and vertical wall are also derived'     

三阶非线性海浪波面斜率的联合概率统计分布

从Longuet-Higgins于1963年建立的非线性随机海浪模型出发,对各向同性波面斜率的联台概率统计分布进行了理论研究.结果表明,在三阶近似下,波面斜率联合概率统计分有为截断的Gram-Charlier级数,截断的项数取决于非线性近似的阶数,每一阶近似均对前一阶近似结果有所修正如果不考虑非线性耦合相互作用的影响,则分布蜕化为高斯分布.     

三阶Stokes型随机波浪载荷谱研究

应用非线性谱分析理论，对三阶Stokes型随机波浪载荷谱进行了分析，将波面方程及海水质点的水平速度用一阶波面的非线性组表示，导出了随机波浪谱的表达式。为了便于求解随机波浪的载荷谱，将阻力项展开为幂级数式，并应用非线性谱分析理论，确定了幂级数的系数，进而将波浪载荷表示为一阶波面及其导数的非线性组合，最后得出波浪载荷谱密度的表达式，并应用数值分析方法，得出单位桩柱波浪力及总波浪力谱密度。     

Second-order theory for coupling 2D numerical and physical wave tanks: Derivation,evaluation and experimental validation

A full second-order theory for coupling numerical and physical wave tanks is presented. The ad hoc unified wave generation approach developed by Zhang et al. [Zhang, H., Schäffer, H.A., Jakobsen, K.P., 2007. Deterministic combination of numerical and physical coastal wave models. Coast. Eng. 54, 171–186] is extended to include the second-order dispersive correction. The new formulation is presented in a unified form that includes both progressive and evanescent modes and covers wavemaker configurations of the piston- and flap-type. The second order paddle stroke correction allows for improved nonlinear wave generation in the physical wave tank based on target numerical solutions. The performance and efficiency of the new model is first evaluated theoretically based on second order Stokes waves. Due to the complexity of the problem, the proposed method has been truncated at 2D and the treatment of regular waves, and the re-reflection control on the wave paddle is also not included. In order to validate the solution methodology further, a series of nonlinear, periodic waves based on stream function theory are generated in a physical wave tank using a piston-type wavemaker. These experiments show that the new second-order coupling theory provides an improvement in the quality of nonlinear wave generation when compared to existing techniques.     

Three-dimensional nonlinear random wave groups in intermediate water depth

High waves at ocean occur during a complex space–time evolution of wave groups. In this paper the nonlinear structure of three-dimensional sea wave groups at intermediate water depth is investigated. To this purpose, the Boccotti's Quasi-Determinism theory is firstly applied to describe the linear wave groups when a given exceptionally high crest occurs. Then, the second-order correction to the linear solution is derived for the general condition of three-dimensional wave groups, at a finite water depth. Several numerical applications, finally, have been carried out in order to show how both the spectral bandwidth and the directional spreading modify the nonlinear high waves at different water depth.     

Dynamics of a Wave Packet on the Surface of an Inhomogeneously Vortical Fluid (Lagrangian Description)

A nonlinear Schrödinger equation (NSE) describing packets of weakly nonlinear waves in an inhomogeneously vortical infinitely deep fluid has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. It is shown that the modulational instability criteria for the weakly vortical waves and potential Stokes waves on deep water coincide. The effect of vorticity manifests itself in a shift of the wavenumber of high-frequency filling. A special case of Gerstner waves with a zero coefficient at the nonlinear term in the NSE is noted.     

Decomposing damped incident and reflected waves using correlation and quasi-linearization methods

Water waves propagating over a layer of soft mud or submerged aquatic vegetation can drastically attenuate over distances comparable to several wave lengths. The attenuation in the case of mud has been found previously to be reasonably described by an exponential decay. Waves reflect from beaches and any structures that they impact. The reflected waves affect wave heights measured in the field or laboratory wave basins.Decomposition of small amplitude waves into incident and reflected waves is a linear problem. However, the presence of the exponential damping introduces nonlinearity to the decomposition problem and requires an iterative process for solving the problem. Despite considerable experimental research on attenuation of waves over mud, none of the existing methods for decomposition of incident and reflected waves have accounted for this case.Here, the Newton Algorithm was used to account for the effect of wave decay over mud by quasi-linearizing the nonlinear equations. Also, a second method using a new error function and a commercial nonlinear solver was proposed in both time and frequency domain. The performance of both methods has been verified using artificial as well as laboratory data.     

Applicability of numerical models to nonlinear dispersive waves

The applicability of three different wave-propagation models in nonlinear dispersive wave fields has been investigated. The numerical models tested here are based on three different wave theories: a fully nonlinear potential theory, a Stokes second-order theory, and a Boussinesq-type theory with an improved dispersion relation. Physical experiments and computations were conducted for wave evolutions during passage over a submerged shelf under various wave conditions. As expected, the fully nonlinear solutions agree better with the measurements than do the other solutions. Although the second-order solution has sufficient accuracy for smaller-amplitude wave cases, the truncation after the third harmonics causes significant discrepancies in wave form for larger waves. In addition, the second-order model markedly overestimates the first- and second-harmonic amplitudes in transmitted waves. The Boussinesq model provides excellent predictions of wave profile over the shelf even in larger wave cases. However, this model also overestimates the magnitudes of several higher harmonics in transmitted waves. These facts may indicate that energy transfer from bound components into free waves in these higher harmonics cannot be accurately evaluated by the Boussinesq-type equations.