Boussinesq方程波浪数学模型的应用

介绍了Ｂｏｕｓｓｉｎｅｓｑ 方程的推导过程和发展过程,基于深水和缓变地形的色散关系,建立了Ｂｏｕｓｓｉｎｅｓｑ方程的波浪数学模型。该模型可以产生波浪,模拟吸收边界和不同反射率的反射边界。该模型可用于研究深水和浅水地区波浪的浅水变形、折射、绕射和反射     

缓坡方程与Boussinesq方程的差异性比较

本文对在缓变水深条件下缓坡方程和Ｂｏｕｓｓｉｎｅｓｑ方程各种不甘落后 差异进行了比较。明确了线性缓坡方程的频散性上，要好于非线性Ｂｏｕｓｓｉｎｅｓｑ方程。而Ｂｏｕｓｓｉｎｅｓｑ方程可讨论非线性的波与波相互作用等问题，而缓坡方程则不能。对Ｂｏｕｓｓｉｎｅｓｑ方程在不规则波计算上的局限性问题本文也进行了讨论，指出对于不规则波而言分解频率的数量和对高频波所产生的混淆误差的抑制是Ｂｏｕｓｓｉｎｅｓｑ方程能     

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.     

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。     

适合复杂地形的高阶Boussinesq水波方程

针对海底坡度较大(量阶为O(1))或海底曲率较大的复杂地形,建立了一个新型高阶Boussinesq水波方程.该方程可用于研究海底存在若干相互平行沙坝引起的Bragg反射问题.方程的水平速度沿水深的分布为四次多项式,色散性和变浅作用性能的精度比经典Boussinesq方程高了一阶.方程在浅水水域可以是完全非线性的.     

二阶Boussinesq方程的孤立波解

基于同量阶迭代法，在保留同阶面的前提下，对林建国等（1998a)得到的二阶Boussinesq类方程进行了求解，得到了与其量阶相对应的取立波解，并春与Euler方程的二阶孤立波解进行了比较，结果显示，本文解比传统Boussinesq方程的孤立波解有明显的改善，扩大了孤立的适用范围。     

一个改进的二阶Boussinesq方程模型在线性波浪反射问题中的适用性研究

基于改进型的二阶Boussinesq方程,在交错网络下建立数值模型.利用模型模拟波浪在常水深情况下的传播,波浪反射系数均低于2％.利用该模型模拟波浪在平斜坡前的反射,并将数值结果与解析解进行对比.结果表明,对于相对水深较大情况,坡度较陡时模拟结果明显偏大;对 于相对水深较小情况,坡度超过1:1时,数值结果仍与解析解有....     

关于波浪Boussinesq方程的研究

对有关波浪 Boussinesq方程的研究成果进行了系统的归纳总结和评述 ,以期对本学科的发展起到一定的引导和促进作用     

二阶全非线性Boussinesq方程的二维数值模拟研究

在非交错网格下采用有限差分法首次对一组非线性精确至O(μ2)阶的全非线性Boussinesq方程数学模型进行了二维数值模拟分析.首先通过在方程的非线性项中引入缓坡假定,考察了其对模型数值精度的影响;其次,在模型中对二阶非线性项采用不同精度,考察了其对模型数值结果的影响.数值模拟结果表明,所建立的二阶完全非线性Boussinesq方程二维数值模型具有良好的适用性,模型非线性项中引入缓坡假定以及在二阶非线性项选用不同的精度对数值模拟结果影响不明显.     

改进的波流相互作用Boussinesq方程

对于波流相互作用的Boussinesq方程,为了考虑水流作用所引起的平均水面变化,通过引入新的计算速度,使方程色散关系中的水深为考虑水流影响后的实际水深,并使方程色散精度达到了Padé[4,4]。通过计算潜堤强水流和裂流两种背景水流流场情况下的波浪运动特征,验证了该模型和数值方法的正确性。     

一种基本Boussinesq方程的近岸区破碎波模型

基于文献「１」Ｂｏｓｓｉｎｅｓｑ方程的近岸区破碎波模型基础,将数值模型中的波高衰减规律由假设改进为Ｄａｌｌｙ的解析公式,使近岸区破碎波模型的应用性更强。并将数值模型计算结果与现场实验资料进行对比,取得了满意的结果。     

One-dimensional numerical models of higher-order Boussinesq equations with high dispersion accuracy

Abstract-Nonlinear water wave propagation passing a submerged shelf is studied experimentally andnumerically. The applicability of the wave propagation model of higher-order Boussinesq equations de-rived by Zou(2000, Ocean Engneering, 27, 557～575) is investigated. Physical experiments areconducted; three different front slopes (1:10, 1:5 and 1:2) of the shelf are set-up in the experimentand their effects on the wave propagation are investigated. Comparisons of the numerical results withtest data are made and the higher-order Boussinesq equations agree well with the measurements since thedispersion of the model is of high accuracy. The numerical results show that the good results can also beobtained for the steep-slope cases although the mild-slope assumption is employed in the derivation of thehigher-order terms in the higher-order Boussinesq equations.     

Alternative forms of the higher-order Boussinesq equations: Derivations and validations

An alternative form of the Boussinesq equations is developed, creating a model which is fully nonlinear up to O(μ⁴) (μ is the ratio of water depth to wavelength) and has dispersion accurate to the Padé [4,4] approximation. No limitation is imposed on the bottom slope; the variable distance between free surface and sea bottom is accounted for by a σ-transformation. Two reduced forms of the model are also presented, which simplify O(μ⁴) terms using the assumption ε = O(μ^2/3) (ε is the ratio of wave height to water depth). These can be seen as extensions of Serre's equations, with dispersions given by the Padé [2,2] and Padé [4,4] approximations. The third-order nonlinear characteristics of these three models are discussed using Fourier analysis, and compared to other high-order formulations of the Boussinesq equations. The models are validated against experimental measurements of wave propagation over a submerged breakwater. Finally, the nonlinear evolution of wave groups along a horizontal flume is simulated and compared to experimental data in order to investigate the effects of the amplitude dispersion and the four-wave resonant interaction.     

基于双层Boussinesq方程的三维波浪数值模型及其验证

Liu等给出的最高导数为2的双层Boussinesq水波方程具有较好的色散性和非线性,基于该方程建立了有限差分法的三维波浪数值模型。在矩形网格上对方程进行了空间离散,采用高阶导数近似方程中的时、空项,时间积分采用混合4阶Adams-Bashforth-Moulton的预报—校正格式。模拟了深水条件下的规则波传播过程,计算波面与解析结果吻合较好,反映出数值模型能很好地刻画波面过程及波面处的速度变化;在kh=2π条件下可较为准确获得沿水深分布的水平和垂向速度,这与理论分析结果一致。最后,利用数值模型计算了规则波在三维特征地形上的传播变形,数值结果和试验数据吻合较好;高阶非线性项会对波浪数值结果产生一定的影响,当波浪非线性增强,水深减少将产生更多的高次谐波。建立的双层Boussinesq模型对强非线性波浪的演化具有较好的模拟精度。     

Numerical Models of Higher-Order Boussinesq Equations and Comparisons with Laboratory Measurement

Nonlinear water wave propagation passing a submerged shelf is studied experimentally and numerically. The applicability of two different wave propagation models has been investigated. One is higher-order Boussinesq equations derived by Zou (1999) and the other is the classic Boussinesq equations. Physical experiments are conducted, three different front slopes (1:10, 1:5 and 1:2) of the shelf are set up in the experiment and their effects on wave propagation are investigated. Comparisons of numerical results with test data are made, the model of higher-order Boussinesq equations agrees much better with the measurements than the model of the classical Boussinesq equations. The results show that the higher-order Boussinesq equations can also be applied to the steeper slope case although the mild slope assumption is employed in the derivation of the higher order terms of higher order Boussinesq equations.     

不规则波Boussinesq型方程的造波,消波和反射

对前人提出的造波、消波和反射边方法分析表明,其方法是极浅水波近似,不适用于任意水深的水域,本文就任意水深变化Ｂｏｕｓｓｉｎｅｓｑ型方程,提出了不规则波新的造波原理、方法和消波边界及部分反射边界波动方程,试验表明,本文提出的造波、消波和反射方程有效而可靠的。     

An application of Boussinesq equations to Bragg reflection of irregular waves

A numerical model based on the second-order fully nonlinear Boussinesq equations of Wei et al. [1995. Journal of Waterway, Port, Coastal and Ocean Engineering 121 (5), 251-263] is developed to simulate the Bragg reflection of both regular and irregular surface waves scattered by submerged bars. Particularly for incident regular waves, the computed results are observed to agree very well with the existing experimental data as presented by Davies and Heathershaw [1984. Journal of Fluid Mechanics 144, 419-446] and Kirby and Anton [1990. Proceedings of the 22nd International Conference on Coastal Engineering, ASCE, New York, pp. 757–768). In the case of incident irregular waves, the simulated results reveal that the distribution of Bragg reflection from irregular waves becomes more flat than that of regular waves. Due to lack of experimental data, the numerical results for incident irregular waves are compared with those of the evolution equation of the mild-slope equation [Hsu et al., 2002 Proceedings of the 24th Ocean Engineering Conference in Taiwan, pp. 70–77 (in Chinese)]. In addition, several parameters such as the number of bars, the relative height of bars and the spacing of bars affecting Bragg reflection are also discussed.     

A Boussinesq Equation-Based Model for Nearshore Wave Breaking

Based on the wave breaking model by Li and Wang (1999), this work is to apply Dally‘ s analytical solution to the wave-height decay instead of the empirical and semi-empirical hypotheses of wave-height distribution within the wave breaking zone. This enhances the applicability of the model. Computational results of shoaling, location of wave breaking, wave-height decay after wave breaking, set-down and set-up for incident regular waves are shown to have good agreement with experimental and field data.     

Numerical Calculation for Nonlinear Waves in Water of Arbitrarily Varying Depth with Boussinesq Equations

Based on the high order nonlinear and dispersive wave equation with a dissipalive term, a numerical model for nonlinear waves is developed. It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/ L0≤ 1. By the application of the completely implicit slagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical solutions and physical models.