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1.
适合中等水流的Boussinesq方程   总被引:2,自引:0,他引:2  
推导了含量阶为O(ε1/2)的瞬变非均匀流的Boussinesq水波方程,讨论了该量阶水流对流场速度和压力分布的影响,采用了Crank-Nicolson格式的预估-校正有限差分法对该方程进行了数值求解.把数值结果与无水流情况的实验结果进行了对比,验证了该方程和数值计算方法的有效性,与经典的Boussinesq方程和含量阶为O(1)的瞬变非均匀流的Boussinesq水波方程的计算结果进行了比较,考察了该方程的适用范围.  相似文献   

2.
含强水流高阶Boussinesq水波方程   总被引:13,自引:3,他引:10  
邹志利 《海洋学报》2000,22(4):41-50
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.  相似文献   

3.
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。  相似文献   

4.
利用Boussinesq方程,采用线性摄动展开法,求解波浪正向通过有限沙坝地形的一阶反射波解,研究比较Boussinesq类方程描述沙坝地形对波浪的反射作用的性能。通过研究反射系数并与势流理论结果及实验结果对比,发现:邹志利的高阶方程、张永刚及Madsen的方程适用的水深范围较广,而Nwogu和Peregrine的方程仅在共振点附近有效;当入射波的波长为沙坝波长两倍时,反射波产生共振效应(即Bragg反射),反射系数与沙坝振幅和水深的比值以及地形中沙坝的条数成正比;相对势流理论的共振时的反射系数,以张永刚为代表的一系列Boussinesq方程色散精度越高,适用水深范围越广,而高阶方程适用的水深很浅。  相似文献   

5.
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.  相似文献   

6.
为模拟潜堤上破碎波浪传播时产生能量的耗散这一特性,在改进的具有四阶色散的Boussinesq水波方程中中入二阶紊动粘性项,建立了考虑波浪破碎的水波数学模型.在非交错网格下建立了有限差分数值模型,并利用三阶Adams-Bash forth格式预报、四阶Adams-Mouton格式校正对数值模型进行求解.通过数值试验,模拟...  相似文献   

7.
在二阶 Boussinesq 方程基础上,通过引入含水深导数项对该方程进行了理论上的改进,使得该方程在应用于无限沙坝 Bragg反射问题时与理论解析解在更大范围内符合.基于该改进的高阶 Boussinesq 方程,在非交错网格下建立了混合 4 阶的Adams-Bashforth- Moulton 格式的数学模型.将数值模型应用到有限个连续沙坝上波浪传播变形问题的数值模拟中,通过两点法给出数值波浪反射系数,将这些反射系数与已有的实验数据进行对比,对比表明改进后的模型计算出的反射系数与实验结果吻合更好,这验证了本文理论改进的有效性.  相似文献   

8.
针对一组近似到二阶完全非线性,四阶色散的Boussinesq方程,在交错网格下建立了数学模型.计算中时间层不交错,模型的求解利用混合四阶Adams-Bashforth-Moulton格式的有限差分法.数值模拟了波浪在潜堤上的演化过程,再现了波浪的浅化、反射以及非线性波能量传递等现象.对数值计算结果采用Friouer变换...  相似文献   

9.
Boussinesq型方程是研究水波传播与演化问题的重要工具之一,本文就1967-2018年常用的Boussinesq型水波方程从理论推导和数值应用两个方面进行了回顾,以期推动该类方程在海岸(海洋)工程波浪水动力方向的深入研究和应用。此类方程推导主要从欧拉方程或Laplace方程出发。在一定的非线性和缓坡假设等条件下,国内外学者建立了多个Boussinesq型水波方程,并以Stokes波的相关理论为依据,考察了这些方程在相速度、群速度、线性变浅梯度、二阶非线性、三阶非线性、波幅离散、速度沿水深分布以及和(差)频等多方面性能的精度。将Boussinesq型水波方程分为水平二维和三维两大类,并对主要Boussinesq型水波方程的特性进行了评述。进而又对适合渗透地形和存在流体分层情况下的Boussinesq型水波方程进行了简述与评论。最后对这些方程的应用进行了总结与分析。  相似文献   

10.
李春雁 《海洋与湖沼》1990,21(3):236-240
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。  相似文献   

11.
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.  相似文献   

12.
Higher order Boussinesq equations   总被引:2,自引:0,他引:2  
A new form of Boussinesq-type equations accurate to the third order are derived in this paper to improve the linear dispersion and nonlinearity characteristics in deeper water. Fourth spatial derivatives in the third order terms of the equations are transformed into second derivatives and present no difficulty in numerical computations. With the increase in accuracy of the equations, the nonlinear and dispersion characteristics of the equations are of one order of magnitude higher accuracy than those of the classical Boussinesq equations. The equations can serve as a fully nonlinear model for shallow water waves. The shoaling property of the equations is also of high accuracy through shallow water to deep water by introducing an extra source term into the second order continuity equation. An approach to increase the accuracy of the nonlinear characteristics of the new equations is introduced. The expression for the vertical distribution of the horizontal velocities is a fourth order polynomial.  相似文献   

13.
A new form of hyperbolic mild slope equations is derived with the inclusion of the amphtude dispersion of nonlinear waves. The effects of including the amplitude dispersion effect on the wave propagation are discussed. Wave breaking mechanism is incorporated into the present model to apply the new equations to surf zone. The equations are solved nu- merically for regular wave propagation over a shoal and in surf zone, and a comparison is made against measurements. It is found that the inclusion of the amplitude dispersion can also improve model' s performance on prediction of wave heights around breaking point for the wave motions in surf zone.  相似文献   

14.
This paper presents the numerical solution of a new nonlinear mild-slope equation governing waves with different frequency components propagating in a region of varying water depth. There are two new nonlinear equations. The linear part of the equations is the mild-slope equation, and one of the models has the same non-linearity as the Boussinesq equations. The new equations are directly applicable to the problems of nonlinear wave-wave interactions over variable depth. The equations are first simplified with the parabolic approximation, and then solved numerically with a finite difference method. The Crank-Nicolson method is used to discretize the models. The numerical models are applied to a set of published experimental cases, which are nonlinear combined refraction-diffraction with generation of higher harmonic waves. Comparison of the results shows that the present models generally predict the measurements better than other nonlinear numerical models which have been applied to the data set.  相似文献   

15.
Enhancements for the Bragg reflection are introduced for three sets of 2D higher order Boussinesq equations to improve the prediction of the Bragg reflection. The extension of the approach to other sets of Boussinesq equations is discussed. The analytical solutions for the Bragg reflection over an infinite number of sinusoidal bars are derived for these Boussinesq models and compared to the exact theoretical solution in order to determine the optimized values of the parameters in the new enhancement terms. Numerical simulations are also carried out for the Bragg reflection over a finite number of sand bars and compared with corresponding measurements to validate the enhancements. Comparisons with other forms of Boussinesq models are made to discuss the applicability of different forms of Boussinesq models to rapidly varying topography with sand bars. The effects of the mild slope assumption on the prediction of Bragg reflection and of wave reflection on a plane self are also discussed.  相似文献   

16.
The elliptic mild slope equation is used to simulate linear wave propagation over variable seabed topography with mild slopes.The governing equation is discretized by the finite difference method.Ba-sed on the BI-CGSTAB technique.an attractive variant of BI-Conjugate Gradients(BI-CG)method,theobtained linear algebraic system of equations is solved.Numerical experiments show that the BI-CGSTABmethod is efficient for solving the elliptic mild slope equation.The results obtained by the BI-CGSTAB-Ba-sed method are much the same as those obtained by other authors with different solution methods,but theconvergence rate is much faster than that of other methods.  相似文献   

17.
任意水深变化Boussinesq型方程非线性波数值计算   总被引:6,自引:2,他引:4  
首先从一个含有耗散项的高阶非线性和频散性波浪理论模型出发,建立了适用于任意底坡变化,相对水深h/Lo≤1的非线性波数学模型。应用全隐式交错网格和二阶精度中心差分法。得到离散方程组。进一步对其一阶导数项进行修正,达到与方程高阶项同量阶精度。精度检验表明本文计算结果与理论解和物理模型结果符合良好。  相似文献   

18.
Two sets of higher-order Boussinesq-type equations for water waves   总被引:1,自引:0,他引:1  
Z.B. Liu  Z.C. Sun 《Ocean Engineering》2005,32(11-12):1296-1310
Based on the classical Boussinesq model by Peregrine [Peregrine, D.H., 1967. Long waves on a beach. J. Fluid Mech. 27 (4), 815–827], two parameters are introduced to improve dispersion and linear shoaling characteristics. The higher order non-linear terms are added to the modified Boussinesq equations. The non-linearity of the Boussinesq model is analyzed. A parameter related to h/L0 is used to improve the quadratic transfer function in relatively deep water. Since the dispersion characteristic of the modified Boussinesq equations with two parameters is only equal to the second-order Padé expansion of the linear dispersion relation, further improvement is done by introducing a new velocity vector to replace the depth-averaged one in the modified Boussinesq equations. The dispersion characteristic of the further modified Boussinesq equations is accurate to the fourth-order Padé approximation of the linear dispersion relation. Compared to the modified Boussinesq equations, the accuracy of quadratic transfer functions is improved and the shoaling characteristic of the equations has higher accuracy from shallow water to deep water.  相似文献   

19.
借助MITgcm模式使用二维非静力近似在水平方向采用不等间距网格,模拟了陆坡非旋转重力羽状流的流动。模拟显示陆坡上的重力羽状流的运动比较复杂。通过数值实验,发现改变地形或调整冷源强度都会影响沿陆坡下沉的低温高密度水的羽状流形态,潮汐亦会对重力羽状流有一定的影响。经计算发现在陆坡处,Richardson数小于1/4,宜发生Kelvin-Helmholtz不稳定性,并由卷挟导致环境流体与高密度流体混合,沿着斜坡加速下滑。  相似文献   

20.
New hyperbolic mild slope equations for random waves are developed with the inclusion of amplitude dispersion. The frequency perturbation around the peak frequency of random waves is adopted to extend the equations for regular waves to random waves. The nonlinear effect of amplitude dispersion is incorporated approximately into the model by only considering the nonlinear effect on the carrier waves of random waves, which is done by introducing a representative wave amplitude for the carrier waves. The computation time is greatly saved by the introduction of the representative wave amplitude. The extension of the present model to breaking waves is also considered in order to apply the new equations to surf zone. The model is validated for random waves propagate over a shoal and in surf zone against measurements.  相似文献   

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