波浪非线性弥散关系分析

Hedges及Kirby等的非线性弥散关系及其修正式在浅水区小波陡时存在较大误差 ,李瑞杰等针对这个问题给出了新的非线性弥散关系式。本文通过对各种非线性弥散关系计算分析可知 ,由李瑞杰等提出的非线性弥散关系除了具有Hedges ,Kirby和Dalrymple等人提出的非线性弥散关系及修正式的优点外 ,还能大大地减小在小波陡相对水深为 1相似文献   

波浪非线性弥散关系及其应用

针对Hedges及Kirby等对Kirby和Dahymple的非线性弥散关系的修正关系,在小波陡时中等水深范围存在较大偏差的问题,给出了一个新的非线性弥散关系。比较可知,新的关系在小波陡时减小了中等水深范围内50％的误差,而在大波陡时能够保持其单调性,且形式上更为简练。将其应用于含弱非线性效应的缓坡方程进行数值验证,结果表明,采用新的非线性弥散关系得到的计算结果与实测结果更为吻合。     

考虑非线性弥散影响的波浪变形数学模型

提出了逼近Kirby和Dalrymple的非线性弥散关系的显式非线性弥散关系的表达式,该显式表达式与他们的非线性弥散关系的精度几乎完全相同.采用显式非线性弥散关系,结合含弱非线性效应的缓坡方程,得到考虑非线性弥散影响的波浪变形数学模型,并对该数学模型进行了数值验证.结果表明,考虑非线性弥散影响的波浪变形数学模型更为精确.     

波浪的非线性显式弥散关系

波浪的非线性弥散关系在应用于求解波浪的变形问题时很不方便，需要与含非线性效应的缓坡方程一起进行迭代运算，往往导致数值计算的计算量太大，计算过于复杂。采用显式形式表达非线性弥散关系，可以克服上述缺点，大为简化波浪变形数值计算的计算量。本文通过将现有的非线性弥散关系进行分析比较，给出了一个更为一般的非线性弥散关系及其显式表达式，经比较可知，该显式弥散关系与相对应非线性弥散关系吻合的很好。本文最后用该显式结合含弱非线性效应的缓坡方程，对复式浅滩地形上的波浪折射绕射进行了计算。结果表明，考虑弱非线性可以得出与实验数据更为相符的结果，而采用显式弥散关系可以有效提高计算效率,在波浪的非线性计算中不失为一种切实有效的方法。     

显式非线性弥散关系在浅水波变形计算中的应用

本文参照Ｚｈａｏ和Ａｎａｓｔａｓｉｏｕ的方法,导出了逼近Ｂｏｏｉｊ的非线性弥散关系的近似显式表达式,该式给出的结果与Ｂｏｏｉｊ的非线性弥散关系相当吻合。用中文显式非线性弥散关系,结合会弱非线性效应的缓坡方程,构成含非线性影响项缓坡方程的一个求解浅水波变形问题的方程组。用实验数据对本文模型进行验证,结果表明,显式非线性弥散关系在求解浅水波变形问题时,给出了更符合实验数据的结果。     

波浪在浅水传播中的弱非线性效应

在波浪从深水向浅水传播过程中,考虑弱非线性效应具有重要的实用价值,因此得到广泛的讨论和研究。本文根据文献「６」导出的考虑能耗的定常缓坡方程,结合文献「５」给出的显式非线弥散关系,得出了含弱非线性效应的缓坡方程,用该方程对浅水中波浪的传播 计算,将计算结果和试验数据进行了比较,结果表明,含弱非线性效应的缓坡方程可以用于讨论浅水中波浪传播的弱非线性效应,所得计算计算结果与试验结果更为吻合。     

非线性效应对浅水水波变形的影响

本文采用波数矢量无旋和波能守恒方程建立了一个考虑非线性作用的浅水水波变形数值模型,模型中采用Ｂａｔｔｊｅｓ关系与波数矢量无旋,波能守恒方程一起来求解波浪在浅水中变形的波浪要素,在波能守恒方程中考虑了底摩擦的影响。利用本文提出的数值模型对一个斜坡浅滩水域波浪折射绕射现象进行了验证,验证计算中用一个非线性经验弥散关系近似浅水水波变形的非线性效应并与用线性弥散关系的计算结果进行了比较,结果说明使用非线性     

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。     

海底边坡稳定性分析中波浪力的求解

针对浅水区波浪的非线性特性,提出了在海底边坡稳定性分析中应用椭圆余弦波理论来研究波浪力的问题,利用非线性弥散关系建立了新的适用于整个水深范围的椭圆余弦波的近似求解方法.结合工程实例,确立了海底边坡波浪力的计算步骤,并编制了计算程序.     

基于波形不对称性的波浪破碎指标

为了探寻波浪破碎与波形不对称性的关系,通过对1/200缓坡上波浪破碎实验研究结果的进一步分析,运用最小二乘法,拟合了波形不对称性参数与相对水深的关系,以及用波形不对称性参数表示的波浪破碎指标表达式。所得规则波的结果与Kjeldsen的深水波结果相同,而不规则波的结果比规则波的小。研究还表明,这一破碎指标与相对水深有关系,随着水深变浅,指标值增大。     

Nonlinear Dispersion Effect on Wave Transformation

—A new nonlinear dispersion relation is given in this paper.which can overcome the limitationof the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple(1986).and which has a better approximation to Hedges'empirical relation than the modified relations by Hedges(1987).Kirby and Dalrymple(1987)for shallow waters.The new dispersion relation is simple in form.thusit can be used easily in practice.Meanwhile,a general explicit approximation to the new dispersion rela-tion and other nonlinear dispersion relations is given.By use of the explicit approximation to the newdispersion relation along with the mild slope equation taking into account weakly nonlinear effect.amathematical model is obtained,and it is applied to laboratory data.The results show that the model de-veloped with the new dispersion relation predicts wave transformation over complicated topography quitewell.     

Nonlinear Dispersion Relation in Wave Transformation

1 .Ｉｎｔｒｏｄｕｃｔｉｏｎ1ＴｈｉｓｗｏｒｋｗａｓｆｉｎａｎｃｉａｌｌｙｓｕｐｐｏｒｔｅｄｂｙｔｈｅＮａｔｕｒａｌＳｃｉｅｎｃｅＦｏｕｎｄａｔｉｏｎｏｆＣｈｉｎａ (ＧｒａｎｔＮｏ .4 0 0 760 2 6ａｎｄ 4 0 0 760 2 8) Ｃｏｒｒｅｓｐｏｎｄｉｎｇａｕｔｈｏｒ.Ｅ ｍａｉｌ:ｒｊｌｉ@ｈｈｕ .ｅｄｕ .ｃｎ　　Ｉｔｉｓａｖｅｒｙｕｓｅｆｕｌａｎｄｅｆｆｅｃｔｉｖｅｗａｙｔｏａｄｊｕｓｔｔｈｅｗａｖｅｄｉｓｐｅｒｓｉｏｎｒｅｌａｔｉｏｎｆｏｒｔｈｅｓｔｕｄｙｏｆｔｈｅｎｏｎ ｌｉｎｅａｒｉｔｙｏｆｗａｖｅｐｒｏ…     

Analysis of Wave Nonlinear Dispersion Relations

1. Introduction The application of the equation taking into account the weak nonlinearity along with the specificboundary condition is a very important and feasible way to study the wave field influenced by weak non linearity, including refraction, diffraction and shoaling. Results of study show that the method can givesufficient accuracy for practical purposes (Booij, 1981; Hedges, 1987; Choi, 1995; Dingemans,1997; Zhu and Hong, 2001; Li and Yu, 2002; Inan and Balas, 2002; Sun and Ga…     

A numerical model for wave propagation in curvilinear coordinates

Using the perturbation method, a time dependent parabolic equation is developed based on the elliptic mild slope equation with dissipation term. With the time dependent parabolic equation employed as the governing equation, a numerical model for wave propagation including dissipation term in water of slowly varying topography is presented in curvilinear coordinates. In the model, the self-adaptive grid generation method is employed to generate a boundary-fitted and varying spacing mesh. The numerical tests show that the effects of dissipation term should be taken into account if the distance of wave propagation is large, and that the outgoing boundary conditions can be treated more effectively by introduction of the dissipation term into the numerical model. The numerical model is able to give good results of simulating wave propagation for waters of complicatedly boundaries and effectively predict physical processes of wave propagation. Moreover, the errors of the analytical solution deduced by Kirby et al. (1994) [Kirby, J.T., Dalrymple, R.A., Kabu, H., 1994. Parabolic approximation for water waves in conformal coordinate systems. Coastal Engineering 23, 185–213.] from the small-angle parabolic approximation of the mild-slope equation for the case of waves between diverging breakwaters in a polar coordinate system are corrected.     

Improved explicit approximation of linear dispersion relationship for gravity waves: Comment on another discussion

Recently, a simple explicit approximation to linear dispersion relationship with an accuracy of 0.044% has been proposed (Beji, 2013). Then, this solution was simplified and improved to an accuracy of 0.019% (Vatankhah and Aghashariatmadari, 2013). Moreover, by considering Beji's approximation as a seed, Newton's method was used (Simarro and Orfila, 2013) to obtain an accurate and explicit two-step solution to linear dispersion relationship with percentage error less than 0.0000082%.Newton's method works very well, if a good seed is given. In this discussion, Beji's expression is simplified and improved as a seed for Newton's method. Using this new expression (initial guess), the solution is improved to an accuracy of 0.00000028% which is 30 times smaller than the solution proposed by Simarro and Orfila (2013).     

水波在软淤泥底床上的衰减

本文研究了二层流体系统中波浪的衰减。上层为理想流体，下层为粘弹性Ｖｏｉｇｔ体。导出了色散关系，计算了波浪衰减系数。对于粘性或弹性很大或很小的情况，导出了各种水深情况下近似的显式的衰减系数表示式。与精确的数值结果比较，近似程度很好。可供工程设计参考、使用。     

Improved explicit approximation of linear dispersion relationship for gravity waves: A discussion

Recently, an accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship (Beji, 2013). The author has nicely improved Eckart's explicit dispersion relationship by introducing an empirical correction function. The resulting expression is valid for the entire range of relative water depths and accurate to within 0.044%.In this discussion, the proposed expression by the author is simplified and improved to an accuracy of 0.019%. Moreover, a near exact solution with 0.001% accuracy is also given.