非线性弥散效应及其对波浪变形的影响

针对Hedges,Kirby和Dalrymple提出的非线性弥散关系的修正式在浅水区存在的较大偏差的问题，给出了一个在整个水深范围内具有单值性的非线性弥散关系。比较可知，它具有在深水与中等水深逼近二阶Stokes波的弥散关系式，在浅水较Hedges,Kirby和Dalymple的修正表达式与Hedges的关系更加吻合的优点，且形式简练，用近似该非线性弥散关系的显式表达式，结合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模型。数值模拟结果表明，用新的非线性弥散关系得到的模型对复杂地形进行模拟的结果和实测结果吻合很好。     

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   

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…     

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。     

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).     

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.     

Improved explicit approximation of linear dispersion relationship for gravity waves

For water waves the transcendental dispersion relationship is solved by iterative methods when wave period and water depth are given and wavelength or wave number is required. A highly accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship. While Eckart's expression is accurate to within 5%, the improved relationship has a maximum relative error of less than 0.05%. A simpler form of the relationship with 0.2% accuracy is also given.     

Nonlinear Effect of Wave Propagation in Shallow Water

—In this paper,a nonlinear model is presented to describe wave transformation in shallow wat-er with the zero-vorticity equation of wave-number vector and energy conservation equation.Thenonlinear effect due to an empirical dispersion relation(by Hedges)is compared with that of Dalrymple＇sdispersion relation.The model is tested against the laboratory measurements for the case of a submergedelliptical shoal on a slope beach,where both refraction and diffraction are significant.The computation re-sults,compared with those obtained through linear dispersion relation.show that the nonlinear effect ofwave transformation in shallow water is important.And the empirical dispersion relation is suitable for re-searching the nonlinearity of wave in shallow water.     

New Numerical Scheme for Simulation of Hyperbolic Mild-Slope Equation

The original hyperbolic mild-slope equation can effectively take into account the combined effects of wave shoaling, refraction, diffraction and reflection, but does not consider the nonlinear effect of waves, and the existing numerical schemes for it show some deficiencies. Based on the original hyperbolic mild-slope equation, a nonlinear dispersion relation is introduced in present paper to effectively take the nonlinear effect of waves into account and a new numerical scheme is proposed. The weakly nonlinear dispersion relation and the improved numerical scheme are applied to the simulation of wave transformation over an elliptic shoal. Numerical tests show that the improvement of the numerical scheme makes efficient the solution to the hyperbolic mild-slope equation. A comparison of numerical results with experimental data indicates that the results obtained by use of the new scheme are satisfactory.     

The dispersion relations for surface plasmon in a nonlinear—metal—nonlinear dielectric structure

In the asymmetric and symmetric nonlinear--metal--nonlinear dielectric structures, this paper studies the analytic dispersion relation for surface plasmon in a system consisting of a thin metallic film covered on two sides media of intensity-dependent refractive indexes by applying a generalised first integral approach. Especially in the symmetric waveguide structure, two possible modes can exist: the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the squared magnitude of the electric field at the interface appears and alters the dispersion relations. Numerical results are compared to those from a certain approximate treatment.     

投影寻踪门限自回归模型在海洋冰情预测中的应用

为预测海洋冰情时序这类非线性动力系统，提出了投影寻踪门限自回归（PPTAR）模型。用自相关分析技术确定预测因子，构造了新的投影指标函数，用门限回归（TR）模型描述投影值与预测对象间的非线性关系，并用实码加速遣传算法优化投影指标函数和TR模型参数。实例的计算结果表明，用PPTAR模型预测海洋冰情时序是可行和有效的，PPTAR模型简便，适用性强，克服了目前投影寻踪方法计算量大，编程实现困难的缺点，有助于投影寻踪方法的推广应用。为解决非线性时序复杂预测问题提供了新的途径。     

Theoretical analysis of equatorial near-inertial solitary waves under complete Coriolis parameters

An investigation of equatorial near-inertial wave dynamics under complete Coriolis parameters is performed in this paper. Starting from the basic model equations of oceanic motions, a Korteweg de Vries equation is derived to simulate the evolution of equatorial nonlinear near-inertial waves by using methods of scaling analysis and perturbation expansions under the equatorial beta plane approximation. Theoretical dynamic analysis is finished based on the obtained Korteweg de Vries equation, and the results show that the horizontal component of Coriolis parameters is of great importance to the propagation of equatorial nonlinear near-inertial solitary waves by modifying its dispersion relation and by interacting with the basic background flow.     

Detection of ocean waves using satellite altimetry: Application to equatorial Kelvin waves

A new method for wave motion detection from satellite altimetric measurements of sea surface height is presented. The essence of the approach is to construct a two‐dimensional traveling‐wave Fourier series representation of the amplitude field within a prespecified oceanic region. The method employs an iterative, nonlinear least‐squares technique based on the Marquardt‐Levenberg algorithm to solve for model parameters describing characteristic features of the evolving wave system. The Marquardt‐Levenberg Fourier series (MLFS) algorithm was applied to Kelvin waves active during the 1986–1987 El Nino event in the equatorial Pacific ocean using GEOSAT Exact Repeat Mission altimetry data. Characteristics of the wave system were found to be in essential agreement with earlier field measurements and the observations of Cheney and Miller (1987) obtained using time series developed from GEOSAT data. The advantage of the present detection scheme lies in its speed and ability to determine a wave system's dispersion relation over a finite range of wavenumbers, and hence the group velocity of that system.     

Wave evolution over submerged sills: tests of a high-order Boussinesq model

A Boussinesq model accurate to O(μ)⁴, μ=k₀h₀ in dispersion and retaining all nonlinear effects is derived for the case of variable water depth. A numerical implementation of the model in one horizontal direction is described. An algorithm for wave generation using a grid-interior source function is derived. The model is tested in its complete form, in a weakly nonlinear form corresponding to the approximation δ=O(μ²), δ=a/h₀, and in a fully nonlinear form accurate to O(μ²) in dispersion [Wei, G., Kirby, J.T., Grilli, S.T., Subramanya R. (1995). A fully nonlinear Boussinesq model for surface waves: Part 1. Highly nonlinear unsteady waves. J. Fluid Mech., 294, 71–92]. Test cases are taken from the experiments described by Dingemans [Dingemans, M.W. (1994). Comparison of computations with Boussinesq-like models and laboratory measurements. Report H-1684.12, Delft Hydraulics, 32 pp.] and Ohyama et al. [Ohyama, T., Kiota, W., Tada, A. (1994). Applicability of numerical models to nonlinear dispersive waves. Coastal Engineering, 24, 297–313.] and consider the shoaling and disintegration of monochromatic wave trains propagating over an elevated bar feature in an otherwise constant depth tank. Results clearly demonstrate the importance of the retention of fully-nonlinear effects in correct prediction of the evolved wave fields.     

Modelling of periodic wave transformation in the inner surf zone

In this paper, we analyse the ability of the nonlinear shallow-water (NSW) equations to predict wave distortion and energy dissipation of periodic broken waves in the inner surf zone. This analysis is based on the weak-solution theory for conservative equations. We derive a new one-way model, which applies to the transformation of non-reflective periodic broken waves on gently sloping beaches. This model can be useful to develop breaking-wave parameterizations (in particular broken-wave celerity expression) in both time-averaged wave models and time-dependent Boussinesq-type models. We also derive a new wave set-up equation which provides a simple and explicit relation between wave set-up and energy dissipation. Finally, we compare numerical simulations of both, the NSW model and the simplified one-way model, with spilling wave breaking experiments and we find a good agreement.     

A fast convolution approach to the transformation of surface gravity waves: Linear waves in 1DH

The transformation of irrotational surface gravity waves in an inviscid fluid can be studied by time stepping the kinematic and dynamic surface boundary conditions. This requires a closure providing the normal surface particle velocity in terms of the surface velocity potential or its tangential derivative. A convolution integral giving this closure as an explicit expression is derived for linear 1D waves over a mildly sloping bottom. The model has exact linear dispersion and shoaling properties. A discrete numerical model is developed for a spatially staggered uniform grid. The model involves a spatial derivative which is discretized by an arbitrary-order finite-difference scheme. Error control is attained by solving the discrete dispersion relation a priori and model results make a perfect match to this prediction. A procedure is developed by which the computational effort is minimized for a specific physical problem while adapting the numerical parameters under the constraint of a predefined tolerance of damping and dispersion error. Two computational examples show that accurate irregular-wave transformation on the kilometre scale can be computed in seconds. Thus, the method makes up a highly efficient basis for a forthcoming extension that includes nonlinearity at arbitrary order. The relation to Boussinesq equations, mild-slope wave equations, boundary integral equations and spectral methods is briefly discussed.     

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。