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。     

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。     

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     

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.     

综合考虑多种变形因素的近岸规则波传播数学模型Ⅰ. 基本方程的导出

推广了Kirby的有环境水流影响的缓坡方程,得到了综合考虑环境水流(水流因子)、非线性弥散影响(非线性因子)、底摩擦波能损失(底摩擦因子)、非缓坡地形影响(地形因子)、折射、绕射、波浪破碎多种变形因素的波浪传播控制方程,并给出了非线性因子、地形因子、底摩擦因子、水流因子的确定方法。基于导出的方程做进一步推导,得到了波高和波向为变量的综合考虑多种变形因素的波浪传播基本方程,该方程有许多优点:1)其绕开了求解波势函数的困难,将椭圆型方程的边值问题化为初值问题;2)直接求解波高和波向;3)可采用有限差分法离散求解,对空间步长没有限制,适合大面积海区波场计算;4)综合考虑了多种波浪变形因素,方程更为合理,5)容易处理波浪破碎问题。     

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。     

强非线性和色散性Boussinesq方程数值模型检验

采用同位网格有限差分法,建立了强非线性和色散性Boussinesq方程数值计算模型。以稳恒波Fourier近似解给定入射波边界条件,对均匀水深深水和浅水域不同非线性的行进波、缓坡地形上深水至浅水域的浅水变形波、以及缓坡和陡坡地形上的波浪水槽实验进行了数值计算,并将计算结果与解析解、解析数值解以及实验值进行了较为详细的比较,从而检验了模型的色散性、非线性以及不同底坡下非线性波的浅水变形性能。     

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   

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     

A Modified Form of Mild-Slope Equation with Weakly Nonlinear Effect

Nonlinear effect is of importance to waves propagating from deep water to shallow water.Thenon-linearity of waves is widely discussed due to its high precision in application.But there are still someproblems in dealing with the nonlinear waves in practice.In this paper,a modified form of mild-slope equa-tion with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation.The modified form of mild-slope equation is convenient to solvenonlinear effect of waves.The model is tested against the laboratory measurement for the case of a submergedelliptical shoal on a slope beach given by Berkhoff et al,The present numerical results are also comparedwith those obtained through linear wave theory.Better agreement is obtained as the modified mild-slope e-quation is employed.And the modified mild-slope equation can reasonably simulate the weakly nonlinear ef-fect of wave propagation from deep water to coast.     

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.     

Comparison between characteristics of mild slope equations and Boussinesq equations

Boussinesq-type equations and mild-slope equations are compared in terms of their basic forms and characteristics. It is concluded that linear mild-slope equations on dispersion relation are better than non-linear Boussinesq equations. In addition, Berkhoffexperiments are computed and compared by the two models, and agreement between model results and available experimental data is found to be quite reasonable, which demonstrates the two models＇ capacity to simulate wave transformation. However they can deal with different physical processes respectively, and they have their own characteristics.     

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。     

Explicit Solution to the Wave Dispersion Equation with Higher Accuracy

Based on the previous study results, two higher accuracy explicit solutions to the dispersion equation for wave length are presented in this paper. These two solutions have an accuracy of 0.1% over all wave lengths, which is sufficiently complete for practical application. At the same time, several previous explicit solutions also have been reviewed and compared herein. In comparison with accuracy, the results show that the present two solutions are as good as Wu and Thornton's solution (which has a good accuracy over all wave lengths, but its calculation formula is so complex that it is hard to be used with a hand calculator), and are better than the other solutions, they may be rather useful in practical calculation with a hand calculator or computer.     

Vertical Distribution of Tidal Flow Reynolds Stress in Shallow Sea

Based on the results of the tidal flow Reynolds stresses of the field observations,indoor experiments,and numerical models,the parabolic distribution of the tidal flow Reynolds stress is proposed and its coefficients are determined theoretically in this paper.Having been well verified with the field data and experimental data,the proposed distribution of Reynolds stress is also compared with numerical model results,and a good agreement is obtained,showing that this distribution can well reflect the basic features of Reynolds stress deviating from the linear distribution that is downward when the tidal flow is of acceleration,upward when the tidal flow is of deceleration.Its dynamics cause is also discussed preliminarily and the influence of the water depth is pointed out from the definition of Reynolds stress,turbulent generation,transmission,and so on.The established expression for the vertical distribution of the tidal flow Reynolds stress is not only simple and explicit,but can also well reflect the features of the tidal flow acceleration and deceleration for further study on the velocity profile of tidal flow.     

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.