基于非线性弥散关系的缓坡方程波浪传播变形模拟研究

Modeling of Wave Propagation and Transformation by the Mild-slope Equation with Nonlinear Dispersion

关键词:  缓坡方程  非线性  弥散关系  波浪变形  Berkhoff地形

Key words:  mild-slope equation  nonlinearity  wave dispersion  wave transformation  Berkhoff experiment

摘要:

[目的]波浪由外海传播到近海时,由于受到地形、建筑物等影响,波浪非线性增强,线性弥散关系不能够很好的描述波浪弱非线性效应。为了对比研究非线性弥散关系的缓坡方程在波浪传播变形的作用。[方法]采用改进型缓坡方程数值模式,并结合Li提出的非线性弥散关系,对Berkhoff椭圆经典地形进行波浪传播变形模拟研究,探讨线性和非线性弥散关系的数值模拟计算结果与实验值的关系,并对两种计算结果进行了比较分析。[结果]非线性弥散关系的计算结果与实验值的误差较线性弥散关系的结果小,非线性模型要优于线性模型。[结论]非线性模型更适合近海海域弱非线性波浪传播变形的研究。

Abstract:

[Objective] As surface waves propagate from deep to shallow water,the nonlinearity of waves would be strengthened due to the effect of topography and various hydraulic structures,which can't be descript well with the linear dispersion relations.The objective of this article is to investigate the effects of the nonlinear dispersion relation.[Methods] In the paper,we attempted to solve this problem by the mild-slope equation with nonlinear dispersion,which will be used to simulate wave propagation and transformation on Berkhoff topography.[Results] The computational results between linear and nonlinear dispersion are presented.The results of nonlinear dispersion agree with the actual measure data,which is better than that of the linear dispersion.[Conclusion] It illustrates that the nonlinear model is suitable for studying the wave transformation with weak nonlinearity in offshore area.