A perturbation method to solve dispersion equations for water waves over dissipative media
A perturbation method to solve dispersion equations for water waves over dissipative media
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DOI：
10.1016/j.coastaleng.2003.12.007
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发表时间：
2004-03
影响因子：
4.4
通讯作者：
F. Méndez;I. Losada
中科院分区：
文献类型：
--
作者：
F. Méndez;I. Losada
本文提出了一种简单而新颖的方法来显式求解耗散介质上水波的频散方程。这个方程的根本身很复杂，很难用标准的数值方法得到。给出了色散关系的一般结构，无量纲波数x取决于耗散参数φ的值，φ是耗散介质的函数。基于耗散参数δφ的小扰动会引起无量纲波数δx的小变化的假设，提出了一种简单的方法，以迭代的方式显式计算复根。新方法改进了标准数值格式在计算耗散介质中根时的不可靠性。
A simple and innovative method to solve explicitly the dispersion equation for water waves over dissipative media is presented. The roots of this equation are themselves complex and difficult to obtain by standard numerical methods. A general structure for the dispersion relation is given, the dimensionless wave number, x, depending on the value of a dissipation parameter, φ, which is a function of the dissipative medium. Based on the hypothesis that a small perturbation in the dissipation parameter, δφ, produces a small variation in the dimensionless wave number, δx, a simple approach is proposed to calculate explicitly in an iterative manner the complex roots. The new method improves upon the unreliability of standard numerical schemes in the calculation of the roots in dissipative media.