任意水深表面张力—重力波的新解法

A New Method of Solving the Equations for Capillary-Gravity Waves in a Arbitrary Water Depth

本文提供了一种新的计算二维任意水深周期性行进的表面张力一重力波的方法。动力学边界条件采用准确的非线性形式。计算域是由Z平面上的一个波长水域变换成ζ平面上的单位圆环域。通过映像法求解出满足一定水深流动条件的Laurent展式,并用该展式有限项表示自由面。其系数用Newton-Raphson方法迭代求解。

In this paper, a numerical method for the computation of two dimensional periodic progressive capillary-gravity waves with a arbitrary water depth is presented. The dynamic boundary condition is exactly nonlinear and the computational domain is transformed from the domain of one wave-length on Z-plane into a unit annulus on ξ -plane. The nonlinear surface is expressed by finite number of the terms of Laurent series which satisfies the boundary condition of finite water depth. The coefficients of the series are solved by Newton-Raphson method.