An Accurate One-Term Approximation for Gravity Waves on Deep Water

精確的深水重力波單項近似解

張憲國(Hsien-Kuo Chang) ； 劉勁成(Jin-Cheng Liou)

《海洋工程學刊》 14卷4期 (2014/12) Pp. 201-213

https://doi.org/10.6266/JCOE.2014.1404.01

摘要

本文只保留非線性波浪級數解的首項，由在波峰及波谷處滿足運動及動力邊界條件的配置法獲得單項近似解，由數學適用性證實本近似解具有稍優於往昔三階攝動近似解的精確度。此近似解呈現波浪的波峰、波速、表面流函數值、柏努力係數等運動及動力特性會隨波浪尖銳度增加而增加的現象，此結果說明本簡單形式的近似解可以適當地描述深水重力波的非線性的特性，並準確地計算運動及動力特性來提供海岸工程的規畫設計的參考。

關鍵字

非線性 ； 深水重力波 ； 數學適用性 ； 動力特性 ； 配置法

並列摘要

Retaining the leading term of a possible Fourier series for the problem of nonlinear gravity waves on deep water we obtain an accurate one-term approximation to exactly satisfy the kinematic and dynamic boundary conditions at the wave crest and wave trough using the collocation method. Examination of mathematical validity indicates slightly better accuracy of the one-term approximation up to an existing third-order Stokes wave theory obtained by the perturbation method. The one-term approximation in simple expressions shows the nonlinearity of gravity waves by an increase of kinematic and dynamic properties, like wave crest, wave speed and Bernoulli's constant with wave steepness. Accurate calculation of kinematic and dynamic properties by the one-term approximation can offer useful references for planning or designing marine structures on coastal engineering.

並列關鍵字

nonlinearity ； deep-water gravity wave ； mathematical validity ； dynamic property ； collocation method