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題 名 | 前進波之折射:通式與等緩坡度底床情況=Progressive Wave Refractions: General Formula and on Gentle Sloping Plane Beach |
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作 者 | 陳陽益; | 書刊名 | 海洋工程學刊 |
卷 期 | 1:1 2001.11[民90.11] |
頁 次 | 頁35-54 |
分類號 | 351.941 |
關鍵詞 | 波浪折射與其位相函數的通式; 等緩斜坡底床; 波向線; 等位相線; 位相函數; 折射係數等之明顯函數表示; 實況的印證; Wave refraction; Wave ray; Phase line; Phase function; Refraction coefficient; |
語 文 | 中文(Chinese) |
中文摘要 | 三度空間中前進波浪的折射現象,已依波浪守衡性的本質簡明地導述出其主控的通式,且與由較繁冗的光學之Fermat 原則所得者完全一致;而最簡單的均勻緩坡度底床的特例情況則退化成Snell 定律者。就此特例情況在波浪的線性分散關係的應用下,前進波浪折射現象的整体特性,包括波向線、等位相線、位相函數與波峰線皆被導述出明確顯然的函數表示;同時引入由沿著波向線與等位相線所構成的完全符合波浪折射幾何通性的正交曲線座標,求出其尺度因子後,由能通量守衡原則定出沿著任一條波向線上的折射係數;並由之對往昔純依兩相鄰的波向線間的幾何類比所給定的折射係數給予導証之。本文結果除與往昔數值計數者相一致外,另為往昔者所無達成的是,與由航空拍照所得的現場波浪折射現象很吻合,因此本文論述得到具体的印證。 |
英文摘要 | A general formula for three dimensional refraction of progressive gravity water waves has been derived using the conservation of waves, which has a form the same as that derived using Fermat’s principle in optics. For the case of gentle sloping plane beach the formula can be degenerated into the famous Snell’s law. And by applying the linear dispersion relation of wave, all the properties of wave refraction including wave rays, constant phase lines, phase function and crest lines etc., can be expressed in explicit functions. By introducing an orthogonal curvilinear coordinate along the wave ray and the constant phase line, and with an estimated scale factor, the refraction coefficients along any wave ray can then be determined. The present results are verified by ordinary wave ray theory and some previous numerical results. Furthermore, the comparisons that agree verywell with refraction phenomena taken from in situ aerial photographs confirm solidly the present statement. |
本系統中英文摘要資訊取自各篇刊載內容。