This study discusses the three-dimensional refraction of progressive wave trains propagating over a bottom of circular concentric contours and the results are expressed in a polar coordinate. First, a general differential formulation of refraction is derived via three different methods: by transferring from its original Cartesian form to the polar coordinate, by applying the Fermat¡¦s principle in polar coordinate, and by applying the conservation of waves in polar coordinate. All three approaches give the same governing equation; hence, its correctness is verified. Based on this governing equation, the wave ray, the phase function, the constant phase line, and the refraction coefficient are all determined.
In the present refraction problem for an originally uniform wave train propagating over a bottom of circular concentric contours, a few special features, including the cusps of constant phase lines due to the effect of bottom, and the envelope composed of these cusps, are present. All these refraction properties can be expressed in terms of both a snapshot and a time evolution of constant phase lines.
In the lee side of the shoal, there exists a sheltered zone that is enclosed by the envelope of the cusps. In this zone, wave rays intersect and the corresponding caustic problem arises, and all possible combinations of intersecting rays are also specifically described in this study. The difficulty of classical ray theory for the caustic problem is overcome and the caustic phenomenon and its refraction coefficients are determined explicitly in this study.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-1102104-215103 |
| Date | 02 November 2004 |
| Creators | Lin, Te-yuan |
| Contributors | Chung-pan Lee, Yang-yih Chen, Jaw-fang Lee, Tai-wen Hsu, Sheng-wen Twu |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | Cholon |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-1102104-215103 |
| Rights | unrestricted, Copyright information available at source archive |
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