Effect of higher-order bottom variation terms on the refraction of water waves in the extended mild-slope equations
- Authors
- Lee, Changhoon; Yoon, Sung Bum
- Issue Date
- May-2004
- Publisher
- Pergamon Press Ltd.
- Keywords
- extended mild-slope equations; higher-order bottom effects; wave refraction; numerical test
- Citation
- Ocean Engineering, v.31, no.7, pp 865 - 882
- Pages
- 18
- Indexed
- SCIE
SCOPUS
- Journal Title
- Ocean Engineering
- Volume
- 31
- Number
- 7
- Start Page
- 865
- End Page
- 882
- URI
- https://scholarworks.bwise.kr/erica/handle/2021.sw.erica/46591
- DOI
- 10.1016/j.oceaneng.2003.08.009
- ISSN
- 0029-8018
- Abstract
- This study investigates how the refraction of water waves is affected by the higher-order bottom effect terms proportional to the square of bottom slope and to the bottom curvature in the extended mild-slope equations. Numerical analyses are performed on two cases of waves propagating over a circular shoal and over a circular hollow. Numerical results are analyzed using the eikonal equation derived from the wave equations and the wave ray tracing technique. It is found that the higher-order bottom effect terms change the wavelength and, ill turn, change the refraction of waves over a variable depth. In the case of waves over a circular shoal, the higher-order bottom effects increase the wavelength along the rim of shoal more than near the center of shoal, and intensity the degree of wave refraction. However, the discontinuity of higher-order bottom effects along the rim of shoal disperses the foci of wave rays. As a result, the amplification of wave energy behind the shoal is reduced. Conversely, in the case of waves over a circular hollow, the higher-order bottom effects decrease the wavelength near the center of the hollow in comparison with the case of neglecting higher-order bottom effects. Consequently, the degree of wave refraction is decreased, and the spreading of wave energy behind the hollow is reduced. (C) 2003 Elsevier Ltd. All rights reserved.
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