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An analytical solution to the extended mild-slope equation for long waves propagating over an axi-symmetric pit

Cited 20 time in Web of Science Cited 21 time in Scopus
Authors
Jung, Tae-Hwa; Suh, Kyung-Duck
Issue Date
2008
Publisher
Elsevier
Citation
Wave Motion 45 (2008) 835-845
Keywords
Long wavesAnalytic solutionExtended mild-slope equationAxi-symmetric pit
Description
author's final version
Abstract
An analytic solution to the extended mild-slope equation is derived for long waves propagating over an axi-symmetric pit, where the water depth decreases in proportion to a power of radial distance from the pit center. The solution is obtained using the method of separation of variables and the method of Frobenius. By comparing the extended and conventional mild-slope equations for waves propagating over conical pits with different bottom slopes, it is shown that for long waves the conventional mild-slope equation is reasonably accurate for bottom slopes less than 1:3 in horizontal two-dimensional domains. The effects of the pit shape on wave scattering are discussed based on the analytic solutions for different powers. Comparison is also made with an analytic solution for a cylindrical pit with a vertical sidewall. Finally, wave attenuation in the region over the pit is discussed.
ISSN
0165-2125
Language
English
URI
https://hdl.handle.net/10371/67642
DOI
https://doi.org/10.1016/j.wavemoti.2008.03.002
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College of Engineering/Engineering Practice School (공과대학/대학원)Dept. of Civil & Environmental Engineering (건설환경공학부)Journal Papers (저널논문_건설환경공학부)
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