Analytical solutions for long waves over a circular island

Tae Hwa Jung, Changhoon Lee, Yong Sik Cho

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In this study, we derive an analytical solution for long waves over a circular island which is mounted on a flat bottom. The water depth on the island varies in proportion to an arbitrary power, γ, of the radial distance. Separation of variables, Taylor series expansion, and Frobenius series are used to find the solutions, which are then validated by comparing them with previously developed analytical solutions. We also investigate how different wave periods, radii of the island toe, and γ values affect the solutions. For a circular island with a small value of γ (e.g. γ = 2/3, as in the equilibrium beach (Bruun, 1954)), the wave rays approaching near the island center reach the coastline, whereas the rays approaching away from the center bend away from the coastline, leading to smaller wave amplitudes along the coast. However, for a circular island with a large value of γ, e.g. γ = 2, all the rays on the island reach the coast, giving large coastline wave amplitudes. If the island domain is small compared to the wavelength, the wave amplitudes on the coastline do not increase significantly; however, when the island domain is not small, the wave amplitudes increase significantly. If γ is also large, the amplitudes can be so large as to cause a disaster on the island.

Original languageEnglish
Pages (from-to)440-446
Number of pages7
JournalCoastal Engineering
Volume57
Issue number4
DOIs
StatePublished - 2010 Apr 1

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Coastal zones
Taylor series
Beaches
Disasters
Wavelength
Water

Keywords

  • Analytical solution
  • Arbitrary bottom slope
  • Circular island
  • Long wave

Cite this

Jung, Tae Hwa ; Lee, Changhoon ; Cho, Yong Sik. / Analytical solutions for long waves over a circular island. In: Coastal Engineering. 2010 ; Vol. 57, No. 4. pp. 440-446.
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Analytical solutions for long waves over a circular island. / Jung, Tae Hwa; Lee, Changhoon; Cho, Yong Sik.

In: Coastal Engineering, Vol. 57, No. 4, 01.04.2010, p. 440-446.

Research output: Contribution to journalArticle

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