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Analytic solution of long wave propagation over a submerged hump

Authors
Journal
Coastal Engineering
0378-3839
Publisher
Elsevier
Publication Date
Volume
58
Issue
2
Identifiers
DOI: 10.1016/j.coastaleng.2010.09.001
Keywords
  • Refraction
  • Long Wave
  • Submerged Hump
  • Analytical Solution
  • Frobenius Method
Disciplines
  • Mathematics

Abstract

Abstract A new analytical solution of the long wave refraction by a submerged circular hump is presented. The geometry of the hump is assumed to be axisymmetric and be described by a power function in the radial direction with arbitrary values of both the exponent and the scaling factor. The submergence of the hump is also variable. The water surface elevation governed by the long wave version of the mild slope wave equation is solved by separation of variables, and a series solution of the Frobenius type is obtained. The solution is shown to be valid when the hump is sufficiently submerged or is of a relatively small height. Matching method is employed to illustrate the refraction of long waves under given conditions of incidence. Effects of the shape, the scale, and the submergence of the hump on wave refraction are discussed.

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