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Title: A numerical model for shoaling and refraction of third-order stokes waves over an irregular bottom
Authors: Cialone, Mary A.
Kraus, Nicholas C.
Keywords: Mathematical models
Water Waves
Publisher: Coastal Engineering Research Center (U.S.)
Engineer Research and Development Center (U.S.)
Series/Report no.: Miscellaneous paper (U.S. Army Engineer Waterways Experiment Station) ; CERC-87-10.
Description: Miscellaneous paper
Abstract: A numerical model for wave refraction and shoaling of third-order Stokes waves over an irregular bottom is presented. The model solves for wave height, angle, and number directly on a rectangular grid. Required inputs are the deepwater wave height, period, and direction and the bathymetry in the region of interest. The model employs a finite difference scheme. The irrotationality equation of the wave number vector is solved for the wave angle, and the conservation of energy flux equation i s solved for the wave height, Iteration is required. A closed form expression, to third-order, for the time-averaged, vertically integrated energy flux is derived. Stokes’ second definition of wave celerity is used in the derivation to reduce the number of intermediate calculations. Expressions for the wave energy and the group velocity are also derived. The model is written such that both first-order (linear) and third-order stokes wave theory model computations may be conducted. The modeling process begins at higher intermediate depth, or deep water, and waves are propagated shoreward until an Ursell number of 25 or another, user-specified, value is reached. The model is applied for the following cases: (a) comparison of small amplitude and finite amplitude wave refraction and shoaling on a plane beach, (b) refraction and shoaling over an irregular bottom configuration, and (c) comparison of the model shoaling predictions to laboratory data of Iversen (1951). The results show that finite amplitude wave shoaling curves consistently lie higher than small amplitude shoaling curves. Finite amplitude waves refract slightly more than small amplitude waves in deep water and refractless than small amplitude waves in shallow water. The model can be applied to transform waves over an irregular bottom as long as caustics do not occur.
Rights: Approved for public release; distribution is unlimited.
Appears in Collections:Miscellaneous Paper

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