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Title: A numerical model for shoaling and refraction of second-order cnoidal waves over an irregular bottom
Authors: Hardy, Thomas C.
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-87-9.
Description: Miscellaneous paper
Abstract: A numerical model for calculating shoaling and refraction of finite-amplitude waves in shallow water is presented. The model is designed to employ second-order cnoidal wave theory, but first-order cnoidal theory can be used also. A brief review of water-wave theory is given, followed by an outline of a second-order cnoidal wave theory derivation. A description is provided of the basic similarities and differences between cnoidal wave theory and the more commonly used small-amplitude wave theory. Methods for the efficient calculation of cnoidal wave theory are derived and used in the model. The model calculates wave height and direction directly at numerical grid points, resulting in a greater ease in calculation over models using the ray tracing method. A derivation is given of an expression for the energy flux of second-order cnoidal waves which is used in the calculation of wave height. The irrotationality wave number equation, adapted for cnoidal wave theory, was used to calculate the wave angle. Model results for shoaling and refraction over a plane bottom showed that second-order cnoidal waves shoaled more than small-amplitude waves but less than first-order cnoidal waves and refracted less than small amplitude waves but more than first-order cnoidal waves. Second-order cnoidal waves were found to match experimental shoaling data more accurately than either small-amplitude or first-order cnoidal waves, Simulations for waves traveling over nonplane bathymetries consisting of a trench and a shoal proved that the model could perform excellently over a nonplanar bottom with reasonably smooth contours.
Rights: Approved for public release; distribution is unlimited.
Appears in Collections:Miscellaneous Paper

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