A numerical model for shoaling and refraction of second-order cnoidal waves over an irregular bottom
Thomas A. Hardy, Nicholas C. Kraus, United States. Army. Corps of Engineers, U.S. Army Engineer Waterways Experiment Station
Dept. of the Army, Waterways Experiment Station, Corps of Engineers, 1987 - Science - 131 pages
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, 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 efficient calculation of cnoidal wave theory are derived. The model calculates water 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 calculating wave height. The irrotationality wave number equation, adapted for cnoidal wave theory, was used to calculate wave angle. Model results for shoaling and reflection over a plane bottom showed that second-order cnoidal waves shoaled more than small-amplitudes 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.
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SURVEY OF WATER WAVE THEORY
USE OF ELLIPTIC FUNCTIONS IN CNOIDAL WAVE THEORY
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amplitude wave Appendix approximation ASCE averaged over wavelength bathymetry boundary conditions boundary value problem breaking criterion Chapter CKNY cnoidal and small-amplitude cnoidal wave theory Coastal Engineering coefficients Comparison with flume cosh curve deepwater wave steepnesses derivation efficient calculation elliptic integrals ENDIF energy flux energy per unit Figure finite-amplitude waves first-order cnoidal wave flume data group velocity Ho/Lo Isobe iterations J=JJ,NJ Jacobian elliptic functions LONGSHORE DISTANCE longshore variation maximum nondimensional nonlinear numerical grid numerical model OFFSHORE percent differences plane bottom 1:50 plots predicted quantities seaward boundary second-order cnoidal model second-order cnoidal wave shallow water wave shoaling and refraction simulations small-amplitude theory small-amplitude wave theory Solitary Wave spherical shoal steeper wave stream function SUBROUTINE trench unit surface area Ursell numbers w2 dz water depth water particle velocity wave angle wave celerity wave energy wave height wave period wave propagation wave refraction wave shoaling wave transformation model wavelength