A NUMERICAL MODEL FOR SHOALING AND REFRACTION OF SECOND-ORDER CNOIDAL WAVES OVER AN IRREGULAR BOTT

Chapter 1. Introduction Chapter 2. Survey of water wave theory 2.1 The boundary value problem for water waves 2.2 Small-amplitude wave theory 2.3 Finite-amplitude wave theory 2.4 Stokes wave theory 2.5 Cnoidal wave theory 2.6 Solitary wave theory 2.7 Numerical wave theory 2.8 Brief outline of a derivation second-order cnoidal wave theory Chapter 3. Use of elliptic functions in Cnoidal wave theory 3.1 An illustration of the role cn function in Cnoidal wave theory 3.2 Efficient calculation of elliptic quantities Chapter 4. Shoaling and refraction over an irregular sea bottom 4.1 Wave refraction 4.2 Derivation of the wave angle equation 4.3 Wave shoaling 4.4 Derivation of the conservation of energy flux equation Chapter 5. Description of the numerical model 5.1 Overview of technique 5.2 Model output and input 5.3 Calculating wave height and wave angle 5.3.1 Subroutine ELLIP 5.3.2 Subroutine LENGTH 5.3.3 Subroutine ANGLE 5.3.4 Subroutine EFFLUX Chapter 6. Numerical model results 6.1 Shoaling over a plane bottom 6.1.1 Comparison of wave shoaling among small-amplitude, first-order Cnoidal and second-order Cnoidal waves 6.1.2 Comparison of theoretical and experimental shoaling rates 6.1.3 The shoaling of second-order Cnoidal wave over a plane bottom 6.2 Refraction over a plane bottom 6.2.1 Comparison of wave refraction among small-amplitude, first-order Cnoidal and second order Cnoidal waves 6.2.2 The refraction of second-order Cnoidal waves over a plane bottom 6.3 Shoaling and refraction over non-plane bathymetry 6.3.1 Shoaling and refraction over a spherical shoal 6.3.2 Shoaling and refraction over a trench 6.4 Comparison of computer time between small-amplitude and second-order simulations

ENG