Nonlinear refraction–diffraction of waves in shallow water
- 20 April 1985
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 153 (-1) , 185-201
- https://doi.org/10.1017/s0022112085001203
Abstract
The parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow-water waves. Two methods of approach are used. In the first method Boussinesq equations are used to derive evolution equations for spectral-wave components in a slowly varying two-dimensional domain. The second method modifies the K–P equation (Kadomtsev & Petviashvili 1970) to include varying depth in two dimensions. Comparisons are made between present numerical results, experimental data (Whalin 1971) and previous numerical calculations (Madsen & Warren 1984).Keywords
This publication has 16 references indexed in Scilit:
- Nonlinear effects on shoaling surface gravity wavesPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1984
- Refraction-diffraction model for weakly nonlinear water wavesJournal of Fluid Mechanics, 1984
- A parabolic equation for the combined refraction–diffraction of Stokes waves by mildly varying topographyJournal of Fluid Mechanics, 1983
- On weak reflection of water wavesJournal of Fluid Mechanics, 1983
- Two-dimensional periodic permanent waves in shallow waterJournal of Fluid Mechanics, 1982
- Refraction–diffraction model for linear surface water wavesJournal of Fluid Mechanics, 1980
- Forward diffraction of Stokes waves by a thin wedgeJournal of Fluid Mechanics, 1980
- On the parabolic equation method for water-wave propagationJournal of Fluid Mechanics, 1979
- Nonlinear resonant excitation of a long and narrow bayJournal of Fluid Mechanics, 1978
- Some numerical solutions of a variable-coefficient Korteweg-de Vries equation (with applications to solitary wave development on a shelf)Journal of Fluid Mechanics, 1972