Nonlinear refraction–diffraction of waves in shallow water

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).

[1]  P. Liu,et al.  Wave‐current interactions on a slowly varying topography , 1983 .

[2]  N. Booij,et al.  Gravity waves on water with non-uniform depth and current , 1981 .

[3]  P. Liu,et al.  Numerical solution of water‐wave refraction and diffraction problems in the parabolic approximation , 1982 .

[4]  P. J. Bryant.  Two-dimensional periodic permanent waves in shallow water , 1982, Journal of Fluid Mechanics.

[5]  Ting-Kuei Tsay,et al.  Refraction-diffraction model for weakly nonlinear water waves , 1984, Journal of Fluid Mechanics.

[6]  Chiang C. Mei,et al.  Nonlinear resonant excitation of a long and narrow bay , 1978, Journal of Fluid Mechanics.

[7]  James T. Kirby,et al.  A note on linear surface wave‐current interaction over slowly varying topography , 1984 .

[8]  J. Kirby,et al.  Wave Diffraction Due to Areas of Energy Dissipation , 1984 .

[9]  Robert W. Whalin,et al.  The limit of applicability of linear wave refraction theory in a convergence zone , 1971 .

[10]  O. Skovgaard,et al.  Computation of Wave Heights Due to Refraction and Friction , 1975 .

[11]  Robert A. Dalrymple,et al.  A parabolic equation for the combined refraction–diffraction of Stokes waves by mildly varying topography , 1983, Journal of Fluid Mechanics.

[12]  Michael H. Freilich,et al.  Nonlinear effects on shoaling surface gravity waves , 1984, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[13]  Performance of a numerical short-wave model , 1984 .

[14]  Carlos J. Lozano,et al.  Refraction–diffraction model for linear surface water waves , 1980, Journal of Fluid Mechanics.

[15]  Ting-Kuei Tsay,et al.  Numerical Prediction of Wave Transformation , 1985 .

[16]  Some numerical solutions of a variable-coefficient Korteweg-de Vries equation (with applications to solitary wave development on a shelf) , 1972 .

[17]  Chiang C. Mei,et al.  Forward diffraction of Stokes waves by a thin wedge , 1980, Journal of Fluid Mechanics.

[18]  P. Liu,et al.  On weak reflection of water waves , 1983, Journal of Fluid Mechanics.

[19]  B. Kadomtsev,et al.  On the Stability of Solitary Waves in Weakly Dispersing Media , 1970 .

[20]  A. C. Radder,et al.  On the parabolic equation method for water-wave propagation , 1978, Journal of Fluid Mechanics.

[21]  O. Skovgaard,et al.  Refraction of cnoidal waves , 1977 .