A parabolic equation for the combined refractiondiffraction of Stokes waves by mildly varying topography
نویسندگان
چکیده
A parabolic equation governing the leading-order amplitude for a forward-scattered Stokes wave is derived using a multiple-scale perturbation method, and the connection between the linearized version and a previously derived approximation of the linear mild slope equation is investigated. Two examples are studied numerically for the situation where linear refraction theory leads to caustics, and the nonlinear model is shown to predict the development of wave-jump conditions and significant reductions in amplitude in the vicinity of caustics.
منابع مشابه
On the gradual reflection of weakly nonlinear Stokes waves in regions with varying topography
Coupled equations governing the forwardand back-scattered components of a linear wave propagating in a region with varying depth may be derived from a second-order wave equation for linear wave motion. In this paper previous studies are extended to the case of weakly nonlinear Stokes waves coupled a t third order in wave amplitude, using a Lagrangian formulation for irrotational motions. Compar...
متن کاملA Note on Linear Surface WaveCurrent Interaction Over Slowly Varying Topography
A mild slope wave equation is derived which governs the propagation of linear surface waves in the presence oflarge ambient currents. The equation is shown to differ from two previously derived models, and arguments for the validity of the new version in comparison to previous versions are presented. A linearizcd evolution equation and parabolic equation approximation are constructed in order t...
متن کاملN ov 2 00 7 On the parabolic equation method in internal wave propagation 1
A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The results of numerical experiments on propagation of an incident plane wave over a circular-type shoal are presented in comparison with the analytical result, based ...
متن کاملAn angular spectrum model for propagation of Stokes waves
An angular spectrum model for predicting the transformation of Stokes waves on a mildly varying topography is developed, including refraction, diffraction, shoaling and nonlinear wave interactions. The equations governing the water-wave motion are perturbed using the method of multiple scales and Stokes expansions for the velocity potential and free-surface displacement. The first-order solutio...
متن کاملNonlinear 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 incl...
متن کامل