Nonlinear refraction - diffraction of water waves: the complementary mild-slope equations. (English) Zbl 1183.76646
Summary: A second-order nonlinear frequency-domain model extending the linear complementary mild-slope equation (CMSE) is presented. The nonlinear model uses the same streamfunction formulation as the CMSE. This allows the vertical profile assumption to accurately satisfy the kinematic bottom boundary condition in the case of nonlinear triad interactions as well as for the linear refraction-diffraction part. The result is a model with higher accuracy of wave-bottom interactions including wave-wave interaction. The model’s validity is confirmed by comparison with accurate numerical models, laboratory experiments over submerged obstacles and analytical perturbation solutions for class III Bragg resonance.
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 86A05 | Hydrology, hydrography, oceanography |
Keywords:
Bragg resonance; coastal and offshore engineering; mild-slope equation; nonlinear waves; streamfunction formulationReferences:
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