The 12th International Conference on Hydrodynamics
18 – 23 september 2016, Egmond aan Zee, The Netherlands
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Go-down ichd2016 Tracking Number 94

Session: Linear and non-linear waves II
Room: Room 2
Session start: 16:00 Tue 20 Sep 2016

Zhili Zou

Topics: - Linear and non-linear waves and current


The fully-dispersive nonlinear mild slope equations for broad-band waves are a newly-developed wave model with full dispersion and nonlinearity to any desired order. It is superior to the higher order Boussinesq equations by its accurate dispersion property, and also superior to the classic mild slope equation by its broad-band spectral feature. Although the mild slope assumption is adopted by this model, the application of the model to a considerable steep topography (the steepness being up to 1:5) is still possible. The present paper presents a comprehensive numerical results to demonstrate the applicablity of fully-dispersive nonlinear mild slope equations mentioned above. Comparison to the numerical results of higher order Boussinesq equations are made in order to show the advantage of the model. Numerical examples include: (1) nonlinear evolution of wave groups. (2) crescent wave generation and evolution. (3) wave propagation over submarine breakwater with different slopes. (4) wave propagation over bottom with a patch of sand bars. (5) wave propagation over a shoal. The first two examples are for the demonstration of the advantage of accurate dispersion and high order nonlinearity of the model. The third is for the illustration of applicability of mild slope assumption. The fourth is for the demonstration of applicability of simulating Bragg-reflection over topography with rapidly-varying depth. The fifth is for the illustration of applicability of wave refraction property of the model. The study's numerical results verify the abilities of the fully-dispersive nonlinear mild slope equations to model the effects of dispersion, nonlinearity and complex bottom topography on wave motions.