Propagation of 3D nonlinear waves over an elliptical mound with a High-Order Spectral method

Abstract

The scattering of nonlinear and non-breaking surface gravity waves propagating over a three-dimensional varying bathymetry is considered in this paper. In a recent study (Gouin et al., 2016) two numerical schemes for propagating waves over a variable bottom in an existing High-Order Spectral (HOS) model have been introduced. Both the computational effort and the accuracy of the model were shown to be conserved with the introduction of these new schemes. Moreover, they have been extensively validated in 2D, but the propagation of regular and irregular waves over 3D varying bottoms remains to be addressed with such spectral methods. In this paper, the three-dimensional formalism is introduced as well as the practical implementation of 3D configurations. Then the method is applied to a three-dimensional varying bathymetry consisting of an elliptical lens, as used in the Vincent and Briggs (1989) experiment. Incident waves passing across the lens are transformed and a strong convergence region is observed after the elliptical mound. The wave amplification depends on the incident wave. Numerical results for regular waves, unidirectional and directional irregular waves are analysed and compared with experimental data, demonstrating the efficiency and practical applicability of the present approach to treat the nonlinear propagation of various sea states over a varying bathymetry.