Development and validation of a non-linear spectral model for water waves over variable depth

M Gouin (1) , Guillaume Ducrozet (1) , P Ferrant (1)

1 LHEEA - Laboratoire de recherche en Hydrodynamique, Énergétique et Environnement Atmosphérique

In the present paper two numerical schemes for propagating waves over a variable bathymetry in an existing High-Order Spectral (HOS) model are introduced. The first scheme was first developed by Liu and Yue (1998), and the second one is an improved scheme which considers two independent orders of non-linearity: one for the bottom and one for the free-surface elevation. We investigate the numerical properties (accuracy, convergence rate, efficiency) of both schemes with respect to the numerical parameters on a simple configuration. To validate the proposed schemes, we first consider Bragg reflection from a sinusoidal bottom patch — as an example of a small bottom variation around a mean water depth. The second validation case focuses on a larger bottom variation with the study of the shoaling of linear waves. Finally, an application is performed to demonstrate the applicability of the proposed model to non-linear cases where the bottom variation is important. In this concern, the very well documented test case of a 2D underwater bar is studied in detail. Comparisons are provided with both experimental and numerical results.

Mots clés: Hydrodynamics; Non-linear water waves; High-Order Spectral method; Variable bathymetry

Domaines: Mécanique des fluides [physics.class-ph]

M Gouin, Guillaume Ducrozet, P Ferrant. Development and validation of a non-linear spectral model for water waves over variable depth. European Journal of Mechanics - B/Fluids, 2016, 57, pp.115-128. ⟨10.1016/j.euromechflu.2015.12.004⟩. ⟨hal-01299482⟩