Fully nonlinear shallow water waves simulation using Green-Naghdi theory

Abstract

Green-Naghdi (G-N) theory is a fully nonlinear theory for water waves. Some researchers call it a fully nonlinear Boussinesq model. Different degrees of complexity of G-N theory are distinguished by “levels” where the higher the level, the more complicated and presumably more accurate the theory is. In the research presented here a comparison was made between two different levels of G-N theory, specifically level II and level III G-N restricted theories. A linear analytical solution for level III G-N restricted theory was given. Waves on a planar beach and shoaling waves were both simulated with these two G-N theories. It was shown for the first time that level III G-N restricted theory can also be used to predict fluid velocity in shallow water. A level III G-N restricted theory is recommended instead of a level II G-N restricted theory when simulating fully nonlinear shallow water waves.

Keywords

Green-Naghdi theory / Boussinesq model / fully nonlinear water waves / shoaling waves