One-dimensional and two-dimensional Green–Naghdi equations for sloshing in shallow basins

Abstract

<jats:p> This paper presents a verified model of weakly non-linear wave sloshing in shallow basins, based on level I Green–Naghdi (GN) mass and momentum equations derived for mild-sloped beds. The model is verified for sloshing of an initially sinusoidal free surface perturbation in a square tank with a horizontal bed. The model is also used to investigate free surface sloshing of an initial Gaussian hump in closed square basins, over horizontal and non-uniform bed topographies. Analysis of the free surface slosh motions demonstrates that the model gives predictions in satisfactory agreement with the analytical solution of linearised shallow water theory obtained by Lamb. Discrepancies between GN predictions and linear analytical solutions arise from the effect of wave non-linearities arising from the wave amplitude itself and wave–wave interactions. </jats:p>