Run up on beaches through simplified shallow water model

Accurate evaluation of wave run-up on beaches is a critical issue for coastal flooding studies. During extreme events, the maximum wave run-up, caused by very long (frequently non-breaking) waves, may exceed the crest of the coastal protection structures or dunes and inundate the protected inland area. This event may be simulated by a flood propagation model, recently published by the authors, that solves a simplified form of the Shallow Water Equations (SWE). The simplification mainly consists of linearizing bottom friction and neglecting advection. This study investigates on the relevance of the latter terms and on the model ability in predicting wave run-up on impermeable beaches. Numerical simulations of run-up induced by solitary non-breaking waves on a gentle-sloping planar beach are compared to the results found by Synolakis (1987) on the basis of an experimental study. For the numerical simulations, only 21 tests of the 40 experiments carried out by Synolakis (i.e. all the non-breaking waves) are considered. A good agreement between the numerical and the experimental maximum run-up was found for all the tested waves. In order to verify the magnitude and the effects of the advection terms in the SWE, some simulations are repeated considering and neglecting this term. The hypothesis of neglecting convective terms is found appropriate.