A flexible z-layers approach for the accurate representation of free surface flows in a coastal ocean model (SHYFEM v. 7-5-71)

We propose a discrete multilayer shallow water model based on z-layers, which, thanks to the insertion and removal of surface layers, can deal with an arbitrarily large tidal oscillation independently of the vertical resolution. The algorithm is based on a classical two-step procedure used in numerical simulations with moving boundaries (grid move- ment followed by a grid topology change, that is, the inser- tion/removal of surface layers), which avoids the appearance of surface layers with very small or negative thickness. With ad hoc treatment of advection terms at nonconformal edges that may appear owing to insertion/removal operations, mass conservation and the compatibility of the tracer equation with the continuity equation are preserved at a discrete level. This algorithm called z-surface-adaptive, can be reduced, as a par- ticular case when all layers are moving, to the z-star coordi- nate. With idealized and realistic numerical experiments, we compare the z-surface-adaptive against z-star and we show that it can be used to simulate coastal flows effectively.