Simulating flow in intertidal areas with the shallow water equations: wetting-drying procedure vs. modified equations for partially dry areas

Accompanying with the back and forth motion of the land-water interface, some parts of the foreshore in estuaries and coastal zones are exposed during low tides and submerged during high tides, which are commonly defined as intertidal areas. Hydrodynamics and sediment transport, hence morphodynamics in intertidal areas are deeply affected by the wetting and drying process. Complex dynamics in such special regions brings difficulties to the field measurements and even more to the numerical simulation. In some numerical models, when solving the classical de Saint-Venant equations over a fixed computational grid, a wetting-drying procedure is needed to simulate the flow in the intertidal areas, which consists of alternating periods in which the corresponding grid cells are covered or uncovered by water. Such a procedure determines when a grid cell (when set “dry”) needs to be removed from the flow domain and when it needs to be reinserted (when the cell becomes “wet” again). It challenges the numerical simulation in terms of robustness, efficiency, and the preservation of physical properties. An alternative approach, proposed by Defina is to numerically solve the modified equations for flow over partially dry areas. In this on-going research, both the classical and the alternative approach are critically evaluated for simple 1D flow configurations. For both approaches, numerical solutions for the water motion are explored in the time domain, as well as in the frequency domain. Harmonic analysis results in the intertidal areas also shed light on the tidal distortion there and on the feasibility of idealized modelling with a limited number of modes. Only the effects of tidal currents are considered in the on-going models.