An SWE-FEM Model with Application to Resonant Periods and Tide Components in the Western Mediterranean Sea Region

A FEM model of Shallow Wave Equations (SWE-FEM) is studied, taking into account the variable bathymetry of semi-enclosed sea basins. The model, with a spatially varying Coriolis term, is implemented for the description of combined refraction–diffraction effects, from which the eigenperiods and eigenmodes of extended geographical sea areas are calculated by means of a low-order FEM scheme. The model is applied to the western Mediterranean basin, illustrating its versatility to easily include the effects of geographical characteristics like islands and other coastal features. The calculated resonant frequencies and modes depend on the domain size and characteristics as well as the location of the open sea boundary, and it is shown to provide results compatible with tide measurements at several stations in the coastal region of France. The calculation of the natural oscillation modes in the western Mediterranean basin, bounded by open boundaries at the Strait of Gibraltar and the Strait of Sicily, reveals a natural period of around 6 h corresponding to the quarter-diurnal tidal components, which are stationary and of roughly constant amplitude on the northern coast of the basin and on the west coast of Corsica (France). On the east coast of Corsica, on the other hand, these components are of very low amplitude and in phase opposition. The semi-diurnal tidal components observed on the same tide gauges north of the basin and west of Corsica are also quasi-stationary although they are not resonant. Resonant oscillations are also observed at lower periods, especially at a period of around 3 h at the Sète station. This period corresponds to a higher-order natural mode of the western Mediterranean basin, but this resonance seems to be essentially linked to the presence of the Gulf of Lion, whose shallowness and the width of the shelf at this point induce a resonance. Other oscillations are also observed at lower periods (T = 1.5 h at station Fos-sur-Mer, T = 45 min in the Toulon harbour station), due to more local forcing.