Bay and harbor resonances are investigated in this work, taking into account the variable bathymetry of the semi-enclosed basin. The Modified Mild-Slope (MMS) equation is implemented for the description of combined refraction-diffraction effects, from which the eigenperiods and eigenmodes are calculated by means of a low-order Finite Element Method (FEM scheme). The model is first applied to a coastal-port region of Toulon, France, illustrating the versatility of the model to easily include coastal structures such as detached breakwater. Next, the present model is applied to the extended nearshore area of Toulon including the Gulf of Giens showing the applicability of the developed MMS-FEM model for the estimation of harbor and bay resonances, as well as more extended nearshore regions where variable bottom topography effects become important. The calculated resonant frequency depends on the domain characteristics and the size of the open sea boundary and accurately reproduces the measurements within Toulon Bay. On the other hand, for open bays such as the Gulf of Giens, a discrepancy is observed between calculated and measured eigenperiods which is due to a very wide opening of the sea boundary that cannot accurately describe the seiching. This underlines the difficulty of accurately calculating the resonance frequency for open bays, in contrast to the classic studies carried out for ports, which are considered virtually closed basins, and confirms the complementary nature of long-term water level measurements and numerical calculations, for better quantification of the risks associated with energetic meteorological and/or oceanographic events.
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