The combined role of bay and shelf modes in tsunamis amplification along the coast

The role of free-modes of oscillation of coastal-areas in tsunami amplification at the coast is investigated here. A finite element numerical model for modal analysis was applied and the numerically calculated natural frequencies were compared to those resulting from the spectra of actually measured sea-level time series. Two case studies have been selected: that of Poverty Bay (New Zealand); and that of Kuluk Bay (Adak Island, Alaska, USA). The natural-modes of the sea-areas that extend in front of these locations are shown to play an important role in tsunami amplification at both the considered bays. In-fact, the enhancement of wave height is found to be related to both the small-scale resonance controlled by the coastal shape, and the large-scale one governed by the continental-shelf bathymetry. In particular, the application to Poverty Bay reveals that some of the continental shelf modes are more energetic and occur at frequencies higher than the bay fundamental one. These modes are identified as both cross-shelf modes and trapped edge-waves. On the other hand, the application to Kuluk Bay shows that geographical entrapment can be relevant for chain islands, making the bay and the continental-shelf modes almost coincident.