On the Resonance Hypothesis of Tsunami and Storm Surge Runup

Abstract. Resonance has recently been proposed as the fundamental underlying mechanism that shapes the amplification in coastal runup for both Tsunamis and storm surges. It is without doubt that the resonance plays a rôle in runup phenomena of various kinds, however we think that the extent at which it plays its role has not been completely understood. For incident waves, the best approach to investigate the rôle played by the resonance would be to calculate the normal modes by taking radiation damping into account and then test how those modes are excited by the incident waves. There are a small number of previous works that attempt to calculate the resonant frequencies but they do not relate the amplitudes of the normal modes to those of the incident wave. This is because, by not including radiation damping, they automatically induce a resonance that leads to infinite amplitudes, thus preventing them from predicting the exact contribution of the resonance to coastal runup. In this study we consider two different coastal geometries: an infinitely wide beach with a constant slope connecting to a flat-bottomed deep ocean and a bay with sloping bottom, again, connected to a deep ocean. For the fully 1-D problem we find significant resonance if the bathymetric discontinuity is large. For the 2-D ocean case the analysis shows that the wave confinement is very effective when the bay is narrow. The bay aspect-ratio is the determining factor for the radiation damping.