Hydrodynamic Characteristics Present in Nonlinear Long Wave Amplification in the Shadow Zone of Offshore Islands

Abstract

Post-tsunami surveys on South Pagai Island in Indonesia (part of the Mentawai Island chain) after the 25 October 2010 tsunami revealed enhanced inundation on the portion of the island coastline in the shadow of Sibigau Island, a 3.2 km long island located 5 km offshore. This amplification of inundation contradicts a widely held local belief that offshore islands can serve as a shield from tsunamis or storm waves. This finding has been the focus of several modeling studies, including a series of laboratory studies conducted at Oregon State University. The characteristics of runup amplification (RA) seen in the Oregon State experiments were investigated using the FUNWAVE-TVD Boussinesq model and a non-hydrostatic wave model (NHWAVE). The model simulations reveal that the maximum runup height on the shoreline in the shadow zone of the island tends to be inversely proportional to distance from the beach to the island (DOI). In addition, FUNWAVE-TVD was used to relate the RA in the shadow zone to the hydrodynamics (specifically, the lateral velocities). The three-dimensional model NHWAVE was further used to help elucidate the runup processes for the Error-Function (ERF) wave representing a long-transient tsunami wave, which (unlike the solitary wave) is not a canonical wave form with analytically-described properties. The NHWAVE model results showed improvement in predicting RA for ERF wave in comparison with FUNWAVE-TVD results. We developed a novel method of obtaining the effective frequency of ERF wave by an intuitive geometric method of integrating the frequencies of successive sech2 waves. As a result of applying the effective frequency obtained in such way to surf similarity for ERF waves, the runup statistics for the ERF wave are equivalent to the runup trends of the solitary wave. We found that the energy and energy-flux density of the furthest DOI case is 10 [tilde] 25 % higher than that of the second nearest DOI case. Furthermore, we discuss the mechanism by which the amplified energy for the furthest DOI case is increased and maintained in the shadow zone, resulting in a higher inundation area on the beach than that of the second nearest DOI case. We investigate how the RA changes as water depth increases. The increased water depth clearly increases the inundation area in the shadow zone by increasing not only the “width” of the RA profile but also the maximum peak of the ratio of amplified runup profile.