Role of shelf geometry and wave breaking in single N-type tsunami runup under geophysical-scale

Over the last several decades, various analytical, numerical and experimental studies have reported that leading-depression N-type tsunamis could be more destructive than leading-elevation N-type tsunamis. However, in many analytical or experimental studies, the effects of shelf geometry and wave breaking under the geophysical scale, which are known to significantly affect tsunami evolution, have been ignored. Therefore, it is still unclear whether leading-depression tsunamis always result in more serious damage than leading-elevation tsunamis if earthquakes with the same magnitude occur at the same epicentre. Thus, this study investigated the runup and wave evolution characteristics of idealized leading-depression and leading-elevation tsunamis, particularly considering the effects of shelf geometry and wave breaking under the geophysical scale. Using a Boussinesq-type model for fully nonlinear, weakly dispersive, rotational and turbulent flow, the evolution of tsunami was simulated, and the energy and momentum of the tsunami were calculated. As a result, on steeply sloped bathymetry, the large momentum and potential energy induced during the rundown process of the leading-depression tsunami results in runup that was higher than that of the leading-elevation tsunami, which was consistent with the results of previous studies. Interestingly, the leading-depression tsunami resulted in a lower runup height on mild and long sloped bathymetry, in contrast to previous studies; this process originated from the energy dissipation caused by the wave breaking of the undular bore and the mass exchange occurring between the positive and negative waves.