Run-up from impact tsunami

Abstract

We report on calculations of the on-shore run-up of waves that might be generated by the impact of subkilometre asteroids into the deep ocean. The calculations were done with the COULWAVE code, which models the propagation and shore-interaction of non-linear moderate- to long-wavelength waves (kh < π) using the extended Boussinesq approximation. We carried out run-up calculations for several different situations: (1) laboratory-scale monochromatic wave trains onto simple slopes; (2) 10–100 m monochromatic wave trains onto simple slopes; (3) 10–100 m monochromatic wave trains onto a compound slope representing a typical bathymetric profile of the Pacific coast of North America; (4) time-variable scaled trains generated by the collapse of an impact cavity in deep water onto simple slopes and (5) full-amplitude trains onto the Pacific coast profile. For the last case, we also investigated the effects of bottom friction on the run-up. For all cases, we compare our results with the so-called ‘Irribaren scaling’: The relative run-up R/H0 = ξ = s(H0/L0)−1/2, where the run-up is R, H0 is the deep-water waveheight, L0 is the deep-water wavelength, s is the slope and ξ is a dimensionless quantity known as the Irribaren number. Our results suggest that Irribaren scaling breaks down for shallow slopes s ≤ 0.01 when ξ < 0.1 − 0.2, below which R/H0 is approximately constant. This regime corresponds to steep waves and very shallow slopes, which are the most relevant for impact tsunami, but also the most difficult to access experimentally.