Tsunami Balls: A Granular Approach to Tsunami Runup and Inundation (Communications in Computational Physics, 2008)
This article develops a new, granular approach to tsunami runup and inundation. The small grains employed here are not fluid, but bits, or balls, of tsunamienergy. By careful formulation of the ball accelerations, both wave-like and flood-likebehaviors are accommodated so tsunami waves can be run seamlessly from deep water, through wave breaking, to the final surge onto shore and back again. In deepwater, tsunami balls track according long wave ray theory. On land, tsunami balls behave like a water landslide. In shallow water, the balls embody both deep water andon land elements. In modeling several 2-D and 3-D cases, we find that wave breakinggenerally causes relative runup to increase with beach slope and wave period and decrease with input wave amplitude. Because of their highly non-linear nature, runupand inundation are best considered to be random processes rather than deterministicones. Models and observations hint that for uniform input waves, normalized runupstatistics everywhere follow a single skewed distribution with a spread between 1/2and 2 times its mean.