COMMUNICATIONS IN COMPUTATIONAL PHYSICS

Abstract. This article develops a new, granular approach to tsunami runup and in-undation. The small grains employed here are not fluid, but bits, or balls, of tsunami energy. By careful formulation of the ball accelerations, both wave-like and flood-like behaviors are accommodated so tsunami waves can be run seamlessly from deep wa-ter, through wave breaking, to the final surge onto shore and back again. In deep water, tsunami balls track according long wave ray theory. On land, tsunami balls be-have like a water landslide. In shallow water, the balls embody both deep water and on land elements. In modeling several 2-D and 3-D cases, we find that wave breaking generally causes relative runup to increase with beach slope and wave period and de-crease with input wave amplitude. Because of their highly non-linear nature, runup and inundation are best considered to be random processes rather than deterministic ones. Models and observations hint that for uniform input waves, normalized runup statistics everywhere follow a single skewed distribution with a spread between 1/2 and 2 times its mean. AMS subject classifications: 76B15 Key words: Water wave, tsunami, run up