Commun. Comput. Phys.,
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Volume 3.


Tsunami Balls: A Granular Approach to Tsunami Runup and Inundation

Steven N. Ward 1*, Simon Day 1

1 Institute of Geophysics and Planetary Physics, University of California, Santa Cruz, CA 95064, USA.

Received 2 January 2007; Accepted (in revised version) 6 June 2007
Available online 14 September 2007

Abstract

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 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 water, 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 behave 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 decrease 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

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Key words: Water wave, tsunami, run up.

*Corresponding author.
Email: ward@pmc.ucsc.edu (S. N. Ward), simonday_ucl@yahoo.co.uk (S. Day)
 

The Global Science Journal