The effects of frequency dispersion in tsunami simulation
Ling-Wan Liao
Abstract
Shallow water wave model is usually used on numerical tsunami simulation. But it can only use when the water depth divided by the wave length is smaller than 0.05 which is called dispersion coefficient. That means when using shallow water wave model to do numerical simulation on tsunami, it ignores the effects of frequency dispersion. So what¡¦s the affection of frequency dispersion in tsunami simulation?
I choose two examples, both of them use two models to check the different results which consider about dispersion term or not; one is Boussinesq model (considered about dispersion term) and another is nonlinear shallow water model (not considered about dispersion term.) The first example is an earthquake tsunami, 2004 Indian Ocean Tsunami. The comparison shows that for practical purpose the NLSW model results are quite reliable because of its low computational cost, maximum wave height, and often overpredicted runup. But the dispersion consideration in the numerical model is necessary for accurate coastal runup prediction. And another example is a submarine landslide tsunami, 1998 Papua New Guinea Tsunami. For this case, dispersion term is not such important in predicting the inundation height, but it¡¦s due to the depth-limited wave breaking, it¡¦s a site-specific phenomena. That indicated that cannot be used as justification to apply it to a future landslide tsunami cases.
Thus, nonlinear shallow water wave model is a reliable model for using on tsunami warning because of its efficiently calculation, but if consider about runup and inundation heights, dispersion term cannot be ignored. It can help for predicting accurate coastal runup.
Reference
P. Lynett, J. Borrero, P. L.-F. Liu, and C. E. Synolakis (2003), Field Survey and Numerical Simulations: A Review of the 1998 Papua New Guinea Tsunami, Pure Appl. Geophys., 160, 2119-2146.
J. Horrillo, Z. Kowalik, Y. Shigihara (2006), Wave Dispersion Study in the Indian Ocean-Tsunami of December 26, 2004, Marine Geodesy, 29:149-166.
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