Numerical modeling of waves for a tsunami early warning system

Numerical modeling of waves for a tsunami early warning system
In the work of Tadepalli & Synolakis (1996) it also appears that some
important features of the tsunamis propagation, such as the fact that the
first wave has a trough traveling in front of the crest, can be predicted by
using model equations that take into account the frequency-dispersion. They
proposed a model which assumes that the solitary wave like tsunami have
the shape of leading-depression N-wave. In the far propagation field they
solve the Korteweg-de Vries equations, while in the near shore field they use
LSWE. Intensification of the height of tsunamis waves can also be induced
by frequency dispersion, as suggested by Mirchin & Pelinovsky (2001).
The NLSWE however, although able of taking into account amplitudedispersion
(i.e. the nonlinear effects) of the waves, cannot reproduce
the frequency-dispersion, which as mentioned before may be of relevant
importance. When studying the propagation of these waves over large
geographical areas it is common that the height of tsunamis is several order of
magnitudes smaller than the water depth. The typical wave height of a large,
destructive tsunamis is of 1 m, while the water depth over which it propagates
may be of 100, 1000 m. The steepness of the waves is also extremely small,
since the length is of the order of the kilometers. This suggests that nonlinear
effects may be neglected or at least may be of secondary importance in
comparison to the proper reproduction of the frequency-dispersion. It is
worth to mention however that the above considerations mostly apply for
the far field and not in proximity of the coast (i.e. in very shallow waters),
where the nonlinear effects become important.
In the last decades the Boussinesq-type equations (Peregrine, 1967;
Madsen et al, 1991; Wei & Kirby, 1995; Nwogu, 1993) have therefore become
the most suitable model for the tsunamis simulation. These equations allow
the reproduction of wave nonlinearity, relevant in the coastal shallow areas,
but they take into account of a weakly frequency dispersion of water waves,
thus being able to simulate its propagation a bit further in the deep water
conditions. Several versions of this type of models are available. The
complexity of the model equations (and therefore the computational costs),
however grows with the increased ability of the models of reproducing the
nonlinear and the frequency-dispersive effects.
Watts and Grilli carried out research studies on tsunami generated by
landslides (Watts et al., 2003; Grilli et al., 2005). They build up GEOWAVE
which is a comprehensive tsunami simulation model formed by combining
the Tsunami Open and Progressive Initial Conditions Sytem (TOPICS),
for the wave maker and tsunami generation, with the FUNWAVE model
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