Numerical modeling of waves for a tsunami early warning system

Numerical modeling of waves for a tsunami early warning system
model results and black solid lines those of the numerical model. An overall
agreement is achieved in terms of wave height and wave period. From the
free surface elevation comparison it can be recognized a first wave train,
that in the numerical simulation is longer (until the 13 rd and 16 th second)
followed by irregular waves (bigger for the physical experiments) which are
due to wave reflection. The first wave crest is slightly underestimated by
the numerical model, this could be due by having approximated a gaussian
landslide model, which enters into the water more smoothly.
ηR1 (m)
ηR2 (m)
20
10
0
−10
−20
0 5 10 15 20
20
10
0
−10
−20
0 5 10 15 20
t(s)
aFourier
aFourier
x 104
4
3
2
1
0
0 1 2 3
x 104
4
3
2
1
0
0 1 2 3
f (Hz)
Figure 4.21: Comparison of the experimental data (red dashed line) and the
numerical one (black solid line)
From the wave energy spectra (right panels) it can be noted that the peak
frequency is about 0.5-0.6 Hz, corresponding to a peak period of about 1.5-2
s, and that the most part of the wave energy content is distributed along
frequencies smaller than 3 Hz. Thus the numerical model was run just for
frequencies up to 3 Hz.
The same results of the numerical model are now compared with the
results of the analytical model of Sammarco & Renzi, (2008). In their model
the landslide shape and kinematics is equal to the numerical one, but the
wave propagation is approximated with the shallow water theory. The figure
4.22 shows the free surface elevation estimated with the analytical model
(thin black lines) and with the numerical one (thick black lines).
Università degli Studi di Roma Tre - DSIC 66