Numerical modeling of waves for a tsunami early warning system

aFourier
filter functions
aFourier
Numerical modeling of waves for a tsunami early warning system
1
0.5
0
0 0.5 1 1.5 2
1
0.5
short landslide
(a
0
0 0.5 1 1.5 2
1
0.5
(c
0
0 0.5 1 1.5 2
f (Hz)
(e
1
0.5
long landslide
(b
0
0 0.5 1 1.5 2
1
0.5
(d
0
0 0.5 1 1.5 2
1
0.5
(f
0
0 0.5 1 1.5 2
f (Hz)
Figure 4.13: Panels a and b: absolute values of the Fourier transform
coefficients of the water surface elevations at point A, computed with the
three dimensional model (thin black line) and with the depth integrated
model, without any filter function (thick black line); panels c and d:
frequency filter (continuous black lines) and landslide filter (dashed red lines);
panels e and f: absolute values of the Fourier transform coefficients of the
water surface elevations at point A, computed with the depth integrated
model, with the frequency filter (continuous black lines) and with the
landslide filter function (dashed red line).
It is however clear that the presence of very high frequency waves is
easily detectable when using a frequency-dispersive model. These waves
would not appear so clearly when employing non-dispersive models. In
order to show this, simulations with the depth integrated model based on
the LSWE have been carried out, which lets each component to propagate at
the same celerity. In particular the same experiments were simulated soving
the following equations
∇h (gh∇hN)+ω 2 1
N = −
cosh (kh) fft(htt) (4.11)
Università degli Studi di Roma Tre - DSIC 58