Geoscience Reference
In-Depth Information
Dependence of the tsunami wave propagation velocity on the depth renders these
waves sensitive to the shape of the sea-floor. Effects peculiar to tsunamis include
the capture of wave energy both by underwater ridges and by the shelf, focusing
and defocusing exhibited when waves propagate above underwater elevations and
depressions. Irregularities of the sea-floor lead to the scattering of tsunami waves.
Actually, the propagation velocity of gravitational waves does not depend only
on the depth, but on the wavelength, also. The formula presented above for the ve-
locity
of long waves
is the limit case (for
λ
H
) of the more general expression
c
=
gtanh(
kH
)
/
k
, where
k
= 2
. Wave dispersion results in transformation of
the initial perturbation into a wave packet, with the most rapid long waves leading.
Note that this effect is manifested in the case of tsunami wave propagation over quite
extended routes (1,000 km or more). Dispersion, resonance properties of the coastal
relief, phenomena such as reverberation (i.e. when the wave perturbation reaches
a certain coastal site via different routes) and the peculiarities of wave formation
at the source, all these, as a rule, result in a tsunami being manifested not as a soli-
tary wave, but as a series of waves with a period amounting to tens of minutes. In
this case, the first wave is often not the strongest. The absence of knowledge of pre-
cisely this property of tsunami waves often leads to human casualties, which could
have been avoided.
The tsunami wave amplitude increases as it approaches the coast—which to a
great extent is what determines the danger of these waves, is also related to the re-
lief of the sea-floor. A decrease in the water depth leads to a decrease in the wave
propagation velocity and, consequently, to compression of the wave packet in space
and an increase of its amplitude. In the case of catastrophic tsunamis the run-up
height reaches 10-30 m, while the wave is capable of inland inundation (runin) of
3-5 km from the coastline. A scheme of the tsunami onshore run-up, explaining
the main parameters of this process, is shown in Fig. 1.3. Note that the maximal
wave height can be achieved at the shoreline, at the inundation boundary or at any
point in between them.
π
/
λ
Fig. 1.3 Scheme of tsunami onshore run-up. Adapted from [UNESCO-IOC. Tsunami Glossary
(2006)]
