Geoscience Reference
In-Depth Information
ν
min
. At small oscillation frequencies of the ocean bot-
tom (which also corresponds to small values of
k
0
), expression (2.102) is essentially
simplified and assumes the following form:
A
(
We shall now determine
ω
)=
η
0
a
ω
. Thus, the quantity
ν
min
a
)
−
1
. Passing to dimensional quantities, we obtain
the following formulae for the limits of the tsunami frequency spectrum:
can be estimated as
ν
min
∼
(20
π
0
.
3
g
H
1
/
2
ν
max
∼
,
(2.103)
(g
H
)
1
/
2
20
ν
min
∼
.
(2.104)
π
a
The lower frequency limit is seen to be related both to the ocean depth and to
the horizontal dimension of the source, while the upper limit only to the depth.
For a depth
H
10
3
m and size of the source equal to
a
10
4
m we obtain
∼
∼
10
−
4
Hz. The spectrum of real tsunami waves lies precisely
within these limits [Murty (1977); Pelinovsky (1996)].
The theoretical dependence (2.102) has been tested experimentally [Nosov,
Shelkovnikov (1992)]. Use was made of the set-up shown in Fig. 2.16. The pneu-
matic generator, 30 cm long, simulated harmonic oscillations of an area of the ocean
bottom. Practically, all the remaining parts of the hydrocanal were occupied by
the wave-damping system representing a gentle slope covered with a plastic mesh.
The wave was registered by the IR wavegraph at a distance of 10 cm from the bound-
ary of the generation area. The results of experiments and of theoretical calculations
for three different water depths in the hydrocanal are presented in Fig. 2.28. The
experimental data are seen to comply with the theoretical dependence.
10
−
2
Hz,
ν
∼
ν
min
∼
max
2.4 Generation of Tsunami Waves and Peculiarities
of the Motion of Ocean Bottom at the Source
In this section we shall deal with the space (3D) problem of tsunami generation by
ocean bottom displacements. Transition from plane (2D) models to the more real-
istic three-dimensional problem makes it possible to investigate the most important
issue of the orientation of wave emission and of its relation to parameters of
the source. The effect of oriented emission of tsunami waves from the source area
can be due to various reasons, which are usually considered to comprise the geomet-
rical shape of the deformation area of the ocean bottom, the transfer of horizontal
momentum to masses of water, and the wave-guide properties of the bottom relief
[Voight (1987); Dotsenko, Soloviev (1990)]. The last reason, generally speaking,
is related to the tsunami propagation, and not to wave generation. The orientation
of tsunami emission, due to source asymmetry, has been studied theoretically [Ka-
jiura (1963, 1970); Dotsenko et al. (1993)], experimentally [Takahasi (1963)] and
numerically [Marchuk, Titov (1993)].
