Geoscience Reference
In-Depth Information
Fig. 3.27 Profiles of gravitational waves formed by a 'non-linear source'. Curves 1-8 are cal-
culated for consecutive moments of time separated by intervals of 100 s. The source parameters:
τ
= 8s,
L
= 40 km,
H
= 4km
Figure 3.27 presents typical profiles of surface waves, formed by a 'non-linear
source'. The action of this source leads to water being 'pushed out' of the source
area, therefore, the waves always originate with a positive phase and finish with
a negative phase.
From the profiles of the formed waves calculation was performed of the
amplitude
Max
x
∗
ξ
∗
)
A
N
=
v
2
max
g
v
2
max
g
ξ
∗
)
A
∗
(
τ
∗
,
L
∗
)
,
−
≡
(
Min
x
∗
(
(3.78)
and of the energy.
∞
H
g
−
1
v
4
max
2
d
x
∗
≡
ρ
H
g
−
1
v
4
max
W
∗
(
τ
∗
,
L
∗
)
.
W
N
=
ρ
ξ
(3.79)
−
∞
The result of calculations carried out for various durations of piston-like dis-
placements,
c
/
H
,
L
∗
=
L
/
H
), were dimensionless
functions of the dimensionless arguments
A
∗
(
τ
∗
, and source sizes
L
∗
τ
∗
=
(
τ
τ
∗
,
L
∗
).
Non-linear effects can, obviously, provide a noticeable contribution to a tsunami
wave only in the case of sufficiently high velocities of the ocean bottom deforma-
tion, which is equivalent to displacements of small durations. Therefore, in calcula-
tions we only dealt with the range of
τ
∗
,
L
∗
) and
W
∗
(
<
8
H
/
c
. From the point of view of tradit
ion
al
ideas, such displacements can be considered instantaneous (
τ
L
/
√
g
H
);
in the case of an instantaneous displacement, on the water surface an initial elevation
is formed, which repeats the shape of residual deformations of the ocean bottom.
Precisely, the evolution of this elevation generates tsunami waves in their classi-
cal sense. We shall term such a tsunami generation mechanism linear. The tsunami
amplitude formed by the linear mechanism can be estimated as the amplitude of
residual deformations of the ocean bottom,
τ
= 8
H
/
c
