Geoscience Reference
In-Depth Information
(a)
(b)
Fig. 2.30 Time-base of waves caused by piston-like displacement. Calculations are performed at
points lying on a circle of radius
r
= 10 (a) and
r
= 30 (b) with its centre at the origin of the ref-
erence frame, for azimuthal angles
α
= 0
,
30
,
60
,
90
◦
(curves 1—4, respectively). The parameters
of the bottom displacement:
a
= 1
,
b
= 5
,
τ
= 1 (a) and
a
= 3
,
b
= 15
,
τ
= 1 (b)
frame. Examples of such time-bases are presented in Fig. 2.30. The azimuthal angle
was counted off from the positive direction of axis 0
x
. From the wave time-bases
amplitude characteristics were determined, and the energy was estimated by the for-
mula proposed in [Kajiura (1970)],
T
g(g
H
)
1
/
2
2
(
t
) d
t
d
W
=
ρ
ξ
γ
.
(2.113)
γ
0
Formula (2.113) yields the energy that passed through the contour
γ
in time
T
.
In our case, the contour
γ
was chosen to be the segment of a circle of radius r,
0
.
The quantity
W
0
corresponds to the potential energy of the initial free-surface ele-
vation, exhibiting the shape of the residual bottom displacement.
Figure 2.31 presents, in the form of directional diagrams, the dependences of
the amplitude of the first crest
A
1
(a, b), of the 'maximum span'
A
max
−
A
min
(c, d),
and of the wave energy
W
α
(e, f) upon the azimuthal angle. Calculations are per-
formed for piston-like and running displacements, the durations of which are cho-
sen so as to satisfy the relationship
= 10
◦
. Energy values were normalized to the quantity
W
0
= 2
given
∆α
ρ
gab
η
= 2
av
−
1
. Thus, the process of wave exci-
tation can be investigated by varying the parameter, common to both piston-like
and running displacements, namely, the duration of the process in the active area.
The dotted line in the figure shows the shape and orientation of the active area.
From Fig. 2.31 the orientation is seen to be manifested most weakly for the ampli-
tude of the first crest. The evolution of directional diagrams differs essentially for
τ
