Geoscience Reference
In-Depth Information
wave of trapezoidal shape, the polarity of which coincides with the polarity of
the seabed displacement. In the case of a membrane-like displacement a bipolar
wave arises that comprises a crest and a trough. We shall present the formulae relat-
ing the main parameters of waves and the characteristics of a displacement:
•
Wave amplitude in the case of piston-like displacement
1
/
2
,
τ
∗
2
,
A
1
max
=
η
0
(2.78)
τ
∗
,
τ
∗
>
2
,
1
/
•
Crest and trough amplitude in the case of membrane-like displacement
1
/
2
,
τ
∗
4
,
A
2
max
=
A
2
min
=
η
0
(2.79)
τ
∗
,
τ
∗
>
4
,
2
/
•
Wave energy (We consider total energy of waves propagating in both positive
and negative directions of the O
x
axis) in the case of piston-like displacement
1
−
τ
∗
/
6
,
τ
∗
2
,
2
0
W
1
=
a
g
ρη
(2.80)
τ
∗
−
τ
∗
)
2
,
τ
∗
>
2
,
2
/
4
/
3(1
/
•
Wave energy in the case of membrane-like displacement
⎨
τ
∗
/
3
τ
∗
≤
2
,
4
/
3
(
τ
∗
/
2)
−
2
/
3
3
2
0
τ
∗
/
3
τ
∗
/
2)
1
/
3
τ
∗
≤
W
2
=
a
g
ρη
(2.81)
−
−
(
,
2
<
4
,
⎩
τ
∗
)(1
τ
∗
)
,
τ
∗
>
4
.
(8
/
−
2
/
•
Period of wave perturbation for piston-like and membrane-like displacements
τ
∗
)
(g
H
)
1
/
2
T
1
=
T
2
=
a
(2 +
,
(2.82)
•
Wavelength of perturbation for piston-like and membrane-like displacements
τ
∗
)
.
λ
1
=
λ
2
=
a
(2 +
(2.83)
τ
∗
=
a
(g
H
)
1
/
2
. Below, we shall make use of dimensionless time, determined by a similar
formula,
t
∗
=
The formulae presented contain the dimensionless displacement duration
t
a
(g
H
)
1
/
2
. The energy of the wave (per unit 'channel' width) was
calculated by the Kajiura formula [Kajiura (1970)]:
