Geoscience Reference
In-Depth Information
C
D
C
D
C
(a)
(b)
C
C
Fig. 4.14 Model shape of perturbation (cavity), resulting from a meteorite falling into the ocean.
D
C
—depth of cavity,
R
C
and
R
D
—internal and external radii of the cavity (Adapted from [Ward,
Asphaug (2000)])
(
D
C
R
D
)
2
1
,
R
D
R
C
R
D
3
R
C
E
T
=
πρ
w
g
2
−
+
(4.37)
ρ
w
is the density of water, g is the acceleration of gravity. When
R
D
=
R
C
√
2,
the general formula (4.37) assumes the more simple form
where
E
T
=
πρ
w
g
3
(
D
C
R
C
)
2
.
(4.38)
of the meteorite's kinetic energy
E
I
is transformed into
the tsunami energy, so we can write
Only a fraction
ε
/
3)
R
I
V
I
2
ε
ρ
I
(4
π
E
T
=
ε
E
I
=
,
(4.39)
ρ
where
I
,
R
I
and
V
I
are the meteorite density, radius and velocity, respectively. The
part of the meteorite energy transferred to the tsunami is not, generally speaking,
a constant, but depends on the properties of the water column and of the falling
body.
Comparison of expressions (4.38) and (4.39) permits to express the depth of
the cavity as follows:
D
C
=
2
1
/
2
I
R
I
V
I
ρ
w
g
R
C
ερ
.
(4.40)
We further assume the relationship between the depth of the cavity and its radius
to be of the form
D
C
=
qR
C
,
(4.41)
where
q
and
are coefficients related to the properties of the meteorite and of
the water column. Substitution of relation (4.41) into formula (4.40) permits to ex-
press the radius of the cavity as follows:
α
1
/
3
⎛
⎝
2
δ
⎞
⎠
,
1
/
3
−
δ
1
qR
α
−
1
I
R
C
=
R
I
2
δ
ρ
I
ρ
w
ρ
w
ρ
I
V
I
g
R
I
ε
(4.42)
