Geoscience Reference
In-Depth Information
distance
x
= 1
.
86 km from the coast, and here the Froud number Fr
max
= 0
.
61 turns
out to reach its maximum at a distance
x
= 0
.
95 km, i.e. much closer to the coast.
From the figure it is seen that the Froud number rapidly reaches its maximum along
the initial length of sliding down and gradually decreases as the landslide reaches
the gently sloping bottom. Ultimately, the landslide stops, when its potential en-
ergy has already been spent on friction and wave generation. The 'path length' of
a solid landslide depends directly on the friction coefficient; thus, for
k
= 0
.
05,
0.10, 0.15 and 0.20 the 'path length' amounts, respectively, to
x
s
= 5
.
19, 3.13, 2.29
and 1.58 km.
When
k
<
0
.
15, the velocity of motion and the Froude number for a solid land-
slide exceed the velocity of motion of the front of a viscous flow everywhere. Here,
the 'path length' of the viscous landslide amounts to 1.6 km.
We draw attention to the velocity of motion of underwater landslides being, as
a rule, smaller, than the velocity of long gravitational waves (i.e. Fr
<
1). This fact
follows from elementary physical arguments. If the motion of a landslide is consid-
ered without account of the wave resistance and of friction (
k
= 0), then its velocity
is determined by the formula
U
=
2g
ρ
2
−
ρ
1
ρ
∆
h
,
(4.6)
2
where
h
is the change in vertical position of the centre of mass of the landslide.
Suppose that, going down the slope, the landslide reaches a certain depth
h
. Clearly,
for an underwater landslide the inequality
∆
h
<
h
is always satisfied. Comparing
the veloci
ty
of the landslide, determined by formula (4.6), and the velocity of long
∆
waves,
√
g
h
, it is not difficult to arrive at the conclusion that equality of these
two quantities is possible, only if
2
>
2
.
0g/cm
3
, i.e. for well-consolidated sedi-
ments and rock. If the force of friction is taken into account, the required density
of the landslide body will be even greater. Thus, a 'resonance' (Fr = 1) is possible
only for landslides, consisting of very dense materials, or when the landslide enters
the water with a certain initial velocity. In the latter case, one can speak of both
subaerial (partially submerged) landslides and of landslides sliding into water from
a 'dry' coastal slope.
ρ
4.2 Tsunami Excitation Related to Volcanic Eruptions
Explosions of volcanic islands (collapses of calderas), explosive (explosion-like)
eruptions of underwater volcanoes and pyroclastic flows landing in water, all these
phenomena are capable of giving rise to waves, which in their destructive strength
are in no way inferior to tsunamis of seismotectonic origin. At present, 66 tsunamis
of volcanic origin are known merely in the Pacific region, and in 10 of the events
wave heights amounted to 10 m and more (up to 55 m).
