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s
s
s
Fig. 4 .9 P rofile of waves excited by underwater eruption. The calculation is performed for t =
100 H / g for two different ratios of the initial perturbation radius and the ocean depth, R S / H
(the values are indicated in the figure)
2
k 0 A ( k 0 ) J 0 ( k 0 r ) cos
,
π
4
( r , t ) =
ξ
ω
( k 0 ) t
(4.15)
t
|
S ( k 0 )
|
where k 0 is the extremum of function S ( k )= g k tanh( kH )
kx / t , which exists
under the condition x < t g H .
As an example, Fig. 4.9 shows the profiles of waves generated as a result of
evolution of the initial perturbation (4.1 1). T he calculation is performed by formula
(4.15) for the moment of time t = 100 H / g for two different radii of the initial per-
turbation. The waves are seen to be strongly dispersive, therefore, the propagation
velocity of the wave packet depends strongly on the radius of the initial perturbation.
The existence of such a dependence leads to an interesting effect (dispersion ampli-
fication), which was first noted in [Mirchina, Pelinovsky (1987)]. Consider two or
more successively amplified eruptions taking place. The radius R S of the perturba-
tion created on the water surface increases with the strength (energy) of the eruption.
In accordance with the growth of the radius the propagation velocity of the wave
packet also increases. Consequently, during the process of wave propagation the su-
perposition is possible of wave packets from different eruptions, which may lead to
significant amplification of the tsunami amplitude. We recall that in August 1883,
three eruptions occurred of the Krakatau volcano, each of which was stronger than
the preceding one.
4.3 Meteotsunamis
Long waves, similar in characteristics to tsunami waves of seismotectonic origin,
can be formed as a result of the influence of various atmospheric processes upon
the water layer. These waves are conventionally termed anemobaric waves or me-
teotsunamis. The term 'meteotsunami' was apparently coined in [Nomitsu (1935)].
The main causes for meteotsunamis to arise are moving inhomogeneities of
the atmospheric pressure or the tension of wind friction. We at once note that, unlike
 
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