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Fig. 3.5 Profiles of surface displacement of a liquid at moment of time t = 10 for different propaga-
tion velocities of the running displacement, v . The thick and thin lines correspond to incompressible
and compressible liquids, respectively
( x ),for
the time moment t = 10, calculated within the framework of models for compress-
ible and incompressible liquids for three displacement propagation velocities, v = 4,
8 and 16. In all cases, an account of the compressibility led to a significantly more
subtly structurized perturbation of the surface, differing from zero only at those
points, at which the elastic wave, formed by the running displacement, had time
to arrive. As it is seen from the figure, when v = 4, the differences between free-
surface perturbations for compressible and incompressible liquids is not so large,
but in the case of high velocities the difference becomes quite significant. When
v
Figure 3.5 presents displacement profiles of the surface of a liquid,
ξ
c , the profile is characterized by the presence of steep fronts and of an original
periodic structure, which is a consequence of multiple reflections from the surface
and from the ocean bottom of the front of the elastic wave, formed by the front edge
of the running displacement. From mathematical physics it is known that, when an
elastic wave is reflected from a free surface, it changes polarity. Thus, for this reason
positive and negative fronts alternate.
The results of calculations of time evolvents
( t ) for the centre of the active zone
( x = 5) are presented in Fig. 3.6. The main feature, distinguishing the behaviour of
a compressible liquid, consists in the rise in the source area of surface oscillations
with a prevalent period equal to four. Oscillations take place against the background
of a developing slower gravitational wave. The rise of surface oscillations is due
ξ
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