Geoscience Reference
In-Depth Information
2
4
π
λ
L
3
=
2
D
.
(5.28)
2
α
Applying expression (5.28), we shall perform a simple estimation showing
the negligible role of wave scattering by small-scale irregulartities of the ocean
bottom. Let the tsunami wave length be 100 km and the ocean depth 4 km. Then,
if the obstacle has a width
D
= 1 km and is 100 m high, then the quantity
L
3
will amount to 6
.
5
10
9
m, which is equivalent to over 160 lengths of the Earth's
·
equator.
5.2 Numerical Models of Tsunami Propagation
The headlong development of computational technologies, taking place in recent
decades, has opened up new possibilities for numerical studies of problems of
the mechanics of continuous media (MCM). The necessary computational facilities
are now available to a wide range of researchers.
Description of tsunami evolution from the moment of generation to arrival of
the wave on the shore represents one of the tasks of MCM. The application of ana-
lytical models for describing real tsunamis is limited, even if only for the complex
topography of the ocean bottom. The only obvious alternative consists in numerical
modelling. The efficiency of such means for studying tsunamis has long been unani-
mously acknowledged by the scientific community. Hopes of resolving the problem
of tsunami prediction are also to a great extent related to the development of numer-
ical models.
The 'age' of numerical simulation of real tsunamis started at the end of the 1960s.
The first works in this direction were performed by Japanese researchers [Aida
(1969), (1974); Abe (1978), (1979)]. One of the first numerical models developed
in Russia was described in [Gusyakov, Chubarov (1982), (1987)] and [Chubarov et
al. (1984)].
As a rule, numerical tsunami models are based on the theory of long waves (in
shallow water), which deals with the equations of hydrodynamics, averaged over
the vertical coordinate. Within the theory of long waves, the total three-dimensional
(3D) problem reduces to the two-dimensional (2D) one, numerical resolution of
which requires a relatively small volume of calculations.
The simulation of tsunami propagation at transoceanic scales within the com-
plete 3D model is not only impossible, at present, but also obviously irrational. The
resolution of such a 3D problem is only of purely scientific, but not practical, inter-
est. The point is that in most cases tsunami wave propagation is quite satisfactorily
described by the linear theory of long waves. Taking into account the insignificant
manifestations of phase dispersion and non-linearity, which are peculiar to tsunami
waves, can also be done within the framework of long-wave non-linear-dispersion
models [Pelinovsky (1996); Satake, Imamura (1995); Rivera (2006); Horrillo et al.
(2006)].
