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recently. Such an approach was first proposed in [Jiang, LeBlond (1992), (1994)].
Numerical methods, based on this approach, were successfully applied in analysing
landslide tsunamis in Nizza of 1979 [Assier-Rzadkiewicz et al. (2000)], in Skag-
way Harbour of 1994 [Fine et al. (1998); Rabinovich et al. (1999)], in Papua New
Guinea of 1998 [Heinrich et al. (2000); Titov, Gonzalez (2001); Imamura et al.
(2001)]. In these studies, it was shown that the notion of a landslide in the form of
a flow of a heavy viscous fluid provides reasonable agreement with data of in situ
observations.
The version of the model described here is based on [Jiang, LeBlond (1994)]
and [Fine et al. (1998)]. We shall consider the horizontal scales of surface waves to
significantly exceed the basin depth, and the thickness of the landslide to be much
smaller than its width and length. In this case it is possible to apply the longwave
(hydrostatic) approximation both in the case of water and in the case of the fluid
forming the landslide. The Coriolis force is usually neglected in such problems.
The scheme of the model is presented in Fig. 4.1. The origin of the Cartesian ref-
erence system 0
xyz
is placed on the unperturbed free surface, the 0
z
axis is directed
vertically upward. The upper layer of water has a density
ρ
1
, a free-surface displace-
ment
(
x
,
y
,
t
), u is the horizontal velocity vector with components
x
and
y
;
t
is time.
The lower layer (the landslide body) has a density characteristic of sedimentary de-
posits,
η
ρ
ν
is the kinematical viscosity and U is the horizontal velocity vector
of the fluid in the lower layer with components
U
and
V
. The slope of the ocean
bottom and the landslide surface are considered small, so that the fluid can be con-
sidered to undergo purely horizontal movement. The landslide body is limited by
the bottom surface
z
=
2
,
−
h
(
x
,
y
,
t
), while its upper surface is given by its thickness
D
(
x
,
y
,
t
)=
h
s
(
x
,
y
)
h
(
x
,
y
,
t
).
The main assumptions concerning landslide properties, substantiated in [Jiang,
LeBlond(1992), (1994)], are adopted in the form:
−
1. A landslide consists of an incompressible viscous fluid, and the sea water is con-
sidered an incompressible liquid of zero viscosity.
2. The difference between the density of the landslide and the density of water must
be large, (
0
.
2g/cm
3
.
3. The flow of a viscous fluid is laminary and quasistationary. For describing
the movement of a viscous fluid over an underwater slope it is, generally
ρ
2
−
ρ
1
)
Fig. 4.1 Geometry of
the model: reference sys-
tem and notation. The shaded
part shows the body of a vis-
cous landslide. Adapted from
[Rabinovich et al. (2003)]
