Geoscience Reference
In-Depth Information
meteotsunami consists in the difference between their maximum periods. The max-
imum period for a tsunami does not exceed several hours, while storm surges may
last several days.
Strong storm surges of heights up to 5 m are observed off the coast of China in
the northern part of the Yellow Sea. This phenomenon results in colossal calamities
for the Republic of Bangladesh—only during recent decades it has brought about
the death of several hundreds of thousands of people. Storm surges are also known
in Europe. The catastrophic storm surge that occurred in the North Sea in the period
between January 31 and February 2, 1953 destroyed protective coastal structures,
flooded an area of 25,000 km
2
and killed 2,000 people in Great Britain and Hol-
land [Gill (1982)]. The famous inundations of St. Petersburg are nothing, but storm
surges. Besides St. Petersburg, strong storm surges in Russia also take place off
the coasts of the Azov and Okhotsk seas, and the Sea of Japan.
The physical mechanism of meteotsunami formation can be related to the influ-
ence upon the water surface of atmospheric pressure and tangential tensions, cre-
ated by the wind. In principle, there exists, also, the possibility of non-linear energy
transfer from the relatively short wind (storm) waves to the longwave components,
but we shall not deal with this mechanism, here.
From the point of view of mathematical description, the influence of the atmo-
sphere upon a water layer is taken into account by the boundary condition on the free
water surface. Instead of the traditional condition of constant pressure on the free
water surface for tsunami problems, we shall now assume this quantity to be vari-
able in space and time,
p
atm
=
p
(
x
,
y
,
t
). Besides the pressure, acting upon the water
surface along the normal direction, there also exists a tangential tension of friction,
caused by the wind. The tangential tension per unit surface area, T, is related to
the speed of the wind, U, by the following approximate relationship:
T
S
=
C
ρ
atm
U
|
U
|
,
where
ρ
atm
is the density of air,
C
is a dimensionless empirical coefficient, the value
of which usually lies within limits from 0.0012 up to 0.003 [Lichtman (1970)].
A similar formula relates the velocity of the water flow near the bottom, v, and
the tension of friction, acting on the water column from the bottom,
T
B
=
−
C
B
ρ
v
|
v
|
,
where
is the density of water,
C
B
is a dimensionless empirical coefficient, the
value of which is usually set equal to 0.0025 [Murty (1984)]. We recall that in
the case of tsunami generation by bottom displacements tangential tensions on
the bottom are not taken into account (owing to the short duration of a displace-
ment). But in the case considered the action of tangential tension of the wind may
turn out to be prolonged (up to several days) and to transfer significant momentum
to the water column.
The presence of tangential tensions on the free water surface and on the bottom
is accompanied by the formation of a pronounced vertical flow structure, which in
real natural conditions is usually turbulent. Owing to the turbulence, the solution of
ρ
