Geoscience Reference
In-Depth Information
7.2 Estimation of the Possibility of Stable Stratification
Disruption in the Ocean Due to an Underwater Earthquake
In this section we investigate whether significant transformation of the stratifica-
tion structure of the ocean can, in principle, result from an underwater earthquake.
As the stratification disruption mechanism we shall consider vertical turbulent ex-
change. The concrete mechanism of energy transfer from the moving ocean bottom
to the turbulent motion remains outside the framework of our estimations. We shall
be interested in the parameters of the hypothetical source of turbulence, which are
necessary for noticeable transformation of the stratification structure, and in the cor-
respondence of these parameters to the possibilities of the seismic energy source.
The characteristic horizontal size of the region, within which transformation of
the stratification structure takes place in the case of an underwater earthquake, sig-
nificantly exceeds the ocean depth, therefore, it is justifiable to consider a one-
dimensionable problem along the 0
z
axis, directed vertically downward. We shall
set the origin of the reference frame on the water surface. The base set of equations
includes the equation of balance for the turbulence energy
b
([
b
]=m
2
s
−
2
) for a strat-
ified liquid and the equation of turbulent heat transfer [Nosov, Skachko (1999)]:
b
3
/
2
L
∂
b
g
ρ
0
K
ρ
∂ρ
∂
z
+
∂
z
K
b
∂
b
−
z
−
β
(
z
,
t
)
,
=
+
(7.1)
∂
t
∂
∂
∂
T
∂
=
∂
∂
z
K
T
∂
T
z
,
(7.2)
t
∂
where g is the acceleration of gravity,
represent the respective average and
current densities of the liquid,
L
is the turbulent motion scale,
K
ρ
,
K
b
and
K
T
are
the turbulent exchange coefficients of mass, turbulence energy and heat. The first
term in the right-hand part of equation (7.1) describes the energy spent on work
against the forces of buoyancy, the second term describes turbulence energy trans-
fer, the third—dissipation of turbulence energy. Generation of turbulence energy is
described by function
ρ
0
and
ρ
β
(
z
,
t
), which we have chosen in the following simple form:
β
0
)
,
β
(
z
,
t
)=
θ
(
t
)
−
θ
(
t
−
τ
where
(t) is the Heaviside step function. Generation (pumping) of turbulence en-
ergy is characterized by power
θ
β
0
]=m
2
s
−
3
) and action duration
. Note, that
attempts at any further determination of the detailed structure of function
β
0
([
τ
(
z
,
t
),
when resolving the estimation problem, is not expedient, since they will only result
in an increase of the number of free parameters. Consider all the turbulent exchange
coefficients to be equal to each other, and assume dimensionality arguments to make
it possible to express them in terms of the turbulence energy
b
and the turbulence
scale
L
:
β
Lb
1
/
2
.
K
ρ
=
K
b
=
K
T
≈
(7.3)
