Geoscience Reference
In-Depth Information
Having chosen the equation of state of water in the linearized form [Monin,
Ozmidov (1981)] (assuming salinity not to vary with depth):
ρ
0
1
T
0
)
,
ρ
=
−
α
(
T
−
10
−
4
(
◦
C)
−
1
m
−
3
, we close the initial set of equa-
where
α
= 2
·
and
ρ
0
= 1
,
000 kg
·
tions (7.1), (7.2).
As boundary conditions we adopt the conditions, that there be no flows of turbu-
lence energy and of heat on the surface and on the bottom:
∂
b
z
= 0
,
z
= 0
,
H
;
(7.4)
∂
∂
T
= 0
,
z
= 0
,
H
.
(7.5)
∂
z
The initial conditions assume the energy of turbulence pulsations to equal zero
at time moment
t
= 0 and the existence of an initial temperature distribution deter-
mining stable stratification (Fig. 7.4):
b
(
z
,
0)=0
,
(7.6)
T
(
z
,
0)=
T
0
(
z
)
.
(7.7)
The set of equations (7.1) and (7.2) with boundary conditions (7.4) and (7.5)
and initial conditions (7.6) and (7.7) was solved numerically by the method of finite
differences with respect to functions
b
(
z
,
t
) and
T
(
z
,
t
).
In all calculations, the temperature difference
T
2
−
T
1
= 10
◦
C. The quantity
h
1
,
characterizing the depth at which the thermocline was to be situated, was set to 10,
45 and 100 m. The thermocline thickness
h
2
−
h
1
= 10 m. The duration of the pro-
cess at the earthquake source usually lies within the range from 1 to 100 s. To cover
the range indicated the action of the turbulence energy source was considered to last
for duration times equal to 1, 10 and 100 s.
Typical values for turbulence energy generation in the ocean,
β
0
, usually lie
within the limits of 10
−
5
-10
−
9
m
2
s
−
3
[Monin, Ozmidov (1981)]. For the purposes
Fig. 7.4 Initial temperature
profile
