Geoscience Reference
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Both the position of the centre of mass and the change in surface temperature
characterize the degree of mixing. Owing to the centre-of-mass position starting to
change, unlike the surface temperature, immediately after generation of turbulence
energy 'switches on', it is more convenient, in a number of cases, to make use of
function f 4 ( t ), instead of f 3 ( t ).
In Fig. 7.7 the two aforementioned development scenarios for the process in
the system investigated are clearly seen:
β 0 = 10 2 m 2 s 3 the maximum gradient decreases
and noticeable changes of surface temperature and of the centre-of-mass position
occur, which signifies destruction of the thermocline and arrival of depth waters
at the surface.
2. When
β 0 = 10 3 m 2 s 3
1. When
and
β 0 = 10 4 m 2 s 3 , the maximal temperature gradient increases monotonou-
sly with time, no noticeable changes of the surface temperature and of the centre-
of-mass position occur, i.e. the thermocline is not destroyed and it serves an
obstacle in the way of depth waters toward the surface.
3. When
β 0 = 10 3 m 2 s 3 , the maximum gradient changes nonmonotonously with
time: after the action of the source terminates a little enhancement of it takes
place; this is due to the energy of turbulence pulsations and, consequently, the ex-
change coefficient in the region of the temperature jump rapidly dropping prac-
tically down to zero. At this time the turbulent exchange in the region above and
below the jump still persists for some time, which precisely leads to enhancement
of the maximum gradient.
The duration of the transient process of 'switching on' ('switching off') pumping,
which can be traced by the behaviour of function f 2 ( t ), depends both on the turbu-
lence scale L and on the value of parameter
β 0 . As it is seen from Fig. 7.7, noticeable
changes in the surface temperature, the centre-of-mass position and the maximum
gradient can occur not only during pumping of turbulence energy, but also when it
is switched off.
In Fig. 7.8 diagrams are presented that in the
β 0 τ
, L plane show the change in
1. Maximum temperature gradient
δ
(Max [grad T ]) by a quantity exceeding 10%
of the initial gradient value
2. Surface temperature
T s
3. the Centre-of-mass position
δ
δ
z .
The data presented in the figures correspond to the final changes in the tem-
perature profile and are not related to any time moment. The calculation is per-
formed for three different durations of the source action,
= 1 , 10 and 100 s, for
h 1 = 10 m and H = 100 m. Similar diagrams, but for a thermocline at the greater
depth h 1 = 45 m, are presented in Fig. 7.9.
Analysis of the figures permits to make the following conclusions. Enhancement
of the duration of the turbulence source action,
τ
τ
, for the same total amount of
energy entering the system,
, leads to an insignificant spread of the range of
noticeable variations in all three parameters studied (
β 0 τ
z ). It
is interesting to note that this range spreads exclusively toward smaller turbulent
δ
(Max (grad T )) ,
δ
T s ,
δ
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