Chapter 4: FINE STRUCTURE AND MICROSTRUCTURE
where
1/ 2
2
2
4
/ 2
B
T
e
T
e
K
w
K
w
D
K
K
ª
º
«
»
¬
¼
,
T
K
K W ,
0
e
z w t h
[
,
(4.29)
z is the depth referenced to the ocean surface, t is time, and 0
h is the depth of
the upper boundary of the thermocline at the initial moment t = 0. The
temperature profile at the point of discontinuity is determined from relation
1/ 2
1
0
2 / 1 1
B
E
ª
º
4
4
¬
¼
,
(4.30)
where
2
4
/
B
e
T
w
K
E
W
. Order of magnitude estimates suggest that the nonstationary effect becomes important in the dynamics of the deepening
thermocline for wB e B > 0.001 – 0.1 cm sP
-1
P
(Barenblatt, 1982).
Average temperature profiles calculated from five individual
temperature profiles are shown in X Figure 4-21 in the depth coordinate [
according to X (4.29)X . Note that [ is referenced to the top of the diurnal mixed
layer rather than to the ocean surface, and that before averaging, the
individual profiles were normalized by the corresponding total temperature
difference across the diurnal thermocline.
Comparison of the model (X Figure 4-22a) and experimental (X Figure
4-22b) profiles shows good qualitative agreement between them. There is a
sharp temperature jump at the top of the diurnal thermocline, and the
temperature profile below the “discontinuity” point in general follows an
exponential law (X Figure 4-22c). The temperature jump constitutes about
16% of the overall temperature difference across the diurnal thermocline.
The estimate of W
D derived from X Figure 4-22c and equation (4.44) is
1
4.16 10
B
D
|
u
mP
-1
P.
From X (4.28)X and X (4.30)X , parameters KB T B and W can be
expressed via 1 0
/
4 4 and B
D as follows:
1
0
e
T
B
w
K
D
4
4
,
(4.31)
0
1
1
B e
w
W D
4 4
4
.
(4.32)
For
0.1
e
w
cm sP
-1
P
and 1 0
/
0.84
4 4
, equations X (4.31)X and X (4.32)X result in
the estimates,
20
T
K |
mP
2
P
sP
-1
P
and W | 460 s.
255
where
1/ 2
2
2
4
/ 2
B
T
e
T
e
K
w
K
w
D
K
K
ª
º
«
»
¬
¼
,
T
K
K W ,
0
e
z w t h
[
,
(4.29)
z is the depth referenced to the ocean surface, t is time, and 0
h is the depth of
the upper boundary of the thermocline at the initial moment t = 0. The
temperature profile at the point of discontinuity is determined from relation
1/ 2
1
0
2 / 1 1
B
E
ª
º
4
4
¬
¼
,
(4.30)
where
2
4
/
B
e
T
w
K
E
W
. Order of magnitude estimates suggest that the nonstationary effect becomes important in the dynamics of the deepening
thermocline for wB e B > 0.001 – 0.1 cm sP
-1
P
(Barenblatt, 1982).
Average temperature profiles calculated from five individual
temperature profiles are shown in X Figure 4-21 in the depth coordinate [
according to X (4.29)X . Note that [ is referenced to the top of the diurnal mixed
layer rather than to the ocean surface, and that before averaging, the
individual profiles were normalized by the corresponding total temperature
difference across the diurnal thermocline.
Comparison of the model (X Figure 4-22a) and experimental (X Figure
4-22b) profiles shows good qualitative agreement between them. There is a
sharp temperature jump at the top of the diurnal thermocline, and the
temperature profile below the “discontinuity” point in general follows an
exponential law (X Figure 4-22c). The temperature jump constitutes about
16% of the overall temperature difference across the diurnal thermocline.
The estimate of W
D derived from X Figure 4-22c and equation (4.44) is
1
4.16 10
B
D
|
u
mP
-1
P.
From X (4.28)X and X (4.30)X , parameters KB T B and W can be
expressed via 1 0
/
4 4 and B
D as follows:
1
0
e
T
B
w
K
D
4
4
,
(4.31)
0
1
1
B e
w
W D
4 4
4
.
(4.32)
For
0.1
e
w
cm sP
-1
P
and 1 0
/
0.84
4 4
, equations X (4.31)X and X (4.32)X result in
the estimates,
20
T
K |
mP
2
P
sP
-1
P
and W | 460 s.
255