THE NEAR-SURFACE LAYER OF THE OCEAN
^
`
1/ 2
0
1/ 2
9
1
1
2
2
0
1
0,
0,
0,
2
exp
1
1 2
0
c
R
R
T
R
T
i i
i
i
R
i
T
t
T t
T
t
T
t
q
t
q
a
e r f
q
N S
N
D
G
G
N S
§
·
'
'
'
¨
¸
©
¹
§
·
ª
º
¨
¸
¬
¼
©
¹
¦
(2.85)
The average temperature difference across the thermal molecular
sublayer of the ocean is defined as follows:
0
0,
w
T
p t T
t dt
f
'
'
³
(2.86)
where
0
1
0,
0, ' '
t
m
T
t
T t dt
t
'
'
³
,
(2.87)
and
p t is the probability density. From (2.85) and (2.87), the following
expression can be obtained:
^
`
1/ 2
0
9
1
2
2
2
1 /2
0
1
1/ 2
0
4
0,
3
exp
1
1 2
1
4
3
m
T
R
i i
l
l
l
l
i
T
R
T
t
T
t
q
q
a
e r f
t
q
N S
D G
G
G
S G
N
N S
§
·
'
¨
¸
©
¹
ª
º
¬
¼
§
·
¨
¸
©
¹
¦
(2.88)
With the Rao et al. (1971) probability density function (2.29), expression
(2.86) can be rewritten in the following way:
2
ln
1/ 2
1
ln
ln
2
exp
0,exp
m
t
m
T
T
t d t
S V
V
f
f
ª
º
«
»
'
'
«
»
¬
¼
³
,
(2.89)
where ln ln
t
t ,
2
ln
/ 4
m
t V
, t is the mean time between bursting
events (renewal time); m and
2
V are the mean value and the variance of the
110