THE NEAR-SURFACE LAYER OF THE OCEAN
Experiments of Rao et al. (1971) on the structure of the boundary-layer
turbulence indicate that the time between bursts is distributed according to a
lognormal law. The probability density for such a process is given by
1
2
1/ 2
2
exp
ln
/
,
0.
p t
t
t m
t
S
V
V
ª
º
!
¬
¼
(2.29)
where m is the mean value and
2
V is the variance for the logarithm of the
random variable t. Garbe et al. (2002) found the lognormal distribution
(2.29) as being in good agreement with the histogram of time intervals
between two successive renewal events derived from infrared images in a
laboratory tank (Figure 2-11).
Inserting (2.29) into relationships (2.26)-(2.28), we obtain:
1/2
1/ 2
2
t
1/ 2
1/ 2
2
0
4
/ 3 exp
/ T
T
t
q
S
V
N
'
,
(2.31)
94
' u 4S
/ 3 exp V
t /Q W ,
(2.30)
/16
/16
Figure 2-11. Lognormal distribution (2.29) fitted to the histogram of the time between two
consecutive surface renewal events t - t 0 for a wind speed of 2 m s
-1 . Reproduced from Garbe
et al. (2002) by permission of American Geophysical Union.