1
1 / 2
Pr
w
v
T
c
w
db
r b b
dz
Q
,
(3.65)
and from accepting the hypothesis that the correlation coefficient c
r = const.
Substituting the Kolmogorov type relationship (3.55) into (3.65) results in
the following equation:
1
/
2
Pr
1
w
w
w
b
z
db
l
b
rL
dz
L
F
V
§
·
¨
¸
¨
¸
©
¹
,
(3.66)
where F is the dimensionless proportionality constant.
Equation (3.64) with relationships (3.55) and (3.66) has an exact solution
in the form:
3/ 2
1/ 3
0
3
3 1
/
exp
/
2
/
1
1
1
/
exp
/
2
z L
z L
z
z L
z L
H
H
ª
º
«
»
«
»
ª
º
«
»
«
»
«
»
¬
¼
¬
¼
,
(3.67)
where
1/ 2
0
/ 48
0.21
s
S
L H
H
E
|
and
0
0 / S
a F H
H
H
,
(3.68)
and a H is a dimensionless coefficient.
2) The turbulence diffusion layer. This layer is a transition zone between
the wave-stirred layer and the layer where the mean shear controls the
turbulent regime,
w s
TD
H
z H
d d
.
(3.69)
In this layer, the wave stirring effect, however, becomes insignificant
compared to the turbulent diffusion, that is,
w
w
db
db
dz
dz
V
!!
.
(3.70)
Chapter 3: NEAR-SURFACE TURBULENCE
191