THE NEAR-SURFACE LAYER OF THE OCEAN
where t
w is the terminal velocity of the particle. For
1
Z t , the vertical
distributions of the horizontal velocity u and concentration C are determined
by the classical laws for the logarithmic boundary layer (Prandtl, 1949):
2
1
ln
,
const
U z
z const C z
z
Z
N
,
(6.39)
which means that the particles do not affect flow dynamics.
For
1
Z , the saturation-limited flow regime is possible, which is
described by the following relation for the velocity and concentration
profiles (Barenblatt and Golitsyn, 1974):
2
ln
,
a
t
u
a K
u z
z const C z
g z
NZ
V
.
(6.40)
For
1
Z ! the vertical mixing coefficient is defined as m
a
K
u z
N ,
while for
1
Z it is given by equation
m
a
t
K
u z wz
ZN
,
(6.41)
which means that the stratification effect reduces turbulent friction by a
factor of
1
Z
.
Equation (6.38) at
1
Z
combined with the formula for the terminal
velocity of raindrops (2.112) gives an equation for the droplet radius
separating the two regimes according to the Barenblatt and Golitsyn theory.
This critical droplet radius r c is as follows:
1/
1 ln
/
c
a
t
r r
u w
O
X
N
ª
º
¬
¼
(6.42)
Dependence (6.42) is shown in Figure 6-18 as a function of the friction
velocity in air. Spray droplets with radii
c
r r
! are the re-entrant spray, while
smaller droplets are effectively transported by turbulence. Note that for 15 m
s
-1 wind speed, which corresponds to the friction velocity in air
0.6
a
u |
m
s
-1 , the critical droplet radius is c
r | 70 Pm. It is interesting that most of the
spray generation functions shown in Figure 6-9 reveal peaks around
100
r
Pm, which may be an indication that the turbulent diffusion is not an
effective mechanism for transporting these relatively large droplets. This,
however, might also be an indication that the known spray generation
functions underestimate the contribution of large droplets, because the
432
u a
where t
w is the terminal velocity of the particle. For
1
Z t , the vertical
distributions of the horizontal velocity u and concentration C are determined
by the classical laws for the logarithmic boundary layer (Prandtl, 1949):
2
1
ln
,
const
U z
z const C z
z
Z
N
,
(6.39)
which means that the particles do not affect flow dynamics.
For
1
Z , the saturation-limited flow regime is possible, which is
described by the following relation for the velocity and concentration
profiles (Barenblatt and Golitsyn, 1974):
2
ln
,
a
t
u
a K
u z
z const C z
g z
NZ
V
.
(6.40)
For
1
Z ! the vertical mixing coefficient is defined as m
a
K
u z
N ,
while for
1
Z it is given by equation
m
a
t
K
u z wz
ZN
,
(6.41)
which means that the stratification effect reduces turbulent friction by a
factor of
1
Z
.
Equation (6.38) at
1
Z
combined with the formula for the terminal
velocity of raindrops (2.112) gives an equation for the droplet radius
separating the two regimes according to the Barenblatt and Golitsyn theory.
This critical droplet radius r c is as follows:
1/
1 ln
/
c
a
t
r r
u w
O
X
N
ª
º
¬
¼
(6.42)
Dependence (6.42) is shown in Figure 6-18 as a function of the friction
velocity in air. Spray droplets with radii
c
r r
! are the re-entrant spray, while
smaller droplets are effectively transported by turbulence. Note that for 15 m
s
-1 wind speed, which corresponds to the friction velocity in air
0.6
a
u |
m
s
-1 , the critical droplet radius is c
r | 70 Pm. It is interesting that most of the
spray generation functions shown in Figure 6-9 reveal peaks around
100
r
Pm, which may be an indication that the turbulent diffusion is not an
effective mechanism for transporting these relatively large droplets. This,
however, might also be an indication that the known spray generation
functions underestimate the contribution of large droplets, because the
432
u a