THE NEAR-SURFACE LAYER OF THE OCEAN
which is based on an assumption that the entire wind stress is transferred to
waves. The ratio / p
c c as a function of
/
a
p
u c
is shown in Figure 1-15.
Here p
c is the phase speed at the spectral peak of wind waves, and u is the
friction velocity in the upper ocean boundary layer defined as
1/ 2
0 /
u
W U
.
Terray et al. (1996) assumed that the waves are “young” (short fetched
or developing waves) when their age
/
13
w
p
a
A c u . The “old” waves
(developed seas) were defined by an opposite inequality,
13
w
A ! . For waves
at very early stages of development, c approaches the peak wave velocity,
while for developed seas it is of the order of the friction velocity in the air,
a
u .
For developed seas, / a
c u can be approximated by a constant; equation
(1.127) thus reduces to
3
0
w
F
u
D
|
,
(1.128)
where
100
w
D |
is a dimensionless constant. For young waves (
13
w
A ! ), D w
can’t be a constant. Kantha and Clayson (2004) proposed the following
approximate formula, which is intended to account for wave age:
3
2
0
*
4.053
(0.037
3.615 / )
w
w
F
u
A
A
|
,
(1.129)
Appreciable kinetic energy can be transferred to the water by rain
droplets. When a droplet impacts water, its kinetic energy is transferred to
the surface layer of the ocean along with its mass. This process is discussed
in more detail in Chapter 2 in relation to the freshwater skin of the ocean.
1.7 Planetary Boundary Layers
The time and length scales of global oceanic and atmospheric processes
are considerably different for reasons related to disparity in the density of the
two media. These differences are bridged in the atmospheric and oceanic
planetary boundary layers that develop adjacent to the air-sea interface.
These boundary layers are subject to strong turbulence, and the turbulent
exchange coefficients are much higher within boundary layers than outside
of these regions. Ekman and Monin and Oboukhov developed onedimensional framework for understanding planetary boundary layers
54
which is based on an assumption that the entire wind stress is transferred to
waves. The ratio / p
c c as a function of
/
a
p
u c
is shown in Figure 1-15.
Here p
c is the phase speed at the spectral peak of wind waves, and u is the
friction velocity in the upper ocean boundary layer defined as
1/ 2
0 /
u
W U
.
Terray et al. (1996) assumed that the waves are “young” (short fetched
or developing waves) when their age
/
13
w
p
a
A c u . The “old” waves
(developed seas) were defined by an opposite inequality,
13
w
A ! . For waves
at very early stages of development, c approaches the peak wave velocity,
while for developed seas it is of the order of the friction velocity in the air,
a
u .
For developed seas, / a
c u can be approximated by a constant; equation
(1.127) thus reduces to
3
0
w
F
u
D
|
,
(1.128)
where
100
w
D |
is a dimensionless constant. For young waves (
13
w
A ! ), D w
can’t be a constant. Kantha and Clayson (2004) proposed the following
approximate formula, which is intended to account for wave age:
3
2
0
*
4.053
(0.037
3.615 / )
w
w
F
u
A
A
|
,
(1.129)
Appreciable kinetic energy can be transferred to the water by rain
droplets. When a droplet impacts water, its kinetic energy is transferred to
the surface layer of the ocean along with its mass. This process is discussed
in more detail in Chapter 2 in relation to the freshwater skin of the ocean.
1.7 Planetary Boundary Layers
The time and length scales of global oceanic and atmospheric processes
are considerably different for reasons related to disparity in the density of the
two media. These differences are bridged in the atmospheric and oceanic
planetary boundary layers that develop adjacent to the air-sea interface.
These boundary layers are subject to strong turbulence, and the turbulent
exchange coefficients are much higher within boundary layers than outside
of these regions. Ekman and Monin and Oboukhov developed onedimensional framework for understanding planetary boundary layers
54