THE NEAR-SURFACE LAYER OF THE OCEAN
In Figure 3-25 the averaged dissipation rate data for Ri < Ri cr are
presented as in Figure 3-23. The averaged data are consistent with the
boundary layer dependence (three points, however, deviate from the
theoretical dependence by more than the 95% confidence interval). The
maximum dimensionless dissipation rate of TKE near the bottom of the
mixed layer
2 3
~ 5 10 /(
)
u
z
H
N
u
, which substantially exceeds the log layer
prediction,
3 /(
)
u
z
H
N
. The strong increase of the dissipation rate as
cr
Ri Ri
o
, which corresponds to ] o f , is in accordance with the
Ri cr is not in contradiction to the decrease of dimensionless mixing
coefficient
)
/( z
u
K
N
predicted by (3.97); this is because K M also depends
on the turbulent mixing scale that rapidly decreases at
cr
Ri Ri
o
.
3.5 Parameterization of Turbulent Mixing
3.5.1 Parameterization of wave-enhanced mixing coefficient
In the framework of the CB94 model, the vertical mixing coefficient due
to wave breaking can be calculated from the following relationship:
1/ 3 1/ 3 4 / 3
1/ 3 4 / 3
M
M
K
S B
l
l
H
H
|
.
(3.99)
With the expression for the dissipation of turbulent kinetic energy in the
form (3.44), and for the length scale defined by equation (3.33), formula
(3.99) is as follows:
1/ 3
0.5
0
0
0
1 3
/
n
n
M
w
q
K
u z z
BS
z
z z
N
D
ª
º
«
»
¬
¼
. (3.100)
Formula (3.100) is shown in Figure 3-26 for surface roughness z 0
parameterized via significant wave height H s according to (3.47) with c 0 =
0.6.
As expected, the main enhancement of the vertical mixing is observed
within the layer of approximately one significant wave height depth. Bubbles
from breaking waves produce density stratification that may affect the
turbulence close to the ocean surface. At this point, however, it is not yet
clear how to include this effect into a mixing parameterization.
208
Wyngaard et al. (1971) formula (1.154). Note that the increase of H at Ri ~
M
In Figure 3-25 the averaged dissipation rate data for Ri < Ri cr are
presented as in Figure 3-23. The averaged data are consistent with the
boundary layer dependence (three points, however, deviate from the
theoretical dependence by more than the 95% confidence interval). The
maximum dimensionless dissipation rate of TKE near the bottom of the
mixed layer
2 3
~ 5 10 /(
)
u
z
H
N
u
, which substantially exceeds the log layer
prediction,
3 /(
)
u
z
H
N
. The strong increase of the dissipation rate as
cr
Ri Ri
o
, which corresponds to ] o f , is in accordance with the
Ri cr is not in contradiction to the decrease of dimensionless mixing
coefficient
)
/( z
u
K
N
predicted by (3.97); this is because K M also depends
on the turbulent mixing scale that rapidly decreases at
cr
Ri Ri
o
.
3.5 Parameterization of Turbulent Mixing
3.5.1 Parameterization of wave-enhanced mixing coefficient
In the framework of the CB94 model, the vertical mixing coefficient due
to wave breaking can be calculated from the following relationship:
1/ 3 1/ 3 4 / 3
1/ 3 4 / 3
M
M
K
S B
l
l
H
H
|
.
(3.99)
With the expression for the dissipation of turbulent kinetic energy in the
form (3.44), and for the length scale defined by equation (3.33), formula
(3.99) is as follows:
1/ 3
0.5
0
0
0
1 3
/
n
n
M
w
q
K
u z z
BS
z
z z
N
D
ª
º
«
»
¬
¼
. (3.100)
Formula (3.100) is shown in Figure 3-26 for surface roughness z 0
parameterized via significant wave height H s according to (3.47) with c 0 =
0.6.
As expected, the main enhancement of the vertical mixing is observed
within the layer of approximately one significant wave height depth. Bubbles
from breaking waves produce density stratification that may affect the
turbulence close to the ocean surface. At this point, however, it is not yet
clear how to include this effect into a mixing parameterization.
208
Wyngaard et al. (1971) formula (1.154). Note that the increase of H at Ri ~
M