are much shorter than the dominant wave. Moreover, in the open ocean
about 98% of breaking waves are of spilling type, which do not penetrate
deeply (Gemmrich and Farmer, 1999). About 2% of breaking events show
deeper penetration. The deeper penetrating events, which are typical for
plunging wave breakers, however, play a minor role in upper ocean
dynamics (even under the condition of swell opposing wind waves, when the
occurrence of deep penetrating events increases to 10% of the total number
of breaking waves). The turbulent kinetic energy produced by spilling
breakers is localized in a shallow layer (also due to intensive bubble
entrainment–see Melville, 1994) and decays quickly with depth (Ly and
Garwood, 2000; Benilov and Ly, 2002). This is consistent with results
shown in Figure 3-19, indicating that the wave-breaking energy mostly
dissipates within less than one significant wave height from the ocean
surface.
The flux of the TKE at the air-sea interface F 0 is the principal component
of the upper ocean parameterization schemes considered above. Although
the direct (eddy correlation) measurement of F 0 is still a challenge, it can be
estimated as the integral of the growth rate over the surface wave spectrum
(see Section 1.6.6). Remote sensing techniques may provide an effective
way for obtaining information about the frequency-direction spectrum of
surface waves on global scale.
In our analysis of wave-enhanced turbulence we have ignored
convection as a source of TKE in the near-surface layer of the ocean.
According to Lombardo and Gregg (1989), the dissipation rate of TKE due
to gravitational convection in the upper ocean
0 /(
)
c
T
p
gQ c
H
D
U
|
,
(3.83)
where D 7 is the thermal expansion coefficient of seawater, g the acceleration
of gravity, and Q 0 is the net surface heat flux. For Q 0 = 200 W m
-2 , we obtain
7
2 10
c
H
| u
W kg
-1
, which is much less than typical dissipation rates
observed in the upper few meters of the ocean under high wind speed
conditions (Figure 3-12). Thus, gravitational convection is not a primary
source of turbulence in this case. Addition of the salinity effect due to
evaporation (see (3.96)) does not change the above estimate substantially.
The models of CB94, Terray et al. (1996), and BL02 do not consider
bubbles. A model of wave-enhanced turbulence incorporating the buoyancy
effect of bubbles, which has yet to be developed, could probably provide a
better insight into the problem of turbulence closure.
Chapter 3: NEAR-SURFACE TURBULENCE
197
about 98% of breaking waves are of spilling type, which do not penetrate
deeply (Gemmrich and Farmer, 1999). About 2% of breaking events show
deeper penetration. The deeper penetrating events, which are typical for
plunging wave breakers, however, play a minor role in upper ocean
dynamics (even under the condition of swell opposing wind waves, when the
occurrence of deep penetrating events increases to 10% of the total number
of breaking waves). The turbulent kinetic energy produced by spilling
breakers is localized in a shallow layer (also due to intensive bubble
entrainment–see Melville, 1994) and decays quickly with depth (Ly and
Garwood, 2000; Benilov and Ly, 2002). This is consistent with results
shown in Figure 3-19, indicating that the wave-breaking energy mostly
dissipates within less than one significant wave height from the ocean
surface.
The flux of the TKE at the air-sea interface F 0 is the principal component
of the upper ocean parameterization schemes considered above. Although
the direct (eddy correlation) measurement of F 0 is still a challenge, it can be
estimated as the integral of the growth rate over the surface wave spectrum
(see Section 1.6.6). Remote sensing techniques may provide an effective
way for obtaining information about the frequency-direction spectrum of
surface waves on global scale.
In our analysis of wave-enhanced turbulence we have ignored
convection as a source of TKE in the near-surface layer of the ocean.
According to Lombardo and Gregg (1989), the dissipation rate of TKE due
to gravitational convection in the upper ocean
0 /(
)
c
T
p
gQ c
H
D
U
|
,
(3.83)
where D 7 is the thermal expansion coefficient of seawater, g the acceleration
of gravity, and Q 0 is the net surface heat flux. For Q 0 = 200 W m
-2 , we obtain
7
2 10
c
H
| u
W kg
-1
, which is much less than typical dissipation rates
observed in the upper few meters of the ocean under high wind speed
conditions (Figure 3-12). Thus, gravitational convection is not a primary
source of turbulence in this case. Addition of the salinity effect due to
evaporation (see (3.96)) does not change the above estimate substantially.
The models of CB94, Terray et al. (1996), and BL02 do not consider
bubbles. A model of wave-enhanced turbulence incorporating the buoyancy
effect of bubbles, which has yet to be developed, could probably provide a
better insight into the problem of turbulence closure.
Chapter 3: NEAR-SURFACE TURBULENCE
197