THE NEAR-SURFACE LAYER OF THE OCEAN
where
96
/
3
2
W
J h
, h is the depth of the mixed layer, W is the vertical
homogenization time scale,
0
0
(
)/
B
g U U U
) is the buoyancy, U is the
fluid’s density (averaged over the mixed layer depth and some time interval),
0
U is a constant reference density, g is the acceleration of gravity, h
is the
horizontal gradient operator, and (
)
h
f
B
is a non-dimensional function
whose form depends on details of the hydrodynamic instabilities that
dominate the flow.
Applying (5.8) to the equations for buoyancy (averaged over the depth
of the upper ocean mixed layer), FY97 obtained the following nonlinear
advection-diffusion equation:
[ (|
|)(
) ]
t
B
B u B
f
B
B B B
J
w
)
G
,
(5.9)
where u
G is the horizontal velocity field, and term B
) relates to the
thermohaline fluxes from the top and bottom of the mixed layer.
5.3.3 Buoyancy flux through the bottom of the mixed layer
Turbulent entrainment, upwelling events, and internal wave effects can
cause the horizontal modulation of the buoyancy flux through the bottom of
the mixed layer. Horizontal wavenumber statistics below the mixed layer
can help to understand this process.
Figure 5-9 gives an example of the horizontal wavenumber spectrum
averaged over 60 to 110 m depth range. These data are also from the western
equatorial Pacific for approximately the same time period as the spectrum in
the mixed layer shown in Figure 5-8. Comparison of the experimental
spectra with the theoretical model of internal waves that accounts for the
isotropic internal wave field and the lower modes of the M 2 baroclinic tide
suggests that the internal wave processes could substantially determine the
wavenumber statistics in this depth range and in the wavenumber range
under consideration.
Internal waves modulate the vertical shear and the density gradient and,
ultimately, the gradient Richardson number, Ri . The spectrum of the
Richardson number associated with the Garrett and Munk model of internal
waves is “white” (i.e., it does not depend on frequency), except for the
lowest few modes that are close to the inertial frequency. Near-inertial
waves are associated with a drop in Ri . Overturning and turbulent
entrainment occurs when Ri drops below it critical magnitude (about 0.25).
The buoyancy influx from the thermocline to the mixed layer caused by the
isotropic internal wave field is therefore more probable on horizontal scales
of inertia-gravity waves.
298
where
96
/
3
2
W
J h
, h is the depth of the mixed layer, W is the vertical
homogenization time scale,
0
0
(
)/
B
g U U U
) is the buoyancy, U is the
fluid’s density (averaged over the mixed layer depth and some time interval),
0
U is a constant reference density, g is the acceleration of gravity, h
is the
horizontal gradient operator, and (
)
h
f
B
is a non-dimensional function
whose form depends on details of the hydrodynamic instabilities that
dominate the flow.
Applying (5.8) to the equations for buoyancy (averaged over the depth
of the upper ocean mixed layer), FY97 obtained the following nonlinear
advection-diffusion equation:
[ (|
|)(
) ]
t
B
B u B
f
B
B B B
J
w
)
G
,
(5.9)
where u
G is the horizontal velocity field, and term B
) relates to the
thermohaline fluxes from the top and bottom of the mixed layer.
5.3.3 Buoyancy flux through the bottom of the mixed layer
Turbulent entrainment, upwelling events, and internal wave effects can
cause the horizontal modulation of the buoyancy flux through the bottom of
the mixed layer. Horizontal wavenumber statistics below the mixed layer
can help to understand this process.
Figure 5-9 gives an example of the horizontal wavenumber spectrum
averaged over 60 to 110 m depth range. These data are also from the western
equatorial Pacific for approximately the same time period as the spectrum in
the mixed layer shown in Figure 5-8. Comparison of the experimental
spectra with the theoretical model of internal waves that accounts for the
isotropic internal wave field and the lower modes of the M 2 baroclinic tide
suggests that the internal wave processes could substantially determine the
wavenumber statistics in this depth range and in the wavenumber range
under consideration.
Internal waves modulate the vertical shear and the density gradient and,
ultimately, the gradient Richardson number, Ri . The spectrum of the
Richardson number associated with the Garrett and Munk model of internal
waves is “white” (i.e., it does not depend on frequency), except for the
lowest few modes that are close to the inertial frequency. Near-inertial
waves are associated with a drop in Ri . Overturning and turbulent
entrainment occurs when Ri drops below it critical magnitude (about 0.25).
The buoyancy influx from the thermocline to the mixed layer caused by the
isotropic internal wave field is therefore more probable on horizontal scales
of inertia-gravity waves.
298