THE NEAR-SURFACE LAYER OF THE OCEAN
surface cooling. These vertical profiles showed that the heating depends
strongly on latitude and could amount to as much as 10 to 30P
o
PC
per day in
the uppermost centimeters of tropical and subtropical oceans. It is interesting
that during midsummer the subpolar ocean in the summer hemisphere can be
exposed to even more radiative energy than near the equator because of the
longer days. These high heating rates do not result in so big actual changes
of the water temperature because internal turbulent processes immediately
transport the absorbed thermal energy into deeper layers, and because some
energy is lost to the atmosphere above.
In the presence of both volume and surface sources of heat, the vertical
flux of heat near the surface is
0
(1
) 1 R
Q z Q
A I
f z
6
,
(4.39)
where I 6 is the insolation, A is the sea surface albedo , function
R
f z
and QB 0 B is the surface heat flux, which is a sum of latent, sensible, and
effective longwave radiation flux ( 0
E
T
L
Q Q Q I
). Q changes sign at
some depth c
z . This is the compensation depth determined from the
equation,
0
0
( 1
) 1 R
Q
A I
f z
6
.
(4.40)
During daytime, c
z often amounts to only a few millimeters (Soloviev,
1979).
The layer 0
c
z z
can become convectively unstable since
0
Q ! .
Discrete convective elements from this layer overshoot the compensation
depth and penetrate into the stably stratified layer below (Kraus and Rooth,
1961). The kinetic energy generated in the convectively unstable layer
0
c
z z
works against the buoyancy forces in the stable layer c
c
z
z h
,
where hB c B is the penetration depth of convection. When z c is very small, the
convection is close to a laminar regime, and, as a first guess, we will ignore
the viscous dissipation of the kinetic energy balance.
Remarkably, c
z does not depend on the ocean turbulence regime.
Equations (4.39)-(4.40), however, imply an unlimited depth of the surface
mixed layer. In fact, this depth is limited and equal to h c .
The depth of penetration of convection into the stably stratified layer, h c ,
can be determined from an integral model including the differential
equations for temperature, salinity, and kinetic energy balance (Soloviev,
1979):
266
characterizes the absorption of solar radiation with depth (see Section 1.4.6),
surface cooling. These vertical profiles showed that the heating depends
strongly on latitude and could amount to as much as 10 to 30P
o
PC
per day in
the uppermost centimeters of tropical and subtropical oceans. It is interesting
that during midsummer the subpolar ocean in the summer hemisphere can be
exposed to even more radiative energy than near the equator because of the
longer days. These high heating rates do not result in so big actual changes
of the water temperature because internal turbulent processes immediately
transport the absorbed thermal energy into deeper layers, and because some
energy is lost to the atmosphere above.
In the presence of both volume and surface sources of heat, the vertical
flux of heat near the surface is
0
(1
) 1 R
Q z Q
A I
f z
6
,
(4.39)
where I 6 is the insolation, A is the sea surface albedo , function
R
f z
and QB 0 B is the surface heat flux, which is a sum of latent, sensible, and
effective longwave radiation flux ( 0
E
T
L
Q Q Q I
). Q changes sign at
some depth c
z . This is the compensation depth determined from the
equation,
0
0
( 1
) 1 R
Q
A I
f z
6
.
(4.40)
During daytime, c
z often amounts to only a few millimeters (Soloviev,
1979).
The layer 0
c
z z
can become convectively unstable since
0
Q ! .
Discrete convective elements from this layer overshoot the compensation
depth and penetrate into the stably stratified layer below (Kraus and Rooth,
1961). The kinetic energy generated in the convectively unstable layer
0
c
z z
works against the buoyancy forces in the stable layer c
c
z
z h
,
where hB c B is the penetration depth of convection. When z c is very small, the
convection is close to a laminar regime, and, as a first guess, we will ignore
the viscous dissipation of the kinetic energy balance.
Remarkably, c
z does not depend on the ocean turbulence regime.
Equations (4.39)-(4.40), however, imply an unlimited depth of the surface
mixed layer. In fact, this depth is limited and equal to h c .
The depth of penetration of convection into the stably stratified layer, h c ,
can be determined from an integral model including the differential
equations for temperature, salinity, and kinetic energy balance (Soloviev,
1979):
266
characterizes the absorption of solar radiation with depth (see Section 1.4.6),