observed zonal flows and fronts, it still does not
explain why Munk’s (1966) estimate of vertical
diffusion in the ocean is an order of magnitude
greater than the generally observed value. Munk
and Wunsch (1998) investigate how much dissipation is needed in the regions of enhanced vertical
mixing to explain the discrepancy. The figure they
find is near 1.9 TW, which they propose is half
due to the wind and half to the tides. The figure is
not impossible but it raises a number of concerns.
Thus it requires most of the energy input from the
wind to be dissipated in the regions of enhanced
vertical mixing, it requires a mixing efficiency
near Osborn’s (1980) upper bound, and it requires
the turbulence affecting Bottom Water in the
Brazil Basin to be typical of all levels of the deep
ocean.
An alternative possibility is that one of the
premises is wrong. In fact this seems to be the solution of the problem. Numerical models (Döös and
Webb, 1994; Döös and Coward, 1997; Toggweiler
and Samuels, 1998) indicate that mixing in the
deep ocean is not essential for the thermohaline
circulation. Instead, as shown in Fig. 4.2.3 (see
Plate 4.2.3, p. 300), the models show that over
half of the North Atlantic Deep Water (NADW)
may be brought up to the surface around Antarctica by Ekman suction acting in regions where the
deep density layers outcrop.
This effect is also discussed by Hasumi and Suginohara (1999b). They find that the production rate
of NADW and the annual mean air–sea heat flux
anomalies are both proportional to the wind stress
over the Southern Ocean. They also show that
these effects are associated with changes in the
stratification of the deep ocean, whose mechanism
is detailed by Tsujino and Suginohara (1999).
Munk and Wunsch (1998) also assume that
deep mixing in the ocean has to upwell approximately 30 Sv across the 3.5°C surface within the
ocean and that this water eventually upwells
through a significant fraction of the ocean’s depth.
As was discussed above, given the area and
stratification of the deep ocean, this requires a
vertical diffusion coefficient of approximately
10
94 m
2 s
91 . Averaged over the whole ocean, this
requires a total energy input of 2.1 TW.
In fact the value of 30 Sv, based on the inverse
model results of Macdonald and Wunsch (1996)
for both Deep and Bottom Water, may be an overestimate. If we take the figure of 3.5°C to roughly
coincide with the boundary between Deep Water
(i.e. North Atlantic Deep Water) and Intermediate
Waters, then Schmitz’s (1995) estimate of the flux
across this surface is 14 Sv. A related estimate
comes from the Atlantic at 30°N where the southward flux of water colder than 4.0°C is of order
17 Sv (see Bryden, Chapter 6.1). To this figure we
should also add an unknown amount of deep
water formed from lighter waters by mixing across
the Antarctic Circumpolar Current. The flux of
Antarctic Bottom Water does not need to be
included in the figures because it is formed at the
surface from water masses in the Deep Water density class (Foster and Carmack, 1976; Olbers et al.,
1992; Schmitz, 1996b).
The models (Döös and Webb, 1994; Döös and
Coward, 1997; Hasumi and Suginohara, 1999b)
indicate that between 9 and 12 Sv of Deep Water is
upwelled and converted to Intermediate Water in
the Southern Ocean. This is a net value, which in
the case of the eddy-resolving models (Döös and
Webb, 1994; Döös and Coward, 1997) includes
the flux in the opposite direction due to eddies. If
this is correct, then it only leaves 5–8 Sv to be
upwelled by diapycnal mixing in the deep ocean.
Using the figures of Munk and Wunsch (1998),
a diapycnal diffusivity of 10
95 m
2 s
91
, due to the
background isotropic internal wave field, can
upwell 3 Sv across the 3.5°C surface. The remaining 2–5 Sv can be upwelled by localized enhanced
mixing as long as the resulting area-averaged
diapycnal diffusivity affecting the deep and intermediate waters is also of order 10
95 m
2 s
91
. On
the basis of the earlier figures this requires around
0.2 TW from the wind or the tides. If these
reduced estimates are correct, they may explain
why regions of enhanced vertical mixing have not
been more widely observed.
Estimates of internal tide dissipation using
barotropic tidal models alone give values near
1.1 TW (Sjoberg and Stigebrandt, 1992; Morozov,
1995). Similar values have recently been obtained
from satellite altimeter observations of the
barotropic tides (Egbert and Ray, 2000). When
satellite altimeter data is used to constrain both
the barotropic and baroclinic tides, the estimate
drops to 0.6 TW (Kantha and Tierney, 1997).
Together with the contribution from the wind,
these dissipation rates are barely sufficient to mix
the 30 Sv of Macdonald and Wunsch through the
full depth of the water column. However, even
SECTION 4 THE GLOBAL FLOW FIELD
212
explain why Munk’s (1966) estimate of vertical
diffusion in the ocean is an order of magnitude
greater than the generally observed value. Munk
and Wunsch (1998) investigate how much dissipation is needed in the regions of enhanced vertical
mixing to explain the discrepancy. The figure they
find is near 1.9 TW, which they propose is half
due to the wind and half to the tides. The figure is
not impossible but it raises a number of concerns.
Thus it requires most of the energy input from the
wind to be dissipated in the regions of enhanced
vertical mixing, it requires a mixing efficiency
near Osborn’s (1980) upper bound, and it requires
the turbulence affecting Bottom Water in the
Brazil Basin to be typical of all levels of the deep
ocean.
An alternative possibility is that one of the
premises is wrong. In fact this seems to be the solution of the problem. Numerical models (Döös and
Webb, 1994; Döös and Coward, 1997; Toggweiler
and Samuels, 1998) indicate that mixing in the
deep ocean is not essential for the thermohaline
circulation. Instead, as shown in Fig. 4.2.3 (see
Plate 4.2.3, p. 300), the models show that over
half of the North Atlantic Deep Water (NADW)
may be brought up to the surface around Antarctica by Ekman suction acting in regions where the
deep density layers outcrop.
This effect is also discussed by Hasumi and Suginohara (1999b). They find that the production rate
of NADW and the annual mean air–sea heat flux
anomalies are both proportional to the wind stress
over the Southern Ocean. They also show that
these effects are associated with changes in the
stratification of the deep ocean, whose mechanism
is detailed by Tsujino and Suginohara (1999).
Munk and Wunsch (1998) also assume that
deep mixing in the ocean has to upwell approximately 30 Sv across the 3.5°C surface within the
ocean and that this water eventually upwells
through a significant fraction of the ocean’s depth.
As was discussed above, given the area and
stratification of the deep ocean, this requires a
vertical diffusion coefficient of approximately
10
94 m
2 s
91 . Averaged over the whole ocean, this
requires a total energy input of 2.1 TW.
In fact the value of 30 Sv, based on the inverse
model results of Macdonald and Wunsch (1996)
for both Deep and Bottom Water, may be an overestimate. If we take the figure of 3.5°C to roughly
coincide with the boundary between Deep Water
(i.e. North Atlantic Deep Water) and Intermediate
Waters, then Schmitz’s (1995) estimate of the flux
across this surface is 14 Sv. A related estimate
comes from the Atlantic at 30°N where the southward flux of water colder than 4.0°C is of order
17 Sv (see Bryden, Chapter 6.1). To this figure we
should also add an unknown amount of deep
water formed from lighter waters by mixing across
the Antarctic Circumpolar Current. The flux of
Antarctic Bottom Water does not need to be
included in the figures because it is formed at the
surface from water masses in the Deep Water density class (Foster and Carmack, 1976; Olbers et al.,
1992; Schmitz, 1996b).
The models (Döös and Webb, 1994; Döös and
Coward, 1997; Hasumi and Suginohara, 1999b)
indicate that between 9 and 12 Sv of Deep Water is
upwelled and converted to Intermediate Water in
the Southern Ocean. This is a net value, which in
the case of the eddy-resolving models (Döös and
Webb, 1994; Döös and Coward, 1997) includes
the flux in the opposite direction due to eddies. If
this is correct, then it only leaves 5–8 Sv to be
upwelled by diapycnal mixing in the deep ocean.
Using the figures of Munk and Wunsch (1998),
a diapycnal diffusivity of 10
95 m
2 s
91
, due to the
background isotropic internal wave field, can
upwell 3 Sv across the 3.5°C surface. The remaining 2–5 Sv can be upwelled by localized enhanced
mixing as long as the resulting area-averaged
diapycnal diffusivity affecting the deep and intermediate waters is also of order 10
95 m
2 s
91
. On
the basis of the earlier figures this requires around
0.2 TW from the wind or the tides. If these
reduced estimates are correct, they may explain
why regions of enhanced vertical mixing have not
been more widely observed.
Estimates of internal tide dissipation using
barotropic tidal models alone give values near
1.1 TW (Sjoberg and Stigebrandt, 1992; Morozov,
1995). Similar values have recently been obtained
from satellite altimeter observations of the
barotropic tides (Egbert and Ray, 2000). When
satellite altimeter data is used to constrain both
the barotropic and baroclinic tides, the estimate
drops to 0.6 TW (Kantha and Tierney, 1997).
Together with the contribution from the wind,
these dissipation rates are barely sufficient to mix
the 30 Sv of Macdonald and Wunsch through the
full depth of the water column. However, even
SECTION 4 THE GLOBAL FLOW FIELD
212