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The Combined Effect of Tidally and Eddy-Driven Diapycnal Mixing
on the Large-Scale Ocean Circulation
OLEG A. SAENKO
Canadian Centre for Climate Modelling and Analysis, Environment Canada, Victoria, British Columbia, Canada
XIAOMING ZHAI
Atmospheric, Oceanic and Planetary Physics, University of Oxford, Oxford, United Kingdom
WILLIAM J. MERRYFIELD AND WARREN G. LEE
Canadian Centre for Climate Modelling and Analysis, Environment Canada, Victoria, British Columbia, Canada
(Manuscript received 11 July 2011, in final form 17 October 2011)
ABSTRACT
Several recent studies have shown that ocean western boundaries are the primary regions of eddy energy
dissipation. Globally, the eddy energy sinks have been estimated to integrate to about 0.2 TW. This is a sizable
fraction of the tidal energy dissipation in the deep oceanic interior, estimated at about 1.0 TW and contributing to diapycnal mixing. The authors conduct sensitivity experiments with an ocean general circulation
model assuming that the eddy energy is scattered into high-wavenumber vertical modes, resulting in energy
dissipation and locally enhanced diapycnal mixing. When only the tidal energy dissipation maintains
diapycnal mixing, the overturning circulation, and stratification in the deep ocean are too weak. With the
addition of the eddy dissipation, the deep-ocean thermal structure becomes closer to that observed and the
overturning circulation and stratification in the abyss become stronger. Furthermore, the mixing associated
with the eddy dissipation can, on its own, drive a relatively strong overturning. The stratification and overturning in the deep ocean are sensitive to the vertical structure of diapycnal mixing. When most of this energy
dissipates within 300 m above the bottom, the abyssal overturning and stratification are too weak. Allowing
for the dissipation to penetrate higher in the water column, such as suggested by recent observations, results in
stronger stratification and meridional circulation. Zonal circulation is also affected. In particular, the Drake
Passage transport becomes closer to its observational estimates with the increase in the vertical scale for
turbulence above topography. Consistent with some theoretical models, the Drake Passage transport increases with the increase in the mean upper-ocean diffusivity.
1. Introduction
Turbulent mixing in a stratified ocean requires mechanical energy. Two primary sources of such energy are
due to winds and tides (Munk and Wunsch 1998; Wunsch
and Ferrari 2004). In global ocean models, the associated turbulence has to be parameterized. Several recent
studies, based on such models, have explored the impact
of tidal energy dissipation in the deep ocean on the
Corresponding author address: Dr. Oleg A. Saenko, Canadian
Centre for Climate Modelling and Analysis, Environment Canada,
3800 Finnerty Road, Ocean, Earth and Atmospheric Sciences Bldg.,
University of Victoria, Victoria BC V8P 5C2, Canada.
E-mail: [email protected]
DOI: 10.1175/JPO-D-11-0122.1
simulated large-scale circulation and stratification
(e.g., Simmons et al. 2004; Saenko and Merryfield 2005;
Jayne 2009). Here, we further elaborate on this topic,
focusing on the combined effect of the tidal energy and
the energy associated with mesoscale eddy field in the
ocean (which essentially comes from the winds).
Eddies can be generated by a number of mechanisms,
such as baroclinic–barotropic instability of mean flows,
localized topographic steering, and direct wind–buoyancy
perturbations. Those eddies with horizontal scales close
to the first baroclinic Rossby radius have their energy
about equally partitioned between kinetic and potential
forms (Gill 1982). At steady state, the sources and sinks of
the eddy energy have to balance. The processes that remove eddy energy remain unclear, but the candidates
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SAENKO ET AL.
FIG. 1. Eddy energy sink in mW m22 (from Zhai et al. 2010). Global integral is ;0.2 TW.
include the ocean bottom drag, air–sea interaction, and
the transfer of eddy energy to the mean flow. It is also likely
that a substantial fraction of the eddy energy gets scattered into high-wavenumber internal waves; the breaking of which results in enhanced diapycnal mixing (e.g.,
Tandon and Garrett 1996; Naveira Garabato et al. 2004;
Marshall and Naveira Garabato 2008; Arbic et al. 2010).
The potential energy generated by the mixing could then
contribute to sustaining the large-scale overturning circulation in the ocean (Huang 1999). Recent estimates (Zhai
et al. 2010; Xu et al. 2011) suggest that western boundary
regions and the Antarctic Circumpolar Current (ACC) are
not only the major eddy source areas but also the places
where much of the eddy energy dissipates (Fig. 1). Globally
integrated, the rate of eddy energy generation/dissipation
has been estimated independently at about 0.2 TW by Zhai
et al. (2010) and by Xu et al. (2011).
Some early models of deep-ocean circulation were
based on the assumption of uniform upwelling (e.g.,
Stommel and Arons 1960). In the real ocean, turbulent
mixing is far from uniform (e.g., Polzin et al. 1997;
Kunze et al. 2006). Microstructure measurements (e.g.,
Gregg 1987) and tracer release experiments (e.g.,
Ledwell et al. 1993) have revealed that, in most of the
upper ocean, below the mixed layer, a representative
value for diapycnal diffusivity is O(1025) m2 s21. However, such diffusivity values would be an order of magnitude too small to maintain the observed stratification
below the pycnocline (Munk 1966). Therefore, it has
been argued that much stronger mixing must be confined to a small number of concentrated areas, including
along the boundaries, from which the water masses are
exported into the ocean interior (Munk and Wunsch 1998).
Ocean general circulation models (GCMs) have
proven to be a useful tool for addressing the impact of
the heterogeneous nature of the small-scale turbulence
on the large-scale circulation (e.g., Simmons et al. 2004;
Saenko and Merryfield 2005; Saenko 2006; Jayne 2009).
Here one such GCM is employed to evaluate the potential impact of the eddy energy sink on diapycnal
mixing and large-scale ocean circulation, separately
and in combination with the tidal energy dissipation. In
section 2, we present some basic arguments suggesting
a link between the kinetic energy dissipation in the
oceanic interior and large-scale overturning circulation
in the abyss. We also provide a brief review of the literature on the role of vertical diffusivity in maintaining
zonal circulation in the Southern Ocean. The model, the
mixing scheme, and the design of numerical experiments
are described in section 3. This is followed by a presentation of main results in section 4 and conclusions
in section 5.
2. Links between small-scale mixing and circulation
a. Overturning circulation
In a stratified ocean at steady state, the link between
the dissipation of turbulent kinetic energy and upwelling
in the abyss can be described by a buoyancy budget of
the form
u $b 1 wbz 5 (Ky N 2 )z 1 Qb ,
(1)
where $ is the two-dimensional gradient operator; b 5
2gr/r0 is the buoyancy, where g, r, and r0 are the acceleration due to gravity, ocean potential density, and
reference density, respectively; Ky is the vertical diffusivity due to small-scale turbulent mixing; N2 5 bz is the
squared buoyancy frequency; and Qb represents buoyancy
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sources and sinks. The velocity field [u(u, y), w] is assumed
to satisfy $ u 1 wz 5 0, and it represents the flows with
scales larger than those associated with the small-scale
turbulence (represented by the first term on the righthand side). Assuming there are no significant buoyancy
fluxes at the bottom and that jQbj is small, one can integrate Eq. (1) globally from the bottom to some horizontal surface in the deep ocean (Gnanadesikan et al.
2005) to obtain
hwbi 5 hKy N 2 i,
Ky 5 G
N2
,
(3)
where G 5 0.2 is the mixing efficiency (Osborn 1980);
combining Eqs. (2) and (3) gives
hwbi 5 Ghi
(4)
In other words, in the presence of stable stratification
there must be a supply of energy to maintain small-scale
turbulent mixing. In turn, the potential energy generated by the mixing maintains the overturning circulation
at larger scales. The mixing efficiency of 20% indicates
that most of the energy dissipates without mixing the
ocean. Only 20% of it could drive the overturning circulation in the abyssal ocean. Munk and Wunsch (1998)
found that, given such a mixing efficiency, a mechanical
energy supply of about 2 TW is required to maintain the
observed stratification in the abyss against 30 Sv (1 Sv [
106 m3 s21) of deep-water formation.
b. Zonal circulation
Zonal circulation, particularly the ACC, also can be
strongly affected by the potential energy generated by
the small-scale mixing. According to Borowski et al.
(2002), the transport through a channel with blocked
contours of f/H (e.g., in the Drake Passage) is to a leading
order determined by the distribution of the baroclinic
potential energy x,
f
J C,
H
1
’ J x,
,
H
with b9 being the buoyancy anomaly relative to its horizontal mean profile. The right-hand side of Eq. (5) represents the joint effect of baroclinicity and relief (JEBAR;
Sarkisyan and Ivanov 1971). In other words, in order for
a vertically integrated flow to cross the contours of f/H,
there has to be a nonzero JEBAR (i.e., the contours of
constant x must cross the contours of constant H). It
therefore follows that x can provide a good proxy for C
in the Southern Ocean (Borowski et al. 2002); that is,
(2)
where hi denotes horizontal integration. This balance
implies that the potential energy created by the smallscale turbulence, through fluxing buoyancy downward,
is removed on the larger scales by transporting buoyancy
upward. Assuming further that Ky can be related to the
kinetic energy dissipation as follows:
C’
x
.
fACC
(6)
Although much of x is likely maintained by the wind
stress (e.g., Saenko 2009), a portion of x could be supplied by diapycnal mixing. Munday et al. (2011) used
a (two layer) version of Eq. (6) to propose a conceptual
model of the ACC. Their model is based on competition
between diapycnal mixing, which tends to deepen the
pycnocline north of ACC, and mesoscale eddies, which
tend to flatten it. According to Munday et al. (2011), in a
realistic situation (with wind stress applied to the ocean)
the transport of the ACC increases with the increase of
global-mean vertical diffusivity at the base of pycnocline,
provided that the diffusivity is relatively large. We shall
test this theory too. In some other theoretical models
the transport of the ACC has been related to the local
diapycnal mixing in the Southern Ocean (e.g., Karsten
and Marshall 2002; Borowski et al. 2002). We shall show
that such a connection may also hold as long as the mean
diffusivity is relatively large.
3. The model and mixing scheme
A parameterization of small-scale mixing in an ocean
GCM has to ensure that the power that maintains such
mixing against gravity does not exceed the power that
may be available locally from different sources (e.g.,
Osborn 1980). One such parameterization has been proposed by St. Laurent et al. (2002) for the case where the
mechanical energy that supports small-scale turbulence
comes from dissipation of internal tides in the deep
ocean.
Here we follow these ideas. Vertical diffusivity in our
ocean GCM is determined by a combined effect of tidal
and eddy energies
(x, y, z) 1 2 (x, y, z)
,
Ky 5 Kb 1 G 1
N2
(7)
1 (x, y, z) 5 q1 Etidal (x, y)F1 (z) (W kg21 ) and
(8)
(5)
where J(,) is the Jacobian; C is the horizontal
Ð 0 streamfunction; f is the Coriolis parameter; and x 5 2 2H zb9 dz,
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where
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FIG. 2. Estimates of vertical diffusivity at about 2200-m depth due to (top) tidal energy
dissipation and (bottom) ocean eddy energy dissipation. In both cases, the decay scale for
turbulence above the bottom is set to 500 m and the observed PHC climatology (Steele et al.
2001) is used to compute the squared buoyancy frequency (see the text for more details).
2 (x, y, z) 5 q2 Eeddy (x, y)F2 (z) (W kg21 ).
(9)
In Eqs. (7)–(9), Kb 5 1025 m2 s21 is the background
diffusivity that is to account for the observational evidence that in most of the upper ocean and away from
rough topography the diffusivity is relatively weak (e.g.,
Gregg 1987; Ledwell et al. 1993; Kunze et al. 2006);
Etidal(x, y) and Eeddy(x, y) are the estimated energy fluxes
provided by internal tides (Jayne and St. Laurent 2001)
and mesoscale eddies (Zhai et al. 2010; Fig. 1), respectively; and q1 and q2 are the fractions of the respective
energies that dissipate locally. Similar to Saenko and
Merryfield (2005), we prohibit Ky in Eq. (7) from exceeding 20 3 1024 m2 s21, which is about 2 times
the global-mean near-bottom diffusivity estimated by
Ganachaud and Wunsch (2000). In the model sensitivity experiments discussed in section 4, we consider the
cases where q1 5 1/ 3 (St. Laurent and Garrett 2002) and
q2 5 1. St. Laurent et al. (2002) argue that 0.3 60.1 value
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for the fraction of the energy that dissipates locally is
reasonable for the Brazil Basin. However, this may
not necessarily hold for any ocean basin (e.g., Althaus
et al. 2003). In our sensitivity experiments the q2 5 1
case corresponds to an extreme situation wherein (i) all
of the eddy energy sinks (that remain after accounting
for G 5 0.2 mixing efficiency) support the diapycnal
mixing in the ocean interior and (ii) they do so locally.
This will be compared with another extreme case where
q2 5 0. Whenever q1 6¼ 1 and/or q2 6¼ 1, an implicit assumption is that the rest of the associated energy (1 2 q1
and 1 2 q2) could contribute to sustaining the background internal wave field.
Ð 0 The verticalÐ 0structure functions F1 and F2 satisfy 2H F1 (z) dz 5 2H F2 (z) dz 5 1.
For simplicity, we assume that F1(z) 5 F2(z) 5 F(z). The
latter has the form that ensures exponential decay of
the mixing energy from the bottom H(x, y) upward (e.g.,
St. Laurent et al. 2002),
F(z) 5
e2(H1z)/h
,
h(1 2 e2H /h )
(10)
where h is the vertical decay scale for turbulence, which
is varied in the sensitivity experiments between 300 and
1000 m: that is, roughly within its uncertainty ranges
(St. Laurent et al. 2002).
Some of the above assumptions and parameters are
likely to be only crude representations of the turbulent
mixing in the ocean. Our motivation, however, is not so
much to examine the most realistic case but to conduct
a set of sensitivity experiments. In these, we aim to make
a step toward estimating the potential role of the tidal and
eddy dissipation energies, separately and in combination,
in maintaining the oceanic stratification and large-scale
overturning circulation. Examples of the vertical diffusivity maps at the middepth ocean due to the tidal energy
dissipation and eddy energy dissipation, obtained using
the above assumptions and climatological distribution of
N2, are shown in Fig. 2. As expected, the largest values of
Ky are found above the major topographic features and
along the western boundaries. Note, in particular, that in
some weakly stratified ocean regions, such as in the
subpolar Atlantic, the vertical diffusivity due to the eddy
energy dissipation can be locally up to an order of magnitude larger than its background value (Fig. 2, bottom),
even though the eddy energy sink in this region is relatively weak (Fig. 1).
The ocean model employed is a version of the National
Center for Atmospheric Research (NCAR) Community
Ocean Model (Gent et al. 1998), which was developed
from version 1 of the Geophysical Fluid Dynamics Laboratory Modular Ocean Model. This is the same model as
in Saenko and Merryfield (2005), but with the horizontal
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resolution of 1.418 3 0.948 (longitude 3 latitude) and 33
vertical levels. The model employs the eddy transport
parameterization of Gent and McWilliams (1990), with
coefficients of thickness diffusivity and isopycnal diffusivity set to 103 m2 s21. Wind stress forcing consists of
daily averages from a 30-yr run of the third-generation
Canadian Centre for Climate Modelling and Analysis
(CCCma) atmospheric general circulation model (AGCM3)
with climatological sea surface temperatures (SSTs).
Surface heat and freshwater fluxes consist of daily averages from the same CCCma AGCM3 run, together
with restoring to (linearly interpolated in time) monthly
climatological fields of SST and sea surface salinity
(SSS) from the Polar Science Center Hydrographic
Climatology (PHC) 2.0 (Steele et al. 2001) with restoring time scales of 30 days for temperature and 180
days for salinity. This climatology is a merged product
that combines data from the World Ocean Atlas and the
Arctic Ocean Atlas. We present results from five sensitivity experiments, all run for 5000 yr (i.e., to near
equilibrium). These differ by the energy sources that
sustain vertical mixing in the ocean and by the value set
for the vertical decay scale h for turbulence (Table 1).
4. Results
a. Impact of eddy energy
The simulated thermal structure in the upper ;2 km
of the ocean is close to that observed (this is illustrated in
Fig. 3, top, for the ‘‘Tidal’’ experiment; see Table 1). It is
largely maintained by the wind stress and its curl
(Saenko 2009), as can be expected based on the theories
of the ventilated thermocline (Luyten et al. 1983). The
deep ocean, however, is too cold in the Tidal model (Fig.
3, top). Based on the arguments presented in Munk and
Wunsch (1998), one reason for this could be related to
insufficient mechanical energy for sustaining diapycnal
mixing in the abyss. According to these arguments, in
the presence of cold water sources in polar regions the
deep ocean is expected to be filled with these waters if
the mixing of heat from the upper ocean is not strong
enough (e.g., Saenko and Merryfield 2005). Consistent
with these arguments, the abyssal ocean becomes
warmer when more energy is supplied to sustain the
mixing in the ‘‘Tidal 1 Eddy’’ experiment (Fig. 3, top).
Furthermore, the different geographic distributions between the tidal and eddy energy sources are an important factor in maintaining the thermal structure in the
abyss. To illustrate this, we conducted an additional
sensitivity experiment (‘‘Tidal*’’) setting q1 5 0.5 and
q2 5 0 in Eqs. (7)–(9). This provides about the same
amount of energy for the mixing as in the Tidal 1 Eddy
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TABLE 1. List of main numerical experiments.
Expt
Energy
source(s)
Vertical decay
scale (m)
Tidal
Eddy
Tidal 1 Eddy
Tidal 1 Eddy1000
Tidal 1 Eddy300
Tidal
Eddy
Tidal and eddy
Tidal and eddy
Tidal and eddy
500
500
500
1000
300
model. As might be expected, the integrated meridional
overturning circulation (MOC) in the Tidal* experiment
(not shown) is largely the same as in the Tidal 1 Eddy
case (see next paragraph). However, in the Tidal* experiment, the largest warming is less widespread and is
mostly confined to the middepth ocean (Fig. 3, bottom).
The rate of MOC differs between the Tidal, Eddy, and
Tidal 1 Eddy experiments but mostly below ;2-km
depth (Fig. 4). This is expected because most of the
energy sustaining the small-scale mixing in the model is
constrained to dissipate below 2-km depth by the vertical profile function. In the Tidal model, about 8 Sv is
transported upward across 3.5-km depth and north of
about 258S (Fig. 4a). This is less than the observational
estimates presented by Talley et al. (2003). She estimated that in the Pacific the bottom water upwelling
is about 10 Sv, with a comparable contribution in the
Indian Ocean. The eddy energy, on its own, can drive as
much as 5 Sv of the bottom water flux across 3.5 km
(Fig. 4b). However, when combined with the tidal energy,
the effect is nonlinear with respect to the overturning
circulation (Fig. 4c). The maximum (in fact the minimum,
as plotted in Fig. 4) overturning in the abyss increases in
the Tidal 1 Eddy model compared to those in the Tidal
and Eddy models by about 1.2 and 4.2 Sv, respectively.
The increase is consistent with the arguments presented
in section 2. The transport associated with the outflow of
North Atlantic Deep Water (NADW) is roughly the same
in all three models.
The observed stratification increases upward. In the
zonal mean, the only region where relatively large values
of N2 penetrate to the abyssal ocean is roughly between
308 and 508S (Fig. 5a). This general structure of the
observed stratification is captured by the Tidal model
(Fig. 5b). The ratio between the simulated and observed
N2 reveals that between 1- and 3-km depth the stratification simulated by the Tidal model is too strong north
of 408S, whereas below 3 km it is too weak (Fig. 5c). The
latter could be indicative of insufficient mixing energy
and hence too weak vertical mixing in the abyss (Saenko
and Merryfield 2005). [On the other hand, too strong
mixing could also lead to unrealistic values for the
vertical scale of stratification. Assuming the so-called
FIG. 3. (top) Zonally averaged potential temperature (solid)
simulated by the Tidal model and (dashed green) as given by the
PHC climatology (Steele et al. 2001). The ocean where the Tidal 1
Eddy run is warmer by 0–0.15 K (relative to the Tidal) is shown
with yellow shading, whereas where this potential temperature
increase is more than 0.15 K is shown with red shading. (bottom)
As in (top), but where the Tidal* run is warmer by 0–0.15 K (relative to the Tidal; see text for details) is shown with yellow shading,
whereas where the Tidal* potential temperature is more than
0.15 K warmer than the Tidal run is shown with red shading.
advective–diffusive balance holds (Munk and Wunsch
1998; Wunsch and Ferrari 2004), this scale is Ky /w, where
w is the vertical velocity. For w 5 1027 m s21 (a realistic
value), the value of Ky 5 1023 m2 s21 gives 10 km for the
vertical scale of stratification.]
Aside from the diapycnal mixing, there are likely many
other physical processes that are represented only approximately by the model. As for the mixing, the available estimates suggest that it would require some 2–3 TW
of mechanical energy to maintain the observed stratification in the deep ocean (Munk and Wunsch 1998; St.
Laurent and Simmons 2006). It is therefore not expected
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that adding ;0.2 TW of the eddy energy to ;1 TW of the
tidal energy dissipation in the deep ocean would correct
for the too weak simulated stratification in the abyss.
Nevertheless, below about 4-km depth the Tidal 1 Eddy
model does tend to simulate a stronger stratification in
the ocean north of the equator and south of 558S (Fig.
5d). In the next subsection, we shall illustrate that, given
the same amount of energy to support the diapycnal
mixing (i.e., tidal plus eddy), the abyssal stratification can
be quite sensitive to the vertical decay scale for turbulence above the topography.
b. Sensitivity to vertical decay scale
FIG. 4. Mean overturning circulation (Sv) below about 1-km depth
in the (a) Tidal, (b) Eddy, and (c) Tidal 1 Eddy experiments. In all
three cases, the vertical decay scale for turbulence is set to 500 m.
Negative values correspond to counterclockwise circulation.
As noted in section 3, some observational studies
on turbulence above rough topography provide evidence for its sharp decay above the bottom (see, e.g., St.
Laurent et al. 2002 and references therein). This is one
of the reasons why some of the related modeling studies
employ Eq. (10) with h 5 500 m to represent the vertical structure of the kinetic energy dissipation that maintains the associated diapycnal mixing (e.g., Simmons
et al. 2004; Saenko and Merryfield 2005; Jayne 2009).
However, results from some other observational studies
suggest a larger decay scale for the turbulence above the
bottom (see Decloedt and Luther 2010, and references
therein). In addition, examples have been presented
where the vertical structure of the dissipation may vary
considerably within the same study region and may even
increase upward (e.g., Naveira Garabato et al. 2004). The
estimates by Kunze et al. (2006) suggest a rather uniform
structure for the mean vertical profile of the dissipation as
a function of height above the bottom.
Motivated in part by this uncertainty in the vertical
structure of the kinetic energy dissipation, we discuss
here two additional sensitivity experiments, ‘‘Tidal 1
Eddy1000’’ and ‘‘Tidal 1 Eddy300.’’ For simplicity, these
are identical to the Tidal 1 Eddy experiment, except
the vertical decay scale for turbulence above the bottom
h in Eq. (10) is either increased to 1000 m or decreased
to 300 m from its 500-m value in the Tidal 1 Eddy
model (see Table 1) (h is most likely a function of location). The corresponding global-mean simulated diffusivity at ;1000-m depth then varies between 0.38 3
1025 m2 s21 and 0.55 3 1025 m2 s21 when h is set to, 300
and 1000 m, respectively. These values of mean diffusivity are within the observational estimates. In particular, the global-mean diffusivity estimates by Decloedt and
Luther (2010) at 1000-m depth range from about 0.15 3
1025 m2 s21 to 0.6 3 1025 m2 s21. The two global-mean
estimates by Kunze et al. (2006) at this depth are 0.15 3
1025 m2 s21 and 0.4 3 1025 m2 s21. In the deep ocean,
the global-mean diffusivity in our model experiments
is within the estimates of Decloedt and Luther (2010),
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FIG. 5. Zonally mean squared buoyancy frequency [N2 5 2(g/r0)›s3/›z; 31027 s22] (a) as given by the observed PHC
climatology (Steele et al. 2001) and (b) as simulated by the Tidal model. Ratio of N2 (c) simulated by the Tidal model to that
represented by the observed climatology and (d) simulated by the Tidal 1 Eddy model to that simulated by the Tidal model.
ranging from about 1024 m2 s21 at 3000-m depth to
1023 m2 s21 at 5000-m depth. Such a range is also consistent with estimates from inverse models (Ganachaud
and Wunsch 2000; see also Lumpkin and Speer 2003). In
contrast, the estimates of Kunze et al. (2006) for the
mean diffusivity in the abyss are ,1024 m2 s21, although they do acknowledge that the lowered ADCP
(LADCP)–CTD data they use do not account for tidal
dissipation and that their sampling may miss major hotspots of enhanced mixing.
The changes in the decay scale for turbulence affect
the MOC in the abyssal ocean (Fig. 6). Compared to the
Tidal 1 Eddy case, the rate of anticlockwise overturning
below about 2-km depth increases in response to the
larger h by about 1.2 Sv and decreases in the case of the
smaller h by about 6.1 Sv. In other words, the rate of
the large-scale overturning can be changed by changing
vertical distribution of the energy dissipation: that is,
without changing the total amount of mechanical energy maintaining the turbulent mixing. An explanation
for this can be provided by assuming locally the vertical
advective–diffusive balance of buoyancy; that is,
wbz 5 (Ky N 2 )z
(11)
so that
w5
(Ky N 2 )z
N2
.
(12)
If Ky is given by Eq. (7), then by substituting (7) into (12)
we obtain
w 5 Kb
›(lnN 2 )
1 G z2 ,
›z
N
(13)
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FIG. 6. Global meridional overturning circulation (Sv) below
about 1-km depth in the (a) Tidal 1 Eddy1000 and (b) Tidal 1
Eddy300 experiments.
where, in this case, 5 1 1 2 and Kb and G are positive
constants. The first term on the right-hand side of Eq.
(13) is positive definite, given the typically observed and
modeled buoyancy distribution, and drives upwelling in
the sense of enhancing the bottom cell. However, the
second term on the right-hand side of Eq. (13) is negative definite and drives downwelling, because decays
upward. Therefore, under the assumption that Eq. (11)
holds, it is the competition between these two terms that
determines the strength of the overturning circulation.
Increasing the decay scale reduces jzj and hence reduces
the downwelling associated with the second term in Eq.
(13), so that the overturning circulation strengthens (assuming the first term does not change much). Similarly,
decreasing the decay scale weakens the near-bottom
overturning (Fig. 6).
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The Tidal 1 Eddy1000 model also simulates the strongest stratification below about 3 km depth. In contrast,
when most of the energy that supports diapycnal mixing
is constrained to dissipate within 300 m above the bottom,
the simulated stratification in the abyss at steady state is
the weakest (Fig. 7).
Increasing the decay scale for turbulence above the
bottom increases the downward diffusion of heat. As a
result, most of the deep ocean becomes warmer (Fig. 8).
It is interesting to note that the largest warming is simulated along the western boundary in the deep Atlantic
Ocean (Fig. 8b), even though the net rate of NADW
overturning is not much affected by the change in the
decay scale. To compensate for the stronger bottom
water upwelling (Fig. 6), the sinking of the Antarctic
Bottom Water becomes stronger with the increase in
the decay scale for turbulence and the deep ocean near
Antarctica becomes colder (Fig. 8).
Zonal circulation, particularly in the Southern Ocean,
is also strongly affected. In our experiments, the net
transport through the Drake Passage increases from
115.4 to 129.8 and 137.5 Sv when the scale for turbulence
increases from 300 to 500 and 1000 m, respectively. For
comparison, we note that Cunningham et al. (2003) estimated the baroclinic transport through Drake Passage
at 136.7 67.8 Sv (relative to the deepest common level
for six hydrographic sections along the World Ocean
Circulation Experiment line SR1b). A recent eddypermitting Southern Ocean state estimate by Mazloff
et al. (2010) gives 153 65 Sv for the net Drake Passage
volume transport.
As argued in section 2b, the distribution of x/f is found
to be a good proxy to the horizontal streamfunction
in the Southern Ocean. The Tidal 1 Eddy1000 model
estimate of x/f is closer to the estimate of x/f based on
the observed ocean hydrography, as compared to the
Tidal 1 Eddy300 and Tidal 1 Eddy model estimates of
x/f (Fig. 9). The Tidal 1 Eddy1000 model also simulates
the largest values of JEBAR northeast of the passage
(Fig. 9): that is, where the JEBAR effect maintains a
deflection of the ACC to the north across the contour of
f/H and forms the Malvinas Current.
The total number of model experiments is not sufficient to come to a robust conclusion about the possible
dependence of the ACC transport on vertical diffusivity
(see also Saenko and Merryfield 2005). Combining the
results from our main experiments (Table 1), the Drake
Passage transport increases with the increase in the
globally averaged diffusivity at roughly the base of the
pycnocline (Ky ), but only for relatively large values of
the diffusivity (Ky . 3 3 1024 m2 s21 ). For Ky , 3 3 1024
m2 s21 , the ACC transport appears to be independent of
the diffusivity (Fig. 10). Both these results are consistent
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535
FIG. 8. Potential temperature difference (K) at about 3.2-km
depth between the Tidal 1 Eddy1000 model and (a) the Tidal 1
Eddy model and (b) the Tidal 1 Eddy300 model (Table 1). Note
the difference in the color scale.
FIG. 7. Ratio of squared buoyancy frequency simulated in (a) the
Tidal 1 Eddy experiment and (b) the Tidal 1 Eddy300 experiment
to that in the Tidal 1 Eddy1000 experiment (Table 1).
with the theory and numerical results presented by
Munday et al. (2011). In particular, according to Munday
et al. (2011), for fixed wind and eddy strength in the
Southern Ocean, the ACC transport is insensitive to the
diffusivity if the mixing-driven upwelling across the base
of pycnocline is sufficiently small (relative to Ekman
transport across the ACC). In our experiments, however, the diffusivity averaged over the whole ocean area
at ;1-km depth essentially follows that averaged for the
ocean south of 408S (Fig. 10). As such, the changes in
the ACC transport may as well be explained based on the
Southern Ocean circulation theories where this transport
has been related to the local vertical diffusivity (e.g.,
Karsten and Marshall 2002). We note that, consistent
with Munday et al. (2011), it is found that in the presence
of wind stress a relatively strong ACC transport can be
maintained even in the limit of relatively low values of
diapycnal diffusivity (Fig. 10). Finally, it should be pointed
that Jayne (2009) also discussed the dependence of the
ACC transport on the vertical diffusivity, but in a context
different from that of Munday et al. (2011).
5. Discussion and conclusions
Using a simple advective–diffusive balance, Munk
(1966) proposed that in order to maintain the observed
stratification in the ocean the diapycnal diffusivity at the
lower part of the pycnocline would have to be O(1024)
m2 s21. However, microstructure measurements (e.g.,
Gregg 1987) and tracer release experiments (e.g., Ledwell
et al. 1993) have revealed an order of magnitude lower
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VOLUME 42
FIG. 9. The baroclinic potential energy scaled by the Coriolis parameter (x/f; in Sv) in the Drake Passage region
(a)–(c) in the models with different decay scale for turbulence h and (d) based on the observed PHC climatology
(Steele et al. 2001). The dashed lines show the contours of f/H, where H(x, y) is the bottom topography resolved by
the model. The dark gray areas indicate the regions with relatively large JEBAR effect: that is, where jJ(x, H21)j .
10211 s22. The baroclinic potential energy was computed using s2 (potential density referenced to 2000-m depth),
based on the model data or the observed climatology.
diffusivity values, below the mixed layer and away from
topography. In an attempt to reconcile the estimated
by Munk diffusivity value with the observations, Munk
and Wunsch (1998) argued that a much stronger (compared to the typically observed) mixing could be confined
to a small number of concentrated areas, including along
the boundaries.
Several recent studies have shown that ocean western
boundaries are the regions of significant sink of mesoscale eddy energy (e.g., Zhai et al. 2010; Xu et al. 2011).
Here, we conducted a set of ocean general circulation
model experiments assuming that this energy is scattered into high-wavenumber vertical modes resulting in
dissipation and enhanced diapycnal mixing. Globally,
the eddy energy sinks integrate to ;0.2 TW (Zhai et al.
2010; Xu et al. 2011), which is a sizable fraction of the
tidal energy dissipation in the deep ocean. The purpose
of the model experiments was to investigate the effect of
the eddy and tidal dissipation energies, in combination
and separately, on the ocean stratification and largescale circulation, through the impact of the dissipation
on diapycnal mixing. We show that, when only the tidal
energy maintains diapycnal mixing, the overturning
circulation and stratification in the deep ocean are too
weak. With the addition of the eddy dissipation, the
deep-ocean thermal structure becomes closer to that
observed and the overturning and stratification in the
abyss strengthen. Furthermore, the mixing associated
with the eddy dissipation can, on its own, drive a relatively strong overturning in the abyss. However, when
combined with the tidal energy, the effect is nonlinear
with respect to the overturning circulation. We also note
that eddy dissipation is not estimated near the equator
because geostrophic balance was used in Zhai et al.
(2010). Including the missing mixing associated with
eddy dissipation near the equator could lead to an even
stronger overturning circulation.
Additional sensitivity experiments show that stratification and overturning in the deep ocean are quite sensitive to the vertical structure of diapycnal mixing. When
most of this energy is constrained to dissipate within
300 m above the bottom, the abyssal overturning and
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SAENKO ET AL.
FIG. 10. The simulated Drake Passage transport plotted against
the mean vertical diffusivity at ;1-km depth, averaged over the
whole ocean and over the ocean south of 408S. The lines are regressions for the values of diffusivity larger than 3 3 1025 m2 s21:
on global mean (dashed) and south of 408S (solid).
stratification are too weak and the deep ocean is too
cold. Allowing for the dissipation to penetrate higher
into the water column, such as suggested by some recent
observations, results in a stronger overturning and stratification in the deep ocean.
Zonal circulation in the Southern Ocean is also strongly
affected by the variations in the vertical scale for turbulence. In particular, the simulated distribution of the baroclinic potential energy, which has been shown to be a
good proxy for the vertically integrated transport, becomes progressively closer to the corresponding observational estimate when more mixing energy is constrained
to dissipate higher above the bottom. In the model, the
Drake Passage transport increases with the increase of the
mean vertical diffusivity at the base of pycnocline, as predicted by some theories of the ACC (Munday et al. 2011).
Acknowledgments. We thank Thomas Decloedt and
two anonymous reviewers for constructive comments.
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