Ocean Modelling 34 (2010) 1–15
Contents lists available at ScienceDirect
Ocean Modelling
journal homepage: www.elsevier.com/locate/ocemod
Modifications of gyre circulation by sub-mesoscale physics
M. Lévy a,*, P. Klein b, A.-M. Tréguier b, D. Iovino a, G. Madec a, S. Masson a, K. Takahashi c
a
LOCEAN-IPSL, CNRS/UPMC/IRD/MNHN, UPMC, BC 100, 4 place Jussieu, 75252 Paris Cedex 05, France
LPO, CNRS/IFREMER/UBO, IFREMER centre de Brest, BP 70, 29280 Plouzane, France
c
ESC, JAMSTEC, Kanazawa-ku, Yokohama 236-0001, Japan
b
a r t i c l e
i n f o
Article history:
Received 27 March 2009
Received in revised form 31 March 2010
Accepted 8 April 2010
Available online 21 April 2010
Keywords:
Sub-mesoscale
Gyre circulation
Thermal equilibrium
a b s t r a c t
The large-scale impacts of sub-mesoscale physics are addressed by comparing mean characteristics of
basin-scale, seasonally varying, subtropical and subpolar gyres in a suite of numerical experiments varying in horizontal resolution (1°, 1/9° and 1/54°) and accordingly, in sub-grid scale mixing. After 100 years
of simulation, and as suggested from earlier studies, the mean circulation and the mean structure of the
ventilated thermocline strongly differ when switching from 1° to 1/9° resolution. Our results emphasize
that increasing the resolution from 1/9° to 1/54° leads to major further changes. These changes ensue
from the emergence of a denser and more energetic vortex population at 1/54°, occupying most of the
basin and sustained by sub-mesoscale physics. Non-linear effects of this turbulence strongly intensify
the jet that separates the two gyres, thus steepening the isopycnals and counter-balancing the strong
eddy-driven heat transport that tends to flatten them. The jet is more zonal, penetrates further to the
east, and is shifted southward by a few degrees, which significantly alters the shape and position of
the gyres. The strengthening of the main jet comes together with the emergence of a regime of energetic
secondary zonal jets, associated with complex recirculations. In parallel, sub-mesoscales restratify both
the seasonal and the main thermocline, inducing in particular a reduction of deep convection and the
modification of the water masses involved in the meridional overturing circulation. Although the results
presented here are presumably highly constrained by the idealized geometry of our basin, they suggest
that sub-mesoscale processes play an important role on the mean circulation and mean transports at the
scale of oceanic basins. At the highest resolution presented here (1/54°), momentum effects are becoming
important so that eddies do not simply cause the slumping of isopycnals but can arrange the flow to form
jet-like structures with steeper isopycnals in places.
Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction
High-resolution satellite images (both infrared and color) and
oceanographic field measurements have revealed intense, transient, sub-mesoscale motions associated with the eddy activity in
many parts of the ocean. Typically, these motions have a horizontal
scale of O(10) km, one order of magnitude smaller than oceanic
mesoscale eddies (O(100) km). Thus, the explicit resolution of
these sub-mesoscale motions in ocean models requires horizontal
grid resolutions of O(1) km. Nowadays, the highest resolution used
in global ocean models is of the order of 1/10° (Maltrud and
McClean, 2005; Sasaki et al., 2008; Le Galloudec et al., 2008), which
is not sufficient to capture the details of the sub-mesoscale.
Nevertheless, the explicit resolution of the sub-mesoscale
range is technically feasible over oceanic domains of limited
extension. Such ‘‘sub-mesoscale resolving” numerical experiments
* Corresponding author. Address: LOCEAN-IPSL, CNRS, 5 Place Jussieu, 75252
Paris, France. Tel.: +33 144272707.
E-mail address: marina.levy@upmc.fr (M. Lévy).
1463-5003/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ocemod.2010.04.001
show significant deviation from eddy-resolving experiments, with,
in particular, the explosion of the number of eddies (Hurlburt and
Hogan, 2000; Siegel et al., 2001). This explosion highlights the
important role of sub-mesoscale physics in sustaining an energetic mesoscale circulation, because sub-mesoscale filaments
form transport barriers that re-inforce the eddies. Very-high resolution model experiments also suggest that sub-mesoscale physics
is an important element of the large scale oceanic circulation. In
particular, the important contribution of sub-mesoscale physics
to the vertical flux of mass, of buoyancy and of tracers in the
upper ocean was illustrated by the studies of Thomas et al.
(2008) and Capet et al. (2008). Moreover, the stratification of
the upper layers by sub-mesoscales and the enhancement of the
connections between the surface and the interior was demonstrated by Fox-Kemper et al. (2008) and Klein et al. (2008). However, the integrated, cumulative effects of sub-mesoscale physics
on the large-scale oceanic circulation could not be addressed in
these studies, either because the large-scale conditions were imposed or because the model integrations were not long enough.
Thus, one question is: how are the large-scale circulation and
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M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
the large-scale thermohaline equilibrium affected by sub-mesoscale physics? In ‘‘eddy resolving” models, sub-mesoscale motions
are generally crudely parametrized by a weak diffusion operator
applied both on tracers and momentum. The Gent-McWilliams
parametrization (Gent and McWilliams, 1990) intends to represent the effects of mesoscales only, and is appropriate for ‘‘noneddy resolving” models. A more physical parametrization of the
sub-mesoscale was recently proposed by Fox-Kemper et al.
(2008), but their parameterization only concerns sub-mesoscales
in the surface mixed-layer. An underlying question is thus the
large-scale consequences of the crude sub-mesoscale cut-off in
present day eddy-resolving models.
The influence of mesoscale eddies on the structure of the ventilated thermocline in an idealized subtropical gyre has been demonstrated in a series of studies (Marshall et al., 2002; Radko and
Marshall, 2003). Henning and Vallis (2004) have used a rectangular
basin, with both a subtropical and a subpolar gyre, to compare
solution without eddies or with eddies (at 1/6°). They note that eddies modify the shape of the ventilated thermocline by moving the
outcrop positions of isopycnals, that eddies mix mode water away,
and tend to thicken the main thermocline. Our goal is to revisit
these results in more realistic, less viscous numerical simulations
at higher resolution.
In this paper, we address the large-scale impacts of sub-mesoscales by comparing mean characteristics of basin-scale, seasonally
varying, subtropical and subpolar gyres in a suite of numerical
experiments varying in horizontal resolution (non-eddy resolving,
eddy resolving, sub-mesoscale resolving) and accordingly, in subgrid scale mixing. The experiments were run over 100 years, which
corresponds to the time required to equilibrate the mean circulation and the mean structure of the main thermocline. Some physics
such as topographic effects or the contribution of water mass formation in marginal seas are not taken into account in our idealized
experiments. In consequence, the results of this sensitivity study
cannot be compared directly to the existing observations either
for example in the North Pacific or the North Atlantic, although
some resemblances may be noted.
2. Model experiments and flow equilibration
A series of simulations have been performed with increasing
horizontal resolution, the highest being two kilometers. Our experiments are carried out in an idealized domain similar to that used
in the studies of Drijfhout (1994a,b) and Hazeleger and Drijfhout
(1998, 1999, 2000a,b), and over several seasonal cycles. This allows
to investigate the spontaneous generation of a large number of
interacting, transient mesoscale eddies and their contribution to
the large scale circulation.
2.1. Domain and forcing
The seasonal cycle of a double-gyre is simulated with the levelcoordinate free-surface primitive equation ocean model NEMO
Fig. 1. Analytical forcings of the model as a function of latitude. (a) Wind stress, (c) penetrative solar radiation, (d) apparent temperature and (e) fresh water flux. The forcings
vary between winter (solid line) and summer (dashed line) in a sinusoidal manner. Panel (b) shows the rotated domain of the model configuration and the mean barotropic
stream function in experiment R1. The dashed horizontal lines mark the latitudes 30°N and 36°N.
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M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
Table 1
Parameters and important features of the model experiments. All computations are performed on the Earth Simulator at Yokohama, Japan. Real computing time is the total
computing time for 100 year simulations (spin-up), multiplied by the number of nodes used (each node is based on eight processors). The terms KM and KT are the eddy viscosity
and eddy diffusivity coefficients, respectively. The slope of the velocity spectra is computed between wave numbers k = 30 and k = 70. EKE is the domain-mean surface eddy
kinetic energy. W2 is the domain-mean 0–500 m vertical velocity variance. MKE is the domain-mean surface mean kinetic energy. The maximum surface velocity is the maximum
velocity in the offshore extension of the main current.
Horizontal resolution
Horizontal grid points
Time step
Number of processors
Real computing time (node hour)
KM
KT
Vorticity maximum (units of f)
Skewness
Slope of velocity spectra
EKE (104 m2 s2)
W2 (m2 d2)
MKE (104 m2 s2)
Separation latitude of the WBC
Maximum surface velocity (m s1)
R1
R9
R27
R54
106 km
20 30
2h
1
3
105 m2 s1
103 m2 s1
–
–
–
1
0.2
44
36° N
0.11
11.8 km
180 270
20 min
7
50
5 1010 m4 s1
109 m4 s1
1.5
1
3.0
199
13.3
129
34° N
0.36
3.9 km
540 810
5 min
78
3000
5 109 m4 s1
109 m4 s1
3
1.8
2.2
290
14.9
141
31° N
0.58
2.0 km
1080 1620
2 min
216
15 000
109 m4 s1
109 m4 s1
4
2
1.9
312
17.4
178
30° N
0.85
(Madec, 2008). The domain geometry is a closed rectangular basin
on the b-plane centered at 30°N and rotated by 45°, 3180 km
long, 2120 km wide and 4 km deep (Fig. 1b). The domain is
bounded by vertical walls and by a flat bottom. The configuration
is meant to represent an idealized North Atlantic or North Pacific
basin.
The circulation is forced by analytical profiles of wind and buoyancy fluxes. The applied forcings vary seasonally in a sinusoidal
manner between winter and summer extrema (Fig. 1). The wind
stress is zonal and its curl changes sign at 22°N and 36°N
(Fig. 1a). It forces a subpolar gyre in the north, a subtropical gyre
in the wider part of the domain and a small recirculation gyre in
the southern corner (Fig. 1b). The net heat flux takes the form of
a restoring toward a zonal apparent air temperature profile
(Fig. 1d). It is given by Q = c (Tw SST), with c = 4 W m2 K1, Tw
the prescribed apparent air temperature and SST the model sea
surface temperature. This value of the thermal coupling coefficient
c ¼ dQ
corresponds to a restoring time scale of 120 days for temperdT
ature within a 100 m depth mixed-layer.
This formulation is dictated by the physical consideration that a
SST anomaly in the ocean interacts with atmospheric fluxes and is
damped through this interaction. A portion of the net heat flux
comes from the solar radiation. This portion is allowed to penetrate
within the water column. The penetrative solar radiation is imposed and varies zonally (Fig. 1c). The fresh water flux is also prescribed and varies zonally (Fig. 1e). The fresh water flux was
determined such as, at each time step, the basin-integrated flux
is zero. This condition insures the conservation of salinity. It is
worth to note that, by construction, all simulations are forced with
the same wind stress, the same solar radiation and the same fresh
water flux but with net heat fluxes that depend on the model solution. For the sake of simplicity, a bilinear equation of state is assumed, q = q0(1 (aT bS)). Here b = 7.7 104 kg m3 psu1
and a = 2 104 kg m3 K1. The resulting vertical stratification is
such that the Rossby radius of deformation ranges from 5 km in
the north of the subpolar gyre to 40 km in the center of the subtropical gyre. This range is consistent with that estimated by Chelton et al. (1998) in the same latitudinal range.
2.2. Model experiments
Four experiments have been performed, with different horizontal resolution (Table 1) and accordingly, lateral sub-grid scale closures. The coarse resolution experiment has a horizontal resolution
of approximately 1° (R1). R1 serves as our reference for a ‘‘noneddying” ocean. In the three other experiments, the resolution is
progressively increased above mesoscale resolution: approximately 1/9° in R9, 1/27° in R27 and 1/54° in R54. The resolution
of R9 is comparable to that of state of the art global eddy-resolving
ocean models (Sasaki et al., 2008; Maltrud and McClean, 2005; Le
Galloudec et al., 2008). More precisely, R1 has 20 30 regular grid
cells on the horizontal, which have a length of 106 km in both
directions. The resolution is progressively increased by dividing
each cell equally into 2 2 or 3 3 matrix as many times as
needed. In all experiments, there are 30 z-coordinate vertical layers, whose thicknesses vary from 10 to 20 m in the upper 100 m,
and increase up to 300 m at the bottom. An additional R27 experiment carried out with 100 vertical layers showed very small differences compared with the standard 30 layers-R27 experiment.
This test showed that relevant high baroclinic modes were captured with 30 layers.
2.3. Model physics
At coarse resolution (R1), laplacian friction dissipates momentum along horizontal surfaces. Temperature and salinity are diffused along isopycnal surfaces without horizontal background. In
the eddy resolving experiments (R9, R27 and R54), bi-harmonic
friction and bi-harmonic diffusion act along horizontal surfaces.
The eddy viscosity coefficients are provided in Table 1. These values have been tuned to remove the numerical noise on the vertical
velocity field. This results in a decrease of the eddy viscosity coefficient approximately like (dx)2, a lower dependency than usually
assumed (Willebrand et al. (2001) advocate a dependency in
(dx)3). For eddy diffusivity, we used a same coefficient for the three
high-resolution simulations. In an early attempt, we used different
eddy diffusivities (i.e. we used eddy diffusivities equal to eddy viscosities for R9, R27 and R54), which led to the undesired consequence of a too-diffusive thermocline in R9. It is presumable that
our results are sensitive to the choice of these coefficients, particularly in the case of R9 where they should be the largest. A systematic sensitivity analysis is beyond the scope here.
Vertical mixing is parameterized by a 1.5 turbulent closure
model (Blanke and Delecluse, 1993), with a background value of
105 m2 s1. Vertical mixing coefficients are enhanced in the case
of convection. Advection of temperature and salinity is performed
with a flux-corrected transport scheme (the TVD scheme used in
Levy et al. (2001) and Penduff et al. (2007)). An energy conserving
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M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
scheme is used for the computation of vorticity trends (Madec,
2008). Free-slip conditions and no heat and salt flux are applied
along solid boundaries, except at the bottom where a non-linear
friction drag is applied.
2.4. Initialization and spin-up
R1 is initialized at rest with vertical profiles of temperature and
salinity uniformly applied to the whole domain. The profiles were
constructed from the World Ocean Atlas climatologies by averaging over 25–30°N and 80–0°W. The profiles were truncated to constant values below 1000 m in order to allow faster equilibration of
deep waters (which are not of interest here) and to facilitate deep
convection in the absence of intermittent forcings. Preliminary R1
experiments revealed very-low frequency oscillations of large
amplitude (of period 1000 years). These oscillations are damped
when a relaxation term on sea surface salinity (SSS) is added.
Pasquero and Tziperman (2004) suggest that such self-sustained
variability result from the interaction between the thermohaline
circulation and the wind-driven circulation.
Thus, R1 was first spun-up for 1000 years (years 1–1000), after
which a SSS relaxation was added for another 1000 years (years
1001–2000). Note that for simplicity the model year is fixed to
360 days. The SSS relaxation is not maintained hereafter. Then,
R9, R27 and R54 are initialized from the spun-up state of R1 and
run for another 100 years to adjust the basin with the new resolutions (years 2001–2100). At this point, an additional 10 year-run is
conducted (years 2101–2110) with annual-mean outputs. Year
2101 is repeated with outputs saved every two days (two-day
averages).
2.5. Equilibration of the experiments
The change in circulation with resolution co-occurs with significant modifications of the thermohaline structure that builds up
during the model spin-up (Fig. 2). After 100 years of integration,
the four experiments have reached different mean state. During
the 100-year spin-up phase, we note a small drift in R1 due
to the removal of the SSS relaxation, while R9, R27 and R54 have
a larger drift due to the adjustment to the new resolution. Fig. 2
shows that, below the main thermocline (at 430 m), the drift declines with time and that a quasi-steady state is reached for all
experiments after 100 years. This is not the case deeper in the
water column where longer integration times would be needed
to reach equilibrium. Nevertheless, the various simulations do differ from each other substantially after 100 years, particularly in the
layer extending from the surface to near the base of the main thermocline, where the water masses are nearly equilibrated. Interestingly, the change is not continuous from R1 to R54: Fig. 2 shows
that the mean domain temperature and salinity at 430 m depth
in R1 is intermediate between those of R9 and R54. This already
indicates that the change of resolution from eddy-resolving to
sub-mesoscale resolving have different impacts than the change
from coarse resolution to eddy-resolving resolution.
There is also evidence of variability at interannual frequencies,
which is an ubiquitous phenomena in eddying double gyres
(Berloff et al., 2007). This interannual variability was noted by
Hazeleger and Drijfhout (2000a) in a similar configuration and
was attributed to both basin-scale internal modes of variability
and to the variability associated with the irregularity of the mesoscale circulation. Of importance here is the fact that the interannual variability is small in comparison with the mean differences
Fig. 2. Averaged salinity and temperature at 430 m depth during the 100-year spin-up phase (years 2000–2100) and during the following 10 years (years 2100–2110) for
experiments R1, R9, R27 and R54.
M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
5
Fig. 3. Snapshot of relative vorticity at the surface of the model domain in experiments R9, R27 and R54. The color intervals are chosen to highlight the structures, but are not
representative of the extremum values (see Table 1). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)
between experiments. This allows us to analyze the differences between experiments regardless of the interannual variability. Unless
specified, the model ‘‘mean state” is defined in the following as the
average of all fields over the last 10-years.
3. Impact of the sub-mesoscales on the gyre circulation
This section focuses on three experiments: the ‘‘coarse resolution” experiment (R1), the ‘‘eddy-resolving” experiment (R9) and
the ‘‘sub-mesoscale resolving” expriment (R54). R27 is an intermediate situation, closer to R54 than to R9, and will not be examined
in details hereafter.
3.1. Mesoscale and sub-mesoscale turbulence
The most visible impact of the resolution is the emergence in
the relative vorticity field (Fig. 3) of smaller and smaller eddies
and filamentary structures resulting from the non-linear interactions. In R9, wave-like ondulations are evident along the inter-gyre
current (mostly on the western side of the domain, between 30 and
35°N). These instabilities occasionally lead to the break out of large
eddies (200 km diameter), essentially close to the western boundary where the current is the most intense. As the resolution is increased (from R9 to R54), more coherent axisymmetric eddies
begin to emerge leading to a denser and well defined vortex population, covering a wide range of scales and populating most of
the basin. The eddies have diameters between 50 and 200 km.
Some are well separated from the jets, others are rapidly re-absorbed into the jet. Dipole vortices and sub-mesoscale filaments
are also present. The emergence with the resolution of more
numerous and smaller eddies is related to the better resolution
of not only the first internal Rossby radius of deformation but also
of the Rossby radius associated with higher baroclinic modes,
which are known to affect the dynamics of the mesoscale turbulence (Barnier et al., 1991).
The velocity spectra (not shown) exhibit significant differences
when sub-mesoscales are explicitly resolved. In R54, a noticeable
shallow (k2, Table 1) spectrum slope is observed over the spectral
band comprised between wavelength 20 km and 100 km. This
slope is significantly steeper in R9 (k3, Table 1). This result is close
to the spectrum slopes reported in the high resolution simulations
of Capet et al. (2008) and Klein et al. (2008).
The eddy kinetic energy (EKE) is multiplied by a factor larger than
1.5 between R9 and R54 (Table 1). The EKE increase is accompanied
by a similar increase in the 0–500 m vertical velocity variance
(Table 1), highlighting that sub-mesoscale turbulence is associated
with intense vertical movements in the upper ocean. The increase
of the vertical velocity variance due to the sub-mesoscales is similar
to that obtained by Klein et al. (2008) in their high resolution simulation of turbulence in a b-plane channel (not shown).
Because eddies are mostly generated through baroclinic instability of the main jet, the spatial distribution of the EKE is highly
heterogeneous (Fig. 4). In R9, the area of high EKE is restricted to
the offshore extension of the inter-gyre current (between 30 and
35°N). In R54, it penetrates further westward and southward within the subtropical gyre, and an area of moderate EKE also develops
in the north (on the western flank of the subpolar gyre). This highlights the strong influence of the sub-mesoscale on the penetration
of EKE.
The shallower spectrum slope and the increase of EKE with resolution illustrate the important role of the sub-mesoscales on the
mesoscale eddies even if these small scales are much less energetic. One role, for example, concerns that of the vorticity gradients
(captured by the sub-mesoscales) surrounding the mesoscale eddies that act as dynamical barriers and therefore prevent these eddies to be deformed and eventually destroyed by the nearby eddies
(Lapeyre et al., 1999). The primary consequence of these dynamical
barriers is thus to obtain stronger (more coherent) and longer lived
eddies, which explains the EKE increase. A second consequence is
that these stronger eddies make the Reynolds stresses (involving
the eddy velocities) to be larger and, as a result, lead to the emergence of more energetic mean zonal jets (Rhines, 1994). This is
seen by the increase of the mean kinetic energy (MKE) by a factor
1.4 (38% between R9 and R54, Table 1). This MKE increase with resolution was not obtained in the quasi-geostrophic double-gyre
experiments of Siegel et al. (2001), although their EKE increase
was similar to ours.
The presence of sub-mesoscales induces strong ageostrophy in
the dynamical field. This is revealed by the probability density
function (not shown) of the surface relative vorticity that exhibits
a significant asymmetry in R54 compared to R9: an exponential tail
is observed for cyclonic structures and a more gaussian distribution for anticyclonic ones. The surface relative vorticity maxima increase from 1.5f in R9 to 4f in R54 (Table 1) and the vorticity
minima are close to f in agreement with Haine and Marshall
(1998). The relative vorticity skewness (Table 1) is equal to 2 in
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M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
Fig. 4. Annual-mean surface eddy kinetic energy (EKE) in experiments R9 and R54. Data from model year 2101 are used. The EKE is defined as the total kinetic energy minus
the mean kinetic energy (i.e. the kinetic energy computed from annual-mean velocities).
R54 (instead of 1 in R9) indicating a strong dominance of the cyclones. This skewness value and the surface velocity spectrum in
R54 are consistent with values observed in other recent high resolution simulations performed with PE models (Capet et al., 2008;
Klein et al., 2008). These properties emphasize that the sub-mesoscales near the surface are strongly associated with frontogenesis
processes (see Capet et al., 2008; Klein et al., 2008), which explains
the increase in the vertical velocity variance as the resolution
increases.
The following sections will focus on the impacts of the sub-mesoscales on the detailed characteristics of the mean circulation.
3.2. The western boundary current and its offshore extension
Our results clearly reveal that sub-mesoscales further amplify
the impact of mesoscale turbulence on the western boundary current (WBC, i.e. the model equivalent of the Gulf Stream or of the
Kuroshio). This impact is known to affect both the WBC separation
latitude (Chassignet and Marshall, 2008) and its offshore extension
(Barnier et al., 1991). Sub-mesoscales make the separation latitude
of the WBC to shift further south by 4° and its offshore extension to
intensify and penetrate farther to the east (Table 1 and Fig. 5).
Thus in R1, the WBC path starts along the south-western
boundary (at 75°W, 25°N), reaches the domain westernmost corner (at 29°N, 85°W), then runs along the north-western boundary
and ultimately separates from the coast at 36°N but hardly heads
off-shore (Fig. 5). In R9, the WBC initially follows the same route
than in R1, but it separates earlier from the coast (at approximately
34°N) and heads off-shore diagonally toward the north-east. Its
off-shore extension is much larger than in R1 and its velocity
amplitude is increased with respect to R1 by more than a factor
of three (Table 1 and Fig. 5). In R54, the WBC separates further
south at 30°N and heads off-shore not diagonally but along the zonal direction; its intensity is more than twice that in R9 (Table 1
and Fig. 5).
The separation latitude of the WBC in R1 coincides with the latitude at which the wind stress curl changes sign (see also Fig. 1a
and b), which agrees with the early linear frictional theory (Munk,
1950). In R9, the southward shift of the separation latitude and the
significant offshore extension agrees with the results of Moro
(1988) and of Barnier et al. (1991), which accounts for non-linear
effects due to the mesoscale turbulence. These effects are further
amplified in R54. Moreover, the southward shift of the WBC separation agrees with observations: the Kuroshio extension is located
Fig. 5. Module of the 10 year-mean surface velocity in experiments R1, R9 and R54.
M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
7
Fig. 6. Annual-mean barotropic velocity in experiments R1, R9 and R54 (vectors). The color shows the intensity of the zonal component of the barotropic velocity (red for
eastward, blue for westward). Data from model year 2101 are used. (For interpretation of the references to color in this figure legend, the reader is referred to the web version
of this paper.)
at about 35°, 7° south of the separation predicted by the linear theory (43°); a similar shift is observed for the Gulf Stream.
Many ocean circulation models fail at reproducing the separation latitude of the Gulf stream correctly, and a number of processes have been proposed to explain this failure. Some studies
(Hugues and de Cuevas, 2001; Zhang and Vallis, 2007) found that
low resolution suffices, provided that topography is present and
that there is a deep western boundary current. Others (Hurlburt
and Hogan, 2000; Chassignet and Marshall, 2008) tend to suggest
that high resolution is necessary, and point out a large sensitivity
to resolution and to sub-grid scale parameterizations. In our model, topography effects are not accounted for, and the differences between R54 and R9 appear to be consistent with these previous
findings about the effects of small scales.
3.3. Alternating mean zonal jets
A consequence of the stronger and more numerous eddies in
R54 is the intensification of the mean current in the form of mean
zonal jets with directions alternating with latitude and speeds of
several centimeters per second. These jets are not visible in instantaneous snapshots of the circulation, which is dominated by mesoscale eddies, and are revealed by the annual mean barotropic
velocity (Fig. 6). They are absent in R1 but occupy the whole domain in R9 and are intensified close to the western boundary. They
are further intensified in R54, particularly in the subtropical gyre.
The signal of the jets persists in the 10 year-mean (not shown),
but is less marked than in the annual mean due to small interannual variations of the latitude of the jets. The main mean jet is
the offshore extension of the WBC. As mentioned before, this main
jet is diagonally oriented in R9, and more zonal in R54. A secondary
eastward jet is found between 34 and 35°N in R54. It is surface
intensified and is apparent in Fig. 5. The emergence of the mean
jets, associated with the strengthening of the WBC extension, explains the MKE increase with resolution (Table 1). The two main
eastward jets are surface intensified, some others are almost perfectly barotropic and a few have only a sub-surface signature
(Fig. 7). The meridional width of the jets is 1.5–2°, consistent with
the Rhines (1975) scale, which varies between 150 and 180 km
with a peak at 250 km in the area of the central jet (not shown).
We note that it is the intensity of the jets rather that the jet width
that differ from R9 to R54. This is explained by the extension of the
energetic area within the interior (Fig. 4).
Alternating zonal jets are ubiquitous features in the world oceans.
They have been observed in the time-averaged anomalies of the
geostrophic velocities estimated from altimeter data (Maximenko
Fig. 7. Vertical section at 75°W of the annual-mean zonal velocity in R54. Contour interval is 0.05 m s1.
8
M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
Fig. 8. Ten-year-mean barotropic stream function in experiments R1, R9 and R54. Dashed lines indicate cyclonic circulations. Contour interval is 10 Sv.
et al., 2005) and were also observed with in situ XBT and float data
(Maximenko et al., 2008). Computational evidence of these zonal jets
is revealed in a 1/4° 1/6° simulation of the North Pacific by Nakano
and Hasumi (2005), as well as in the global ocean 1/10° simulation
using the OFES model (Maximenko et al., 2005; Sasaki et al., 2008).
However, alternating zonal jets estimated from altimetry and float
data appear to be more numerous, stronger and more zonal than
those revealed by the eddy resolving (with a 1/10° resolution) simulations (Maximenko et al., 2005). These differences are similar to
those that emerge between R9 and R54 and that are entirely due to
the switch from eddy resolving to sub-mesoscale resolving model.
Such jets are ubiquitous properties of turbulent flows on the
b-plane (Rhines, 1994). Their formation mechanism in the ocean
is still under investigation (Berloff et al., 2009a,b); whether zonal
jets result from the tendency of b-plane turbulence to organize
itself (Panetta, 1993; Treguier and Panetta, 1994; Galperin et al.,
2004), from free Rossby waves arresting this inverse cascade of energy and redirecting it into zonal modes (Nadiga, 2006), from the
baroclinic instability of weak meridional currents (Spall, 2000) or
from the result of the time-averaging of eddies following preferred
pathways (Schlax and Chelton, 2008) is still unclear. However,
there is a consensus on the fact that mesoscale eddies play a central role in supporting them (Kamenkovich et al., 2009). Our results
confirm that the jets emerge when mesoscale turbulence is well
established, and that they get more numerous and more intense
when turbulence is more energetic.
3.4. Barotropic transport
A consequence arising from the presence of the alternating
zonal jets is the strong modification of the barotropic transport
(Fig. 8). In R1, the barotropic stream function (BSF) is characterized
by an anticyclonic circulation in the south and a cyclonic circulation in the north and thus forming two distinct gyres, in agreement
with the linear Sverdrup theory. In R9, the BSF still displays two
main gyres, although some weak and smaller scale recirculations
appear. In R54, the BSF strongly deviates from the typical double-gyre structure. In the north, the mean cyclonic circulation
(dashed lines in Fig. 8) is perturbated by an anti-cyclonic re-circulation between 40°N and 45°N. This anti-cyclonic structure was already present in R9, but it is intensified in R54. In the south, the
mean anticyclonic circulation (plain lines in Fig. 8) is strongly perturbated by a cyclonic re-circulation around 30–32°N. We note
that the zero-contour of the BSF is located at 36°N in all experiments: this latitude is forced by the change of sign of the wind
stress curl (Fig. 1a and b). Thus, the deviation from the typical double-gyre structure in R54 originates both from the existence of the
alternating zonal jets, and from the fact that the main current sep-
arating the two gyres is located 6° to the south of the zero-contour
of the BSF. In realistic model simulations of the Kuroshio current
system, Nakano et al. (2008) find two recirculation gyres in 1/10°
runs (one on each flank of the Kuroshio) that are absent in 1/2°
runs. Here, the resolution of sub-mesoscales and the development
of alternative zonal jets generates more numerous recirculation
gyres with smaller scales: the southern and northern boundaries
of these recirculation gyres are set by the alternate zonal jets.
The maximum transport in the subtropical gyre is increased
with resolution: from 29 Sv in R1, to 73 Sv in R9, and 123 Sv in
R54. The increase in the subpolar gyre is less significant (Table 1).
Treguier et al. (2005) found an increase similar to the one from R1
to R9: from their 1° to their 1/6° model runs of the North Atlantic,
the Gulf Stream recirculation grew by about 70 Sv. The additional
increase due to the sub-mesoscales (i.e. between 50 Sv and between R9 and R54) revealed by our results points out the necessity
to explicitly resolve these small scales.
3.5. The surface mixed-layer
Important differences in the winter mixed-layer depth (MLD)
result from sub-mesoscale physics. The first one concerns the
intensity of deep-convection in the north of the domain (Fig. 9).
In R1, deep convection occurs north of 43°N, mainly on the west
side of the gyre. In R9 and R54, it occurs in the center, but most
of all it is much reduced in R54 with respect to both R9 and R1.
The other differences concern the mid-latitudes (between 30°N
and 43°N), where the MLD significantly shallows when sub-mesoscales are explicitly resolved (by 20–30 m on average between R9
and R54). However, south of 30°N, the resolution of sub-mesoscales implies deeper MLDs (Fig. 9), since the WBC is moved southward and since deep mixed-layers (200–300 m) are found south
of the WBC in agreement with existing observations (de Boyer
Montgut et al., 2004).
The shallowing of the MLD by mesoscale eddies and by frontogenesis associated to sub-mesoscale structures is a well known feature that has been documented by several studies (Spall, 1995;
Nurser and Zhang, 2000; Lapeyre et al., 2006). In these previous
studies, however, the seasonal stratification was not accounted
for. Our experiments extend these findings in presence of a seasonal cycle, with the dynamical restratification due to sub-mesoscales acting significantly both in the subpolar gyre (reduction of
deep convection in winter) and in the subtropical gyre.
3.6. The large scale density field
The large scale density field displays a strong N–S gradient with
the subtropical gyre involving saltier and warmer waters than the
M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
9
Fig. 9. Ten-year-mean mixed-layer depth (MLD) in experiments R1, R9 and R54. The MLD is computed as the interface of the surface layer whose density does not exceed the
surface density by more than 0.01.
subpolar gyre. The modification of this large-scale density field by
mesoscales and sub-mesoscales is intimately linked to the related
changes in the mean circulation (mentioned in the preceding sections) through the thermal wind balance.
The outcropping position of the isopycnals differs markedly
from one run to the other. In the western part of the basin, isopycnal outcrops in R1 (Fig. 10a) significantly deviate from the zonal
direction because of the circulation in the subtropical gyre
(Fig. 8a). As the resolution increases, this deviation significantly
shrinks in concord with the emergence of the zonal jets, which
makes the isopycnal outcrops to be much better aligned in the zonal direction (Fig. 10c).
The vertical density structure is also significantly modified.
Fig. 11a shows, along a vertical section, the typical bowl shape of
isopycnals in the subtropical gyre, outcropping in the subpolar
gyre. Resolution modifies both the isopycnal depths and the isopycnal slopes. In accordance with the thermal wind balance, the
strengthening of the WBC extension in R9, with respect to R1, is
associated with the steepening of the isopycnal slopes (Fig. 11b).
In addition, deeper isopycnals in the subtropical gyre and shallower isopycnals in the subpolar gyre correspond to a southward
shift of the bowl shape. This shift is associated with the WBC separation latitude that goes south from R1 to R9. Impact of the submesoscales (R54) further reinforces the steepening of the isopycnal
slopes, as revealed by the differences between R9 and R54 (Fig. 11c
and d). In the case of R54, step-like patterns emerge (Fig. 11d),
which are the signature of the alternating zonal jets on the mean
density structure. Moreover, the displacement of the WBC extension, further south in R54, induces an additional southward displacement of the bottom of the subtropical bowl from 31° to 28°
between R9 and R54 (Fig. 11b). All together, the main impact of
resolution leads to deeper isopycnals in the subtropical gyre, shallower isopycnals in the subpolar gyre and steeper isopycnal slopes.
The sub-mesoscales strongly reinforce the impact of the mesoscales in terms of these changes in the density field.
Fig. 11 contrasts with the results of Henning and Vallis (HV,
2004, their Fig. 6), which compare coarse resolution and eddy-permitting double-gyre experiments, even though we have chosen a
section which is located in a similar position to theirs, relative to
the gyres. The first difference to note is that in HV simulations, isopcynals (isotherms, in their figure) outcrop vertically in the subpolar gyre. In our case, with a seasonal cycle present in the
atmospheric forcing, the isopycnals outcrop vertically in winter
only, and a seasonal thermocline is present in the time-mean.
The main result of HV is that eddies tend to push the outcrop latitude to the north, with only a slight deepening in the subtropical
gyre, and thus the net effect is to reduce the isopycnal slope. The
reverse is true in our experiments: the subtropical gyre deepens
with higher resolution consistently with the increase of the upper
layer circulation and with the inertial recirculations that are
Fig. 10. Ten-year-mean surface density in experiments R1, R9, and R54.
10
M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
Fig. 11. Ten-year-mean density (black contours) along a section at 72°W in experiments R1, R9 and R54. The colors show the intensity of the vertical density gradient. To
facilitate the comparison, the depth of the 25.0 isopycnal is reported in panel (d) for the three experiments. (For interpretation of the references to color in this figure legend,
the reader is referred to the web version of this paper.)
apparent in the barotropic stream functions of Fig. 8. This deepening is less marked in HV because their run has a lower resolution
and is more viscous than even R9, and therefore the increase in circulation is confined to the west of their section, closer to the western boundary, with no significant impact on the mean circulation
(their Fig. 3). The steepening of the isopycnal slope with resolution
may seem surprising, since it is widely accepted that eddies draw
their energy primarily from the available potential energy of the
mean flow, and thus tend to flatten isopycnal surfaces (Gent and
McWilliams, 1990); indeed HV find that isopycnal slopes are less
steep at eddy permitting resolution and they interpret their results
within the GM framework. On the other hand, the increased slope
with resolution in our experiments is a well known effect of eddy
fluxes on a baroclinically unstable eastward jet, on a b-plane. Eddy
momentum stresses tend to concentrate the momentum in the jet
core, thus creating a potential vorticity barrier in the upper
(directly forced) layer. This effect is discussed for example by
McWilliams and Chow (1981) in an oceanic context but it also
well-known in the case of the atmospheric mid-latitude jet stream
(Panetta, 1993). This eddy-driven rectification of the eastward jet,
not taken into account by the GM parameterization, is found here
to be important at the scale of an ocean basin (namely, the scale of
the intergyre boundary), especially when the mesoscale eddies are
better resolved.
3.7. Stratification of the main thermocline and mode waters
The vertical density gradient is strongly affected by resolution
(Fig. 11). Besides the vertical stratification in the surface layers
(discussed in the section on the MLD), presence of the mesoscales
and sub-mesoscales significantly affects the main thermocline,
that is centered between 200 and 400 m depth in the density range
24.8–25.2, and which outcrops at high latitudes. In the main thermocline, the main impact of the sub-mesoscales (differences between R9 and R54) is to strengthen the stratification by almost a
factor of two (see Fig. 11c and d). Interestingly, the opposite result
is found between R1 and R9: presence of the mesoscales alone
makes the stratification to significantly decrease. This result actu-
ally agrees with those from HV in a similar resolution range. Here
we point out a new effect due to the sub-mesoscales on the stratification of the main thermocline, that was not apparent in eddypermitting simulations. It is interesting to note that this result is
similar to that related to the MLD in the northern part of the domain. The emergence of the strong zonal jets in R54 may explain
this stratification increase since these jets (through the thermal
wind balance) make the isopycnals slopes to be steeper. Another
explanation is that sub-mesoscales (through the restratification
of the upper layers in the subpolar gyre) create a source of high potential vorticity which affects the restratification of the main
thermocline.
The main thermocline is separated from the surface layers by a
region of weakly stratified fluid (see Fig. 11), which is typical of
‘‘mode waters” in the subtropical ocean basins (Polton and Marshall, 2003). The detrainment of well mixed waters combined with
a strong meridional mixed-layer depth gradient in the boundary
current extension is one of the reasons of mode-water formation
south of the WBC extension (Hazeleger and Drijfhout, 2000b).
Within the mode waters, vertical stratification increases from R1
to R54, and the mode waters tend to be lighter with higher resolution. Similar results where found in a model of mode water formation in the NE atlantic (Paci et al., 2007). Karleskind (2008) suggest
that this is due to subduction occurring over a larger range of densities when sub-mesoscales are present. The increase of stratification within the mode waters also agrees with HV, although in our
case it is much less dramatic. HV had a complete erosion of the
mode waters in the eddy permitting case, that might be due to
the absence of a seasonal cycle in their forcing.
3.8. The meridional heat transport
Recently, regional modeling studies have demonstrated a
dependence of the meridional heat transport on resolution, with
coarse-resolution models generating poleward transports that are
significantly less than those observed (Fanning and Weaver,
1997) and less than those obtained at eddy-permitting resolution
(Spence et al., 2008). In these studies, nearly all of the increase in
M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
the total transport was accounted for by changes in the time mean
flow (due to a better resolution of the WBC), rather than by direct
contribution from eddies (Hecht and Smith, 2008).
In our idealized model, and as expected, the total northward
heat transport is positive for all latitudes (plain lines in Fig. 12)
and is of course entirely explained by the heat fluxes at the surface.
The maximum transport is located south of 35°N and goes from 85
TW for R1 to 60 TW for R54. Thus, increasing the resolution (from
R1 to R54) has a conspicuous negative impact on the total transport south of 35°N. Near 40°N, however, the total heat transport
for R54 is higher (45 TW) than R1 and R9 (respectively, 35 and
25 TW). This actually results from the resolution effects on the surface heat fluxes and therefore on the SST (because of the restoring
to a prescribed apparent air temperature, see Section 2.1). In summary, taking into account the impact of the mesoscales and submesoscales does not lead to a systematic increase of the total heat
transport, but on the contrary appears to slightly decrease this
transport in some regions and to increase it in some others.
This impact appears to emphasize a subtle competition between large and small scales in the ocean interior. For a better
understanding, we have estimated the respective impact of large
and small scales by splitting the total transport into a mean contribution, due to the time-mean flow, and an eddy contribution that
is the difference between the mean contribution and the total heat
transport (dotted and dashed curves in Fig. 12, respectively). As it
is defined, the eddy contribution actually involves the effects of
transient eddies as well as that of seasonality. The eddy contribution for R1 results mainly from the seasonal cycle. It is positive and
11
much smaller than the mean contribution. On the contrary, for R9
and R54, the eddy contribution is negative over a large latitude
band, with a much larger amplitude than the total heat transport,
and therefore is strongly compensated for by the mean contribution. The importance of the eddy contribution versus the total contribution found here is much larger than previously estimated in
North Atlantic models at resolution of 0.1°N (Hecht and Smith,
2008). It is also much larger than that estimated in a similar model
configuration at 1/6° by Drijfhout (1994a,b). Drijfhout (1994b)
noted that compensation between mean and eddy contributions
occurs for values of the thermal coupling coefficient (c) smaller
than 70 W m2 K1, which is the case in our experiments.
South of 30°N, the negative eddy contribution is consistent with
the positive large-scale meridional temperature gradient in the
ocean interior in this region (see Fig. 11 where density structure
is in fact dominated by temperature) since the impact of the eddies
is to decrease the large-scale temperature gradient. But the increase of this eddy contribution with the resolution is explained
by the significant increase of the eddy activity in this region as
the resolution increases (as displayed in Figs. 3 and 4). This eddy
contribution, with a much larger amplitude than the total heat
transport, therefore must be strongly counter-balanced by the
mean circulation effects, a property that well characterizes energetic turbulent eddy fields. Indeed, for these fields, the horizontal
divergence of the meridional heat flux is mostly compensated for
by the mean vertical advection of heat (see Panetta, 1993). In our
simulations, this compensation leads in this region to an equilibrium characterized by steeper isopycnal slopes in R54 than in R9
Fig. 12. One-year-mean northward heat transport (in W) in experiments R1 (black), R9 (green) and R54 (red). The plain line shows the ‘‘total” heat transport, computed from
the integration of 1 year-mean meridional heat fluxes. The dotted line shows the ‘‘mean” heat transport, computed from the 1 year-mean flow and 1 year-mean temperature
distribution. The dashed line shows the ‘‘eddy” contribution, computed as the difference between the ‘‘total” and ‘‘mean” contributions. (For interpretation of the references
to color in this figure legend, the reader is referred to the web version of this paper.)
12
M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
at depths. This indicates that the corresponding mean circulation
concerns a significant depth. This property is further discussed in
the next section. In the latitude band between 30°N and 37°N,
the eddy contribution to the heat transport becomes smaller
than the total heat transport and therefore the mean contribution
is still positive when the eddy contribution becomes positive. The
varying behavior (as a function of latitude) of the eddy and mean
contribution appears to be strongly related to the presence of the
energetic zonal jets discussed in the preceding paragraphs (see
Figs. 6 and 7). The sign change of the eddy contribution in this region is consistent with the sign change of the large-scale temperature gradient observed in the ocean interior in this latitude band
(see Fig. 11). North of 37°N, the eddy contribution becomes very
much weaker than the total heat transport and does not seem to
be significantly affected by the resolution. This is in agreement
with Figs. 3 and 4 that do not display any significant increase of
the eddy activity in this region. It should be noted that a tendency
for compensation between mean and eddy heat transport contributions is often found in realistic models (Bryan, 1996). In our case,
the details are probably dependent on the model geometry.
3.9. The meridional overturning circulation
The residual mean stream function, which characterizes the
meridional overturning circulation (r-MOC), is estimated from
the instantaneous meridional velocity (binned over instantaneous
density layers) integrated from the bottom to a given density layer,
integrating zonally and averaging in time. Besides the surface
trapped overturning cell led by the wind stress and the associated
Ekman transport (Fig. 13a–c, grey shading), the major feature of
the r-MOC in all experiments consists of two dominant cells (in
white). The first cell, in the northern part, is mostly trapped in
the deeper layers (isopycnal values larger than r = 25, the isopyc-
nal r = 25 actually corresponding to the region where the stratification is the strongest as seen in Fig. 11). This cell comprises a
northward flow above 350 m, a sinking flow near 45°N, associated
with the deep convection, and a southward return flow at depth.
The other cell, in the southern part, is within the subtropical gyre.
It is mostly trapped in the upper layers (isopycnal values smaller
than r = 25 and located above 350 m depth) and is connected with
the secondary circulation associated to the eastward extension of
the turbulent WBC. We can note that, in all experiments, the intensity of the MOC is much weaker than in the real ocean, due to the
simplications made in the model (in particular, the small latitudinal extension and the weak deep vertical mixing). However, the
conspicous modifications of the MOC in presence of mesoscales
and sub-mesoscales point out a very significant sensitivity that is
worth to be discussed.
The transport associated with the r-MOC does not vary much
as the resolution increases. The main impact is that the water
masses (characterized by their density class) involved in the
MOC vary, with the northern and southern cells located within
lighter density layers when the resolution increases. Regarding
the northern cell, maximum transport occurs at the density of bottom waters in R1 and R9 (r = 26), while it is shifted to lighter densities in the case of R54 (r = 25.5). This is consistent with the
strong decrease of deep-wintertime convection due to the restratification effect of the sub-mesoscales (see Fig. 9). We also note a
significant upwelling across isopycnals at the southern limit of
the northern cell which, surprisingly, appears larger in R9 and
R54 than R1. This is not due to the change in lateral diffusion
parameterizations (laplacian isopycnal diffusion in R1 versus horizontal biharmonic in R9 and R54) because we have verified that
the cross-isopycnal flow remains the same in a sensitivity experiment with laplacian isopycnal diffusion in R9 (not shown). The
model vertical diffusion, or diffusive effects due to advection
Fig. 13. One-year-mean meridional overturning circulation (MOC) in experiments R1, R9 and R54, plotted in r-coordinates (from 23.0 to 26.0). Contour interval is 0.5 Sv. The
dotted line shows the 1 year-mean density at 350 m depth. The dashed line shows the bowl, defined as the maximum zonal-mean density, and delimiting the waters masses
that have been in contact with the atmosphere along the seasonal cycle. Left panels show the total MOC, middle and left panels show the ‘‘mean” and ‘‘eddy” contributions to
the total MOC.
M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
schemes at high resolution (Griffies et al., 2000) could play a part,
although the advection scheme used here has weak inherent diffusivity (Levy et al., 2001; Penduff et al., 2007). Regarding the southern cell, its northward extension is shifted to the south with
increased resolution, and this shift corresponds to the southward
displacement of the WBC with resolution (the descending branch
occurring at the latitude of the WBC extension). The southern cell
is also shallower (the maximum transport in this cell is located at
r = 24.3 in R1, 24.2 in R9 and 24.1 in R54) and it occupies a reduced
density range with increased resolution (Dr = 1.9 in R1, 1.5 in R9
and 1.0 in R54). These changes are consistent with the reduced
density range of surface waters in the subtropical gyre (Fig. 10),
primarily because of the southward displacement of the main jet
and thus of the subtropical gyre (Fig. 5). We can also note that
the downwelling branch of the southern cell is displaced from
35°N to 30°N from R1 to R54, consistently with the displacement
of the main jet.
In order to reveal the role of eddies we have split the r-MOC
into an Eulerian mean stream function and an eddy stream function following McIntosh and McDougall (1996) (Fig. 13d–i). The
Eulerian mean stream function is obtained by using the meridional
velocity, averaged in the zonal direction and over a year, as a function of the density also averaged zonally and over a year. Then the
eddy stream function simply results from the residual mean
stream function minus the Eulerian mean stream function. The
eddy stream function thus includes the contribution of the stationary and time-varying mesoscale and sub-mesoscale eddies as well
as that of the seasonality. In R1, the eddy stream function is due to
the seasonality and is confined to the upper layers. This seasonality
effect is mostly confined within the density layers which are in
contact with the atmosphere along the seasonal cycle (the ‘‘bowl”,
delimited by the dashed line in Fig. 13). Seasonality appears most
clearly in the upper envelop of the southern cell which is more
spread for the total r-MOC (Fig. 13a) than for the mean r-MOC
(Fig. 13b), as a result of seasonality in the formation and destruction of water masses. It is also clearly seen in the bowl for R9
and R54.
Below the bowl, the effects of the mesoscale largely prevail over
seasonality effects. In R9 and R54 the mean and eddy stream functions well extend at depth and exhibit significant upwellings and
downwellings across isopycnals, in particular in the region of the
subtropical gyre. South of 35°N, the eddy circulation is anticlockwise while the Eulerian mean circulation is clockwise with a northward flow in the upper layers and southward flow in the lower
layers. These dynamical features are similar to those related to
the Ferrel cell in the atmosphere except the different sign due to
the different isopycnal slope. North of 35°N the eddy stream function is almost zero, consistent with the weak eddy activity leading
to a small eddy heat flux. There is a strong compensation between
eddy and mean transports, which are both much stronger than the
total residual mean transport. This is in agreement with the nonacceleration theorem (Andrews and McIntyre, 1976) valid for no
diabatic effect. One interesting feature observed in Fig. 13 is the almost perfect compensation of the small-scale structures. This is
particularly true for R54. On the other hand, such compensation
is not verified for the large-scale structures in particular in the
upper layers where the Eulerian mean contribution dominates.
This is due to the thermohaline and momentum forcings that drive
the residual mean circulation (Andrews and McIntyre, 1976).
4. Conclusion
In this paper, we have computed long (100 years) integrations
of an idealized double-gyre circulation at sub-mesoscale resolving
resolution (1/54°) that allowed us to demonstrate the cumulative
13
effects of sub-mesoscale dynamics. Our configuration is characteristic of mid-latitudes oceanic gyres, such as the Gulf Stream system
in the North Atlantic or the Kuroshio system in the North Pacific.
When horizontal resolution is increased from eddy-resolving to
sub-mesoscale resolving, a strongly turbulent eddy field emerges
with the consequence of significant modifications of the model
mean fields. Our 1/54° resolution simulation is characterized by
the emergence of a regime of zonal jets which are particularly intense between the latitude of zero wind stress curl and the latitude
of the separation of the western boundary current, as the latter
moves to the south. These mean zonal jets result from the submesoscale impact on the mesoscale eddies that makes these eddies
to become more energetic and their related Reynolds stresses to be
stronger. Such a zonal jet regime appears to exist in the Western
part of the North Pacific as shown by Maximenko et al. (2005)
and hinted by the numerical simulations of Sasaki et al. (2008)
but probably not so well in the Gulf Stream area, because of the
topography not taken into account in our study. Another original
aspect is the restratification of the upper layers when sub-mesoscales are taken into account. This much reduces the deep convection in the Northern part of the domain.
The modification of the gyre-scale density structure by the eddies is much more complex to decipher in our experiments than in
the ones of Henning and Vallis (HV, 2004), who contrasted a coarse
resolution and an eddy permitting model. HV could interpret the
effect of eddies invoking baroclinic instability alone (using the concept of eddy-induced velocities described in Gent et al. (1995)).
Their eddy fluxes fit neatly into classical scalings for the wind driven gyres and the stratification within the internal thermocline. It
is not so as the circulation is pushed into a fully eddy resolving regime and sub-mesoscales are allowed to develop, because the
mean circulation changes substantially. Contrary to HV, we find
that the wind-driven subtropical gyre is deeper at high resolution,
due to the rectifying effect of eddy fluxes that was not represented
in their 1/6° model.
Furthermore, although we find (like HV) that the stratification
within the internal thermocline decreases from coarse resolution
to eddy permitting, the reverse is true when the resolution is further enhanced. One explanation may be related to the emergence
of the strong zonal jets that make (through the thermal wind balance) the isopycnals slopes to be steeper at depth. Another explanation is that sub-mesoscales (through the stratification
enhancement of the upper layers in the subpolar gyre) create a
source of high potential vorticity which affects the restratification
of the internal thermocline. A more thorough interpretation of the
modification of the internal thermocline would require a detailed
analysis of the mechanisms involved, which is beyond the scope
of the present study.
Our idealized experiments display, quite unexpectedly, a decrease of the meridional heat transport as the resolution is refined.
Impact of sub-mesoscales appear to reduce the meridional heat
transport at mid-latitudes and to increase it in the North. This
emphasizes that eddy-driven changes in transport are not generic,
but rather depend on the detailed characteristics of the mean circulation and atmospheric forcing. Moreover, both the meridional
heat transport and the meridional overturning circulation are characterized by a large compensation between eddy and mean fluxes,
highlighting that the total circulation and total transport result
from a subtle competition between large and small scales.
Our experiments are idealized in two ways which may make
them especially sensitive to the role of the sub-mesoscale. The first
one is our choice of a flat-bottom basin: in the real ocean the mean
flow is strongly constrained by the bathymetry. The second simplification is the hypothesis of a fixed atmospheric state (fixed air
temperature, winds and freshwater fluxes), rather than a coupled
ocean-atmosphere model. Isopycnal outcrops move as resolution
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M. Lévy et al. / Ocean Modelling 34 (2010) 1–15
is refined due to circulation changes and the establishment of the
zonal jets. This modifies the air temperature and thus the air-sea
fluxes, and different water masses are formed. The large changes
of the mean state make it difficult to analyze the eddy effects in
a more quantitative fashion at the basin scale: this is the reason
why the present paper is rather descriptive. More in-depth analysis
will focus on specific regions or specific water masses.
Acknowledgements
This work is a contribution to the MOU between the Earth Simulator Center, CNRS and IFREMER. It is supported by ANR (INLOES
project), MERCATOR (Multicolor project) and CNRS-INSU-LEFE
(TWISTED project). All the computationally expensive experiments
analysed in the study were performed on the Earth simulator. M.A.
Foujols is thanked for developing the code on the Earth Simulator,
A. Koch Larrouy for her help in setting up the configuration. Many
thanks to R. Benshila, C. Talandier, F. Pinsard, P. Brockmann, A. Caubel, E. Maisonneuve, C. Deltel, C. Ethé. M. Kolasinski, S. Denvil, J.
Ghattas and P. Brochard who have come to the ESC to run the simulations. Their visit at the ESC was greatly facilitated by the kind
help of A. Kurita, R. Itakura, A. Toya and M.-E. Demory.
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