Journal of Oceanography, Vol. 63, pp. 125 to 134, 2007
Mixed Layer Depth Front and Subduction of Low Potential Vorticity Water in an Idealized Ocean GCM
S HIRO NISHIKAWA* and ATSUSHI KUBOKAWA
Graduate School of Environmental Earth Science, Hokkaido University, Sapporo 060-0810, Japan
(Received 13 December 2005; in revised form 15 September 2006; accepted 20 September 2006)
It is known that there is a front-like structure at the mixed layer depth (MLD) distribution in the subtropical gyre, which is called the MLD front, and is associated with
the formation region of mode water. In the present article, the generation mechanism
of the MLD front is studied using an idealized ocean general circulation model with
no seasonal forcing. First, it is shown that the MLD front occurs along a curve where
∇ Ts = 0 is satisfied (u g is the upper ocean geostrophic velocity vector, Ts is the sea
u g·∇
surface temperature and ∇ is the horizontal gradient operator). In other words, the
∇ Ts > 0) and the region where
front is the boundary between the subduction region (ug·∇
∇ Ts < 0). Second, we have investigated subduction of
subduction does not occur (u g·∇
low potential vorticity water at the MLD front, which has been pointed out by past
∇ Ts = 0 at the MLD front, the water particles do not cross the outstudies. Since u g·∇
crop at the MLD front. The water that is subducted at the MLD front has come from
the deep mixed layer region where the sea surface temperature is higher than that at
the MLD front. The temperature of the water in the deep mixed layer region decreases as it is advected eastward, attains its minimum at the MLD front where
∇ Ts = 0, and then subducts under the warmer surface layer. Since the deep mixed
u g·∇
layer water subducts beneath a thin stratified surface layer, maintaining its thickness, the mixed layer depth changes abruptly at the subduction location.
Keywords:
⋅ Mixed layer depth
front,
⋅ subduction,
⋅ low potential
vorticity water,
⋅ subtropical gyre,
⋅ idealized ocean
GCM.
locities at the base of the mixed layer:
1. Introduction
In the subtropical gyre region, water is transfered
from the surface mixed layer into the thermocline below
by downward Ekman pumping. This process is called
subduction. The subducted water flows along an isopycnal
surface, isolated from the direct effect of wind stress, and
is advected by Sverdrup flow, conserving its potential
vorticity. The thermocline structure in the subtropical gyre
region is mainly determined by this process. This view
of the wind-driven circulation in the subtropical gyre was
first given by Luyten et al. (1983) and is called the ventilated thermocline theory.
The ventilated thermocline theory implies that the
lateral distribution of the mixed layer depth (MLD) is
important in the determination of thermocline structure.
Williams (1989, 1991) formulated the effect of the mixed
layer depth distribution on the subducted fluid and combined it into the ventilated thermocline model. He expressed the potential vorticity (PV) of the ventilated fluid,
q, in terms of the mixed layer depth, density, and the ve-
q=
f ub ⋅ ∇σ θ
,
ρ wb + ub ⋅ ∇h
(1)
where f is the planetary vorticity, ρ is a reference density, u b and wb are the horizontal and vertical velocities
at the base of the mixed layer, σθ is the potential density
of the mixed layer, h is the mixed layer depth, and ∇ is
the horizontal differential operator. Williams’ formula
indicates a low PV of subducted water where the gradient of MLD, ∇h, is large.
Recent studies based on the ventilated thermocline
theory, including Williams’ study, have shown that the
subtropical ocean interior structure is affected by the MLD
distribution. Among these studies, Kubokawa and Inui
(1999) studied the MLD distribution in an ocean general
circulation model (GCM) and its effects on the upper
ocean structure, and Kubokawa (1999) gave a theoretical
discussion of the ventilated thermocline, strongly affected
by the mixed layer distribution. They showed that there
is a front-like structure in the MLD distribution (where
∇h is large) and low PV water is formed around the inter-
* Corresponding author. E-mail: [email protected]
Copyright©The Oceanographic Society of Japan/TERRAPUB/Springer
125
section of the outcrop and this front-like structure in each
isopycnal layer. They referred to this front-like structure
as the mixed layer front. The low PV waters formed at
each isopycnal layer are advected southwestward along
the subtropical gyre, converge in the horizontal plane and
accumulate vertically, as a result forming thick low PV
pool (mode water) in the central western subtropical gyre.
Furthermore, they explained that the isopycnal surfaces
in the upper layer are raised by the formation of the mode
water and this structure drives a surface eastward current
(subtropical countercurrent) along the southern edge of
the mode water.
Several studies indicate that the mechanism presented
by Kubokawa and Inui (1999) and Kubokawa (1999) is
important for the formation of some mode waters observed
in the real ocean. It is known that there are three mode
waters in the North Pacific: subtropical mode water
(STMW), central mode water (CMW), and eastern subtropical mode water (ESTMW). Xie et al. (2000) reproduced these three mode waters in their realistic GCM
simulation. They showed that low PV water is formed at
the intersection of the MLD front (mixed layer front) and
the outcrop of each isopycnal surface in their model. They
suggested that such low PV waters are the sources of
STMW and CMW.
The role of the MLD front in determining the
thermocline structure presented by Kubokawa and Inui
(1999) and Kubokawa (1999) has been applied to other
problems. One example is the problem of oceanic
thermocline response to an intensification of the Westerlies. It is known that a sudden change in the atmospheric
circulation over the North Pacific during the mid-1970s
caused a cooling of the subsurface ocean interior. Inui et
al. (1999) investigated the cooling mechanism using an
idealized ocean GCM. They showed that when westerly
intensification occurred, the MLD front shifts northward
by the anomalous change of the MLD distribution, the
location of the mode water shifts westward, and as a result, isopycnals of the subsurface rise, which causes the
cold anomaly. On the other hand, Kubokawa and Xie
(2002) presented a somewhat different mechanism for the
problem. They argued that the westerly intensification
strengthens the Sverdrup flow in that region and this
causes the westward shift of the low PV water (mode
water) without the anomalous change of the MLD distribution.
As mentioned above, the effect of the MLD front on
the ocean interior structure has been investigated in several studies. However, the structure and determination of
the MLD front itself have not been studied so far. Since
the MLD distribution is one of the boundary conditions
of the ventilated thermocline model, an exact understanding of the MLD distribution in an idealized situation is
important for theoretical studies. In addition, since past
126
S. Nishikawa and A. Kubokawa
studies have considered the MLD front as a source region of low PV water (mode water), the subduction process at the MLD front is also important. The purpose of
this paper is to investigate the MLD front in an idealized
situation. We focus on the following two points: what
determines the location of the MLD front? And how is
the low PV water subducted at the MLD front, in the absence of seasonal forcing? The location of the MLD front,
the subduction of the low PV water and the generation of
the sharp MLD front are three aspects of the same phenomenon. Investigation of the subduction process will
lead us to an interpretation of why the MLD front is so
sharp.
In this study, for simplicity we use an idealized ocean
GCM with no seasonal variation, similar to models used
by Kubokawa and Inui (1999), Inui et al. (1999), etc. We
adopt Stommel’s mixed layer demon concept (Stommel,
1979), that is, the surface density condition is fixed in
late winter where the mixed layer is deepest and the annual mean wind forcing is used. Although seasonality is
important for the subduction process in the real ocean
(e.g., Woods, 1985; Williams et al., 1995), such a simple
model would be helpful in understanding the essence of
the mechanism of MLD front generation and its relation
to the subduction of low PV water.
The rest of this paper is organized as follows. Section 2 describes the configuration of the model. Section 3
briefly discusses the model’s upper ocean structure. In
Section 4 we discuss the determination of the location of
the MLD front, while in Section 5 we discuss the subduction at the MLD front. Finally, a summary and discussion are given in Section 6.
2. Model Description
The model used in this study is the Center for Climate System Research (CCSR) Ocean Component Model
(COCO, described by Hasumi, 2000) ver. 3.3 developed
at University of Tokyo. COCO is a Bryan-Cox type ocean
GCM (e.g., Bryan, 1969; Cox and Bryan, 1984). This
model solves the three dimensional primitive equations
under hydrostatic and Boussinesq approximations. Spherical coordinates are used horizontally and geopotential
height coordinate is used vertically. The free surface is
explicitly treated by a method similar to that introduced
by Killworth et al. (1991). COCO uses UTOPIA (Leonard
et al., 1993) as a tracer advection scheme, and isopycnal
diffusion with weak background horizontal diffusion.
When the density stratification is unstable, the convective adjustment scheme is applied to the density field.
The model domain is a rectangular basin with no
bottom topography, which is 60° wide in longitude, extends meridionally from the equator to 60°N, and has a
constant depth of 3000 m. The horizontal resolution is
1.2° × 1.2°. There are 30 vertical levels. The vertical reso-
Fig. 1. Meridional profiles of τx (left) and Ta (right). Unit of τx is dyne cm –2 and unit of T a is °C.
lution is high in the upper ocean and low near the bottom. For example, the thickness of the uppermost layer is
10 m and that of the lowest layer is 400 m. The viscosity
and diffusivity coefficients are constant spatially and temporally. The horizontal and vertical viscosity coefficients
are AH = 2.0 × 108 cm 2s –1 and AV = 1.0 cm2s –1, respectively. The isopycnal diffusion coefficient and vertical
diffusion coefficient are KHI = 1.0 × 107 cm2s–1 and KV =
0.3 cm2s–1, respectively.
The model ocean is driven by surface wind stress
and surface temperature flux. The surface wind stress,
(τx, τy), is
 

π 
τ 0 0.35 cos 15 ϕ  − 0.65

τx =  
π
π


τ 0 cos
ϕ+
 30

2
(0 < ϕ ≤ 15)
(15 < ϕ ≤ 60),
(2 )
(3)
τ y = 0,
where ϕ is latitude, and τ0 = 0.7 dyne cm–2. Its functional
form is based on Hellerman and Rosenstein’s (1983) annual and zonal mean data. The surface temperature flux
is
Q = γ (Ta − Ts ),
( 4)
where Ta is a reference temperature and Ts is the sea surface temperature of the model ocean (Haney, 1971). T a in
this study is
27.0

Ta =  23
104
− ϕ+
3
 45
(0 < ϕ ≤ 15)
(15 ≤ ϕ < 60),
(5)
and γ = 100 cm day –1. The functional forms of (τx, τy) and
Ta are the same as those used in Sumata and Kubokawa
(2001). The meridional profiles of τx and T a are shown in
Fig. 1.
Initially, the model ocean is at rest and has a temperature stratification. The initial temperature stratification is zonally uniform, given by the zonal average of
northern hemisphere winter climatology of World Ocean
Atlas 94 (Levitus and Boyer, 1994). The salinity in this
model is constant at 34.9 psu.
The reference temperature, T a, in (5) mimics a zonal
mean of the winter sea surface temperature, while the wind
stress, τx, in (2) mimics the annual mean τx. This is based
on the idea of “Stommel’s mixed layer demon” (Stommel,
1979; Williams et al., 1995). Although the mixed layer
depth has seasonal variability, Stommel (1979) argued that
only the water leaving the mixed layer in wintertime irreversibly enters the permanent thermocline. This means
that the properties of the main thermocline are controlled
by the winter mixed layer rather than by the annual-mean
state.
The model is integrated for 80 years. The time step
is 1 hour. After 80 years, the wind-driven circulation fully
spins up and the model ocean reaches a quasi-steady state.
We analyze the 1-month averaged data after 80 years’
integration.
3. Model’s Upper Ocean Structure
Before discussing the location and the formation
mechanism of the MLD front, let us fist survey the model
results. Figure 2 shows the barotropic stream function.
The barotropic ocean current system consists of three
gyres. The region from 15°N to 44°N is an anticyclonic
subtropical gyre region. To the north is a cyclonic subpolar
gyre region and to the south is also a cyclonic gyre region. These are the result of the applied wind stress (see
the left panel of Fig. 1).
Mixed Layer Depth Front in an Idealized Ocean GCM
127
Fig. 2. Barotropic stream function. Unit is Sv = 106 m3s–1.
Dotted contours denote negative.
Fig. 3. Horizontal velocity field at z = –40 m.
Figure 3 shows the velocity field at z = –40 m. Except for the uppermost layer in which Ekman flow is dominant, the upper layers (shallower than about –200 m) have
a similar horizontal flow structure vertically in the northern part of the subtropical gyre (not shown).
Figure 4 shows the sea surface density field. Since
salinity is constant in this model, the density distribution
corresponds to the temperature distribution. Figure 5
shows the mixed layer depth (MLD) distribution. The
MLD in this study is defined as a depth at which the density difference from that of the sea surface is 0.01σ θ to
resolve the thin surface stratified layer. If we use 0.1σ θ,
as many studies have (e.g., Kubokawa and Inui, 1999),
the location of the MLD front cannot be obtained cor128
S. Nishikawa and A. Kubokawa
Fig. 4. Sea surface density σθ field (at z = –5 m).
Fig. 5. Mixed layer depth (MLD) distribution. MLD is defined
as a depth where the density is 0.01σθ heavier than that on
the sea surface. Contour interval is 20 m. Contours deeper
than 500 m are omitted and shaded. It should be noted that
there is no wind-induced mixed layer in this model.
rectly. The mixed layer is very shallow in the south and
deep in the north. Between 30°N and 40°N, there is a
front-like region where the MLD varies sharply. This is
the MLD front.
Figure 6 shows the potential vorticity (PV) distribution on isopycnal surfaces, σ θ = 25.6, 25.8, 26.0, 26.2.
The potential vorticity in this study is given by
q=−
f ∂σ θ
.
ρ ∂z
(6 )
Fig. 6. Potential vorticity (PV) distribution on isopycnal surfaces, (a) 25.6 σθ, (b) 25.8σ θ, (c) 26.0σθ, and (d) 26.2 σθ (thin solid
contours), with Bernoulli function (thick dotted contours) and the location of the MLD front denoted by diamonds (䉫).
Outcrops are denoted by dashed lines. Unit of PV is 10–10 m –1s–1 and the region lower than 1.6 × 10–10 m–1s –1 is shaded.
Contour interval of the Bernoulli function is 4.0 × 102 kg m –1s–2.
The streamlines are superimposed on these isopycnal surfaces. They are given by the Bernoulli function, B = p +
ρgz, where p is the pressure, ρ is the potential density, g
is the gravitational acceleration and z is the vertical coordinate. Low PV water is formed at the intersection of the
MLD front and the outcrop of each isopycnal surface. The
low PV water formed at the intersection is advected along
the streamline. This result is consistent with that of
Kubokawa and Inui (1999) and Inui et al. (1999).
4. Location of the MLD Front
In the steady state the occurrence of subduction and
convection depends on the upper ocean geostrophic velocity distribution (Fig. 3) and the sea surface temperature distribution (Fig. 4). Using them, we here discuss
the location of the MLD front.
We can divide the subtropical gyre region into two
regions according to the relation between the direction of
the upper ocean geostrophic velocity, ug, and that of the
horizontal gradient of the sea surface temperature, ∇T s.
In the northwestern region of the subtropical gyre, ug·
∇T s is negative (Fig. 7). In this region, southern warm
water is advected northward by the western boundary current and the subsurface (the depth of 10–200 m where
Ekman flow is small enough) is warmed, while there is a
surface cooling; therefore convection tends to occur and
the deep mixed layer is developed and maintained in this
region. On the other hand, in the rest of the subtropical
gyre, u g·∇T s is positive (Fig. 7). Marshall and Nurser
(1992) and Marshall et al. (2001) showed that the vertical component of potential vorticity (PV) flux in ocean
surface mixed layer can be written as J z = fug·∇σθ in the
steady state. In the region where ug·∇Ts is positive, the
PV flux is negative. This means that water particles with
Mixed Layer Depth Front in an Idealized Ocean GCM
129
Fig. 7. Distribution of u g·∇T s, where ug is given by the horizontal velocity at z = –40 m and T s is the sea surface temperature. Shaded region denotes negative. Contour interval
is 3.0 × 10–7 K s –1. Location of the MLD front is denoted
by diamonds (䉫).
some PV enter into thermocline through the surface outcrops, that is, subduction occurs. In this region, colder
(denser) water is subducted below warmer (lighter) water along the isopycnal surface. Thus, the surface stratification is developed, convection cannot occur and a mixed
layer is not formed. The relation ug·∇T s > 0 can be considered to be a condition of subduction. The boundary,
u g·∇Ts = 0, between the subduction region and the region
where subduction does not occur coincides with the MLD
front (Fig. 7).
The location of the zero surface temperature flux
(Q = 0) differs slightly from that of ug·∇T s = 0, because
Ekman advection is important for the surface temperature flux (e.g., Nurser and Marshall, 1991; Marshall et
al., 1993) and the line of Q = 0 does not coincide with the
location of the MLD front (Fig. 8). Whether or not the
convection occurs is determined by the relation between
the upper most layer temperature (T s) and temperature in
the adjacent subsurface layer (T g). The uppermost layer
temperature is determined by the surface temperature flux
Q, temperature flux to subsurface and the horizontal
advection including the Ekman flow, while the subsurface temperature is determined by the convection and the
geostrophic advection ug·∇Tg. On the northern side of the
MLD front where the mixed layer is deep, the subsurface
temperature is equal to the surface temperature (T g = Ts).
Therefore, the subsurface geostrophic advection is given
by ug·∇Ts. In this region, since ug·∇Ts < 0, the geostrophic
advection tends to warm the subsurface layer and
destabilize the stratification, leading to convection. The
130
S. Nishikawa and A. Kubokawa
Fig. 8. Distribution of surface temperature flux. Shaded region denotes negative. Contour interval is 10–5 K m s –1.
Location of the MLD front is denoted by diamonds (䉫).
boundary where ug·∇Ts = 0 is satisfied is the southern
boundary of the convective region with a deep mixed
layer. This boundary corresponds to the MLD front. Since
there is cooling by the Ekman advection, Q = 0 lies a
little north of the MLD front (Fig. 8). It should be noted
that the Ekman flow effect does not enter the subsurface
temperature balance; instead, Ekman flow indirectly affects the MLD front through the surface temperature balance.
The above discussion allows us to describe the MLD
distribution and the location of the MLD front as follows:
1) In the region of ug·∇σ θ > 0, the stratification
tends to be unstable and a deep mixed layer develops.
2) In the region of ug·∇σ θ < 0, the ordinary ventilation occurs, and the stratification tends to be stabilized.
3) At the boundary between these two regions,
which satisfies ug·∇σθ = 0, the mixed layer depth abruptly
changes: This is the mixed layer depth front.
5. Subduction at the MLD Front
As shown in Section 3, low potential vorticity (PV)
water is formed and subducted at the intersection of the
MLD front and the outcrop of each isopycnal surface.
Here a problem arises. How is the low PV water subducted
at the MLD front where the horizontal velocities are parallel to the outcrop lines, i.e., u g·∇Ts = 0? In this section
we examine the subduction process at the MLD front using a trajectory of a water particle. It will also be shown
that the subduction process is closely related to the reason why the MLD front is so sharp.
Figure 9(a) shows an example of a water particle trajectory starting from the deep mixed layer region and Figs.
Fig. 9. (a) Example of the trajectory of a water particle (thick solid line) which is subducted at the MLD front, with the MLD
distribution (dotted contours). Symbol × denotes the starting point of the trajectory and dashed line denotes the outcrop of the
isopycnal into which the particle is subducted. (b) Vertical potential density distribution along the trajectory (solid contours).
Dash-dotted line denotes the depth of the particle and the arrow denotes the position of the MLD front. (c) Value of up·∇T s
along the trajectory, where u p is the horizontal velocity of the particle and T s is the sea surface temperature (SST). Unit is
10–8 K s–1. (d) Temperature of the particle (dash-dotted line) and SST along the trajectory (dotted line).
9(b)–(d) show the particle’s depth, u p·∇Ts, and temperature along the trajectory, where up is the horizontal velocity of the particle. The particle tracing method is the
same as that presented in Masuda (2003). At about 1150
km from the starting point the particle is considered to be
subducted at the MLD front (Fig. 9(b)) and up·∇Ts changes
from negative to positive (Fig. 9(c)). From this result, we
can describe the subduction process along the water particle as follows:
1) Before the particle reaches the MLD front, u p·
∇Ts < 0: The particle is in the deep mixed layer. It flows
from warmer to colder and is approaching the outcrop.
The temperature at the position of the particle decreases
and the MLD gradually becomes deeper.
2) At the MLD front, u p·∇T s = 0: The particle
reaches the outcrop and the velocity direction is parallel
to the outcrop. Here, the temperature of the water particle coincides with that of the outcrop and the MLD
abruptly becomes shallower.
3) After the particle passes the MLD front, u p·
∇T s > 0: The particle flows toward the higher sea surface
temperature (SST) region and is subducted beneath a shallow stratified layer.
Figure 9(a) indicates that the trajectory (thick solid
line) does not cross the outcrop (dashed line), but just
contacts it tangentially, as already suggested above. BeMixed Layer Depth Front in an Idealized Ocean GCM
131
front. Since water is subducted along the outcrop, the
vertically homogeneous water, which has the thickness
of MLD, is subducted under the thin surface stratified
layer, maintaining its thickness as implied by Williams’
formula (1). This forms the abrupt change in the MLD
distribution. If the water is not subducted at the location
of ug·∇T s = 0, the mixed layer gradually deepens and does
not form the MLD front. Such a case will be discussed in
Section 6.
Fig. 10. Diagram showing the relation between the outcrops
(solid contours) and the water particle trajectories (dotted
contours) in the subduction process at the MLD front (diamonds).
fore getting to the tangent point, water temperature is
decreasing because of the surface cooling. At the tangent
point, the temperature attains its minimum. Since the temperature of the water particle is unchanged while the SST
along the trajectory increases, the subduction occurs (Fig.
9(d)). In the present model, one tangential point exists
for each outcrop. This is because the surface temperature
decreases eastward and becomes zonally uniform while
the current is anticyclonic. Figure 10 schematically illustrates this relation among the streamlines, SST and the
MLD front.
The potential vorticity of the water subducted at the
MLD front is zero from Williams’ equation (1), as the
numerator ub·∇σ θ = 0 gives q = 0 in his formulation. On
the other hand, Marshall and Nurser (1992) and Marshall
et al. (2001) show that the subduction rate in the steady
state is given by
S=−
fug ⋅ ∇σ θ
Jz
.
=−
ρq
ρq
(7)
If this formula and Williams’ PV formula (1) are both
valid, these two give the subduction rate, S = –w b – u b·
∇h (e.g., Marshall et al., 1993). Estimation of the subduction rate at the MLD front will be possible using this
equation. The subduction rate is extremely high at the
MLD front because the lateral induction term (ub·∇h) is
extremely large there. Lateral induction is dominant and
vertical pumping (wb) will be negligible at the MLD front.
The subduction process when ug·∇Ts = 0 is satisfied
is closely related to the generation mechanism of the MLD
132
S. Nishikawa and A. Kubokawa
6. Summary and Discussion
In this paper we have studied the mixed layer depth
(MLD) front and its relation to subduction using an idealized ocean GCM. The MLD front is a remarkable structure in the MLD distribution in the subtropical gyre region. Its importance was pointed out by past studies, such
as Kubokawa and Inui (1999) and Kubokawa (1999). They
showed that low PV water is formed at the intersection of
the MLD front and the outcrop of each isopycnal surface.
However, the structure and determination of the MLD
front itself has not been studied hitherto. We first investigated the relation of the MLD front to subducting and
non-subducting regions, and second, we investigated the
subduction of the low PV water at the MLD front.
The occurrence of the subduction and convection
depends on how the upper ocean geostrophic velocity
vector ug crosses the contour of the sea surface temperature field Ts. Using this, we discussed the location of the
MLD front. In the northwestern region of the subtropical
gyre where ug·∇T s < 0, convection tends to occur and the
deep mixed layer is formed and maintained. On the other
hand, in the remaining part of the subtropical gyre where
ug·∇T s > 0, subduction occurs and the surface stratification is developed. The boundary, ug·∇Ts = 0, gives the
boundary of subduction. We compared the location of the
MLD front with the location of ug·∇T s = 0 and found that
they coincide.
The above result shows that the MLD front is formed
where the upper ocean geostrophic velocities become
parallel to the outcrops of the isopycnals. This means that
there are no velocity components normal to the outcrops
at the MLD front. The question then is how subduction
occurs at the MLD front. We investigated this using a
water particle that is subducted at the MLD front. Before
a particle reaches the outcrop of the ventilated isopycnal,
ug·∇T s is negative and it approaches the outcrop from the
south through the deep mixed layer region. At the MLD
front, ug·∇Ts vanishes, that is, the horizontal velocity of
the particle becomes parallel to the outcrop. After that,
u g·∇T s is positive and it leaves the outcrop and flows
southeastward along the isopycnal under thin surface
stratification. In this subduction, the trajectory of the water
particle does not cross the outcrop; instead, it is subducted
parallel to the outcrop at the MLD front (see Fig. 10).
Fig. 11. Example of surface density made by controlling surface temperature condition (left), and MLD distribution corresponding to that case (right). MLD is defined using the density difference 0.01σθ.
The present experiment allows us to outline how the
mixed layer depth is determined, and why the sharp front
occurs in the mixed layer depth, as follows: The western
boundary current advects a thick warm water northward
and the surface is cooled in this region. The mixed layer
depth there will be determined by the sea surface temperature (SST) and the stratification; that is, the mixed
layer depth is the depth of the isopycnal whose temperature is the same as SST. Therefore, it increases northward
in the western boundary region. Since SST tends to be
high in the west because of the temperature advection,
the water flowing eastward after leaving the western
boundary still experiences the decrease of SST and the
mixed layer continues to deepen. While flowing eastward,
the current direction gradually changes from eastward to
southward as the Sverdrup theory predicts, and the development of the mixed layer ceases where the current
direction is parallel to the SST contour. After that, since
the SST is higher than that of the water flowing from the
western boundary region, the water is subducted under a
thin stratified surface layer. This causes the abrupt change
in MLD.
This survey suggests that, if the SST increases eastward, the subduction described above will not occur and
the deep mixed layer will lie only in the western boundary region. Figure 11 shows that case, in which Ta is increased eastward to control the SST distribution. Although
the mixed layer is deep in the subpolar gyre (north of
44°N) and near the western boundary, there is no MLD
front in the interior region of the subtropical gyre. It
should also be noted that there seems to be an MLD front
in the subpolar gyre region but the MLD changes rather
gradually. In this region, water particles flow from the
southern region where u g·∇Ts > 0 to the northern deep
mixed layer region where ug·∇Ts < 0. The flow direction
in this case is opposite to that in the subtropical gyre.
Therefore, the surface temperature gradually decreases
along the flow trajectories and the mixed layer gradually
develops northward to the north side of u g·∇Ts = 0. That
is, the sharp MLD front such as is seen in the subtropical
gyre region is not formed.
Here we have defined the MLD as a depth at which
the density difference from that of the sea surface is
0.01σθ. In model studies, 0.1σθ is often used as the density difference (e.g., Kubokawa and Inui, 1999). When
we use 0.1σ θ, the MLD front comes out a little to the
south (about 2–3 degrees) compared with that defined by
0.01σθ. This means that there is thin surface stratification in the area between the MLD front defined by 0.01σθ
and that defined by 0.1σθ. In other words, the density difference 0.1σθ is too large to resolve the important surface stratification which is associated with the MLD front.
Thus, 0.01σθ is a better value for this study.
In the present study we used an idealized ocean GCM
in which the formation of the mixed layer occurs only by
convective adjustment, the ocean is driven by steady forcing and meso-scale eddies are not permitted. These
simplifications yield a clear result. Qu et al. (2002), using an eddy-permitting GCM, found that meso-scale activities enhance the subduction rate. The relation between
the mean location of MLD front and mean upper layer
current/SST may also be affected by meso-scale eddies.
Time-dependent forcing may have similar effects to the
eddies. These points should be clarified in a future study.
Acknowledgements
The authors would like to thank Prof. L. D. Talley
for valuable comments and advice. Dr. H. Hasumi kindly
Mixed Layer Depth Front in an Idealized Ocean GCM
133
permitted us to use COCO, and Dr. Y. Masuda gave us
helpful advice about the particle tracing method. The authors also thank two anonymous reviewers for helpful
comments. The numerical experiments were performed
on the HITACHI SR8000 computer at the Information
Initiative Center, Hokkaido University. The GFDDENNOU Library was used to draw the figures. This work
was partly supported by a Grant-in-Aid for Scientific
Research from the Japan Society for the Promotion of
Science.
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