# **The Eddy-Driven Thermocline**

## Paola Cessi, Scripps Institution of Oceanography -- UCSD

***Summary***

***We examine the role of time-dependent eddies with horizontal scales
of about 100 km in the maintenance of the oceanic deep thermocline and
abyssal stratification. The hypothesis is that eddy heat-fluxes balance
the diapycnal mixing of heat and thus determine the vertical scale of
penetration of horizontal thermal gradients imposed at the surface (i.e.
the depth of the thermocline). This conjecture is in contrast with
current theories that the deep stratification arises from a balance
between diapycnal mixing and the large-scale overturning circulation.***

**1. Introduction**

Unlike the atmosphere, which is heated \`\`internally\'\' by radiative
processes, the ocean is differentially heated (and freshened) only at
the top boundary. A fundamental question in physical oceanography is how
the thermal (and haline) gradients are transferred from the surface of
the ocean to the abyss. To this day, the processes that mantain the
oceanic deep thermocline and the abyssal stratification are not
understood. The thermal structure crucially determines the meridional
heat transport by the ocean, and the latter is an important component of
the earth climate system. Without a clear understanding of the
mechanisms that determine the thermal stratification of the ocean, any
claim to predict future climate scenarios is on shaky grounds.

Classical theories posit that the oceanic stratification stems from a
balance between diapycnal mixing and the advection of density by the
large scale circulation that arises in response to the large-scale
thermal (and haline) gradients. Diapycnal mixing occurs when internal
gravity waves break and overturn a stable stratification. Breaking
internal gravity waves have horizontal scales of 10 cm. The large scale
meridional overturning considered by the classical theories is
associated with flows on the planetery scale of 107 m. Thus in classical
theories, and in coarse resolution climate models, the oceanic density
structure arises from a balance between two extreme ends of the
dynamical scales in the ocean. All the flows at scales intermediate
between 10-1 m and 107 m are neglected.

**2. A minimal model**

To examine the role of eddies in their simplest setting, we consider a
cartesian oceanic domain of 1000 × 1000 × 2 km3, periodic in both
horizontal directions, resolved by 128 × 128 × 100 grid points. The
Coriolis parameter is constant. At the rigid top, we impose the
temperature, characterized by a large-scale, steady pattern of heating
and cooling and a no-stress condition. At the rigid bottom, we impose no
flux of temperature and no-slip. The diffusivity, κ, and viscosity, ν,
are uniform and isotropic in all three dimensions. Thus κ measures the
diapycnal diffusivity which parametrizes breaking gravity waves.

The problem thus formulated is the simplest process model which enables
us to study the role of eddies in the formation of the thermocline. Our
numerical results to date show that the time-dependent eddying flows are
characterized by horizontal scales of 50 to 100 km. The eddies are
associated with a lateral heat transport which balances vertical
diffusion of heat mantaining a zonally averaged temperature, T, with a
well-defined thermocline, as illustrated in figure 1.

![](media/image1.png){width="3.0027777777777778in"
height="2.311111111111111in"}Figure 1. The zonally averaged temperature,
T, for κ=8 × 10-5 m2 s-1 and ν=4 × 10-3 m2 s-1 as a function of y and z.
The rotation rate is f=1 × 10-4 s-1. The contour interval is 0.2 oC and
negative values are dashed.

We have performed extensive computations (at Oak Ridge National Lab and
in-house) to determine the dependence of depth of the thermocline on
different parameters. A summary of the results is shown in figure 2. We
find that the viscosity, ν, as well as the diffusivity, κ, determine the
depth of the thermocline.

**3. Future plans**

We intend to examine how the eddy-driven thermocline is mantained in the
presence of wind-stress at the surface. Without lateral boundaries
wind-driven gyres are not possible, but the wind-stress generates Ekman
flow, whose mean meridional heat transport is upgradient for conditions
appropriate to the Antarctic Circumpolar Current. The equatorward mean
heat transport is largely cancelled by the eddy heat transport. In this
case, the \`\`residual circulation\'\', equal to the sum of the mean and
eddy-induced heat transport, balances the diabatic terms in the heat
equation. Our plan is to sistematically examine the dependence of the
thermocline depth and of the net heat transport on the diffusivity,
κ, and on the strength of the wind-stress. We also intend to change the
domain configuration to include lateral boundaries. In a closed domain,
the role of the mean large scale circulation is potentially as prominent
as that of the eddies and the thermocline structure that emerges when
both processes are present can be determined. This last part of the
project is very ambitious and we anticipate that it will require large
computational resources.

![](media/image2.png){width="3.004166666666667in"
height="2.3916666666666666in"}Figure 2. The depth of the thermocline as
a function of κ,  for different values of the domain depth, H, and of
the Prandtl number, Pr=ν/κ.

**For further information contact:**

Dr. P. Cessi

Scripps Institution of Oceanography --UCSD

La Jolla, CA 92093-0213

Phone: 858-534-0622

E-mail: <pcessi@ucsd.edu>