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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 10cm. The large scale meridional overturning considered by the classical theories is associated with flows on the planetery scale of 10⁷m. 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^-1m and 10⁷m are neglected.

2. A minimal model

To examine the role of eddies in their simplest setting, we consider a cartesian oceanic domain of 1000 x 1000 x 2km³ , periodic in both horizontal directions, resolved by 128 x 128 x 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, k , and viscosity, n, are uniform and isotropic in all three dimensions. Thus k 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 100km. 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.

Figure 1. The zonally averaged temperature, T, for k =8 x 10^-5 m² s^-1 and v =4 x 10^-3 m² s^-1 as a function of y and z. The rotation rate is f=1 x 10^-4 s^-1 . The contour interval is 0.2 °C 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, n, as well as the diffusivity, k, 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 , k, 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.

Figure 2. The depth of the thermocline as a function of k, for different values of the domain depth, H, and of the Prandtl number, Pr= n/k .

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

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