An extra dimension to mixing

According to a new theory, stratification of the oceans is controlled by a balance between heat input at the surface and heat redistribution by eddies. But it is early days for this sea-change in thinking.

In the oceans, buoyant surface water lies above denser deep water. In most parts of the world there is a well-defined boundary between the two in which, at depths typically between 100 m and 1,000 m, the temperature changes rapidly between surface and deep values. This sharp temperature gradient is known as the permanent thermocline. Its depth and sharpness vary around the world, and control the speed at which the ocean circulation adapts, for example, to winds, and to the currents that result from these and other 'forcing' phenomena. Understanding what sets the depth and form of the thermocline is therefore one of the fundamental aims in oceanography.

The short answer is heating and cooling, as warmer water is less dense. But two papers by Marshall and colleagues, published in the Journal of Physical Oceanography1,2, provide a challenge to the usual textbook answers. The authors suggest that the limiting term in the ocean budget for water buoyancy, and therefore the factor that determines the steady state for the thermocline, is the rate at which eddies are formed and transfer heat.

In one model, known as the ventilated thermocline3, wind action causes surface water to circulate to intermediate depths, resulting in vertical temperature transfer. The variation of temperature with depth, which defines the thermocline, arises as horizontal temperature variations at the surface are 'mapped' onto the vertical plane by this circulation. When the influence of these 'ventilated' waters on water that circulates without reaching the surface is taken into account4, the theory is quite successful in explaining many observed features of the ocean.

But the ventilated thermocline model nonetheless remains incomplete. It describes a wind-driven circulation only, and does not account for the processes that actually set up the large-scale temperature gradients in the ocean. These processes include the greater heating from the Sun in the tropics than at the poles, and the effect that this has on water movement. Certain issues of water dynamics are also swept under the carpet by assuming the existence of 'passive western boundary currents', such as the Gulf Stream, which flow near to the western edges of ocean basins. These currents are needed to 'close' the circulation, making it hard to talk about such things as heat budgets when a part of the closed circulation lies outside the theory.

An alternative to the ventilated thermocline is the 'diffusive thermocline' model5, in which the maintenance of large-scale temperature differences is explicitly taken into account. This is essentially a one-dimensional theory. The deep waters of the ocean are formed at only a few sites in the North Atlantic and near to Antarctica, where surface water cools, becomes denser and less buoyant, sinks to the bottom, and spreads around the world by flowing at great depth. The denser water is formed mostly by cooling, although salinity also determines density and can be important in the formation of these deep waters.

To complete the circuit, the deep water must upwell, becoming less dense as it does so. The diffusive thermocline theory assumes that downward diffusion of heat counteracts the upward movement of dense water to maintain stratification in the ocean. In subtropical regions, the wind pumps water downwards near the surface, resulting in a confluence of shallow and deep water at a certain depth. The resulting temperature discontinuity, which is smoothed by diffusion, gives rise to the thermocline.

The principal shortcoming of the diffusive thermocline model is in reconciling the observed sharpness of the thermocline with measurements of turbulent diffusion (molecular diffusion is on a much smaller scale and can be neglected in the absence of small-scale turbulence). Measured diffusion rates6,7,8 are ten times too small to match thermocline structure, except in a few regions where the topography of the ocean floor is rough or currents are particularly strong, enhancing the turbulence.

The new theory proposed by Marshall and colleagues1 offers a variation on the 'closed heat budget' idea of the diffusive thermocline. It extends the one-dimensional idea of vertical diffusion to three dimensions by describing how large, horizontal eddies can transport heat across a mean temperature surface. The key to this theory is to consider the heat budget of a bowl of water, bounded by a surface on which the temperature is constant (Fig. 1). In a long-term steady state, the surface heating must be balanced by a combination of diffusion and advection of heat across the bowl. Assuming the diffusion by small-scale turbulence to be negligible outside a shallow, surface mixed layer where the flow is directly driven by wind (the Ekman layer), a three-way balance results. The heat drawn into the bowl by surface heating and advection in the Ekman layer must be balanced by loss of heat in eddies breaking off from the bowl. Although small-scale turbulence or diffusion is then required to dissipate the eddies, the factor that controls the heat budget is the rate of formation of large eddies which carry heat away from the bowl.

Figure 1: An oceanographic mixing bowl.

The bowl shape represents a surface on which the temperature is constant, capped by an Ekman layer in which the wind directly drives water flow and mixing. The sum of the heat input due to direct surface heating and to Ekman flow must be balanced by heat transport out of the bowl's sides below the mixed layer. Marshall and colleagues1,2 propose that eddies breaking away from the bowl transport this heat at a rate that is determined by the bowl's shape. Applying this heat budget to a series of bowls nested inside one another (inset) results in a temperature pattern involving a region where temperature varies with depth: the thermocline.

To estimate this rate, Marshall and colleagues assume that eddy heat flux is proportional to the temperature gradient, and to the tangential flow speed of the eddies. The tangential flow results from the pressure gradient associated with the temperature anomaly inside the bowl. The flow that arises from this radial pressure is deflected by the Coriolis force, which is due to the Earth's rotation and here creates a circulation around the bowl, so the flow speed can also be described in terms of temperature. By calculating the heat budgets of the water inside the bowl and of the surface mixed layer, a complete theory can be derived which determines the stratification that results from the imposed heating and Ekman flow — laboratory experiments show that it works. Interestingly, Ekman flow turns out to be a more important heat source for the deep ocean than direct surface heating.

The laboratory is one thing, but the real ocean is quite another. The laboratory experiments mimic a flat Earth, but the Earth's curvature and the topography of the ocean floor can both have a large impact on eddy generation, and ocean-floor topography can produce strong, narrow currents, effectively turning the neat bowl of Fig. 1 into something more like a squid with long, convoluted tentacles. Nonetheless, as Marshall and colleagues describe in their second paper2, this simple approach gives a reasonable scaling for stratification in the Southern Ocean and the resulting strength of the Antarctic Circumpolar Current (in which it is generally thought that eddy fluxes are indeed a significant factor9). Moreover, predictions for other ocean basins give reasonable thermocline structures, hinting that this concept has much wider applicability than in just the Southern Ocean, and that a complete thermocline theory must consider the role of eddies.

It is early days for an idea that has not yet been adapted to realistic ocean conditions. But the first signs are encouraging: it may be large, horizontal eddies — rather than small, vertical ones — that control the ocean.


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Correspondence to Chris W. Hughes.

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Hughes, C. An extra dimension to mixing. Nature 416, 136–139 (2002). https://doi.org/10.1038/416136a

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