The overturning circulation maintained by mixing

How do the above considerations apply to the circulation of the ocean? For simplicity, we consider only the effects of temperature and not of salinity, and a schema of the circulation is given in the top panel of figure 4.6. The ocean, is, roughly speaking, a big basin of water for which the temperature of air just above the sea surface decreases with latitude. Air-sea exchange of heat heats or cools the water at the sea surface so that it has, approximately and on average, the temperature of the air above it. The sea-surface temperature thus decreases more or less monotonically from the equator to the pole, and as a consequence the density of the water at the sea surface increases from the equator to the pole.

CHARTER 4 Warm surface

Cold surface

) Heat diffuses in from warm surface, warming deep water water is warmed and rises

Polewards return flow

Sinking dense i water

Dense water displaces light water, and moves equatorward

Equator Eastward wind

Latitude

Pole

Cold surface

Shallow northward flow

Sinking dense water

Deep southward flow

South

Latitude

North

Figure 4.6. Schema of the two main components of the Moc. Top: The mixing-maintained circulation. Dense water at high latitudes sinks and moves equatorward, displacing warmer, lighter water. The cold, deep water is slowly warmed by diffusive heat transfer (mixing) from the surface in mid- and low latitudes, enabling it to rise and maintain a circulation. Bottom: Winds over the Antarctic circumpolar current (outlined by dashed lines) pump water northward, and this pumping enables deep water to rise and maintain the circulation. In the absence of both wind and mixing, the abyss would fill up with the densest available water and the circulation would cease.

As we mentioned, a fluid parcel itself sinks if it is cold and sufficiently dense. This is just what happens to water at high latitudes, especially in winter in the North Atlantic and near Antarctica, and this process is known as convection. Some lighter water at depth comes up to the surface to take the place of the dense, sinking water, as indicated by the dashed lines in figure 4.6, and as this water comes into contact with the cold atmosphere, it too cools and sinks, so that eventually the whole column of water at high latitudes is cold and dense. What happens then? Recall that the pressure at some level in a fluid is equal to the weight of the fluid above that level, so that if a column of fluid is cold and therefore dense, then the column weighs more than does a column of lighter fluid. Thus, the pressure in the deep ocean is largest at the high latitudes because the cold water weighs more than the warmer water at low latitudes. Thus, in the deep ocean there is a pressure force acting to push fluid from high latitudes to low latitudes, and the water begins to circulate, flowing at depth from high latitudes to low latitudes.

If no other physical processes occurred, the dense water would displace light water until the entire deep ocean were filled up with cold, dense water with polar origins. Nearer the surface, there would be a region of strong vertical temperature gradients, linking the low temperature of the abyss with the warmer surface waters. However, the deep, abyssal waters would eventually stop circulating because the water in the deep ocean would be as cold and dense as the coldest and densest waters at high latitudes at the surface. That is, the surface water would no longer be denser than the water beneath it, and convection and the deep circulation would cease. This state would be the "cold death" of the ocean.

So what enables a deep circulation to continue? The circulation continues because the deep water in low and midlatitudes is continually, albeit weakly, warmed by the transport of heat from the surface. This warming enables the water to rise and the circulation to continue. If there were no such heat transport, the deep ocean would simply fill up with cold, dense polar water. There would then be no convection because the cold surface waters at high latitudes would not be negatively buoyant. Thus, although the circulation can be thought of as being set up by a buoyancy gradient at the surface, its continuation relies on the effect of transport of heat down into the abyss, and without that, this part of the overturning circulation could not be maintained.

What physical process causes the downward heat transfer? In a quiescent fluid, the heat is transferred by molecular diffusion, in which molecules of water pass on their energy to neighboring molecules without any wholesale transport of fluid itself. However, the molecular diffusivity is very small and molecular diffusion is a slow process indeed, requiring thousands of years for a significant amount of heat to be diffused from the surface to the abyss. In fact, the ocean is a turbulent fluid, and the downward transport of heat is mainly effected by small-scale turbulent eddies. This process is sometimes called turbulent diffusion because the process is similar to that of molecular diffusion but with parcels of water replacing individual molecules. (Turbulent diffusion arises in large part from internal gravity waves that break and mix the fluid. Such waves, analogous to waves on the surface of the ocean but interior to the fluid, are generated by mechanical forcing—by the winds and the tides. Thus, without the effects of mechanical forcing, this component of the MOC would be weak indeed because the diffusion would be small.) Thus, to summarize, the following two effects combine to give an overturning circulation.

1. A meridional buoyancy gradient between the equator and the pole enables dense water to form at the surface at high latitudes and then potentially to sink in convective plumes and move equatorward. In today's ocean, the buoyancy gradient is predominantly produced by the temperature gradient.

2. The slow warming of the abyssal waters by turbulent diffusion of heat from the surface in mid- and low latitudes imparts buoyancy to the deep water and enables it to rise. Without this warming, the abyss would fill with cold, dense water and circulation would cease.

It is natural to think of the meridional buoyancy gradient as being between the equator and the pole, mainly caused by temperature falling with latitude. In this case, we can envision a meridional circulation in each hemisphere, with sinking at each pole and rising motion in mid- and low latitudes, in both hemispheres.

If one hemisphere were to be significantly colder than the other, then the abyss in both hemispheres could be expected to fill up with the water from the colder and denser hemisphere, which would create an interhemi-spheric circulation (more on that later). Finally, although we've couched our description in terms of the temperature effects on buoyancy, the effects of salinity can also be important. Salty water is heavier than freshwater at the same temperature, so adding salt can have a similar effect to that of cooling the surface. in today's climate, temperature has a larger effect than salinity on the variations in buoyancy so that the circulation is thermally driven, rather than salt driven. However, variations in salinity turn out to be the key difference in the overturning circulation of the Atlantic and the Pacific—the North Atlantic is saltier than the North Pacific, and so it can more easily maintain an overturning circulation.

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