The dynamics of global ocean circulation

Roughly 70% of the earth's surface is covered with ocean. From the window of a plane the ocean looks tranquil and calm, as if nothing seems to go on there. But the ocean is far from a stagnant body of water. Instead, it is constantly in motion, at speeds from a few centimetres per second to two metres per second in the most vigorous currents.

The ocean circulation is governed by the Navier-Stokes equations. This set of coupled partial-differential equations cannot be solved analytically for non-trivial solutions, which is one of the reasons physical oceanography is so fascinating. Physical oceanography is where climate meets fluid dynamics, where observations are extremely difficult to obtain, and where physicists can make a great contribution to the understanding of our planet.

Two modes of large-scale motion in the ocean

Most of the motion in the ocean can either be classified as current or wave.

Most people are familiar with waves (including the tides) but it is the ocean currents that are most relevant to climate. It is for this reason that most physical oceanographers study currents and how water moves around on timescales of years to millennia.

Historically, researchers have distinguished two types of currents based on their driving mechanism: the wind-driven horizontal circulation and the buoyancy-driven vertical circulation.

Until recently, these two circulations were thought to be reasonably well separate. Scientists would study the vertical circulation without bothering too much about the detail of the horizontal circulation and vice versa.

Wind driven horizontal circulation

Of the two types, wind-driven circulation is the best understood as sailors have charted it for centuries. Water circulates in gyres, circulation patterns that span the entire width of an ocean basin. Bands of alternating easterly and westerly winds set the latitudinal scale of these gyres.

The Gyre Circulation

This gyre circulation is very well understood from a geophysical fluid dynamics perspective. The theoretical framework of the wind driven gyres was developed in the mid-twentieth century and is considered one of the biggest triumphs of the field, most notably because it perfectly explains the existence of western boundary currents.

Western boundary currents are among the strongest ocean currents in the world (the Gulf Stream is one, and so are the Kuroshio and the Agulhas). They are always found on the western boundary of a wind-driven gyre.

It will go too far here to completely explain why they must exist in a wind-driven gyre, but basically their existence is related to the conservation of potential vorticity, the equivalent of angular momentum for a fluid. The input of potential vorticity by the wind in the basin has to be dissipated somewhere in order to satisfy mass balance closure in the basin, and this can (due to the rotation of the earth) only be done in a strong boundary current on the western side of the basin.

Buoyancy-driven vertical circulation

The other type of circulation, the buoyancy-driven overturning circulation, is much less understood. Perhaps therefore, it is much more notorious.

In the simplest, and most popular, picture of the overturning circulation, water around Greenland gains buoyancy (“gets heavier”) because it is cooled by the strong, cold winds overhead. Since the ocean should always be stably stratified (i.e. dense water should be below less dense water), the very heavy cold water will sink.

Once this cooler water descends 2km, it slowly spreads southwards and eventually exits the Atlantic Ocean into the Indian and Pacific Oceans. In these oceans, the water mixes back up into the water column, until it is near the surface again. Once at the surface, the water returns back to the North Atlantic, where the loop is closed.

From this rather general description it is apparent why the buoyancy-driven circulation is popularly called the conveyor-belt circulation.

Conveyer belt circulation model

However, it should be clear this is not what physical oceanographers truly think is happening.

There are a number of major problems with the conveyor concept outlined above. It does not explain the unknown source of energy that magically drives the water up in the Pacific and Indian Oceans.

Neither does it account for the fact that when water sinks in the North Atlantic it will be directly replaced by underlying water. With this in mind, the water should overturn locally within the water column. There is no apparent need for it to flow southward across the Atlantic.

Yet there is strong evidence that an overturning circulation exists. Physical oceanographers go out to sea (one of the best perks of the job) to measure properties of the water around the world’s oceans. By linking temperature, salinity and oxygen at different places, a clear picture emerges of water moving away from the North Atlantic and slowly mixing in with the surrounding waters.

Furthermore, there are a number of rapid climate changes in the past (hundreds of thousands of years ago) that can best be explained by a conveyor-type circulation. The time scale of these climate events – around a thousand years – does not appear anywhere else in the climate system.

Thus, until very recently, many physical oceanographers found it very convenient to separate ocean circulation into a horizontal wind-driven part and a vertical buoyancy-driven part. The first of these was well understood and a celebration of geophysical fluid dynamics, while the second one was only understood in vague terms, a little mysterious, but potentially crucial to rapid climate change.

Eddies and the intertwining ocean circulation

However, there was one key aspect of the ocean that was not taken into account in these two types of circulation.

In the original description, both the horizontal and vertical circulation moved sluggishly and steadily over time. This idea of a highly viscous flow was corroborated by the earliest computer model outputs that, due to a lack of resources, couldn't run at a high enough resolution and so produced velocity fields that were rather smooth.

But oceanographers that went to sea have known for a long time that the ocean is neither sluggish nor steady in time. There is a lot of variability on the scales below 100km. Unfortunately, observations were so sparse that it was not clear how widespread and persistent this variability was.

And then, around 1992, the American and European space agencies started launching a series of altimeter satellites. These satellites used lasers to measure sea surface height to an accuracy of a few centimetres.

Sea surface height is tightly linked to circulation, because pressure is higher under areas where the sea surface is more elevated. This is similar to what happens in the atmosphere, where high and low pressure areas control how air blows from one location to the other. Therefore, measuring sea surface height directly yielded an estimate of water movement in the ocean.

When the first altimetry satellite results came in, the ocean circulation was not as expected. Yes, there were western boundary currents, and some hints of a gyre circulation. But most dominantly, the ocean was literary filled with eddies.

Satellite visualisations showing ocean eddies

These eddies were relatively small (in the order of 100 km) vortices, some rotating cyclonically and others anti-cyclonically.

More and more, physical oceanographers started to appreciate that these eddies are crucial in maintaining the large-scale circulation. Eddies mix water in and out of the wind-driven gyres, and can induce vertical transports due to residual circulations. There are ideas that eddies change the time scales of ocean circulation, although it is not known yet whether they extend or shorten it.

Perhaps most importantly, it has become clear that eddies can be a considerable source of downward momentum transfer, thereby directly linking the circulation in the upper and lower ocean.

As a result of these measurements, the contemporary view of the world ocean circulation is one of an inherently chaotic soup of eddies, where some circulation patterns emerge only in the time-mean.

The Navier-Stokes equation, the century-old foundation of our field now have to be re-interpreted to include the effects of eddies and time-varying behaviour on the time-mean circulation. Every time we go to sea or we increase the resolution of our models, we observe new phenomena. It makes the ocean a wonderful place to be for a scientist and a beautiful subject to study.

Dr Erik Van Sebille

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