Fig. 10.1 This NASA satellite image shows the warm surface water moving eastward to the South American coast during the severe El Niño episode in 1997–98.
Thus far we have discussed ocean waves that are easily visible at the surface. But there is another kind of wave that, although predicted 70 years ago, remained undetected until recently. These “internal waves” propagate on the thermocline, the narrow boundary between the warm surface layer of the ocean and the cold deeper waters. They cause barely a ripple at the surface, a few centimeters at most. And yet they affect weather and climate conditions around the world.
Two main types of these so-called planetary waves—Kelvin waves and Rossby waves—were discovered by our old friend, Lord Kelvin in 1879, and explained mathematically by Carl-Gustaf Rossby, a Swedish meteorologist, in 1939. These ocean waves participate in a dramatic global climate phenomenon, the El Niño–La Niña cycle. We’ll begin our story with it.
One of the most productive fishing grounds in the world lies off the coasts of Peru and Ecuador. Fish are abundant there because of a favorable weather pattern. During normal years, the strong trade winds from the southeast blow the warm surface waters far out to sea. Cold water wells up from the deep to replace the warm water. The cold water brings plankton and algae up from the depths, ensuring an abundant supply of food for small fish. As a result the coastal waters are filled with dense clouds of sardines and anchovies.
For many years Peruvian fisherman have made a good living from the sea. They could depend on a steady, constantly renewing crop of fish. But every five years or so, generally around Christmas, the trade winds fade for a few months. The offshore waters turn warm, the food supply shrinks, the fish migrate north or south, and the Peruvian fishing industry crashes. The fishermen call these episodes “El Niño,” meaning “the Christ Child.” They last for about a year and cause misery and deprivation among the fishermen. But then the trade winds start blowing, the cold water wells up at the Peruvian coast again, and the fish return.
El Niño events often have disastrous consequences far away from the Peruvian coast. In the severe El Niño episode of 1997–98 (the strongest in 100 years), significant details were learned about both ocean and atmospheric conditions from temperature data collected by instrumented buoys and meteorological stations.
Throughout most of 1997 La Niña was in force. As is typical of that situation, early in that year a low-pressure zone sat over Indonesia while violent thunderstorms and heavy rain battered eastern Asia. A pool of warm water (30°C) extended to a depth of about 200m on the equator of the western Pacific. The warm sea caused moist air to rise by convection. The air traveled eastward and descended on the opposite side of the South Pacific, near Easter Island. The descending air produced a high-pressure zone, causing drought in Peru and Chile but also causing the trade winds to blow the warm waters away from the coast. A cool layer (22°C) of upwelling water only 50m deep lay off the eastern Pacific along the equatorial coast of South America, providing the Peruvian fishermen with excellent fishing.
But by November 1997 the southeast and northeast trade winds had weakened considerably and the temperature distribution had reversed. Now, an El Niño event was in full force, with warm waters replacing the cooler waters and extending to a depth of about 70m on the eastern equator of the Pacific (fig. 10.1).
In the western Pacific, Australia, Indonesia, and the Philippines suffered devastating drought, while in the United States, the change in weather was dramatic. The Northwest and the Midwest were warmer and drier than normal with much less snow. Large waves during the El Niño winter months eroded 41 of 47 beaches on Washington State’s coast. High storm waves stripped sand from the shore, leaving many beaches narrower and steeper.
In the Northeast, warmer than usual temperatures minimized the snowfall. It may be that Quebec’s terribly destructive ice storm that winter was exacerbated by El Niño’s warming effects, which turned the normally dry snow into wet mush that froze overnight on trees and power lines, pulling them down in a tangle of branches and wires. At the same time both California and the southeastern states experienced very heavy rain. Altogether, the damage to industry, crops, and property cost billions of dollars.
Fig. 10.1 This NASA satellite image shows the warm surface water moving eastward to the South American coast during the severe El Niño episode in 1997–98.
By March 1998, the trade winds had recovered and began to push the warm surface water back across the Pacific, bringing back La Niña.
Peruvian fishermen would like to think that La Niña periods are “normal” and El Niño events are the anomalies. But in fact both El Niños and La Niñas are part of an irregular cycle of atmospheric pressures called the Southern Oscillation. The Southern Oscillation is not strictly periodic. El Niños occur at intervals of 3–7 years, and an El Niño may be followed by two or more La Niñas. It is an infuriatingly difficult phenomenon to model. But what role do ocean waves play in it?
Oceanographers have made good progress in revealing the mechanisms involved in El Niño events. Theoretical studies over the past 30 years suggest a crucial role for two unusual types of ocean waves: Rossby waves and Kelvin waves. These waves were predicted to have wavelengths of hundreds or thousands of kilometers. Unlike gravity waves at the surface, these interior waves move very slowly. They take months or years to cross the full width of the Pacific. It is the long crossing time of these waves that seems to determine the interval between El Niños.
Thanks to the efforts of a number of theory groups we now have several numerical models of how Kelvin and Rossby waves participate in the El Niño cycle. Perhaps the most complete model is the “delayed oscillator” model of Stephen Zebiac and Mark Cane (Columbia University) and another model by David Battisti (University of Washington). Their models, constructed in the late 1980s, couple the atmosphere and the ocean in a complex sequence of events. The stages of their model are shown in figure 10.2.
The basic picture evolves as follows. Imagine that we are in a La Niña year. The strong southeast trade winds drive warm surface water to the western end of the equatorial Pacific, around Indonesia. This warm water accumulates in a deep pool, whose upper surface rises about half a meter above the mean sea surface. The warm water is separated from the cold deep water by a thin layer, called the thermocline, at a depth of a few hundred meters.
Moist air rises over the warm water in the west Pacific, leaving low pressure at the surface. The air flows eastward in a large convection cell, drying out as it travels, and descends near South America. This hot, dry air produces a high-pressure area near the surface which drives the strong trade wind toward Asia. So in a La Niña period, the trade winds drive the warm water westward, and the warm waters drive the atmospheric circulation eastward, which drives the trade winds, in a closed loop.
Now imagine that a change occurs in the atmospheric pressures at the east and west coasts of the tropical Pacific that causes the southeast trades to fade in strength. As the wind’s push on the sea decreases, the mound of warm water near Asia begins to slide eastward under the force of gravity. The movement of the warm water is controlled by a Kelvin wave, which is a kind of long-wavelength gravity wave (fig. 10.2, top) that propagates along the thermocline. As the wave travels eastward on the equator, it depresses the ther-mocline, allowing the warm water to slide eastward. The Kelvin wave travels at a speed of a mere 3m/s, so it takes about 70 days to arrive at the South American coast (the right-hand border of the figure). Its height above the mean surface of the sea is only a few centimeters, but the theory predicts an amplitude of about 50m at the thermocline.
Fig. 10.2 The stages of the El Niño–La Niña cycle in the delayed oscillator model. The left and right sides of the drawing represent the Asian and tropical South American coastlines of the Pacific Ocean. (Drawn after International Research Institute for Climate and Society, “Advanced ENSO Theory: The Delayed Oscillator,” http://iri.Columbia.edu/climate/ENZO/theory/evolution.html.)
As the warm pool moves eastward, warm surface water north and south of the equator is sucked toward the equator. This inflow leaves a shallower warm layer in two regions on either side of the equator (fig. 10.2, top). The inflow launches a pair of Rossby waves toward the west in the opposite direction to the Kelvin wave. Rossby waves transport vortices in the water and are sensitive to the Coriolis force, as we shall see. (If you need to recall how the Coriolis force arises, take a look at the two paragraphs at the end of this chapter.) As they travel westward, at about 1m/s (thus, three times slower than the Kelvin wave), the Rossby waves raise the thermocline and thin the warm layer in their paths. They also depress the surface of the sea by a few centimeters from the mean as they pass by.
So the original pool of warm water in the western Pacific is being urged toward the east by the combined action of the Kelvin wave (traveling eastward) and the Rossby waves (traveling westward). When the faster Kelvin wave reaches the eastern coast of the Pacific, the warm water it brings triggers the onset of an El Niño event (fig. 10.2, middle). Then the Kelvin wave divides. One part moves north along the coast; another part moves south. In addition, part of the Kelvin wave is reflected back as a slow Rossby wave, which propagates westward along the equator (fig. 10.2, bottom). This third Rossby wave acts to depress the thermocline and therefore deepen the surface layer of warm water. It also raises the surface of the ocean a few centimeters as it travels.
Now the atmosphere enters the picture. The warm surface water, newly arrived at the coast of South America, causes the overlying air to rise by convection. As a result the air pressure at the surface decreases, and that change further weakens the trade winds. So the development of the El Niño leads to changes that enhance the El Niño effect. This is a positive feedback mechanism that would tend to lock in the El Niño permanently. But there is more to come.
After 125 days (in the model) the Rossby wave in the west reaches the Asian coast and is reflected eastward as a Kelvin wave. But the reflection causes the new Kelvin wave to act differently: now it pulls up on the thermocline. Figure 10.2, bottom, shows this reflection at 175 days. When this Kelvin wave arrives at South America, at 275 days in the simulation, it thins the warm layer, allowing cold deep water to well up. The warm water is displaced by cold water. With cold water near the surface, the El Niño event ends. The original pattern of high atmospheric pressure in the Pacific’s far west and low pressure in the east is slowly restored, and a La Niña phase begins again. As David Battisti put it, the El Niño effect bears the seeds of its own destruction.
This delayed oscillator model correctly predicted the sequence of events, but the times required for waves to cross the Pacific were far too short. Such defects have been addressed in recent work by adding the role of ocean currents and atmospheric waves.
In the early 1990s, these models were controversial. Rossby waves were familiar phenomena in the polar atmosphere (as we will see a bit later in the chapter), where they play an important role in generating the jet stream and the cyclonic weather fronts. But neither Rossby nor Kelvin waves had ever been observed in the oceans. The reason was that most of their action takes place at the boundary between the warm surface water and the colder water at depths of around 100–200m. Moreover, their surface amplitudes were predicted to be only a few centimeters. No known technique was capable of searching for them at that time.
Then in August 1992, the French space agency, CNES (Centre national d’études spatiales), launched the Topex/Poseidon satellite from its base in equatorial French Guiana. (The name comes from “Topography Experiment” combined with the name of the god of the seas, Poseidon.) The satellite was a joint project of NASA and CNES, conceived at a seminar in 1981. NASA supplied the primary instruments, and CNES built the craft and launched it with its Ariane rocket. Walter Munk, the preeminent oceanographer whom we have already met in previous chapters, described this satellite as “the most successful ocean experiment of all time.”
This spacecraft was the fourth satellite designed specifically for research in oceanography, and it was the best equipped by far. Its primary mission was to measure the hills and valleys of the ocean surface (the ocean’s topography) as they vary over months and years. For this purpose the spacecraft was equipped with a novel dual-frequency radar altimeter. It was capable of measuring the height of sea level with an accuracy of 3cm from an altitude of 1,300km. Another instrument could measure the temperature of the ocean. The spacecraft could scan more than 90% of the ocean surfaces, repeating the same track on the sea every 10 days. Topex/Poseidon operated without a flaw and generated a mountain of data until a malfunction in 2005 ended its life.
From the measurements of sea level and temperature, scientists were able to follow changes in the major currents of the oceans, such as the Gulf Stream. The combined observations yielded estimates of the heat transported by the currents, a crucial quantity for climate research. In addition, the spacecraft was able to monitor the development of an El Niño cycle, so important for the global climate.
Early on, two keen researchers at Oregon State University, Dudley Chelton and Michael Schlax, realized that they could process the massive data set for signs of Rossby and Kelvin waves. After three years of continuous operation, the satellite had accumulated enough data for a comprehensive analysis. All the fast, random motions could be averaged out, and the predicted centimeter-height waves might be revealed. On April 12, 1996, Chelton and Schlax published their discovery of Rossby and Kelvin waves in Topex data. Their results created a sensation among oceanographers.
Topex detected the alternating positive and negative sea-level pattern and the western propagation that theory had predicted for Rossby waves. The wave periods ranged from 6 to 24 months, and wavelengths varied from 10,000km in the tropics to 500km at latitude 50 degrees.
In figure 10.3 we see the evolution of a Rossby wave in two global sea-level maps, dated April 13 and July 31, 1993. The height of the sea varies from point to point by less than 4cm. In both maps, the white curved line marks the trough of a wave that is traveling westward. From the latitude variation of its speed, it was identified as a Rossby wave. The speed and direction of another wave trough, traveling eastward on the equator (marked by an X on the map), suggested that it was a Kelvin wave.
Topex saw a weak El Niño event in 1994–95. This was sufficient to confirm the basic sequence of events as described by the delayed oscillator model. But there was a problem: the observed wave speeds were twice as fast as the standard linear theory predicted. Since 1997, theorists have introduced a host of factors to explain the discrepancy but there is no consensus as yet.
Fig. 10.3 Two maps of the sea level, made three and a half months apart by the Topex/Poseidon satellite. The curved line and light gray shading mark the trough of a westward-traveling Rossby wave. (Courtesy of D. B. chelton and M. G. Schlax, Science 272 [1996]: 234, fig. 4.)
Now that we have some idea of the importance of Rossby and Kelvin waves, let’s examine them more closely. We’ll begin by comparing their basic properties.
Both Kelvin and Rossby ocean waves propagate along the thermocline, just 50–200m below the surface. Strange to say, Rossby waves travel only from east to west and at the equator; Kelvin waves travel only from west to east. But as we saw earlier, each wave can transform into the other when they are reflected back at a coastal boundary.
Both are transverse waves, in which water blobs oscillate in a direction perpendicular to the direction of propagation. In both waves, gravity acts as the restoring force in the vertical direction, as might be expected, but interestingly, the Coriolis force acts as the restoring force in the horizontal direction. It is this unfamiliar force that dictates the waves’ east-west movements at the equator.
Kelvin waves oscillate primarily vertically and transmit energy like normal gravity waves. Rossby waves, on the other hand, oscillate primarily in the horizontal direction. They transport changes of rotation (or “vorticity”) in the form of eddies. Both types of waves oscillate vertically by a few tens of meters on the thermocline and by a few centimeters at the sea surface.
Both have long wavelengths, up to thousands of kilometers, and extremely slow phase speeds. Kelvin waves travel at about 3m/s and cross the Pacific in about 10 weeks. Rossby waves travel at a snail’s pace, about 1m/s, and take about 7 months to cross the Pacific.
In 1879, more than a century before internal waves were confirmed by data from the Topex satellite, Lord Kelvin described a wave that oscillated under the joint forces of gravity, water pressure, and the Coriolis force. Kelvin waves were later named after him. There are two varieties: coastal trapped waves and equatorial trapped waves. Each of these types is divided into surface waves and internal waves. Surface waves oscillate vertically through the full depth of the water, with decreasing amplitude at greater depths, much like ordinary gravity waves. Internal Kelvin waves oscillate differently above and below the thermocline.
A coastline prevents a Kelvin wave from oscillating horizontally. At the same time the Coriolis force presses the wave against the coast so that the wave can only propagate parallel to the coast. In this sense the waves are trapped. So the blobs in a surface Kelvin wave oscillate in vertical planes that are parallel to the coast, much like an ordinary gravity wave. The wave amplitude decreases very rapidly in the offshore direction, meaning that the wave is a thin ribbon stretched along the coast. The speed of the wave is the same as for a shallow-water gravity wave and varies as the square root of the water’s depth. For example, on a coastal shelf 30m deep, a surface Kelvin wave would travel at a brisk 17m/s, or 62km/h.
Internal Kelvin waves are similar to surface Kelvin waves except that their motions are different above and below the thermocline. At a coast, they are trapped by the Coriolis force in the same manner as a surface wave and can only travel parallel to the coast. However, their speed is determined by the difference of water density across the thermocline, a difference of about 0.3%. As a result, the speed of an internal Kelvin wave is much smaller (about 3m/s) than that of a Kelvin surface wave.
At a coast the Coriolis force ensures that a Kelvin wave can travel only in preferred directions. So, for example a wave must travel toward the equator along the western coast of an ocean and poleward along an eastern coast. Therefore, a Kelvin wave can travel counterclockwise around the north and south borders of an ocean in the Northern Hemisphere and clockwise in the Southern Hemisphere.
At the equator, the Coriolis force reverses direction abruptly, from a deflection to the right, to a deflection to the left. That means that both northern counterclockwise Kelvin waves and southern clockwise Kelvin waves are trapped in a narrow east-flowing band.
Rossby waves are named after Carl-Gustaf Rossby, a Swedish-American meteorologist who was one of the first to model the large-scale motions of the atmosphere, using fluid mechanics. He was a pupil of the great Vilhelm Bjerknes, the Norwegian scientist who developed the theory of weather fronts, around 1913.
In 1939 Rossby noticed that the high-speed jet streams that circle the North Pole meander southward in wide excursions. The meanders seemed to have a wavelike structure, with two to four maxima around the perimeter of the wind system. The meanders also propagated eastward along the jet, like a wave, at much slower speeds than the air within the jet stream. Rossby recognized that the meanders were wide enough and slow enough for the Coriolis force to act as the restoring force for a wave. So he analyzed the properties of the meander and gave them a physical and mathematical explanation. His work has become an essential part of modern-day forecasting of weather fronts.
Rossby was apparently unaware that his type of wave had been predicted in 1897 by Sydney Samuel Hough, a mathematician at Cambridge University. Hough had discovered the wave during his investigation of the tides on a rotating sphere. (We will come to the spiral pattern of tides again in chapter 11.)
Rossby also speculated in 1939 that his type of wave might be observed in the oceans. He would have been delighted to see the Topex/Poseidon experiments confirm that, indeed, these planetary waves are as important in the oceans as they are in the atmosphere.
Now let’s see how Rossby waves are generated and how they propagate. We’ll focus on the horizontal motions in the wave.
Imagine a column of water a few hundred kilometers in diameter somewhere in the North Pacific. It is slowly rotating in an arbitrary direction about its vertical axis. Let’s call this rotation its relative spin (i.e., relative to the static water around it). An observer floating in space would see that the column has an additional spin. It is rotating as a whole about the earth’s axis, as the earth turns from west to east. We’ll call that rotation its planetary spin.
The size of the column’s planetary spin depends on its latitude, or, more accurately, the angle between its vertical axis and the axis of the earth. If the column is near the North Pole, its vertical axis aligns exactly with the earth’s, and so it absorbs the full planetary spin of the earth, a counterclockwise 360 degrees per day. If the column is near the equator, its axis is perpendicular to the earth’s axis, and so it receives no planetary spin. That is, the planetary spin of a column increases with increasing latitude, in either the Northern or the Southern Hemisphere.
A most important principle, discovered by Lord Kelvin, is that the total spin (planetary plus relative) of a column of fluid is constant, independent of its movements in latitude. This concept is called the conservation of vorticity (or spin).
Now imagine that a sustained wind pushes our column of water north from its present latitude in the Northern Hemisphere (fig. 10.4A). As a result, the column enters a region of larger planetary spin (fig. 10.4B). Because its total spin has to remain constant according to Kelvin’s principle, and because its planetary spin has increased, its relative spin must decrease by an equal amount. This decrease of spin represents a braking action, which generates a clockwise rotating eddy in the top of the column (shown as arrows in fig. 10.4B). This shallow eddy pulls water northward on its west side and pulls water southward on its east side.
The water moving north loses relative spin in the same way as before; the water moving south gains an additional amount. The result is that the rotating eddy moves to the west (dashed circle in fig. 10.4C). Notice that the water in most of the column doesn’t move west; only the clockwise rotating eddy does. In effect, the change in relative spin (or vorticity) is being transmitted to the west by a traveling eddy. We can think of this eddy as part of a Rossby wave that carries information to the west.
At the same time, the Coriolis force pushes on the northernmost and southernmost segments of the clockwise eddy (fig. 10.4B). Because the Coriolis force is larger at the northern segment, the net force is toward the south (as shown), and therefore the column is driven south toward its original position (fig. 10.4C).
When the column passes south of its original position, another eddy of the Rossby wave is generated. Because the planetary spin decreases in this move south, the relative spin increases, and therefore the eddy rotates counterclockwise (fig. 10.4D). The net Coriolis force on the column is northward. In short, the Coriolis force acts as a restoring force, maintaining a north-south oscillation of the column after an initial push by a wind.
So we can visualize the Rossby wave as the wake of a kayak that is being paddled westward, with alternating eddies on either side where the paddle has stirred up the water.
Rossby waves can travel westward along any parallel of latitude, unlike Kelvin waves, which are trapped at the equator and along the coasts. It turns out that the speed of a Rossby wave depends on the latitude gradient of the Coriolis force, so the speed is smaller at higher latitudes. You can see this effect in the Rossby wave of figure 10.3. The trough of the wave bends backward at higher latitudes. At the same time these horizontal motions are in play, the water is oscillating vertically as well under the force of gravity, causing the thermocline to undulate up and down.
Fig. 10.4 The origin and propagation of a Rossby wave. The horizontal line represents the initial latitude of a column of water. A, the column is pushed farther north from original location; B, the column enters a region of greater planetary spin and is subjected to the Coriolis effect; C, the rotating eddy (dashed circle) moves to the west, while the column of water returns to original position; D, another eddy is created when the water column moves south.
Rossby waves have now been detected in all the oceans of the world. They are recognized as the prime mechanism for transmitting changes in the ocean’s circulation in response to changes in atmospheric pressures and winds. For instance, they transmit changes in the tropical oceans to higher latitudes and modulate the Pacific Ocean over periods of a decade or more. They also intensify western boundary currents, such as the Gulf Stream and the Kuroshio Current off Japan, with important consequences for the climate of Europe and North America. Recent research has shown that these slow-moving waves play an essential role in global climate change.
Rossby waves also may play an unexpected role in feeding the tiny phytoplankton of the tropical seas. These miniscule algae contain chlorophyll, which allows them to store solar energy in the form of sugar. Phytoplankton are the basic producers of food in the ocean; all other creatures depend directly or indirectly on them. The little plants require nutrients to grow and multiply, and in their vast numbers they can rapidly deplete water of nutrients. How are these nutrients replenished? One proposal is that the turbulence that accompanies currents churns the sea and brings up nutrients from the deeps. But this mechanism seems to be too weak to fit the facts.
Recent research suggests that Rossby waves may help in “plowing” the sea, turning over the water and bringing up nutrients (the “rototiller effect”). The evidence is a correlation between sea level (as measured by satellite altimetry) and the amount of green color in the water. Depressions of sea level are proxies for Rossby waves, and the green color is an indicator of chlorophyll. So the idea is that Rossby waves produce sufficient upwellings of cold, nutrient-rich water to feed the algae. However, new data upset this idea, as we shall see later.
In the past five years, more precise satellite observations of the sea level have revealed a huge, previously undetected population of eddies. Oceanographers are now challenged to interpret these observations.
We saw how Topex observations revealed, for the first time, the propagation of Rossby waves at all latitudes. Or to put it another way, that’s how Chelton and Schlax interpreted the observations of ocean topography. Indeed, their interpretation was wholly consistent with the contemporary Internal Waves and El Niño theory. Their work was hailed as a breakthrough—except for the seemingly small problem that the observed propagation speeds were twice as fast as predicted.
Fig. 10.5 A global map of nonlinear mesoscale eddies, obtained from observations of sea level over 16 years by two satellites. (Courtesy of D. B. chelton et al., Progress in Oceanography 91 [2011]: 167, fig 1.)
A number of theorists immediately pitched in to explain this puzzling factor of 2 in speeds. Several ingenious ideas were proposed, and there seemed to be no serious difficulty in finding an explanation. Then in 2011, Chelton and his colleagues combined 16 years of sea level observations from two satellites, Topex/Poseidon and ERS-1. The additional data improved the spatial resolution of the images by a factor of 2, and an entirely new picture emerged (fig. 10.5).
These images showed that all the oceans, poleward of 10 degrees latitude, are sprinkled with eddies that had not been resolved before. The eddies are either depressed or raised above mean sea level by about 10cm. They range in size between 100 and 200km and, with the exception of one major stream, they travel nearly due west. They turn either clockwise or counterclockwise in the same hemisphere, and they have lifetimes of less than 3 weeks to more than 12. Some 30,000 eddies have measured lifetimes averaging 32 weeks.
Eddies with the longest lives could be tracked to obtain their westward speeds. These vary with latitude, from 2cm/s at 50 degrees to 15cm/s at 10 degrees latitude. This variation of speed with latitude is consistent with predictions for long-wavelength Rossby waves.
Chelton and co-workers conclude that these eddies are nonlinear, in the sense that their speeds of rotation are larger than their propagation speeds and that they preserve their shape as they travel. Such eddies can trap and transport seawater, an important mechanism for carrying heat throughout the oceans. Also, some eddies are green, which suggests that they, not Rossby waves, encourage the growth of algae.
Few eddies were found at latitudes below 20 degrees, where objects with much larger sizes are streaming westward at Rossby wave speeds but are not necessarily being carried by Rossby waves. However, in the higher latitudes near Antarctica, Dudley Chelton and his colleagues at Oregon State University identified a broad stream of eddies flowing westward from Australia, bouncing off the southern tip of Africa, and streaming into the eastward circumpolar current around Antarctica (fig. 10.5). What could this eastward streaming imply?
As you can see in the illustration, eddies seem to concentrate in dense clusters at the western boundaries of ocean basins, where major currents are found, such as the Gulf Stream; the Kuroshio, off Japan; the Agulhas, off Africa; and the Brazil, off South America. The researchers suggested that these eddies “are likely generated by the instability of background currents.” These new results will provide theorists much to think about. The relationship between Rossby waves and the eddies seems to be fundamental in the dynamics of the oceans and cries out for a comprehensive explanation. We look forward to a clearer picture.
It is a curious fact that the current at a western boundary of an ocean basin (for example, the Kuroshio Current) is thinner and faster and carries more water than the current at the eastern boundary (such as the California Current). Rossby waves are partly responsible for this asymmetry. Let’s see how this happens.
As we have seen, Rossby waves are generated by transients in the prevailing winds. These long-wavelength waves propagate westward and carry energy (and vorticity) at their group speed. When they reach the western boundary of the ocean, they are reflected. At the equator they transform upon reflection into eastward-propagating Kelvin waves, as we saw in the delayed oscillator model of the El Niño. But over most of the mid-latitudes, long-wavelength Rossby waves are reflected as short-wavelength Rossby waves.
So far I haven’t mentioned these short wavelengths. But it should not be a surprise that Rossby waves can have a wide range of wavelengths, from hundreds to thousands of kilometers. And their group speeds and directions depend upon their wavelengths. Short wavelengths have smaller group speeds than long wavelengths and travel only eastward. That means that when a long Rossby wave is reflected at a western boundary, its reflection (a short-wavelength Rossby) carries off less energy than the incident wave brought. This phenomenon creates a steadily increasing surplus of wave energy at the boundary. To balance the energy input and outgo, the boundary current accelerates. It carries off the surplus energy in the form of kinetic energy of its waters. This process aids in the intensification of a western boundary current.
What is lacking in this simple explanation is the role of the eddies that are observed at the western boundary currents. Are these related to short-wavelength Rossby waves? Or are they related to the instability of the boundary current?
It would appear that Rossby waves are only partly responsible for the intensification of western boundary currents. Henry Stommel, a scientist at the Woods Hole Oceanographic Institute, provided an effective explanation of the phenomenon in 1948, without any reference to Rossby waves. He employed Kelvin’s principle of the conservation of total vorticity (just introduced earlier in this chapter) and Sverdrup’s result on the role of wind stress in accelerating a current (as we’ll see in chapter 12). He demonstrated how the circulation around a gyre is generated and how the streamlines of the flow bunch together at the western boundary. This was the intensification of the boundary current. Then in 1950, Walter Munk built on Stommel’s work and showed how all the gyres in the ocean fit into a global pattern of circulation. These three researchers laid the foundations of the science of dynamic oceanography.
Imagine that a gunner and his cannon are located on the equator. He fires the cannon, intending to reach a target that lies 5km to the north. The shell leaves the cannon at high speed aimed straight toward the North Pole. However, while the shell was held in the breech of the cannon, it also acquired the speed of the earth’s rotation toward the east, which is 1,600km/h at the equator. Now in flight, the shell retains its eastern component of velocity. As it speeds north, it passes areas at (slightly) higher latitudes whose eastern rotation speeds are less than 1,600km/h. So when the shell finally lands, it has traveled further east than its intended target. The chagrinned gunner might think the shell has been pushed east by some unknown force.
This unknown force is called the Coriolis effect or Coriolis force, and it is purely the result of the gunner’s ignorance that he stands on a rotating body like the earth. An observer floating calmly in space would see the shell going straight and would recognize that the Coriolis force is only apparent. The shell is actually following Newton’s laws of motion as expected. But to an observer on earth, a body moving in the Northern Hemisphere seems to be deflected to the right, regardless of the original direction, and to the left in the Southern Hemisphere. But even though the Coriolis force is based on perception, it does have real-world impacts on the movements of objects on rotating bodies. For instance, the Coriolis force is exactly why a bathtub drains and a hurricane swirls counterclockwise in the Northern Hemisphere and clockwise in the Southern. And it also has impacts on tidal motions.
