EDDIES

Ocean currents are not continually getting faster and faster, and this is because an equilibrium has been reached whereby the rate at which energy is supplied is being balanced by the rate at which it is being dissipated.

Ultimately, the ocean's kinetic energy is converted to heat, through frictional interaction with the sea-bed (this is particularly true of tidal currents in shallow shelf seas) or internal friction at the molecular level, i.e.

molecular viscosity. There is a continual transfer of energy from the identifiable currents (i.e. the mean flow) to eventual dissipation as heat, via a succession of eddies of generally decreasing size. The frictional effect of these eddies is the eddy viscosity discussed in Section 3.1.1. Eventually, within small eddies a few centimetres across or less, kinetic energy is converted to heat energy by m o l e c u l a r viscosity.

This idea of a 'cascade' of energy flow, from large-scale features down to the molecular level, was neatly summarized by the dynamicist L.F.

Richardson ( 1881-1953), in the following piece of dogerell:

'Big whirls have little whirls which feed on their velocity.

Little whirls have lesser whirls and so on to viscosity.'

(A paraphrase of Augustus de Morgan, who had himself paraphrased Jonathan Swift.)

Richardson was in fact referring to atmospheric motions, but could as well have been referring to flow in the ocean.

Eddies form because flowing water has a natural tendency to be turbulent and chaotic. Theoretically, it would be possible for an idealized uniform current to flow smoothly, as long as the current speed was below a certain critical value. In reality, wherever there are spatial variations in flow velocity (i.e. horizontal or vertical current shear), any small disturbances or perturbations in the flow will tend to grow, developing into wave-like patterns and/or eddies. Such effects are described as n o n - l i n e a r because they are not predictable simply by adding together flow velocities.

Although the formation of eddies generally results in energy being removed from the mean flow (i.e. from the identifiable current system), eddies may also interact with the mean flow and inject energy into it. They may also interact with one another, sometimes forming jets or plumes, but more often producing a complex pattern of eddies flowing into and around one another, forming more and more intricate swirls (as illustrated by the images in Figure 3.31 and Figure 1.1 ).

Figure 3.31 Examples of eddies in the oceans.

(a) Eddies in the Mediterranean off the coast of Libya. They were photographed from the Space Shuttle and (like those in Figure 1.1) show up because of variations in surface roughness. The picture shows an area about 75 km across; the white line isa ship's wake or bilge dump.

(b) Eddies in the North Atlantic Current to the south of Iceland. The eddy pattern is made visible by an extensive bloom of cocco- lithophores, phytoplankton with highly reflecting platelets. The distance from top to bottom of the image is about 350 kin.

(c) The complex eddying currents around Tasmania, made visible by means of the Coastal Zone Color Scanner carried aboard the Nimbus-7 satellite. The colours are false and represent different concentrations of phytoplankton carried in different bodies of water, estimated on the basis of the amount of green chlorophyll pigment in surface water. Australia can be seen at the top of the image, which is about 1000 km across.

73 The pattern of large-scale current systems like the Gulf Stream or the Antarctic Circumpolar Current - i.e. the average current pattern (or mean flow) we attempt to represent geographically in maps like Figure 3.1 - is the oceanic equivalent of climate. Only relatively recently have oceanographers begun to get to grips with the study of the ocean's variability over short time-scales- i.e. with the ocean's 'weather'. In fact, the random fluctuations and eddies so characteristic of the ocean were formerly regarded merely as a nuisance, obscuring the mean flow.

Although eddies occur over a wide range of space- and time-scales, it became clear in the 1970s that variable flows with periods greater than the tidal and inertial periods are dominated by what are now called mesoseale eddies (the prefix "meso-" means 'intermediate'). Mesoscale eddies are the oceanic analogues of weather systems in the atmosphere, but the differing densities of air and water mean that while cyclones (depressions) and anticyclones have length-scales of about 1000 km and periods of about a week, mesoscale eddies generally have length-scales of 50-200 km and periods of one to a few months. Mesoscale eddies travel at a few kilometres per day (compared with about 1000 km per day for atmospheric weather systems), and have rotatory currents with speeds of the order of 0.1 m s -~.

In most mesoscale eddies, but not all, flow is in approximate geostrophic equilibrium.

Figure 3.32 The kinetic energy possessed by various oceanic (blue) and atmospheric (black) phenomena. (Atmospheric Rossby waves were discussed in Section 2.2.1 .) (Note that for convenience both vertical and horizontal scales are logarithmic.) (For use with Question 3.10, overleaf.)

The term 'mesoscale eddy' is often used to refer specifically to 'current-rings' that form from meanders in fast currents like the Gulf Stream, the Kuroshio and the Antarctic Circumpolar Current. Such intense currents flow along regions with marked lateral variation in density, i.e. fronts, which are often boundaries between different water masses. Like fronts in the atmosphere (Figure 2.8), oceanic frontal boundaries slope and are intrinsically unstable, with a tendency to develop wave-like patterns and eddies. As a result, frontal currents continually 'spawn' eddies which travel out into the quieter areas of the ocean. (We will come back to this topic in Chapter 4.)

It is clear that mesoscale eddies are an intrinsic part of the ocean circulation.

They are particularly numerous in certain regions of the ocean (i.e. close to frontal currents) but no part of the ocean has been shown to be without them.

Kinetic energy spectra that extend into periods greater than 30 days nearly always show a bulge in the mesoscale part of the curve. Indeed, it is believed that m o s t of the kinetic energy of the ocean - perhaps as much as 99% - is contained in the ocean's 'weather'. The extent to which the energy of mesoscale eddies feeds back into the general large-scale circulation is not clear. Insight into this and other related problems can only be obtained through computer models with the ability to predict basin-wide flow patterns on time-scales and space-scales that are small enough to 'resolve' mesoscale motions. Such computer models (described as 'eddy-resolving') only began to be feasible in the mid-1980s, when computers with sufficient power to run them were developed.

As might be expected, mesoscale eddies play an important role in the transport of heat and salt across frontal boundaries, from one water mass to another. For example, it has been estimated that eddies are responsible for transporting heat polewards across the Antarctic Circumpolar Current at a rate of about 0.4 x 1015 W (1 watt = 1 J S -l) (cf. Figure 1.5). Generally, they lead to the dispersal of water properties and marine organisms, and through their 'stirring" motions they contribute to the homogenization of water characteristics within water masses.

Mesoscale eddies are an exciting and relatively new discovery.

Understanding them, and how they interact with the mean flow, will immeasurably improve our understanding of the oceanic circulation as a whole. However, mesoscale eddies are only one part of a continuous spectrum of possible motions in the oceans, and by no means all eddies (or even all mesoscale eddies) form from meandering frontal currents. Eddies may be generated by the bottom topography (notably seamounts), and commonly form down-current of islands. They may also be formed as a result of the interaction of a current with the coast, or with other currents or eddies, or as a result of horizontal wind shear. Some of the wide variety of eddy types will appear in later chapters.

75

1 The global surface current pattern to some extent reflects the surface wind field, but ocean currents are constrained by continental boundaries and current systems are often characterized by gyral circulations.

2 Maps of wind and current flows of necessity represent average conditions only" at any one time the actual flow at a given point might be markedly different from that shown.

3 The frictional force caused by the action of wind on the sea-surface is known as the wind stress. Its magnitude is proportional to the square of the wind speed: it is also affected by the roughness of the sea-surface and conditions in the overlying atmosphere.

4 Wind stress acting on the sea-surface generates motion in the form of waves and currents. The surface current is typically 3% of the wind speed.

Motion is transmitted downwards through frictional coupling caused by turbulence. Because flow in the ocean is almost always turbulent, the coefficient of friction that is important for studies of current flow is the coefficient of eddy viscosity. Typical values are 10 -5 to 10 -l m 2 s -! for A:

and 10 to 10 5 m 2 s -i for Ah.

5 Moving water tends towards a state of equilibrium. Flows adjust to the forces acting on them so that eventually those forces balance one another.

Major forces that need to be considered with respect to moving water are wind stress at the sea-surface, internal friction (i.e. eddy viscosity), the Coriolis force and horizontal pressure gradient forces; in some situations, friction with the sea-bed and/or with coastal boundaries also needs to be taken into account.

Although deflection by the Coriolis force is greater for slower-moving parcels of water, the magnitude of the force increases with speed, being equal to n ~ . 6 Ekman showed theoretically that under idealized conditions the surface current resulting from wind stress will be 45 ~ cure sole of the wind, and that the direction of the wind-induced current will rotate cum sole with depth, forming the Ekman spiral current pattern. An important consequence of this is that the mean flow of the wind-driven (or Ekman) layer is 90 ~ to the right of the wind in the Northern Hemisphere and 90 ~ to the left of the wind in the Southern Hemisphere.

7 When the forces that have set water in motion cease to act, the water will continue to move until the energy supplied has been dissipated, mainly by internal friction. During this time, the motion of the water is still influenced by the Coriolis force, and the rotational flows that result are known as inertia currents. The period of rotation of an inertia current varies with the Coriolis parameter f - 2 ~ sin ~, and hence with latitude, ~.

8 The currents that result when the horizontal pressure gradient force is balanced by the Coriolis force are known as geostrophic currents. The horizontal pressure gradient force may result only from the slope of the sea- surface, and in these conditions isobaric and isopycnic surfaces are parallel and conditions are described as barotropic. When the water is not homogeneous, but instead there are lateral variations in temperature and salinity, part of the variation in pressure at a given depth level results from the density distribution in the overlying water. In these situations, isopycnic surfaces slope in the opposite direction to isobaric surfaces; thus, isobars and isopycnals are inclined to one another and conditions are described as baroclinic.

9 In geostrophic flow, the angle of slope (~)) of each isobaric surface may be related to u, the speed of the geostrophic current in the vicinity of that isobaric surface, by the gradient equation: tan e =fidg. In barotropic flow, the slope of isobaric surfaces remains constant with depth, as does the velocity of the geostrophic current. In baroclinic conditions, the slope of isobaric surfaces follows the sea-surface less and less with increasing depth, and the velocity of the geostrophic current becomes zero at the depth where the isobaric surface is horizontal. The types of geostrophic current that occur in the two situations are sometimes known as 'slope currents' and "relative currents', respectively. In the oceans, flow is often a combination of the two types of flow, with a relative current superimposed on a slope current.

10 In baroclinic conditions, the slopes of the isopycnals are very much greater than the slopes of the isobars. As a result, the gradient equation may be used to construct a relationship which gives the average velocity of the geostrophic current flowing between two hydrographic stations in terms of the density distributions at the two stations. This relationship is known as the geostrophic equation or (in its full form) as Helland-Hansen's equation. It is used to determine relati~'e current velocities (i.e. velocities relative to a selected depth or isobaric surface, at which it may be assumed that current flow is negligible) at right angles to the section. This method provides information about a~'erage conditions only, and is subject to certain

simplifying assumptions. Nevertheless, much of what is known about oceanic circulation has been discovered through geostrophic calculations.

11 Departures of isobaric surfaces from the horizontal (i.e. from an equipotential surface) may be measured in terms of units of work known as dynamic metres. Variations in the dynamic height of an isobaric surface (including the sea-surface) are known as dynamic topography On a map of dynamic topography, geostrophic flow is parallel to the contours of dynamic height in such a direction that the 'highs" are on the right in the Northern Hemisphere and on the left in the Southern Hemisphere. Dynamic topography represents departures of an isobaric surface from the (marine) geoid, which itself has a relief of the order of 100 times that of dynamic topography.

12 Surface wind stress gives rise to vertical motion of water, as well as horizontal flow. In particular, cyclonic wind systems lead to a lowered sea- surface, raised thermocline and divergence and upwelling, while anticyclonic wind systems give rise to a raised sea-surface, lowered thermocline and convergence and downwelling. Relatively small-scale linear divergences and convergences occur as a result of Langmuir circulation in the upper ocean.

13 Flow in the ocean occurs over a wide range of time-scales and space- scales. The general circulation, as represented by the average position and velocity of well-established currents such as the Gulf Stream, is known as the 'mean flow' or 'mean motion'.

14 Most of the energy of the ocean, both kinetic and potential, derives ultimately from solar energy. The potential energy stored in the ocean is about

100 times its kinetic energy, and results from isobars and isopycnals being displaced from their position of least energy (parallel to the geoid) as a result of wind stress or changes in the density distribution of the ocean. If the ocean were at rest and homogeneous, all isobaric and isopycnic surfaces would be parallel to the geoid. The ocean's kinetic energy is that associated with motion in ocean currents including tidal currents (plus surface waves). The kinetic energy associated with a current is proportional to the square of the current speed, and for any given area of ocean, the total kinetic energy associated with a range of periods/frequencies may be represented by a kinetic energy density spectrum.

77 15 The ocean is full of eddies. They originate from perturbations in the mean flow, and their formation has the overall effect of transferring energy from the mean flow. There is effectively a "cascade" of energy through (generally) smaller and smaller eddies, until it is eventually dissipated as heat (through molecular viscosity). Mesoscale eddies, which have length scales of 50-200 km and periods of one to a few months, represent the ocean's 'weather" and contain a significant proportion of the ocean's energy. Current flow around most mesoscale eddies is in approximate geostrophic equilibrium. They are known to form from meanders in intense fi'ontal regions like the Gulf Stream and the Antarctic Circumpolar Current, but may form in other ways too. Eddies of various sizes are generated by interaction of currents with the bottom topography, islands, coasts or other currents or eddies, or as a result of horizontal wind shear.

Now try the follo~t'ing qltestions to consolidate vottr understanding of this Chaptel:

Figure 3.33 Kinetic energy density spectrum for flow in the Drake Passage, between South America and Antarctica.

Figure 3.34 Variability in sea-surface height, as computed from satellite altimetry data. Colours represent different deviations from mean sea- level (for key, see bar along the bottom).

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During the 1600s, the eastern coast of North America was colonized by Europeans and the Gulf Stream was traversed countless times and at various locations. In the following century the experience gained in the great whaling expeditions added further to the knowledge of currents, winds and bottom topography. This accumulating knowledge was not, however, readily accessible in technical journals, but handed down by word of mouth. Charts indicating currents did exist - the first one to show the 'Gulf Stream' was published in 1665 - but they were of varying quality and showed features that owed more to the imagination than observation.

The first authoritative chart of the Gulf Stream was made by William Gerard De Brahm, an immensely productive scientist and surveyor who, in 1764, was appointed His Majesty's Surveyor-General of the new colony of Florida.

De Brahm's chart of the Gulf Stream (Figure 4. l(a)) and his reasoned speculation about its origin were published in The Atlantic Pilot in 1772.

At about the same time, a chart of the Gulf Stream was engraved and printed by the General Post Office, on the instructions of the Postmaster-General of the Colonies, Benjamin Franklin. This chart was produced for the benefit of the masters of the packet ships which carried mail between London and New England. A Nantucket sea captain, Timothy Folger, had drawn Franklin's attention to the Gulf Stream as one cause of delay of the packet ships, and had plotted the course of the Stream for him (Figure 4.1(b)).

The theories of oceanic circulation that had evolved during the seventeenth century were seldom as well constructed as the charts they sought to explain.

During the eighteenth century, understanding of fluid dynamics advanced greatly. Moreover, the intellectual climate of the times encouraged scientific advances based on observations, rather than fanciful theories based in the imagination. Franklin, who had observed the effect of wind on shallow bodies of water, believed that the Trade Winds caused water to pile up against the South American coast: the head of pressure so caused resulted in a strong current flowing "downhill" through the Caribbean islands, into the Gulf of Mexico, and out through the Straits of Florida.

Franklin was also one of those who hit upon the idea of using the thermometer as an aid to navigation. Seamen had long been aware of the sharp changes in sea-surface temperature that occur in the region of the Gulf Stream. More than a century-and-a half earlier, Lescarbot had written:

"I have found something remarkable upon which a natural philosopher should meditate. On the 18th June, 1606, in latitude 45 ~ at a distance of six times twenty leagues east of the Newfoundland Banks, we found ourselves in the midst of very warm water despite the fact that the air was cold. But on the 21st of June all of a sudden we were in so cold a fog that it seemed like January and the sea was extremely cold too.' Franklin made a series of surface temperature measurements across the Atlantic and also attempted to measure subsurface temperatures: he collected water for measurement from a depth of about 100 feet using a bottle, and later a cask, with valves at each e n d - a piece of equipment not unlike the modern Nansen bottle.

The next intensive study of the Gulf Stream was made by James Rennell, whose authoritative work was published posthumously in 1832. R e n n e l l - who is often referred to as 'the father of o c e a n o g r a p h y ' - studied large amounts of data held by the British Admiralty Office and carefully

81

Figure 4.1 (a) De Brahm's chart of Florida and the Gulf Stream. On this projection, lines of latitude (not shown) are parallel to the top and bottom of the map, and the curved lines are lines of longitude. In the small circles along the path of the Gulf Stream are indicated the bearings of the current read against magnetic north.

(b) The chart of the Gulf Stream and North Atlantic gyre (inset), made by Timothy Folger and Benjamin Franklin.

documented the variability found in the Gulf Stream. He distinguished between 'drift currents', produced by direct stress of the wind, and 'stream currents" produced by a horizontal pressure gradient in the direction of the flow (the term "drift current" is still used occasionally). Rennell agreed with Franklin that the Gulf Stream was a 'stream current'.

The current charts shown in Figure 4.1 were produced mainly from measurements of ships' drift. By the time of Franklin and De Brahm, accurate chronometers had become available and ships' positions could be fixed with respect to longitude as well as latitude. Position fixes were made every 24 hours; between fixes, a continuous record of position was kept by means of dead-reckoning, i.e. the ship's track was deduced from the distance travelled from a known (or estimated) position and the course steered using a compass. The accumulated discrepancy after 24 hours between the dead-reckoning position and the accurately fixed position gave an indication of the average 'drift' of the surface water through which the vessel had passed (Figure 4.2). However, sailing vessels were themselves strongly influenced by the wind, and there could be considerable difficulties in maintaining course and speed in heavy seas. These inherent inaccuracies, combined with any inaccuracies in position-fixing, meant that estimates of current speeds so obtained could be very unreliable.

Figure 4.2 Diagram to illustrate how the mean current may be determined from the ship's drift, i.e. the discrepancy between the ship's track as steered using a compass and dead-reckoning, and the course actually followed (determined by celestial navigation, or known coastal features or islands). In this example, the ship has been steered straight according to dead-reckoning, but in reality has been displaced to the south by a current between fixes 1 and 2, and again by a (stronger) current between fixes 3 and 4. In each case, the speed of the mean southerly current was the southward displacement divided by the time between fixes (24 hours). (The displacement caused by the wind ('leeway') was ignored.)

Although single estimates of current speed obtained from ship's drift were unreliable, accumulations of large numbers of measurements, as compiled by Rennell, could be used to construct reasonably accurate charts of current flow, averaged over time and area. Collection of such data from commercial shipping has continued to the present day and this information has been used to construct maps of mean current flow (e.g. Figure 5.12). Current speeds estimated by dead-reckoning are now considerably more accurate, thanks to position-fixing by radar and navigational satellites, and the use of automatic pilots.

Systematic collection of oceanographic data was given a great impetus by the American naval officer and hydrographer, Matthew Fontaine Maury. Maury arranged for the US Hydrographic Office to supply mariners with charts of winds and currents, accompanied by sailing directions; in return, the mariners agreed to observe and record weather and sea conditions and to provide Maury with copies of their ships' logs. In 1853, on Maury's initiative, a conference of delegates from maritime nations was convened in Brussels to devise a standard code of observational practice. It was agreed that observations of atmospheric