4.1 Introduction4The Gulf StreamSystem

N. P. Fofonoff

In the two decades since the first publication of Stom-mel's (1965) monograph on the Gulf Stream, ourknowledge of the Gulf Stream System has been ex-panded dramatically through the development and ap-plication of new, powerful measuring techniques. Mul-tiple ship surveys of the type organized by Fuglister(1963) provided the first systematic descriptions of thespatial structure between Cape Hatteras and the GrandBanks that included the surrounding slope waters tothe north and the Sargasso Sea waters to the south ofthe Gulf Stream. Several major theoretical and inter-pretative studies grew from the base of data and de-scriptions provided by this study. During the sameperiod, instrumented buoys, both moored and drifting,were beginning to reveal some of the complexities ofthe subsurface and deep fields of temperature and cur-rents. Among the new techniques implemented in the1960s was infrared-radiation imaging to map the ther-mal patterns of the ocean surface from satellites orbit-ing the earth (Legeckis, 1978). The two-dimensionalsurface thermal maps that have been obtained haveadded rich detail to our knowledge of the strongly vary-ing thermal structure associated with the Gulf Streamthroughout its path. Yet, despite these advances in ourability to measure, our understanding of the dynamicmechanisms by which the Gulf Stream forms, developsin intensity, decays, and finally merges into the large-scale circulation of the North Atlantic have notevolved as satisfactorily. Even the mechanism control-ling the position of the Gulf Stream after leaving thecontinental shelf at Cape Hatteras has not yet beenfirmly established. Is the Gulf Stream controlled bybottom topography, by the distribution of mean windstress, or by a mechanism yet to be determined? Thedynamics by which meanders of the Gulf Stream am-plify and develop into large rings and eddies and thesubsequent movement and evolution of these entitiesare not well understood. In spite of the impressiveprogress of the past decades, much remains to be doneto resolve and understand the particular mechanismsthat determine the character and behavior of the GulfStream along its entire path from the Gulf of Mexicointo the central North Atlantic.

In preparing material for this review, I concludedthat my initial plans for a comprehensive discussion ofthe literature since 1958 were unrealistic. As over 200references plus numerous technical reports and articleswere identified, it became obvious that only a fewaspects of the Gulf Stream System could be covered ina single short review. Given the necessity for choice,it is clear that the selection must reflect my prefer-ences, interests, and perhaps, biases. I hope my effortto trace particular lines of research in the literature

II2N. P. Fofonoff

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will prove of interest to readers and will serve as aguide to a part of the rapidly growing body of literaturethat represents our collective knowledge of the GulfStream System. That other, equally important, aspectsof research are omitted is unfortunate but inevitable.

4.2 The Gulf Stream System

The subdivisions of the Gulf Stream System proposedby Iselin (1936), reproduced in figure 4.1, although notentirely accepted in practice, serve as a convenientframework for grouping the research literature. Startingfrom the Gulf of Mexico, the Florida Current was la-beled by Iselin as the portion of the Gulf Stream Systemflowing through the Florida Straits northward pastCape Hatteras to the point where the flow leaves thecontinental slope. Objections had been raised by Niel-son (1925) and Wust (1924) to using the word "Gulf"in reference to the Florida Current, as they consideredthat the water flowed directly across from the YucatanChannel into the Florida Straits rather than from theGulf of Mexico. This distinction seems less justifiednow because the flow through the Yucatan Channelhas been observed to loop well into the Gulf of Mexicoon occasion (Leipper, 1970; Behringer, Molinari, andFesta, 1977), although the Florida Current does notoriginate there. After leaving the Florida Straits, theFlorida Current presses close to the continental slopeand in the upper layers forms a relatively continuoussystem. The flow is augmented on the seaward side byinflow of water of essentially the same characteristics

as the Florida Current. Iselin included both sourcesunder the same label. Oceanographers frequently referto the Florida Current between the Florida Straits andCape Hatteras as the Gulf Stream. However, becausemeasurements and theoretical studies have tended torelate this portion of the Gulf Stream System moreclosely to the current in the Straits rather than to thecurrents downstream from Cape Hatteras, Iselin's no-menclature is more convenient in the present review.

North of Cape Hatteras, the current begins to flowseaward off the slope into deeper water. Freed of theconstraints of the shelf, the Gulf Stream developsmeanders of increasing amplitude downstream. Bowingto popular usage, Iselin retained the name Gulf Streamfor the section between Cape Hatteras and the GrandBanks. The name North Atlantic Current had alreadybeen widely accepted for easterly flows at mid-latitudesbeyond the Grand Banks. Even though an extension ofthe Gulf Stream, the North Atlantic Current, accordingto Iselin, becomes separated into branches and eddiesto form a distinctly different regime of flow. Its easternlimit is not clearly defined, though Iselin assumed thatthe branches extended into the eastern North Atlantic.A composite view of the western portion of the GulfStream System (figure 4.2) has been assembled byMaul, deWitt, Yanaway, and Baig (1978) from infraredsatellite images and surface tracking by ships and air-craft. The sharp thermal contrasts between the warmcurrents and the neighboring waters are detectablefrom space and reveal the variability of the Gulf StreamSystem throughout its length. The complexities intro-duced by the near-surface spatial and temporal varia-bility of the Gulf Stream System are only beginning tobe described. Comparatively little is known of the var-iable subsurface and deep structure, particularly down-stream of Cape Hatteras.

4.3 The Florida Current

Iselin (1936) defined that Florida Current as all thenorthward-moving waters with velocities exceeding10 cms - 1 starting along a line south of Tortugas andextending to the point past Cape Hatteras where thecurrent ceases to follow the continental shelf. Thethree chief characteristics of the Florida Current notedby Iselin are that it greatly increases in volume as itflows north, that it flows most swiftly along the con-tinental slope, and that over most of its length it isrelatively shallow, transporting water no colder than6.5°C until passing the northern limit of the BlakePlateau. The surface thermal structure of the FloridaCurrent between Miami and Cape Hatteras can be seenin the infrared image reproduced in figure 4.3.

II3The Gulf Stream System

Figure 1

Figure 4.I A schematic diagram showing the Gulf StreamSystem as described by Iselin (1936). Each streamline repre-sents a transport interval of about 12 x 106 m3 s- .

850 800

Figure 4.2 A composite of thermal fronts of the Gulf StreamSystem showing variability for a 9-month period betweenFebruary and November 1976. [Courtesy of G. Maul from

4.3.1 Sea-Level Slope from Tide GaugesMontgomery (1938b) assumed that the intensificationof the Florida Current as it flowed into the Straits ofFlorida is produced by a hydraulic, or pressure, headbetween the Straits and the Gulf of Mexico. Althoughthe differences in sea level corresponding to the pres-sure head could not be measured directly, tide-gaugemeasurements could show variations in the slope andhence, in the Florida Current itself. The recent devel-opment of precision altimetry from satellites capableof resolving the shape of the sea surface has renewedinterest in the possibility of monitoring major oceancurrents remotely. A brief review is given of the use ofsea-level records to infer variations of the Florida Cur-rent (see also chapter 11).

Iselin (1940a) in his report on the variations of trans-port of the Gulf Stream noted that sea-level measure-ment by tide gauges "provides a continuous and inex-pensive record of the variations in the cross-current

400

35°

300

25°

20°

750 700

Geostationary Operational Environmental Satellite (GOES)infrared observations.]

density gradient, if it is assumed that the average sur-face velocity varies with the total transport of the cur-rent." The relation between sea-level and ocean cur-rents had been used to infer variations of ocean cur-rents (and vice versa) much earlier by Sandstr6m (1903).Montgomery (1938b) first applied the method to theFlorida Current using data from tide-gauge stations atKey West and Miami, Florida, and at Charlestown,South Carolina, from the eastern coast of the UnitedStates and from St. Georges harbor in Bermuda on theseaward side of the Florida Current. Variations in rel-ative differences (absolute differences in heights of tidegauges were not determined) were examined as indi-cators of the strength of the mean surface current. Sealevel, although reflecting tidal variation primarily andto a lesser extent local atmospheric pressure and winds,contains significant contributions also from the cross-stream slope necessary to balance Coriolis forces actingat the surface and the downstream slopes associated

II4N. P. Fofonoff

�LI� 1--· �� � �_�_

Figure 4.3 The Florida Current between Miami and Cape Hat-teras as seen in the infrared on February 26, 1975, fromNOAA-4 satellite. A large eastward deflection occurs southof 32°N, possibly as a result of a topography feature. (Courtesyof R. Legeckis, NOAA-NESS.)

II5The Gulf Stream System

*-~~~~~~ I~~~~~~~~~~~~~~~~~~~~~·~

I -- , - I Ia6( rP, I

with accelerations or decelerations between stations.Montgomery (1938b) concluded from a 47-month studyof mean differences of Bermuda minus Charleston thata seasonal cycle was present with the maximum dif-ference and, hence, maximum surface current occur-ring in July and a minimum in October. The down-stream difference of Key West minus Miami, based on67 monthly values, showed a maximum hydraulic headin July with minima in November and February. Asthe gauges were not connected by geodetic leveling,the total hydraulic head was not known. Montgomerynoted that the difference of 19 cm measured by levelingacross the northern part of the Florida Peninsula wouldbe adequate to accelerate the current off Miami to193 cms - , corresponding to maximum speeds ob-served. When leveling data were obtained, however,the drop in mean sea level from Key West to Miamiwas found to be only 4.9 cm, too small to account forthe observed increase of speed between the two sta-tions. Stommel (1953a) estimated that a difference of20 cm is required to produce the observed accelerationto satisfy simple geostrophy and Bernoulli's equation.The lack of confirmation of the driving head by directleveling forced Montgomery (1941) to conclude thatthe downstream differences between Key West andMiami could not be regarded as an indicator of thestrength of the Florida Current. The cross-stream dif-ferences, however, clearly indicated a seasonal varia-tion.

Schmitz (1969) reexamined Stommel's estimate us-ing data from free-fall instruments obtained in the Flor-ida Straits off Miami. He noted that the measured rel-ative vorticity was considerably smaller than the valueused by Stommel (0.lf rather than 0.4f, where f is theCoriolis parameter). Furthermore, the change of theCoriolis parameter between the Key West-Havana andthe Miami-Bimini sections is approximately 0.1f, off-setting the change in layer thickness necessary to con-serve potential vorticity. Based on vorticity estimates,it apparently is not necessary to have a drop in headmuch larger than that found by land leveling. However,the observed maximum surface speeds in the Straitswould indicate a considerably larger drop of 20 cm ormore. It seems likely that the horizontal pressure gra-dient does not vanish with depth, so that the two-layerassumption of both Stommel (1953a) and Schmitz(1969) of a resting lower layer appears to be overlyrestrictive. Furthermore, the geodetic leveling maycontain errors, and the actual drop in sea level couldbe larger than reported.

The disagreement between land-leveling and sea-level differences expected from the distribution of cur-rents and density was examined by Sturges (1968).Using historical surface-current and wind observations,he calculated a surface topography for the western At-lantic near the Gulf Stream that represented a best fit

to the slopes estimated from the data. He concludedthat the northward rise in sea level found by precisegeodetic leveling along the east coast of the UnitedStates was inconsistent with his results. Sea levelwithin the Gulf Stream must drop northward to main-tain the northward flow. In a later paper, Sturges (1974)estimated the north-south slope from hydrographic-station data to be 0.8 cmdeg -1 (centimeters per degreeof latitude) upward to the north seaward of the FloridaCurrent. From the estimated downstream increase intransport and the increase in magnitude of the Coriolisparameter, the cross-stream difference in level wouldrequire the inshore edge of the Gulf Stream to slopedown 2.8 cm deg-' relative to the seaward edge or a netdownward slope of 2.0 cm deg-' in the direction oppo-site to the land-survey results. Sturges concluded thatthe precise leveling surveys must contain systematicerrors of undetermined nature that gave rise to theslight bias in meridional geodetic leveling.

4.3.2 Variability of the Florida CurrentSpeculation about the variability of the Florida Currentwas inspired not only by evidence from tide gauges butalso from measurements of electrical potential usinga telegraph cable from Key West to Havana, Cuba(Wertheim, 1954). The electrical potential induced byflow of sea water through the earth's magnetic field,shunted partially by the conducting sea floor, providesa signal that is correlated with the transport. The var-iations of nontidal flow appear to be exaggerated in theelectrical potential (Schmitz and Richardson, 1968) be-cause of shifts of the Florida Current relative to thebottom topography. The cause of these shifts was notdetermined. Maul et al. (1978) have speculated thatmeanders of the Loop Current in the Gulf of Mexicomay affect the Florida Current. Sanford and Schmitz(1971) concluded that induced electrical potential wasmore closely correlated with the transport at theMiami section. The estimated error was found to beabout 10% of the mean compared to a factor of twochanges for the Key West section.

Supporting evidence for the seasonal variation of theFlorida Current found by Montgomery (1938b) in thetide-gauge data came from other sources. Fuglister(1951) used monthly mean current speed and directioncharts from an atlas published by the U.S. Navy Hy-drographic Office (1946) to estimate seasonal variabil-ity in 10 regions following the Gulf Stream Systemfrom Trade Wind Latitudes to beyond the Grand Banks.He found that the maximum currents occurred in sum-mer (July) in southern portions and in winter in north-ern portions, while the minimum tended to occur infall (September to November) in all regions. The sea-sonal variability first seen on tide gauges was also con-firmed by direct measurements. Niiler and Richardson

iI6N. P. Fofonoff

(1973), using a 7-year study of volume-transport meas-urements at a cross-stream section at Miami, foundthat the annual variation accounted for 45% of thetotal variability, with transports ranging from an earlywinter low of 25.4 x 106 m 3 s-1 to a summer high of33.6 x 106 m3 s- l. The average transport was29.5 m3 s- 1. They also reported a strong short-period (2weeks or less) modulation of the velocity and densitystructure that was as strong as the seasonal change.These rapid fluctuations have been studied intensivelysince (Brooks, 1975; Wunsch and Wimbush, 1977;Schott and Duing, 1976).

Wunsch, Hansen, and Zetler (1969) extended theanalysis of sea-level record and sea-level differencesover the remainder of the frequency range contained inthe tide-gauge data. They examined simultaneous rec-ords from Key West and Havana (1953-1956), Key Westand Miami (1957-1962), and Miami and Cat Cay(1938-1939). The power levels below tidal frequencieswere low at all sites. About half the power was inseasonal variations with no detectable peaks betweenseasonal and tidal frequencies. Coherences betweenstations were small and, where detectable, showed zerophase across the Florida Current, consistent possiblywith a Bernoulli effect or large-scale atmospheric forc-ing. Lack of downstream coherence was attributed toDoppler shifting because of different mean speeds be-tween stations. An inverted-barometer response to at-mospheric-pressure forcing could be detected at lowerfrequencies (periods 10-128 days), and a direct responseat higher frequencies.

4.3.3 Eddy-Mean Flow InteractionA downstream pressure gradient is called for in inertialmodels of westward intensification. In the simplestmodel of this type, the frictionless, homogeneous cir-culation on a -plane described by Fofonoff (1954), thepressure and free surface drop along the western bound-ary as the flow intensifies. The lowest pressure is foundat the boundary where the highest speeds are attained.Along each streamline, pressure is related to speed bythe Bernoulli equation. In the model, the highestspeeds and lowest pressures (and hence sea levels) arefound at the boundary. In the real ocean, the sea surfacewithin the Florida Current has to be matched to acoastal boundary region, implying that the pressuregradient is continued into the coastal region. This, inturn, implies an active dynamic regime inshore of theFlorida Current. Several studies have described thefluctuations within and adjacent to the Florida Currentin some detail.

Von Arx, Bumpus, and Richardson (1955) observeda succession of short, overlapping segments that theydescribed as "shingles" extending from the FloridaStraits past Cape Hatteras. These shingles wer:e firstnoted during an attempt to follow the Florida Current

with an airborne infrared radiometer. The inshore edgewas found not to be continuous in its thermal structurebut made up of a series of fronts. They speculated thatthe cause might be tidal modulation of the FloridaCurrent emerging from the Florida Straits, but admit-ted that no sound basis had been found for a relationbetween tides and the short-term fluctuations ob-served. These structures in the thermal field could beinterpreted as instabilities of the Florida Current andevidence for exchange of energy between the meanflow and a time-dependent field.

Webster (1961a, 1961b, 1965) analyzed these andother surface-velocity measurements made during re-peated crossings of the Florida Current at sections offMiami and Jacksonville, Florida, and off Onslow Bayand Cape Hatteras, North Carolina, to estimate Rey-nolds stresses associated with the nontidal velocityfluctuations present in the flow. One of the objectivesof the study was to evaluate the magnitude of eddy-mean flow interactions within the Florida Current. Thesurface currents were estimated using a towed GEK(Von Arx, 1950), which responds to the current com-ponent perpendicular to the ship's track. In some cases,currents were inferred from the ship's set during cross-ings. The repeated crossings enabled Webster to com-pute means and fluctuations of the cross stream flu, u'),the long-stream (, v') components of surface flow, andthe momentum-flux component pui!7 in several zonesacross the Florida Current. The Reynolds-stress com-ponent T,, corresponding to this eddy momentum fluxis -pu'v'. At nearly all sections, the velocity correla-tions were positively correlated (pu'v' > 0), implyingthat momentum was being transported offshore andthat the Florida Current was exerting a negative (south-ward) stress on the coastal region. As the northwardflow increases offshore, the momentum has to betransported into regions of increasing mean flowagainst the mean-velocity gradient. Thus, the slower-moving coastal waters appear to exert an acceleratingstress on the swiftly moving Florida Current offshore,a result that is opposite to the intuitive expectationthat the Florida Current might tend to be retarded bythe coastal boundary and lose momentum to it. Web-ster calculated also the rate of work W done by theReynolds stresses on the mean flow from the term

W = x = ax e ax .

Integration from a straight coast x = 0 to the axis ofthe current x = L (Webster integrated across the entirecurrent) yields the total work per unit time within thecoastal strip inshore of the current axis:

w dx = VTanUIx=L -_ a dx.

II7The Gulf Stream System

-

Assuming v to be zero at the coast, the total workdone in the coastal strip is equal to the work done onthe seaward boundary (vi,}) plus the eddy work on themean flow within the strip. For a steady state to exist,the two terms must balance; otherwise, the mean flowin the strip would have to gain or lose energy at a rateequal to the difference between the two terms, assum-ing that other terms, such as work against pressuregradients, neglected above, remain small. Webster ex-amined the eddy-mean flow term at each section andconcluded that the net energy transfer was from eddyto mean flow for all sections. As a consequence of theeddy-mean flow interaction, the inshore strip is doingwork on the Florida Current and therefore must con-tain an energy source to supply the offshore flux ofmomentum and energy. Schmitz and Niiler (1969)reexamined Webster's estimates and analyzed addi-tional measurements made by free-fall instrumentsthat confirmed the earlier conclusions about signifi-cant eddy-to-mean energy flux within the coastal re-gion of cyclonic shear. They found, in addition, a regionof negative velocity correlation in shallow depths closeto shore, indicating a region of retarding stress and flowof momentum to the shore. This feature was not ob-served by Webster in Onslow Bay presumably becausehis sections did not approach close enough to the coast.Lee (1975) and Lee and Mayer (1977) describe recentmeasurements in this dissipative near-shore strip inthe Florida Straits. Schmitz and Niiler (1969) foundthat the total energy flux integrated across the entirewidth of the current was not significantly differentfrom zero within each section. They concluded thatalthough a region of intense energy transfer from eddyto mean flow existed, it was offset by a wider region ofmean-flow-to-eddy transfer over the rest of the current,resulting in a redistribution of energy that required noexternal energy source.

Brooks and Niiler (1977) carried out a comprehensivestudy of historical and new transport-profile data for asection across the Florida Current in the vicinity ofMiami. Their estimates showed that statistically sig-nificant conversions of kinetic and potential energybetween fluctuations and mean flow occurred in eitherdirection in parts of the section, but the net conversionrates were too small to be dynamically important.Based on these rates, the decay time for the total per-turbation energy was about 50 days, much longer thanthe residence time for the Florida Current in the FloridaStraits. They concluded that pressure gradients mustbe present to balance the energy flow. The couplingbetween mean flow and fluctuations may, in fact, berather weak compared to the major energy conversionbetween mean potential energy and mean kinetic en-ergy, with the fluctuations playing a minor or negligi-ble role. Such a model is also suggested by the distri-bution of surface velocity and kinetic energies of the

mean and eddy flow tabulated for the Florida Currentby Hager (1977) from ship-drift reports collected by theU.S. Hydrographic Office for the period 1900-1972.While these data are not of the same quality as directmeasurements, they reveal clearly the spatial extent ofthe Florida Current and its region of intensification asit flows into the Florida Straits. The peak currents andkinetic energies appear to be underestimated by thedead reckoning used to compute ship drift because ofthe spatial averaging involved. Hager found that theeddy kinetic energy was comparable to the mean-flowkinetic energy in the Loop Current and in the GulfStream past Cape Hatteras. However, within the Flor-ida Straits, the eddy kinetic energy (1-2 x 103 cm2 s -2 )

was much smaller than the mean-flow kinetic energy(>104 cm2 s-2) and showed little similarity in its spatialdistribution. These results suggest that the fluctua-tions are not essential to the intensification of themean flow in the Florida Straits.

4.3.4 The Downstream Pressure GradientThe downstream pressure gradient is important to theenergetics of the Florida Current because it providesthe simplest mechanism for converting potential tokinetic energy within the Florida Current (Webster,1961a). The development of satellite radar altimetrywith precision and resolution capable of detecting dif-ferences in surface elevation of less than a meter (Von-bun, Marsh, and Lerch, 1978) has created the oppor-tunity to use sea-level slopes to infer behavior ofcurrent fluctuations in considerably greater detail thanpossible with surface observations only. The interpre-tation of surface slopes and internal pressure gradientsrelated to these slopes will become increasingly im-portant as altimetry measurements are accumulated(see figure 4.11).

The Florida Current increases in transport as it flowsnorthward along the continental slope to Cape Hatteras(Iselin, 1936; Richardson, Schmitz, and Niiler, 1969;Knauss, 1969). Its momentum, energy content, and fluxincrease, implying the presence of strong energysources within the Florida Current and perhaps thesurrounding regions. As the increasing momentum andenergy within the Florida Current is most likely pro-duced by a downstream pressure gradient acting toaccelerate the flow, the most probable source of energyfor the inshore region is a continuation of this down-stream gradient into the coastal region.

Godfrey (1973) has given a clear physical interpre-tation of the effects of a downstream (northward) pres-sure gradient based on an examination of a six-layernumerical model reported by Bryan and Cox (1968a,b).The longshore pressure gradient was well developed inthe upper layers and weakened with depth along thewestern wall. The drop was equivalent to about 1 m atthe 100-m level and had reversed sign at 1600 m. Be-

II8N. P. Fofonoff

I ___ I___ _�

cause a balancing geostrophic flow would have to beoutward from the coast, a complete geostrophic bal-ance is impossible. The gradient must be balancedpartly by an outflow, causing upwelling along theboundary, and partly by downstream acceleration. Theupwelling along the coastal boundary implies shore-ward motion at depth. Godfrey used the model to in-terpret eddy formation in the East Australian Current,but it had been developed originally by Bryan and Coxwith application to the Gulf Stream in mind.

Blanton (1971, 1975) presented evidence for a vigor-ous movement of shelf water into the Florida Currentand intrusion of Gulf Stream Water from the FloridaCurrent along the bottom onto the North CarolinaShelf off Onslow Bay in summer. A section taken onJuly 22, 1968, showed Gulf Stream Water covering theentire shelf, with shelf water forming an isolated lensin the upper layer at mid-shelf. A month earlier, GulfStream Water had shown only a slight intrusion at theshelf break (40-m depth). Many other factors may bepresent. The driving mechanism, whether dominatedby pressure gradients originating in the Florida Currentas described by Godfrey (1973) or by local winds, hasnot been clearly established. The occurrence of strongupwelling and exchange with the coastal region is ap-parent, however, and may be evidence of a current-induced pressure gradient on the shelf.

The mechanism by which the pressure gradient cansupply momentum to the eddies and not to the meanflow remains obscure. Because the meanders describedby Webster (1961b) move downstream in the directionopposite to the propagation of topographic Rossbywaves, the mechanism of wave-momentum transportsuggested, for example, by Thompson 11971, 1978) doesnot appear to be appropriate.

Pedlosky (1977) studied the radiation conditions fora linear two-layer ocean model to propagate wavesaway from a forcing region consisting of a sinusoidalmoving zonal boundary. Eastward-moving meanderscan radiate into the ocean interior only if their phasespeed is less than the local interior velocity. If the localinterior velocity is westward, the eastward-movingmeanders cannot radiate in either baroclinic or baro-

tropic Rossby-wave modes. For nondivergent flowsover a sloping north-south boundary, such as the con-tinental shelf, these results seem to imply that topo-graphic waves in the shallow coastal region cannot becoupled to northward-moving meanders. Other mech-anisms may be possible. Webster (1961a) noted that"each of the meanders resembles a sort of skewed wavemotion and consists of an intense offshore runningcurrent (time 1 to 4 days) followed by a broad diffuseflow onshore time 4-7 days then followed by anotherintense offshore current." The intense offshore jetsshown in figure 4.4 may be similar to inertial jetsformed along western boundaries. The sloping shelfprovides a strong topographic /3-effect in the coastalstrip. Currents that flow offshore down a pressure gra-dient and across depth contours on the shelf so as toconserve potential vorticity would intensify into nar-row jets with strong cyclonic relative vorticity thatmay be incorporated into the cyclonic inshore regionof the Florida Current. Such jets could carry momen-tum and energy offshore. If the instantaneous down-stream (northward) pressure gradient were concen-trated across a narrow jet, the transfer of momentuminto the Florida Current would be readily accom-plished. The existence of intensifying jets detachedfrom solid boundaries has not been established, how-ever, so that this line of reasoning must be consideredspeculative. Most theoretical studies applicable to theFlorida Current assume that the basic flow is nondi-vergent with zero downstream pressure gradient. It ispossible that the neglect of the pressure gradient ex-cludes relevant mechanisms of meander formation andmay exaggerate the role of eddy-mean flow interac-tions in numerical models.

4.3.5 Stability and Atmospheric ForcingMechanisms for the conversion of kinetic and potentialenergy associated with the mean flow to perturbationshave been examined in several studies of the stabilityof the Florida Current.

Orlanski (1969) developed a two-layer model for twocases of bottom topography in the lower layer resem-bling the continental slope under the Gulf Stream and

MAr UN£20 21 22 23 24 25 2 27 28 29 30 1 i 2 1 t 4 ,6 7 9 10 11 12 13 14 15 16 17 18

Figure 4.4 Space-time variation of temperature off OnslowBay, showing movement of temperature fronts with 4-7-daytime scale. Note that the offshore motion was discontinuous

or more rapid than the onshore motion of the front. (Webster,1961b.)

I19The Gulf Stream System

the continental rise in the open ocean further down-stream. The model has a constant Coriolis parameterwith no downstream variation of the basic current,pressure fields, or topography. Orlanski found that anecessary condition for instability to occur is that thegradient of potential vorticity of the basic flow be ofopposite sign in the two layers. As only cross-streamvariation occurs, the stability depends critically on theslope of the interface between the two layers relativeto the bottom slope. The change of thickness of thebottom layer across the current can determine the signof the potential-vorticity gradient and hence the sta-bility. The most unstable modes found by Orlanski aregiven in table 4.1. Orlanski and Cox (1973) reexaminedthe stability of the western boundary current in a three-dimensional numerical model. The model had betterresolution in the vertical (15 levels) but was periodicalong the coast, thus excluding a downstream pressuregradient. Nonlinear terms and a -effect were includedin the model. Instabilities developed as predicted bylinear theory but with a growth rate about double thatof the simpler two-layer model. The growth rate de-creased by an order of magnitude as finite amplitudewas attained.

Niiler and Mysak (1971) analyzed a barotropic, con-stant-f model in which the velocity distribution andbottom topography of the continental shelf were ap-proximated by segments of constant potential vorticityand depth. Unstable barotropic waves were possible inthe model because the potential vorticity was chosento contain maxima in its distribution across the cur-rent. The arguments for these extrema are that thecyclonic shear in the inshore region raises the relativevorticity sufficiently to overcome the opposing effectof increasing depth of the shelf and slope. Thus if theslope is small enough, a maximum occurs in potentialvorticity. A region of anticyclonic shear on the seawardside of the Florida Current over a slowly varying depthyields a minimum in the cross-stream distribution.

These extrema in the potential-vorticity distributionsimply the existence of unstable barotropic modes. Withno basic current, the solutions are shelf and topo-graphic waves already discussed by Robinson (1964)and Rhines (1969a) (see chapters 10 and 11). With abasic northward current, the southward-travelingwaves can be reversed and made unstable. The mostunstable barotropic mode on the Blake Plateau has aperiod of about 10 days and a wavelength of 140 kmand can reach finite amplitude in a few wavelengthsdownstream. Because these barotropic waves requirebottom topography to induce regions of instability,their growth is not sustained in deep water. Here theunstable waves were found to have a period of 21 daysand a wavelength of 195 km. The authors suggest thatthe unstable shelf modes can be triggered by narrowfast-moving frontal systems. These short-period wavesincrease in amplitude as they move northward to deepwater, where they are no longer unstable because ofthe change in potential-vorticity structure of the basicdeep flow but may persist as a smaller-scale structureon the longer and slower meanders that develop down-stream.

Brooks (1978) has also pointed out the importance ofwind stress and its curl as a forcing mechanism forshelf waves. He concludes that strong coupling canoccur for periods that are less than or greater than thezero group-velocity period of barotropic shelf waves forthe continental shelf off Cape Fear (i.e., 2.5-3.5 and> 10 days, respectively). The model was used to inter-pret correlations between atmospheric-pressure varia-tions and winds and sea-level variations from tidegauges at Beaufort and Wilmington, North Carolina.Recently, Brooks and Bane (1978) reported that deflec-tions of the Florida Current are induced by a smalltopographic feature in the continental slope offCharlestown, South Carolina. Satellite observations ofthermal patterns (figure 4.3, for example) show consid-erable difference in amplitude upstream and down-

Table 4.1 Characteristics of Perturbations Found for the Florida Current and Gulf Stream

Wavelength Period Growth rate Phase speedAuthor (km) (days) (days-') (cm/s) Type

Orlanski (1969)

Shelf waves 220 10 1/5 BaroclinicDeep ocean 365 37.4 1/7.23 Baroclinic

Orlanski and Cox (1973) 246 1/12.1

Niiler and Mysak (1971)Shelf 140 10 1/13 14 BarotropicOcean 195 21 1/13 9 Barotropic

Brooks (1975) 190 12 0 South

South From currentSchott and Diing (1976) 170 10-13 0 (17 cm s-1) measurements

I20N. P. Fofonoff

stream of the "Charlestown Bump" located near 32°N.Stumpf and Rao (1975) suggested possible topographicinfluences in studying a sequence of infrared images ofmeanders off Cape Roman and Cape Fear. They pointout that a well-coordinated field experiment would benecessary to distinguish wind forcing from topographicinfluences or instability of the Florida Current.

Schott and Diing (1976) found southward-travelingwaves in the Florida Straits based on velocity meas-urements from three moored buoys located close to thesame isobath at 335 m near the "approximate locationof the axis of Gulf Stream" according to nautical charts.Records were obtained for a duration of 65 days froma depth of about 300 m. The most likely wave param-eters were fitted by least-square methods to 36 inde-pendent auto- and cross-spectra. A significant fit wasfound in the 10-13-day spectral band for a wavelengthof 170 km traveling south at 17 cm s-l. These are iden-tified as stable continental-shelf waves probably gen-erated by passage of atmospheric cold fronts. The pa-rameters obtained agree well with a model by Brooks(1975) that included realistic topography and horizontalcurrent shear to yield a southward-propagating wave of12-day period and 190-km wavelength at maximumresponse to forcing by cold fronts. The characteristicsof these wave models are summarized in table 4.1.

The observed coherence with meteorological eventsnoted by Wunsch and Wimbush (1977) and Diling,Mooers, and Lee (1977) may be a consequence of theweak coupling between mean flow and the fluctua-tions. The perturbations apparently can receive a sig-nificant fraction of their energy from atmospheric forc-ing rather than from the mean flow and consequentlyshow measurable correlation with wind events.

Several mechanisms for generation of meanders inthe Florida Current have been identified: barotropicand baroclinic instability in the presence of topogra-phy; bottom features forcing deflections and down-stream lee waves; and excitation of propagating wavesby atmospheric forcing. Nonlinear mechanisms are yetto be explored, as are the effects of the downstreaminhomogeneity of the Florida Current.

Richardson et al. (1969) found that the transport ofthe Florida Current increased relatively slowly (17%)through the Florida Straits from Miami to Jacksonvillewith a slight increase in surface speeds and a shift towestward of the current axis. A larger increase in trans-port (67%) was found from Jacksonville to Cape Fearwith a slight decrease of maximum surface velocityand a broadening of the current. The effects on theinstability modes of the downstream increase in trans-port are not known. Other intermittent perturbationsto the Florida Current are the passage of rings andeddies seaward of the Florida Current. These appar-ently can be swept into the current (Richardson, Strongand Knauss, 1973). The consequences of such events

are not known. The deep western boundary currentpredicted by Stommel (1957b) and the first observed bySwallow and Worthington (1957, 1961) has been foundin recent studies to contain strongly time-dependentcomponents (Riser, Freeland, and Rossby, 1978). Theeffects on the Florida Current are not adequatelyknown at present but may be profound.

4.3.6 The Deep Western Boundary CurrentIf an upwelling velocity of broad horizontal scale isassumed in the deep interior flow of an ocean, Stommel(1957b) showed that the conservation of mass and po-tential vorticity cannot be satisfied by geostrophic flowalone. A deep western boundary current is necessary toallow both constraints on the deep flow to be met. Inthe North Atlantic, Stommel concluded that a south-ward flow should be present along the continentalslope. This prediction together with the developmentof the neutrally buoyant float for measuring current bySwallow (1955) led Swallow and Worthington (1957,1961) to measure the deep flow off Cape Romain, SouthCarolina, near the northern end of the Blake Plateau,where the flow was expected to lie seaward of thestrong surface current over the Blake Plateau. South-ward flows of 9-18 cm s- l measured over a period of amonth led them to conclude that the deep westernboundary current is a persistent feature of the circu-lation along the continental slope. The transport of theundercurrent was estimated to be 6.7 x 106 m3 s-.

Subsequent measurements by a number of investi-gators (Volkmann, 1962; Barrett, 1965; Worthingtonand Kawai, 1972; Richardson and Knauss, 1971; Amos,Gordon, and Schneider, 1971; Richardson, 1977) re-ported transports ranging from 2 to 50 x 106 m3 s-

with an average of 16 x 106 m3 s- . The flow is per-sistent, though apparently quite variable. Westwardand southward deep currents along the continental risenorth of the Gulf Stream have been reported by Web-ster (1969), Zimmerman (1971) and Luyten (1977). Re-cent measurements using SOFAR floats (Riser, Free-land, and Rossby, 1978) show flow south of the Blake-Bahama Outer Ridge along the Blake Escarpment. Thesouthward flow may be simply a consequence of a deepwestward flow onto the sharply rising topography.Steady slow geostrophic flows are constrained to followcontours of f/h, where h is depth, which are concen-trated along the slope. Near Cape Hatteras, where theGulf Stream crosses over the deep current (Richardson,1977), the combined effect of vortex stretching withinthe northward-moving current and the deep flow cross-ing the bottom slope would be felt. Holland (1973) hasexamined the enhancement of transport in the westernboundary current in a numerical model including bar-oclinicity and topography. The vortex stretching in thestratified upper layers must counteract changes of fonly to conserve potential vorticity, whereas the deep

12IThe Gulf Stream System

water can be subjected to a much larger stretching bycrossing depth contours. Thus a relatively weak deepflow crossing depth contours can have a vertical veloc-ity equal and opposite to a large meridional baroclinicflow. This type of flow was described briefly by Fofon-off (1962a) under a general class of thermohaline trans-ports.

Slow steady barotropic flow must be along contoursof f/h or must cross contours of f/h at a rate that bal-ances the combined divergence of baroclinic and Ek-man flow. For deep flow onto the continental slope,the intensification of the current on the slope can beestimated from the potential-vorticity equation alongeach streamline:

fo fo+ yho h - sx - s'

where f0, h are open-ocean values of Coriolis param-eter and depth, and s,, s, the (constant) bottom slopes.For a slope width Ax, the deep streamlines are displacedequatorward by an amount Ay, where

Ay = Ax = fos.ho}10. (,O + fh

and f3,, fl, are the horizontal gradients of f/ho. From thesketch in figure 4.5, it is seen that the narrowing orintensification over the slope is

h hfos2\ 2UUh Ax Uoh 1

U&fosr,. (for s = 0).ph0

For h = 2500 m, f0 = 10-4 S-l,

= 1/100 (continental rise),

U = 20U0.

fo°

AY

U --

.-- AY

W

U

= 2 x 10-13 cms - 1, s

Wo U 0

F·igur X . D///////"/// o

Figure 4.5 Displacement dYo"' a current flowing over a bot-tom slope of width Ax on a -plane. The velocity U, on theslope is magnified by the ratio of widths w/w,. Relative vor-ticity is assumed to be small.

For the continental slope (e.g., s = 1/15, h = 1500 m),

U = 200U,.

The intensification even over the gentle continentalrise is sufficient to magnify flows U0 that are below ameasurable level in the interior to observable velocitieson the rise and slope. Thus, it is very difficult to de-termine by direct measurement whether the flow overthe continental rise is being forced by an upslope ordownslope component.

The main thermocline deepens northward (Iselin,1936) on the seaward side of the Florida Current, in-tensifying the apparent B-effect below the thermocline.The deep flow must move southward to conserve po-tential vorticity. Within the Gulf Stream itself, thethermocline rises sharply downstream. The rise isequivalent to s, < 0 in the lower layer. Furthermore,the thermocline slopes sharply downward in the x-di-rection because of the shear across the thermocline. Ifthe thermocline slopes are denoted by T, T,, thelower-layer-displacement equation becomes

- fo(T - slhoThe displacement Ay is no longer necessarily south-ward along the western boundary. Northward deepflows are permitted by the vorticity equation if

/3hoT, - s < 0 or T - s > fo

These flows would likely be unstable because the po-tential-vorticity gradient would then be of oppositesign in the two layers.

According to simple potential-vorticity conserva-tion, westward deep flow on reaching the continentalrise should turn southward and continue to have asouthward component as long as the main thermoclineslopes downward to the north. The decreasing thick-ness of the deep-water layer has to be compensated bydecreasing the Coriolis parameter. In the region of theaccelerating western boundary current, the thermnno-cline slope is reversed and the constraint on the deepflow is altered. The current may then turn northwardif the thermocline slope is sufficiently large. The cir-culation diagram given by Worthington (1976) for thedeep water (potential temperature 0 < 40C) reproducedin figure 4.6 has southward flow along the continentalslope with northward flow further to the east oppositeto the deep flow expected based on the elementarypotential-vorticity arguments given here. The presentinterpretation of the deep circulation in western NorthAtlantic and its interaction with the deep boundarycurrent is not consistent with potential-vorticity con-servation and needs further development.

122N. P. Fofonoff

... 8.. 6, 4 , 0 0.... ........ ., ... .. ., . . -- -- -- - --2__11 1 _ ' I

I :=

4 1L1~~~m

N -

0

IM

100 ° 80 60'

Figure 4.6 Circulation diagram for the deep (0 < 4C) circu-lation in the North Atlantic. Worthington estimates a flow of62 x 106 m3 s - x in the recirculation gyre with 6 x 10 m3 s-l

4.4 The Gulf Stream

The portion of the Gulf Stream System from CapeHatteras to the Southeast Newfoundland Rise is theGulf Stream according to the nomenclature introducedby Iselin (1936). The Gulf Stream is separated from thecontinental shelf to the north by a band of westward-flowing Continental Slope Water (McLellan, 1957;Webster, 1969) and bounded to the south by the west-ward recirculation gyre described by Worthington(1976) and Schmitz (1978). Thus, the Gulf Stream is aneastward-flowing current flanked on either side bybroader regions of westward flow. As the Gulf Streamis assumed not to be locally driven, enough energy andmomentum must be carried by the flow into the regionto maintain the eastward motion and the eddy andcirculation fields in the surrounding areas. Fuglister(1963) noted that the Gulf Stream leaving Cape Hat-teras flows approximately along a great circle while thecontinental slope turns northward. There is no pro-nounced curvature of the Gulf Stream on entering deep

40' 20° 0° 20'

flowing southward inshore of the recirculation. (Worthington,1976.)

water, as might be expected from the increasing depth.The lack of a mean curvature at a point of rapid deep-ening of the ocean bottom is interpreted as an indica-tion that the Florida Current is injected into the upperlayer above and into the main thermocline and mayonly contact the bottom intermittently. Richardson(1977) found that the Gulf Stream did not extend tothe bottom off Cape Hatteras for direct current meas-urements from six moorings over periods ranging from5 to 55 days. Other measurements Barrett, 1965; Rich-ardson and Knauss, 1971) show northeast flow near thebottom under the axis of the Gulf Stream. After leavingCape Hatteras, the Gulf Stream gradually developsmeanders, clearly visible in the infrared image in figure4.7. The meanders become progressively larger down-stream (Hansen, 1970), but are especially marked aftercrossing the New England Seamounts (Fuglister, 1963;Warren, 1963). The most intense horizontal thermaland density structures are found between Cape Hat-teras and the Seamounts. Strong horizontal density gra-dients are found throughout the entire depth. These

I23The Gulf Stream System

60°

40-

20'

0

60°

40-

20°

0

............. - -·

.. , - ----...-------.---.-.. .. .. .. .. .. .. .. .. .II I...I I

_..-

100° 80 60, 40' 20' 0 20°

,.,,,.1, ,,,1I I I I I I I I I E-Ll- ._l t 1 1 1 1 1 11 I ll l l I l l L , .,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.,...I

Figure 4.7 The Gulf Stream south of Cape Cod, showing well-developed meanders with several eddies formed in the slopewater to the north (Courtesy of R. Legeckis, NOAA-NESS,from NOAA-4 satellite November 12, 1975.)

I24N. P. Fofonoff

__ �

gradients begin to weaken in the deep water after cross-ing the Seamount chain (Fuglister, 1963). The mean-ders become sufficiently large to form detached coldeddies (rings) to the south as shown in figure 4.8 (Fug-lister, 1972; Parker, 1971) and warm eddies to the north(Saunders, 1971) of the Gulf Stream at irregular inter-vals. The meander amplitudes probably do not con-tinue to grow eastward because of the confining effectsof the Grand Banks and Southeast Newfoundland Rise.These topographic features appear to lock the GulfStream into quasi-stationary spatial patterns similar tothose described by Worthington (1962) and Mann(1967) that are more constrained than the meandersfarther to the west.

4.4.1 Gulf Stream Separation MechanismsThe mechanism of separation of the Gulf Stream fromthe continental slope at Cape Hatteras remains ambig-uous. The early theories of mean ocean circulationdeveloped by Stommel (1948) and Munk (1950) re-quired an intensifying current along the westernboundary only to the latitude of maximum wind-stresscurl. Poleward of the maximum, the current weakenedand returned into the ocean interior as a broad slowflow specified by the meridional scale of the wind-stress curl field. It was soon recognized that the lackof even qualitative agreement with the Gulf Streamcould be attributed to the neglect of nonlinear terms

in the western boundary. Munk, Groves, and Carrier(1950) showed by a perturbation analysis that the non-linear terms acted to shift the point of maximum ve-locity downstream past the maximum in the stresscurl.

The inertial models that were developed subse-quently indicated that an intensifying current withwestward flow from the interior (Charney, 1955b; Mor-gan, 1956) could be extended well past the latitude ofmaximum curl of the wind stress by inertial recircu-lation. In two-layer inertial models, the northward ex-tent is limited by surfacing of the inshore isopycnaland ending of the potential to kinetic-energy conver-sion in the boundary current [Veronis (1973a) and chap-ter 5]. By increasing the size of the recirculation gyre,the boundary current can be extended to the latitudewith zero wind-stress curl that separates the majorocean gyres (Munk, 1950). Leetmaa and Bunker (1978)recomputed the curl of wind stress from recent dataand found that the zero stress-curl contour lies nearCape Hatteras on the average. Thus the separation maybe a consequence of the larger-scale mean wind fieldrather than the local dynamics at Cape Hatteras. More-over, Stommel, Niiler, and Anati (1978) point out thatall of the transport in excess of about 30-36 x106 m3 s- required by the wind-stress-curl distributioncan be attributed to recirculation without violatingconservation of mass and heat. The possibility that the

Figure 4.8 Diagram of Gulf Stream ring generation frommeander formation to separation. (Parker, 1971.)

Iz25The Gulf Stream System

mean Gulf Stream path may be determined by themean-wind pattern deserves further study. It is notobvious why the Gulf Stream should separate from thecontinental slope to allow formation of the slope-waterregion extending from Cape Hatteras to the GrandBanks, rather than flow along the slope to the Banksand beyond (for further discussion, see chapter 5).

4.4.2 Gulf Stream Trajectory ModelsDifferent mechanisms for determining the shape of theGulf Stream have been proposed in terms of path ortrajectory models. These will be examined briefly.

The systematic measurements in a series of 11 mer-idional hydrographic sections through the Slope Waterand Gulf Stream carried out in 1960 under Fuglister'sguidance (Fuglister, 1963) provided the basis for a num-ber of theoretical studies in the following years, in-cluding the development of the trajectory or path the-ories. The observations during the 3-month duration ofGULF STREAM '60 showed rather small changes ofthe large meander found in the Stream path. Fuglisterstated that no evidence was found in the data for shiftsin the meanders by more than the Gulf Stream width.Moreover, neutrally buoyant floats tracked at '2000 mdepth to provide reference velocities for the computa-tion of geostrophic currents yielded currents extendingto the ocean bottom flowing in the same direction asthe surface Gulf Stream. These characteristics of theGulf Stream prompted Warren (1963) to develop amodel based on bulk or integrated properties of theGulf Stream. By assuming that the Gulf Stream couldbe treated as a narrow current or jet and integratingbetween streamlines over a section across the current,the vorticity equation was converted to a form relatingpath curvature to vortex stretching by the changingdepth along the path of the current and by changes inthe Coriolis parameter resulting from a change of lat-itude. Given initial conditions of position and direc-tion, as well as the bulk properties of volume transport,momentum transport, and volume transport per unitdepth, the subsequent path is determined by the to-pography and change of latitude encountered enroute.The simple model applied to five observed paths ex-hibited remarkable agreement in shape in the region oflongitude between 65 and 73°W. The path computationcould not be continued eastward because of the obviousbreakdown of the model in describing meanders overthe New England Seamounts. Warren noted, as didFuglister (1963), that the New England Seamount Arcunderlies the region where large meanders develop.

The model possessed several attractive features. Theseparation from the continental shelf at Cape Hatterasoccurred as a natural consequence of the topographyand was not related to a wind-stress mechanism assuggested by earlier theories. Moreover, the meanderscould develop as a consequence of the initial angle of

injection relative to the topography and would not nec-essarily indicate an instability of the current. Subse-quent elaboration of the theory by Niiler and Robinson(1967) brought to light several shortcomings of the ap-proach. The narrow-jet trajectory theory assumed asteady state, whereas later observations revealed theGulf Stream to exhibit strong time dependence in itsmeanders. Neither the simple model studied by Warrennor the more elaborate models developed later couldbe fitted simultaneously to the mean-path and meanderdata (Robinson, 1971). Robinson concluded that "vor-tex-line stretching will undoubtedly play some role inthe vorticity balance" in a properly posed nonlineartime-dependent theory of meanders. Hansen (1970)obtained a series of measurements of Gulf Stream pathsto describe the occurrence and progressive develop-ment of meanders in an effort to discriminate betweenthe inertial-jet theories and dynamic-wave models withpossible unstable modes that can extract energy fromthe basic flow. The paths were mapped over a periodof a year by towing a temperature sensor along the15°C isotherm at 200 m depth supplemented as nec-essary by bathythermograph observations. Hansen con-cluded that although no model then available couldaccount for all of the major features of the Gulf Stream,the most likely models would have to include topo-graphic influences that are clearly seen in some, butnot all, observed paths as well as energy conversionprocesses such as baroclinic instability necessary toaccount for meander development at least, where to-pography is too weak to influence the path. Pathmodels alone were not adequate to account for themeanders.

Time-dependent extensions of the path model havebeen given by Luyten and Robinson (1974) and Robin-son, Luyten, and Flierl (1975). A consistent dynamicquasi-geostrophic model was developed in which thevelocity field is resolved into a jet velocity, a velocityof the jet axis, and a transient adjustment velocityassumed small relative to the geostrophic velocities.The model was applied to Gulf Stream data collectedduring 1969 near 70°W (Robinson, Luyten, and Fuglis-ter, 1974). Using parameters appropriate to the GulfStream for 70°W, Robinson et al. (1975) found that aninlet period of 31 days had a spatial wavelength of560 km and a downstream growth (e-folding) scale of200 km, in agreement with the observed large-scalemeanders of the Gulf Stream. In the local vorticitybalance, advection and transient terms dominated thetopographic and -effects. The model contains mech-anisms analogous to ring or eddy formation. Becausethe path displacements are not constrained to be small,the path equations can, at least in the case of the purelybaroclinic limit and no -effect, yield solutions inwhich the meanders grow spatially and close uponthemselves to form isolated eddies. For the thin jet

I26N. P. Fofonoff

models to be applicable, however, the transient flowsmust be small.

4.4.3 Deep Currents of the Gulf StreamThe vertical coherence of the thermal and density fieldwithin the Gulf Stream and the slow evolution ofmeanders noted by Fuglister (1963) made plausible theassumption that the Gulf Stream extended to, and in-teracted with, the ocean bottom. A vertically coherentGulf Stream, however, was not substantiated by sub-sequent direct current measurements. These showeda vigorous velocity field in the deep water (Schmitz,Robinson, and Fuglister, 1970) that was not a simpledownward extension of the near-surface flow.

Luyten (1977) designed a current-meter array con-sisting of 15 moorings deployed in two meridional linesabout 50 km apart at 70°W to measure the deep flowon the continental rise and beneath the Gulf Stream.Current meters were placed 1000 m above the oceanbottom on each mooring with a second instrument200 m above bottom on some moorings as shown infigure 4.9. Data for 240 days were obtained on 30 of the32 current meters. The measurements revealed a re-markable and unexpected feature of the deep flow inthat the downstream coherence scale was very small(less than 50 km) while the meridional or cross-streamscale was found to be several times as large (- 150 km).

The currents contained strong meridional bursts ofspeeds reaching 40 cms;-' and lasting for about amonth. The highest intensity of flow occurred nearestthe Gulf Stream, with four to six bursts in individualrecords. Hansen (1970) calculated (figure 4.10) an av-erage eastward phase speed of 8 cms -1 and a meanwavelength of 320 km for meanders of the 15°C iso-therm at 200 m depth. This corresponds to a period of46 days, agreeing approximately with the interval be-tween events (four to six events in 240 days) in Luy-ten's array shown in figure 4.9. Because the measure-ments were not simultaneous, a correlation betweenthe motion in the deep water and the upper levels hasnot been firmly established. The agreement of timescales is suggestive of a strong coupling between them.

The mean flow for depths shallower than 4000 m onthe continental rise is westward with speeds 2-5 cm s- land apparently dominated by the bottom slope. Deeperthan 4000 m, the mean flow vectors tend to have asmall eastward component with an erratic or perhapsrapid spatial variation of the meridional component,reflecting the burst structure of the variable flow. TheGulf Stream, if it exists near the bottom above 70°Was suggested by Fuglister (1963) and Robinson, et al.(1974), is nearly completely masked by the strong deepmeridional eddy field. The lack of coherence down-stream is puzzling. It may be a consequence of havingonly two points of measurement along the Gulf Stream

direction. The deep fluctuations may be locked in somemanner by local topography, resulting in an inhomo-geneous spatial pattern of coherence. Luyten found theinteraction between eddies and mean flow to be smallnorth of the Gulf Stream on the continental rise. Thehorizontal eddy-stress divergence vector was nearlyperpendicular to the mean flow. Under the Gulf Streamitself, the mean flow appeared to be gaining energyfrom the eddies (figure 4.11).

4.4.4 Dynamical Gulf Stream ModelsThe instability and subsequent evolution of a thinzonal jet in the upper layer of a two-layer model de-scribed by Rhines (1977) has several points of similaritywith the observations taken by Luyten (1977) andSchmitz (1978) of the velocity field near the GulfStream. Rhines investigated numerically the evolutionof an eastward jet imbedded in a broad westward flowin the upper layer of a two-layer ocean model. Theinitial field was perturbed by broadband noise. Thesequence of development is shown in figure 4.12. Inless than 20 days, organized meanders become visiblein the upper layer and elliptical eddies with predomi-nantly north-south motion in the lower layer resem-bling the meridional motions observed by Luyten(1977). In the early stages, the pattern moves down-stream with the motion in the deep layer leading theupper layer as required by baroclinic instability. Afterthe meander exceeds unit steepness (about 42 days),the nonlinear eddy-eddy interactions become evident,causing distortion and stretching of vorticity contoursby horizontal velocity shear. In the lower layer, eddiesof like sign begin to coalesce, producing a north-southdisplacement and creating an abyssal flow in the samedirection as the upper layer jet.

As the eddy field develops, the jet is no longer rec-ognizable in the velocity or streamfunction field, butis still visible in the topography of the interfacial sur-face. At later stages (t = 62 days), the eddies in theupper and lower layer begin to lock together and be-come more barotropic in structure. Rhines suggests, asillustrated in figure 4.12, that the time evolution of themodel resembles the downstream development of theGulf Stream with the injection of the jet into the upperlayers of the ocean corresponding to initial conditionsin the model. Downstream migration of the eddies inthe lower layer, however, was not observed by Luyten(1977). Instead, the phase propagation appeared to besouthward, probably dominated by the bottom slope.The downstream motion of the surface meander hasbeen documented by several authors, notably Hansen(1970), as seen in figure 4.10. Coupling of the surfacemeanders and eddies to the lower layer drives a meanflow below the main thermocline and the developmentof barotropic eddies. Schmitz (1977, 1978) has found aneastward deep flow and increased barotropic signature

I27The Gulf Stream System

; _

E

I0o

LAT. (N)

Figure 4.9A Distribution of current meters and temperature-pressure recorders on the Luyten (11977) Continental Rise ar-ray. The solid lines refer to 700W, dashed to 69°30'W. (Luyten,1977.)

NORTH

5232 ,

(983 m) '-'-,-(105 m)

5261 (2006) - --- r ' -

5291 J ~ . . . , ..(2483 m) ;' _ -..

(2818 m) _ _

-__- q - (19777I?m)

.. , ~ - .. -_( ~ _~ ~ ~, 5282I.: Nx` (2329m)I I i ,~~~/

5312'- 9 2925 m)

5331(3182 m)

Jt , '//&/1p '

5341(3337 m)

5373(4262 m)

APR' MAY' JUN' JULY' AUG ' SEPT' OCT' NOV'DEC74

·. Z-A ~l/Ai'tIf( 55322(3213 m)

'1¥ x, / ',5352

I/ O cm/s vs~in~.~7/( v\5&71'sP~b~srl (3453 m)

... \ /,~ _ &.!-t. 53617,V-j -71 ' 34Y6 m)(3466 m)

APR ' MAY JUNE' JULY' AUG SEPT' OCT 'NOV' DEC74

Figure 4.9B Time sequence of 1-day averaged current. Thenumbers identify mooring and instrument. Instrument depthsin meters are shown in parentheses. (Luyten, 1977.)

128N. P. Fofonoff

L JC-·I L_-~~ - 527:x

- ~ ~ ~ ~ ~I

- 4/.ILW~MYE ~~~ A .. _,,,l o .....

. ,.-- ·------ ��--- - -- --

` 7 -1 1 1 7 1 -' _ --- _ _

I .bAL - - - _

1h,

141, -, 11_�\ t /, .. � 'o,11,461A\

Figure 4.10 Inferred progression and evolution of meandersrelative to the mean Gulf Stream path. The diagonal lines

Figure 4.11 Vector acceleration of mean flow by eddy Rey-nolds stress gradients. The "eddy forces" tend to oppose themean flow on the continental rise and to accelerate it underthe Gulf Stream at the southern portion of the array. The

500 km. I

JUNE 15-20

JULY 15-23

AUG 16-23

SEPT 14-16SEPT 21-23

SEPT 30OCT 12-15OCT 16-20

NOV 15

3

PHASE PROGRESSION JUNE 966-NOVEMBER 1966

show phase propagation (solid where supported by other evi-dence). (Hansen, 1970.)

eddy forces are estimated by grouping the data in depth in-tervals and from neighboring values in the array at a commondepth for the spatial grouping. Luyten, 1977.)

I29The Gulf Stream System

DEPTH SORTED SPATIALLY GROUPED

N

E 2000 1 EDDY FORCE

5

.5

/3000 MEAN FLOW5

/5 ' Scm/s

/4000

-50 km

4000 Z 50km (

. *. .

QN-1 _\1\

I

I

h,6--j-

�1_-`I - I

1%, -,III

/

tl_�

t = 16 daysII~1 III I IIIIIfll llllllllllllllllll m

............. · :: ........... -: ..:;: ......

:ii:';: : :.. .... ... ...

ii Ac1 ii .2011 II11L n

ai =.20

0

3 Q

A*? =-.03

t =26

t =37 t =49"lllllllllllllllllllllllllllllllnneplnnr

A1\Y 2.26

,W . . ..

. ' 3At2, =.13

IiII'IIIgII I IIIIIInIIIIrimiinTrUi

A I =.33

AI 2 =.20

t =49

t =62;' ,,l ,/llllIlllIlll llI lll mr

I A; Y $.35

AP1I =.35

A' 2 =.23

t =62

Ar) =.16 A7 =.15

Figure 4.I2 Evolution in time of a two-layer spatially periodicmodel. The figure shows upper-layer streamfunction 1,,lower-layer streamfunction q,2, and interface height -q. Theinterface height retains the strong slope across the initial jetlong after the jet has been obscured by barotropic flows in thevelocity field. Contour intervals are indicated for relativecomparison. Dimensions are 1250 km on each side with aspeed of 50 cm s- 1 averaged across the jet. (Rhines, 1977.)

I30N. P. Fofonoff

\1"

ilTrmhT.nln.nTrln.,

....... ....

X/ - ;i~

I

A 7 =.19Figure 12

.. ,,,,.,.,,...,,,.,.,,,,.

~.JlllllIl l 1 il il l li IillI JIJi

i _,n,.. .. 1X1ll

I.........,,;,,,,,, ..... .......-.~

� �---

to the velocity field (figure 4.13) in a long-term moored-array experiment along 55°W designed to examine themesoscale eddy field in the vicinity of the Gulf Stream.[The array is part of a long-range program developedunder the cooperative experiments MODE carried outin 1973 and in POLYMODE (1974-1979). The readeris referred to chapter 11 for a discussion of mesoscale

eddies in the ocean.]Although it is evolving and not stationary in time,

Rhines's model is attractive and suggestive of processesthat may be acting in the actual Gulf Stream. However,the model lacks an explicit recirculation mechanismand has no bottom topography. Both may affect thebehavior significantly and may need to be incorporatedas essential elements in a more complete Gulf Streammodel. The simpler models must be explored andunderstood before the combined effects of several

N. LATITUDE42 40 38 36 34 32 30 28

1:5 Axis ^ 600m

10

-5 -

_ -10

E -I

10- Axis

= 5-

z p----.N -5O-W 10 Axis- . 1500m

E 5

0-J

-5z0N -0

z] 5 i I \

current at four depths along 55°W fro m the first POLYMODE5 -

42 40 38 36 34 32 30 28

- N. LATITUDE

Figure 4.I3 Meridional distribution of time-averaged zonalcurrent at four depths along 550W from the first POLYMODEarray shown by circles 0 and from the combined first andsecond setting of the array shown by squares 0. The approx-imate mean axis of the Gulf Stream is indicated. The west-ward mean flow shows little depth dependence. The meanflow is eastward under the Gulf Stream at 4000 m depth.(Schmitz, 1978.)

mechanisms can be interpreted in the more complexgeneral circulation models.

The mass flux of the Gulf Stream has been estimatedto be in the range of 100-150 x 106 m3 -1 south of CapeCod (Fuglister, 1963; Warren and Volkmann, 1968;Knauss, 1969). Stommel et al. (1978) concluded thatmost of the transport in the Gulf Stream is recirculatedin the western North Atlantic. The net transport north-east, assumed to be wind driven in the ocean interior,is only 38 x 106 m3 s-l. Thus the recirculating portionmay be as much as 60-110 x 106 m3 s-. The highrecirculation rate implies that a relatively small frac-tion of the energy is lost by the Gulf Stream in flowingbetween Cape Hatteras and the Grand Banks. Most ofthe kinetic energy is converted back to potential energyto form the recirculation to the south. Just as the con-version from potential to kinetic energy requires anaccelerating pressure gradient along the westernboundary, the conversion from kinetic to potential en-ergy requires an opposing or decelerating pressure gra-dient. The details of the conversion process must becomplicated because of the large-amplitude meander-ing and eddy formation that takes place between CapeHatteras and the Grand Banks. Because it can be as-sumed that the recirculation is relatively stationaryand does not change its size and intensity rapidly, itsenergy content is essentially constant. Energy is con-verted from potential to kinetic in flowing through theGulf Stream and is converted back to potential energyon entering the westward gyre. As the recirculationtransport is larger (perhaps twice) than the wind-driventransport, the kinetic-energy flux in the Gulf Streamprobably contains only a minor contribution, depend-ing on the velocity profile, attributable to direct forc-ing, and only this amount of energy needs to be dissi-pated to maintain a steady state. The magnitudesinvolved can be estimated very roughly from availabledata. The average wind-stress magnitude over the sub-tropical North Atlantic is about 0.5 dyn cm-' (Leetmaaand Bunker, 1978). Assuming that the curl of the windstress drives a transport of 40 x 106 m3 s-' into thewestern boundary current through a section of averagedepth 500 m deep and 2000 km in length, the averageinflow current would be 4 cm s-l. Assuming that4 cm s- ' is also typical of interior geostrophic velocitiesand that wind stress-eddy forcing is small, the workdone by wind stress would be 11 * Ivl - 2 ergcm- 2 s- '.Over the entire basin (area 1 x 10'7 cm2), the rate ofenergy input by the wind is 2 x 1017 ergss-; it isconverted entirely to potential energy. The interior fluxof kinetic energy by the mean flow is negligible. Nonet work is done by Ekman velocities in the frictionallayer because the work by surface stresses must bedissipated within the Ekman layer for a steady state toexist. Only the surface geostrophic currents need be

I3IThe Gulf Stream System

considered in estimating net wind work (Stern, 1975a).If T is wind stress and

1Vg = (k x VHp)

pf

the surface geostrophic current, the net rate of windwork on the ocean surface is

1v,* =- (k x VHP) 7

1= -- (k x 7). VHP

pf

1Ve ' VHP

P

where Ve = -1/f (k x T) is the Ekman mass transport,VHP the horizontal pressure gradient, and p density ofthe surface layer. The net work by wind stress can beinterpreted as the rate at which mass is transported upthe pressure gradient in the Ekman layer. Because pres-sure gradients are produced hydrostatically, the"uphill" Ekman flow represents an increase of poten-tial energy at a rate equal to the wind work. Thus,except for the portion dissipated in the Ekman layer,the wind work is converted entirely to potential energyin the ocean interior. If no interior dissipation is pres-ent, all of the input wind energy must be removedthrough the western boundary current and dissipatedwithin the recirculation region. Assuming a width ofthe boundary current of 80 km and a depth of 500 m,the energy and mass fluxes require a mean speed of100 cm s-' in the western boundary current. These arejoined near Cape Hatteras by recirculation fluxes ofmass and energy, resulting in a deepening and inten-sification of the flow, but leaving the scale width ofthe Gulf Stream unchanged. Suppose the recirculatingtransport is 80 x 106 m3 s-', making a total transportof 120 x 106 m3 s-'. The total kinetic energy flux wouldbe three times the interior value or 6 x 1017 ergs s- ifthe section deepened with no change of mean velocity.Only 2 x 1017 erg s - must be dissipated and 40 x106 m3 s-1 transport returned to the interior circulationto maintain a steady mean state. The kinetic-energyfluxes into the western boundary layer and out of thedissipation region are assumed to be negligible com-pared to conversion rates of potential energy to kineticenergy. The kinetic-energy flux is proportional to thecube of speed and is, therefore, very sensitive to thevelocity profile in the intensified Gulf Stream. For agiven mean flux, the kinetic-energy flux is least if theflow is spread throughout the entire water column. Amore detailed calculation is required to improve theestimate. An essential point of the argument is thatthe conversion of kinetic energy to and from potentialenergy is an exchange between mean fields. These con-

versions are not usually examined in numerical modelsbecause their basin average is zero.

An approximate estimate of the rate of energy dis-sipation in the Gulf Stream can be obtained from theinitial decay rate of Gulf Stream rings, as these areformed from segments of the Gulf Stream itself (Fug-lister, 1972). Cheney and Richardson (1976) found de-cay rates in Gulf Stream rings of 1.7 0.2 x102' ergs day-', or about 37 ergs cm -2 s-1 averaged overthe ring area, from the observed decrease of availablepotential energy of the ring. If the same dissipation rateis assumed in the Gulf Stream, it would require over7000 km of path or about 80 days to dissipate the ki-netic energy transported in the boundary region fromthe ocean interior. The distance from Cape Hatteras tothe Grand Banks is about 2300 km-too short to getrid of the kinetic energy by internal dissipation andradiation. Meandering will increase the Gulf Streampath significantly, perhaps by a factor of two or more.Some of the energy is removed into the rings and ed-dies.

The flux of mass and energy in the Gulf Stream issufficient to form a cyclonic ring of 100-km radius perweek or about 50 rings per year. Many fewer are be-lieved to form. Fuglister (1972) and Lai and Richardson(1977) estimated that as many as 10 to 16 rings of

either anticyclonic or cyclonic type may form annuallynorth and south of the Gulf Stream. If so, the formationof rings, although a spectacular manifestation of theGulf Stream decay mechanism, is not the major mech-anism for dissipating the kinetic energy. Some, possi-bly a considerable fraction, of the kinetic energy istransferred to the lower layers to replace the energyloss in the recirculation gyre through instability, radia-tion, and dissipation from the gyre, as indicated insome numerical models or by other dispersive proc-esses within the gyre. The bulk of the kinetic-energyflux, however, appears to be converted back into po-tential energy.

4.4.5 Numerical Gulf Stream ModelsThe complete energetics of the Gulf Stream are farfrom obvious. The development of numerical modelswith sufficient spatial resolution to permit significanteddy-mean flow and eddy-eddy interactions to takeplace has revealed energy conversion and dissipationmodes to help interpret Gulf Stream behavior.

The first series of ocean-scale general circulationmodels to exhibit baroclinic instability in the westernboundary current and recirculation gyre were describedby Holland and Lin (1975a,b). They found that if lateralfriction was taken sufficiently small or wind forcingsufficiently strong, a steady-state flow was not attainedin the numerical integration. The flow remained timedependent but statistically stationary, in that meansand variances approached constant values with time.

I32N. P. Fofonoff

-·111��---- ----�1----�-�--�- _ ,,� ___

Thus, the time-varying eddy flow appeared to be anessential part of the momentum-transfer mechanismin the model. Their model was chosen with a "single-gyre" wind-stress distribution so that the westernboundary current was constrained by both western andnorthern boundaries and did not exhibit strong insta-bilities. The next step was taken by Semtner and Mintz(1977), who developed a five-level primitive equationmodel with shelf topography and surface heat exchangeto simulate the Gulf Stream and mesoscale eddies inthe western North Atlantic. Their model containedtwo novel features not included in the Holland and Linmodel: a biharmonic friction to prevent a "violet ca-tastrophe" resulting from a transfer of mean squarevorticity (enstrophy) to high wavenumbers (enstrophycascade), and a bottom frictional Ekman layer to allowdissipation at the ocean bottom. These mechanismshad been introduced and explored earlier by Brethertonand Karweit (1975) and Owens and Bretherton (1978)in the study of open-ocean mesoscale eddy models. Theprimitive equation model showed that the dominantinstability occurred within the simulated Gulf Streamover the continental rise. Over the flat abyssal plain,energy was transferred from the eddies to the meanflow.

Reduction of the effective lateral friction using thebiharmonic dissipation allowed the eastward jet (GulfStream) to develop intense meanders, some of whichformed ringlike eddies that separated from the jet anddrifted westward in the recirculation gyres. Strong deepgyres developed in the vicinity of the meandering east-ward jet as a consequence of downward flux of mo-mentum associated with the meanders. The energeticsof the primitive equation model were studied in detailby Robinson et al. (1977) to evaluate the types and ratesof energy transfers in several regions of the basin. Theprimitive equation models are expensive to run andSemtner and Holland (1978) concluded after compari-son that most of the behavior of the western boundarycurrent and the free eastward jet used to simulate theGulf Stream is contained in the simpler quasi-geo-strophic two-layer model. Holland (1978) carried out aseries of experiments using this latter model to explorethe effects of horizontal diffusion and bottom frictionon energy flow to the eddy field. For low lateral diffu-sion, most of the energy input by wind stress wastransferred via upper-layer eddies to eddies in the lowerlayer, to be dissipated by bottom friction. For highlateral viscosity, the energy is dissipated by diffusionin the mean flow, with much smaller fractions beingtransferred to eddies in the upper and lower layers. Anocean basin with a "double-gyre" wind forcing pro-duced a free mid-ocean jet with behavior recognizablycloser to that of the Gulf Stream. Momentum and en-ergy were transferred to the lower layer through thecoupling of eddies across the interface, to be dissipated

by friction at the bottom. A strong recirculating gyreis developed in the lower layer as seen in the stream-function and interface topography and total transportsshown in figure 4.14. The results are sufficiently prom-ising to attempt a comparison (figure 4.15) with currentmeasurements along 55°W by Schmitz (1977). Goodagreement was obtained with the mean zonal currentsin deep water. However, the north-south variations ofmodel eddy kinetic energy u'2 + v' 2 and Reynolds-stress term u' v' were considerably broader than meas-ured by Schmitz. Holland attributed the broader dis-tribution of eddy variables to the absence of bottomtopography in the model. A similar comparison for theSemtner-Mintz model was given by Robinson et al.(1977). Further comparisons with measurements arenecessary to define the limits of applicability and tolocate the parameter ranges for best fit of the numericalmodels to the Gulf Stream. The initial results are en-couraging.

4.5 The North Atlantic Current

The Gulf Stream undergoes a radical change on reach-ing the Southeast Newfoundland Rise, a ridge runningtoward the Mid-Atlantic Ridge from the Tail of theGrand Banks. According to Iselin (1936), the GulfStream divides, with the major branch flowing northacross the Southeast Newfoundland Rise parallel andopposite to the cold Labrador Current running southalong the eastern face of the Grand Banks. Anotherpart of the Gulf Stream continues eastward to dividefurther into northward and southward branches beforecrossing the Mid-Atlantic Ridge. The southern branchrecirculates into the Sargasso Sea. The northern branchturns eastward after reaching a latitude of about 50°Nto become the North Atlantic Current. Details of theseparation into branches were not available to Iselin.Even today little is known of the time-varying featuresof this critical-breakdown region of the Gulf Stream.The sharp thermal contrast between the Labrador Cur-rent and the warm waters originating from the GulfStream is seen vividly in the infrared images repro-duced in figures 4.16 and 4.17. The ribbon of cold(white) Labrador Water marks the eastern wall of theGrand Banks. A narrow strip of cold water (figure 4.17)is entrained along the edge of the northward-turningcurrent, heightening the contrast.

Worthington (1962, 1976) proposed a fundamentallydifferent interpretation of the hydrographic data, inwhich the Southeast Newfoundland Rise acts to sepa-rate the circulation into two independent anticyclonicgyres (figure 4.6). A trough of low pressure near to, andparallel with, the Southeast Newfoundland Rise, as-sumed to be continuous, marks the boundaries be-tween the gyres. Worthington reached this conclusion

I33The Gulf Stream System

0 500 1000 0 500 1000 0 500 1000 0 500 1000X (km) X (km) X (km) X (km)

Figure 4.I4 The mean fields for Holland experiment 3: (A)upper-layer streamfunction (contour interval CI = 5000m 2s-L); (B) lower-layer streamfunction (CI = 1000 m 2s-); (C)interface height (CI = 20m); (D) total transport (CI = 50 x106 m3 s-L). (Holland, 1978.)

KM

0 400 800 1200 1600 2000

30" 34°

38' 42 ° 46*LATITUDE

12

za:

le -Z

W

8

KMKM

30* 34 38' 42"LATITUDE

g,

1.

30* 34: 38' 42*LATITUDE

Figure 4.I5 Comparison of meridional distributions of (A)zonally averaged mean flow U, (B) eddy kinetic energyu32 + v 2, and C) Reynolds stress u3v3 in the lower layer (sub-script 3) for experiment 3 compared with observed distribu-tion (Schmitz, 1977) along 55°W. (Holland, 1978.)

I34N. P. Fofonoff

10

0

0

0O

tO

Figure 4.I6 The Gulf Stream and North Atlantic Current asseen from an infrared image taken November 2, 1977. Thefigure shows the colder shelf and slope water responding to acomplex meandering of the Gulf Stream. The cold ribbon ofLabrador Water is seen flowing south along the eastern edgeof the Grand Banks. (Courtesy of R. Legeckis.)

I35The Gulf Stream System

I

Figure 4.I7 A detailed infrared image of the circulation in thevicinity of the Grand Banks showing the southward flowingcold Labrador Water. (Courtesy of P. La Violette, NORDA.)

I36N. P. Fofonoff

I I _ _I_�_ � __�_

· z···. �i�-::-":.

::��-r."�:4m�r

.I�:�·.;�·%:�·;�8�1r�

d

"Pli·: : : .c; 1·�d

from the observation that the northern gyre transportedwater about 1 mll -1 richer in dissolved oxygen thanthe water of the same temperature and salinity typecarried by the Gulf Stream. The source of water of thesame density with higher oxygen content is availableto the west but it is fresher and colder and would haveto be entrained in large amounts to produce the ob-served concentration of oxygen in the North AtlanticCurrent. Moreover, a large flow into the Northern La-brador Basin from the Gulf Stream would require acompensating return flow of equal magnitude passingeast and south of the Gulf Stream. Worthington arguedthat the close proximity of the saline MediterraneanWater anomaly is evidence against such a strong returnflow from the Northern gyre. Mann (1967), using morerecent data obtained on cruises of C.S.S. Baffin duringApril-May 1963 and June-July 1964, disagreed withWorthington's interpretation and proposed a splittingof the current analogous to Iselin's (1936) scheme.Analysis of the hydrographic stations indicated that abranch transporting about 20 x 106 m3 s- joined byabout 15 x 106 m3 s- ' originating in the slope waterformed the branch of the North Atlantic Current tothe north. A southward-flowing branch of about 30 x106 m3 s- x carried the remainder of the Gulf Streamback into the Sargasso. A weak anticyclonic eddy cen-tered over the Labrador Basin appeared to be a persist-ent feature of the circulation. Mann suggested thatmixing between waters in the eddy and the currents tothe west could supply the additional dissolved oxygenobserved in the northern basin. A similar interpretationhas been constructed using data from subsequentcruises to the area in 1972 (Clarke, Hill, Reiniger, andWarren, 1980). These authors estimate that the oxygengradient of 2 mll -1 per 100 km across the northwardcurrent is sufficient to enrich the waters north of theSoutheast Newfoundland Rise by horizontal diffusionalong isopycnals given an eddy diffusion coefficient of107 cm2 s- acting along the 700-km length of thenorthward current. They point out also that the sepa-rate gyres postulated by Worthington would requiresignificant departures from geostrophic flow. The dy-namic topography relative to 2000 db shown in figure4.18 is consistent with the branching hypothesis de-scribed by Mann (1967).

Although the weight of evidence available todayseems to favor the general interpretation given byMann, the definitive answer is not yet in. Evidencefrom the hydrographic cruises and infrared surfacethermal structure indicate strong time dependence inthe region. The flow across the Southeast Newfound-land Rise may be intermittent, so that the dynamictopography may show a varying degree of couplingacross the Southeast Newfoundland Rise. The inter-pretation of mean flow across the Southeast New-foundland Rise can be modified considerably by time

dependence. It seems less likely that the interpretationof water-type characteristics will be altered signifi-cantly as these are inherently conservative and lessaffected by time variations than the spatial distribu-tions.

4.6 Summary and Conclusions

The growing literature describing the Gulf Stream Sys-tem and its dynamics is impressive in its diversity anddetail. The author recognizes that the treatment ofmany of the topics included in this review is superficialand may not reflect accurately all of the accomplish-ments and directions of current research. The numberof papers and their detail and complexity necessitatedrather brutal simplification to reduce the length of thereview and the time needed for its preparation. Manytopics could not be discussed at all. The general cir-culation of the North Atlantic leading into the GulfStream System is bypassed. The reader is referred toStommel's (1965J monograph on the Gulf Stream, inwhich much of the classical oceanographic material issummarized, and to Worthington (1976) for his detailedexamination of the water masses and their sources andsinks in the North Atlantic (see also chapter 2). TheLoop Current in the Gulf of Mexico has been excludedfrom the Gulf Stream System. Yet the dynamics of theLoop Current may have significant downstream effects.The exclusion seems arbitrary.

The deep western boundary current remains a mys-tery. How does it coexist with the Gulf Stream and therecirculation gyre? The topic of warm- and cold-corerings has been omitted. Both theory and observationsof rings are being pursued vigorously at present and asubstantial body of literature has accumulated (Lai andRichardson, 1977; Flierl, 1977, 1979a). Their formationby the Gulf Stream is of obvious importance for re-moving mass, momentum, and energy from the GulfStream and for exchanging Continental Slope Waterand Sargasso Water across the Gulf Stream, eventhough their overall contribution to the kinetic-energyflow from the Gulf Stream may prove to be relativelysmall compared with the energy loss by other proc-esses.

The transport of heat, salt, and other quantities bythe Gulf Stream is omitted. The literature on transportof heat by the Gulf Stream is surprisingly meagre. Heatexchange for the North Atlantic has been estimated byBunker and Worthington (1976). Newton (1961) con-cluded that rings represented the principal mechanismfor transporting heat between the Sargasso and theContinental Slope Water. Vonder Haar and Oort (1973)estimate that 47% of poleward transport of heat in thenorthern hemisphere at latitudes 30-35°N is carried byocean currents such as the Gulf Stream. It is expected

I37The Gulf Stream System

146'

44'

Figure 4.I8 Dynamic topography from the North AtlanticCurrent showing the separation of the Gulf Stream into anorthern branch flowing around a weak, anticyclonic eddy inthe Labrador Basin. (Clarke et al., 1980.)

138N. P. Fofonoff

%6£6

44° 42°

_ _

that interest in heat transport by the Gulf Stream willgrow because of the need to develop more comprehen-sive and realistic models of world climate.

The Continental Slope Water to the north of the GulfStream is not adequately explained. Is the separationof the Gulf Stream from the continental slope at CapeHatteras a consequence of a local dynamic process re-lated to local topography, as suggested by many of theinertial models (Greenspan, 1963; Pedlosky, 1965a;Veronis, 1973a)? Is the separation a consequence of thelarge-scale wind-stress pattern? Leetmaa and Bunker(1978) show that the mean curl of the wind stressreverses sign near Cape Hatteras and is zero over a paththat is surprisingly like the mean Gulf Stream acrossthe Western North Atlantic. Is the path simply deter-mined by the mean wind field? It is conceivable thatthe presence of the Gulf Stream with its strong lateralthermal contrast may significantly affect the wind-stress gradients in its vicinity. The position of the lineof zero curl of the wind stress may be a consequence,as well as a cause, of the observed Gulf Stream location.Another possibility is an upstream influence of theGrand Banks jutting southward into the path of theGulf Stream and possibly forcing it away from thecontinental slope as far back as Cape Hatteras.

The Florida Current emerges as the part of the GulfStream System that is best documented, analyzed, andunderstood. The Gulf Stream itself is likely to be morecomplex, but is as yet poorly measured by comparison.The systematic program of moored current and tem-perature measurements developed by Schmitz (1976,1977, 1978) are slowly building a foundation of time-series data that will enable the next interpretive stepsto be taken. Because of the complexities of the GulfStream System, understanding of the behavior in termsof dynamics will rely heavily on numerical modelingand analysis. It is essential that the observational andnumerical studies of the Gulf Stream System proceedcooperatively.

I39The Gulf Stream System