Transport driven by eddy momentum fluxes in the Gulf StreamExtension region

R. J. Greatbatch,1 X. Zhai,2 M. Claus,1 L. Czeschel,1,3 and W. Rath1

Received 13 September 2010; revised 14 October 2010; accepted 19 October 2010; published 16 December 2010.

[1] The importance of the Gulf Stream Extension region inclimate and seasonal prediction research is being increasinglyrecognised. Here we use satellite‐derived eddy momentumfluxes to drive a shallow water model for the North AtlanticOcean that includes the realistic ocean bottom topography.The results show that the eddy momentum fluxes can drivesignificant transport, sufficient to explain the observedincrease in transport of the Gulf Stream following itsseparation from the coast at Cape Hatteras, as well asthe observed recirculation gyres. The model also capturesrecirculating gyres seen in the mean sea surface heightfield within the North Atlantic Current system east of theGrand Banks of Newfoundland, including a representation ofthe Mann Eddy. Citation: Greatbatch, R. J., X. Zhai, M. Claus,L. Czeschel, and W. Rath (2010), Transport driven by eddymomentum fluxes in the Gulf Stream Extension region, Geophys.Res. Lett., 37, L24401, doi:10.1029/2010GL045473.

1. Introduction

[2] The importance of correctly representing the GulfStream and Kuroshio Extension regions in both climate andseasonal forecast models is increasingly being recognised[Rodwell and Folland, 2002; Minobe et al., 2008], yet ourunderstanding of the dynamics of these regions is still farfrom complete. A common feature of both the Gulf Streamand Kuroshio Extensions is the presence of recirculationgyres north and south of the main current [Hogg et al., 1986;Jayne et al., 2009]. These recirculation gyres are thought tobe driven by eddies. Indeed, recirculation gyres are a char-acteristic feature of quasigeostrophic eddying ocean modelsthat use a flat bottom [e.g., Holland, 1978; Holland et al.,1984]. The similarity between the recirculation gyres inthese models and Fofonoff gyres [Fofonoff, 1954] led toextensions of the Fofonoff gyre concept to stratified oceansand their application to explain the observed recirculationregions [e.g.,Marshall and Nurser, 1986; Greatbatch, 1987].A particular feature of the model of Greatbatch [1987] is aregion of deep recirculation, extending throughout the depthof the ocean not dissimilar to the observed Gulf Streamrecirculation gyres [e.g., Worthington, 1976; Schmitz, 1980;Richardson, 1985]. The transport in Fofonoff‐type modelsof the recirculation regions can exceed by many times theflat‐bottomed Sverdrup transport, given by integrating the

wind stress curl westwards from the eastern boundary, afeature consistent with observations [Gill, 1971]. The reasonfor the increase in transport is the shielding of the recircu-lation to the east by a region in which the advection of meanrelative vorticity by the mean flow is important, breaking thetraditional linear Sverdrup constraint. In the present paper,we take the alternative point of view and ask how muchtransport can be driven by linear Sverdrup balance when theforcing is provided by the eddy momentum fluxes, herecomputed from satellite altimeter data. Our model calcula-tions show that significant transport can be driven by theeddy momentum fluxes and that this transport is comparableto observed transport in the Gulf Stream Extension region.[3] The importance of the eddy momentum fluxes in the

dynamics of the atmospheric jet stream is well known [e.g.,Marshall and Plumb, 2008]. The role of the eddy momen-tum fluxes in the ocean is much less clear; in some regionsthe eddies appear to accelerate jets and in other regions todecelerate jets [Hughes and Ash, 2001]. The reason for thedifferent behaviour in the ocean seems to be the rough andsteep bottom topography seen by eddies [Ducet and LeTraon, 2001; Hughes and Ash, 2001; Greatbatch et al.,2010]. The atmospheric storm tracks, on the other hand, aretypically found over the oceans [Hoskins and Valdes, 1990]where eddies see an effectively flat bottom. Greatbatchet al. [2010] have used the 13 years of available satellitedata to compute eddy momentum fluxes for the Gulf Streamand Kuroshio regions. Greatbatch et al. [2010] argue thatwhile locally it is hard to see evidence that eddies system-atically flux momentum into jets, after suitable averaging, aclearer picture emerges. Since the eddies themselves extendto the bottom of the ocean, these authors also emphasise theimportance of the variable bottom topography for under-standing the ocean response to the eddymomentum fluxes, theidea we take as our starting point here.

2. Model

[4] The long‐time averaged, steady state horizontal momen-tum equations for a Boussinesq ocean, written for conve-nience in Cartesian coordinates and neglecting advectionby the mean flow, are

�f v ¼ � 1

�o

@ p

@x� @ u 0u 0

@x� @ u 0v 0

@y� @ u 0w 0

@zþ F

x

�oð1Þ

and

f u ¼ � 1

�o

@ p

@y� @ u 0v 0

@x� @ v 0v 0

@y� @ v 0w 0

@zþ F

y

�oð2Þ

where r · is the divergence operator, u = (u, v, w) is veloc-ity (the zonal and meridional components are u and v,

1Leibniz Institute of Marine Sciences at Kiel University (IFM-GEOMAR), Kiel, Germany.

2Atmospheric, Oceanic and Planetary Physics, University of Oxford,Oxford, UK.

3Now at KlimaCampus, Hamburg, Germany.

Copyright 2010 by the American Geophysical Union.0094‐8276/10/2010GL045473

GEOPHYSICAL RESEARCH LETTERS, VOL. 37, L24401, doi:10.1029/2010GL045473, 2010

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respectively, and w is the vertical component), p is the pres-sure, (Fx, Fy) represents the forcing associated with three‐dimensional turbulence (including the wind forcing), theoverbar denotes a long time average at fixed height andprime deviations from that average. The terms @

@zw0u 0,

@@zw

0v 0 play no role in the vertically integrated momentumbudget and will not be discussed further. The horizontaleddy fluxes u 0v 0, u 0u 0 and v 0v 0 are the subject of this paperand have been calculated at the surface using geostrophicvelocity anomalies for the period January 1995 to December2008 computed from the global sea surface height anomalydataset compiled by the CLS Space Oceanographic Divisionof Toulouse, France [see Le Traon et al., 1998]. The meanover the whole time series was removed from the zonal andmeridional velocity anomalies before computing the fluxes.However, no attempt was made to remove the seasonal cycle(the seasonal cycle of the mean flow is, in fact, weak comparedto the eddy variability and can be safely neglected). u 0v 0 isplotted by Greatbatch et al. [2010, Figure 2] [see also Ducetand Le Traon, 2001, Plate 8]. The seemingly chaotic natureof the plotted field can be attributed to the underlying var-iable and rough bottom topography.[5] In order to estimate the transport driven by the eddy

momentum fluxes, we exploit the fact that the eddy momentumfluxes act over the full depth of the ocean and use a linearbarotropic model for an ocean of uniform density but includ-ing the realistic bottom topography and coastlines, i.e.,

ut � f v ¼ � g

a cos �

@�

@�þ Z � � x

b

�oHð3Þ

vt þ f u ¼ � g

a

@ �

@ �þM � � y

b

�oHð4Þ

�t þ 1

a cos �

@ Huð Þ@�

þ @ cos �H vð Þ@ �

� �¼ 0: ð5Þ

Here � is latitude, l is longitude, a is the radius of the Earth,H is the ocean depth, (t b

x, t by) represents the bottom stress,

and Z and M are the vertical average of the forcing for thezonal and meridional momentum equations, respectively,that arises from the eddy momentum fluxes (note that directwind forcing is not included). The particular form we use forZ and M is given by

Z ¼ � 1

2Ha cos �

@

@�H u 0u 0js� �þ @

@ �cos �H u 0v 0js� �� �

ð6Þ

and

M ¼ � 1

2Ha cos �

@

@�Hu 0v 0js� �þ @

@�cos �Hv 0v 0js� �� �

ð7Þ

where u 0u 0js, v 0v 0js and u 0v 0js are the surface fluxes derivedfrom the satellite data and to write (6) and (7) it has beenassumed that each of the fluxes, u 0u 0, v 0v 0 and u 0v 0 varieslinearly from the computed value at the surface to zero at thebottom. This choice for the vertical structure is based on theobservation that eddies in the ocean generally have anequivalent barotropic vertical structure, as noted by Wunsch[1997]. It should be noted that use of a different verticalstructure for the momentum fluxes will change only the

amplitude of the forcing term, as long as the verticalstructure is everywhere self‐similar (i.e., a function only ofz/H). For example, assuming the fluxes are everywherevertically uniform removes the factor of 2 from (6) and (7),doubling the forcing amplitude. Schmitz [1982] providesevidence from 55°W that near the Gulf Stream, u 0v 0 is, infact, remarkably uniform in the vertical. Indeed the valuesshown in his Figure 2 for 4000 m depth are similar in mag-nitude to the surface values used for our model forcing. Wealso note that in writing (3) and (4), we have neglected anypossible feedback on the barotropic mode from the projec-tion of the forcing on to the internal baroclinic modes. Toinvestigate this issue would require the use of a much morecomplex model than we are using here. For the bottom fric-tion we use a quadratic formulation (the only source of non-linearity in the model)

ð� xb; �

ybÞ=�o ¼ kðu2 þ v2Þ1=2ðu; vÞ ð8Þ

where k = 5 × 10−2. The model domain covers the NorthAtlantic between 100°W to 0° and from 15°N to 55°N anduses realistic bottom topography taken from the ETOPO1data set. The horizontal resolution is 1/6° in latitude andlongitude. It should be noted that extending the modeldomain further north has no effect on the model results. Theresults shown in the next section are obtained by running themodel to steady state.

3. Results

[6] Figure 1 shows the transport streamfunction computedfrom the model together with the mean sea surface heightcontours taken from Niiler et al. [2003] to indicate the meanflow by geostrophy. We focus only on the Gulf StreamExtension region since this is where the significant modelresponse is found. A striking feature is the tendency forpositive/negative streamfunction values on the south/northside of the Gulf Stream axis, similar to the schematic drawnby Hogg [1992, Figure 10]. The corresponding recirculationgyres carry 50 Sv or more in transport, enough to accountfor the observed transport in the Gulf Stream Extensionregion [Gill, 1971; Hogg, 1992; Johns et al., 1995], althoughit should be noted that the magnitude of the computed trans-port depends on the vertical structure that has been assumedfor the eddy momentum fluxes (confining the fluxes nearerthe surface leads to lower transport). Between 50°W and60°W, the recirculating gyres resemble the observed recir-culation gyres [e.g., Schmitz, 1980; Hogg et al., 1986]. Inparticular, there is a cyclonic gyre circulation bounded by theGrand Banks to the east and the continental slope to thenorth corresponding to the northern recirculation gyre [Hogget al., 1986]. The pattern of recirculating gyres straddling theGulf Stream is also similar in character to that given by Zhaiet al. [2004, Figure 2]. Zhai et al. [2004, Figure 2] shows thetransport that is driven directly by the eddies in their model.Zhai et al. [2004] attribute the eddy‐driven transport toforcing from the Reynolds stress terms although they do notdemonstrate this explicitly. It is also striking how the trans-port streamfunction shown in Figure 1 resembles the totalstreamfunction found in the 1/10th degree eddy‐permittingmodel of Smith et al. [2000], reproduced here as Figure 2using the version by Bryan et al. [2007, Figure 4c]. Indeed,

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while not exact, there is an interesting correspondencebetween some of the maxima and minima in Figures 1 and 2,e.g., the “gap” in the streamfunction pattern extendingsoutheastwards from the Grand Banks of Newfoundland atthe location of the Southeast Newfoundland Rise, as well asthe locations of maxima and minima further to the north andto the west. The similarity between the two streamfunctionsalmost certainly reflects the influence of the variable bottomtopography and supports our assumption that the forcingfrom the eddy momentum fluxes projects strongly on to thebarotropic mode. Looking at Figure 1 in the region imme-diately to the east of the Grand Banks, we see that the model

reproduces a gyre circulation corresponding to the MannEddy at 43°N, 42°W [Mann, 1967], be it that the model gyreis displaced slightly northeastwards from the surface signa-ture of the Mann Eddy in Niiler et al.’s [2003] product. Themodel also indicates several eddy‐driven gyres embedded inthe North Atlantic Current, east of Newfoundland, withcorresponding gyre circulation indicated in Niiler et al.’s[2003] data set, including in the northwest corner [Lazier,1994] where the North Atlantic Current takes a sharp turneastwards to pass through the Charlie‐Gibbs Fracture zone.[7] We have run the model using forcing from each of the

four terms separately that make up the divergence of the

Figure 2. As Figure 1, but for the barotropic streamfunction in the Gulf Stream region from the model of Smith et al.[2000]. Courtesy of Frank Bryan.

Figure 1. Model‐computed transport streamfunction (colour shading in units of Sverdrups) in the Gulf Stream Extensionregion. The contours show the mean sea surface height from Niiler et al. [2003] with an interval of 0.1 m.

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momentum flux in equations (6) and (7). It should be notedthat despite our use of quadratic bottom friction, the sum ofthe four individual streamfunctions adds up to give a fieldalmost the same as that shown in Figure 1. It is clear fromFigure 3 that the model response to the u 0u 0js and v 0v 0jsterms show a large cancellation. Nevertheless, the modelresponse to the sum of these terms, also shown in Figure 3,

is significant and comparable in magnitude to the modelresponse forced by the u 0v 0js term in the zonal momentumequation. The corresponding term in the meridional momen-tum equation can play a role locally but is more noisy thanthe model response to the other terms. It should be notedthat the model response is not particularly sensitive to thespecified friction (as long as this is not too large). This is

Figure 3. As Figure 1 but for the model‐computed transport streamfunction (Sv, colour coding) when the model is forcedseparately by each of terms that appear in equations (6) and (7). Also shown is the sum of the model response to the u 0u 0jsand v 0v 0js terms and each of the u 0v 0js terms. The contour interval for the mean sea surface height is here 0.2 m.

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because the model response is dominated by the integral ofthe topographic Sverdrup balance

J Y; f =Hð Þ ¼ @M

@�� @ cos �Zð Þ

@�ð9Þ

along the f /H contours from the equator at the easternboundary where Y = 0. An interesting implication of (9) isthat the model response is not local but rather depends onthe “upstream” forcing along the f /H contours in the direc-tion of the eastern boundary.

4. Summary and Discussion

[8] We have used a simple, barotropic shallow water modelto show that the eddy‐momentum fluxes can drive signifi-cant circulation and transport in the Gulf Stream Extensionregion analogous to the observed recirculation gyres [Hogget al., 1986; Schmitz, 1980]. The model also captures severalgyre circulations in the North Atlantic Current east of theGrand Banks of Newfoundland that have a surface signaturein the mean sea surface height derived by Niiler et al.[2003], including the Mann Eddy [Mann, 1967] (be it dis-placed slightly northeastwards in the model). The computedtransport streamfunction in the Gulf Stream Extension/NorthAtlantic Current region is also quite similar to the barotropicstreamfunction found in the 1/10th degree eddy‐permittingmodel of Smith et al. [2000]. One reason for the successof the calculation appears to be the influence on the under-lying variable bottom topography on both the structure ofthe eddy fluxes themselves [Ducet and Le Traon, 2001;Greatbatch et al., 2010] and on the model‐computed stream-function. As we have noted, the model response is domi-nated by the topographic Sverdrup response integrated alongthe f /H contours, indicating a strong non‐local aspect to themodel solution. We noted that early theories of the recir-culation gyres emphasised the role of advection of meanvorticity for shielding the recirculation gyres from the eastand allowing the transport to increase above that givenby the flat‐bottomed Sverdrup prediction. Here, the modelsolution is dominated by the topographic Sverdrup responseto the forcing imposed by the eddy momentum fluxes, withno need to invoke the mean flow, a possible reason beingthe variable bottom topography not included in the earlierwork. A third approach to explain the increase in transport isto appeal to bottom pressure torque, as by Mellor et al.[1982] or Zhang and Vallis [2007], a factor that may playa role in reality and requires further exploration. It is diffi-cult to assess the impact of the spatial and temporalsmoothing inherent in the satellite data used to compute theeddy momentum fluxes that force our model but the generalagreement between Figures 1 and 2 suggests that the essenceof the forcing is being captured. Only a future study using amuch higher resolution satellite data set will be able toanswer this question, although studies using the new gen-eration of high resolution models might also help. Finally,we note that there is growing interest in the possible impactof the Gulf Stream Extension region on the atmosphere[e.g., Rodwell and Folland, 2002; Minobe et al., 2008] andthere are clear implications from our results for attempts torepresent the recirculation gyres in climate or seasonal fore-cast models. In particular, there is the need to parameterisethe eddy momentum fluxes, a potentially daunting task that

requires including the impact of the underlying variablebottom topography on these fluxes. It may be that a simplerand more effective alternative is the use of bias‐correctiontechniques, such as the so‐called semi‐prognostic methodreviewed by Greatbatch et al. [2004].

[9] Acknowledgments. This work has been funded by IFM‐GEOMARand a grant from the Deutsche Forschungsgemeinschaft. We are grateful toFrank Bryan for providing the data used to plot Figure 2 and to threeanonymous reviewers for comments on an earlier version of the manuscript.

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M. Claus, R. J. Greatbatch, and W. Rath, Leibniz Institute of MarineSciences at Kiel University (IFM‐GEOMAR), Dusternbrooker Weg 20,D‐24105 Kiel, Germany. (rgreatbatch@ifm‐geomar.de)L. Czeschel, KlimaCampus, Bundesstrasse 53, D‐20146 Hamburg,

Germany.X. Zhai, Atmospheric, Oceanic and Planetary Physics, University of

Oxford, Parks Road, Oxford OX1 3PU, UK.

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