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8/19/2019 lagrangian flow
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GEOPHYSICAL RESEARCH LETTERS, VOL. 24, NO. 16, PAGES 2035-2038, AUGUST 15, 1997
Lagrangian flow at the foot of a shelfbreak front using a dye
tracer injected into the bottom boundary layer
RobertW. Houghton
Lamont Doherty Earth Observatory,Palisades,NY 10964
Abstract. Convergent low at the foot of the shelfbreak ront n
the Middle Atlantic Bight has beendetectedusinga dye tracer,
Rhodamine-WT, injected into the bottom boundary ayer. The
observations ubstantiatemodel simulationsby Chapman and
Lentz (1994) of convergentlow in the vicinity of the front which
would be very difficult if not impossible to detect with
conventionalmoored current measurements. y tollowing the
dispersal of the dye patch over a 4 day period Lagrangian
velocitiesof the order of 0.015 m/s with respect o the front were
resolved even as the frontal boundary was displaced 12 km
onshore. The water-following properties of the dye tracer
provides a useful technique for studying the small-scale
circulationand mixing at the frontal boundary.
Introduction
Understanding he processesesponsibleor the positionand
structureof the shelfbreak front, a continuous baturealong the
northeast ontinentalmargin from Nova Scotia o Cape Hatteras,
has been a focus of much research.Typical springtimestructure
of this front, separatingcold, fresh Shelf Water from denser
warm, salty Slope Water is shown n Fig. 1. Numerical model
calculations by Gawarkiewicz and Chapman [1992] and
Chapmanand Lentz [ 1994] highlight he dynamical ole of the
bottom Ekman layer (BBL) by which the offshore flow is
arrested at a convergent zone generated by the cross-shelf
buoyancy lux and then separatesrom the bottom o shoalalong
the frontal boundary.
This convergent low has not been detected. n fact all mean
Eulerian cross-shelf velocities, as measured by current meters
moored in the BBL on the outer shelf and upper slope, are
offshore anging n magnitude rom 0.01 to 0.04 m/s [Beardsley
et al., 1985; Aikman et al., 1988; Bum•an, 1988; Houghtonet al.,
1994]. A continuous offshore flow across he shelfbreak without
any convergences difficult to reconcilewith the persistence f a
narrow frontal boundary.The fact that the foot of the front often
undergoes ross-shelf xcursions reater han 20 km [Houghton
et al., 1994] makes observationof a small scaleconvergent low
at the frontal boundary by an array of current meters neither
feasiblenor cost effective. For these easons new technique,
dye tracer, was proposed as a means of observing the
convergencendperhaps ven he detachment f the BBL flow at
the frontal boundary.The resultsof a pilot cruisewhich not only
tested this technique but also produced some striking
observations re presented ere.
Experiment
Both injectionand detectionof the dye were accomplished
using a sled (0.5 m high, 2 m long, weighing -150 kg and
ballasted o remainhorizontal) owedat speeds anging rom 1 to
4 kts. The sled was fitted with a downward ooking altimeter,a
Sea Cat SBE-19 CTD, and two Chelsea MK II Aquatracka
fluorometerswith optical filters suited o detect Chlorophyll a
and Rhodamine-WTdye. The chlorophyllmeasurement as used
to remove spuriousbackground ignal n the dye channeldue to
in situ chlorophyll. hirty-five kilograms f Rhodamine-WT ye
in a 20% water solutionmixed with isopropylalcohol o achieve
in situ densitywas pumped nto the BBL producing n initial
streak1 km in lengthparallel o the 100 m isobath n 8.9øC water
on the shoreward side of the center of the front. The vertical
temperature radientat the top of the BBL at the Ibm of the front
wasmuchgreater han depicted n Fig. 1. Above a mixed ayer4-
7 m thick, the transition to cool, fresh water above was a 2.4øC
decreasen 3 m correspondingo a 0.4 kg/m density ecrease
and a Brunt-V•iis•il•i period of 2.9 minutes. Because of the
fluctuationsn sleddepthand he unexpected harpnessf the top
of the BBL approximately alf of the dye was actually njected
into the BBL. Within 24 hours all evidence of streakiness in the
dye patch disappearedand dye injected above the BBL was
advected out of the study area by the vertical shear of the
horizontalvelocity.
lOO
15o
200
•1 ' ß ß ß
4O 50 6O 70 8O 90 lOO
Distance kin)
250
i
30 140
10 120 130
Copyright 997by theAmericanGeophysical nion.
Papernumber 7GL02000.
0094-8534/97/97GL-02000505.00
Figure 1. Cross-shelfalonga PRIMER transect 0ø from the
cross-shelfaxis with CTD stations ndicated by crosses)
temperaturesection across he shelfbreak ront south of Martha's
Vineyard wo weeksbefore he pilot cruise,courtesy f Bob
Pickart.
2035
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2036 HOUGHTON' LAGRANGIAN FLOW AT THE FOOT OF A SHELFBREAK FRONT
40.•
40.4
was derivedusing he temperature t the peak dye concentration
to represent he temperatureof the center of massof the patch
and constructing a mean cross-shelf front BBL temperature
profile from a compositeof all the cross-front ections.Over the
3-day periodof the surveys he dye patch,and hence he tagged
water parcel n the BBL, moved onshoreby 3.5 km with a mean
speedof 0.015 m/s. Thus the water moved n a directionopposite
to that expected.
The situation s clarified by considering he spatialvariations
ß ' of other variables n the BBL structure Table 1). Although the
i .' ' .......................... tandardeviationssociatedithndividualeasurementss
• '••.•,• "•;i :iii approximately0o0%ftheean,herendreel
•100, defined.ovingnshoreocolderemperatures,he ross-shelf
,q4o.a........ . ................'•It-• :•-fl"'h.•,a,......................... temperatureradient,x, increases,heverticalemperature
'-' ; ß ': R... • .......7-,. i
40.•....... 40
......._ ..............................5
. kiltieters ', '.
-70.7 -•ot -•o_s -70.4 -•o.a
Figure2.ruiserackduringtheinjectionanddetectionofC3•15[-i T?•/ 'l'i 1....
ye patch. Three surveysare identified as TR3, TR4, and TR5.
Bottombathymetry s indicated.Contoursof dye concentrationn
unitsf10- are , 12, nd 0 orTR3 nd .5 nd forTR5. 1
Note the onshoredisplacementof the dye patch and hence the
frontal boundary rom the 100m to 80m isobathbetweenTR3 and
TR4.
0 •,"•'• i i i ,"' i "• i \ I
6.5 7 7.5 8 8.5 9
Tempe atu e degC)
Theubsequentispersalf heyeatchn he BLas 45 : T
appedor henext daysFig. ).Measurableye
detection was a concentrationof 10 11b
concentrationlevelf .... y 40 .... ... .... .... ....... .... ........ ....
volume) was confined to the BBL. The sled altitude was '
maintainedetweento5 m aboveottomith rief ertical 35- '
excursions to measure the B BL thickness and stratification by
adjustingheowingpeedndengthf ableeployed.he
estwardriftf he atch-0.06 /s),oughlyarallelo he 30.... ........ ............... '...........
local isobaths,was expected, he sudden nshore isplacement f
approximately2mn 4ionrs-0.14/s)wasot.hereas i 25................/..................concurrentdisplacement f the frontal boundary nferred rom
theross-shelfositionf heøCsotherm.inceuringhis • 20 : ' : ß i '"'" '
eventross-shelfemperatureradientsithinheBBL idnot
change,t s nferredhat t eastheowerortionf herontal O• 5 ... .... .... .... ' 'Ti ' : .
boundaryasdisplacednshorendnot uststretched. >, : : ....
As the dye patch dispersedts mean temperature ecreased. 10 .... : ... : .... : .... : -' .... : ......... : ...
Thesalinity lsodecreasedithT-S values f thedyepatch /::l _
evolving along the mean T-S mixing curve for the BBL water
across the front. This cooling is illustrated by representative
sections cross he dye patch Fig. 3) measured uringsuccessive
surveysof the dye patch. The dye inventory derived from the
final survey indicates that 11.5 1 or approximately 70% of the
original dye injected into the BBL was still in the dye patch.
Therefore the dye patch is truly a Lagrangian ollower, and this
temperature hange epresents oolingof the waterparcel agged
by the dye. The dye patchposition elative o the front (Table 1)
o
-5 -4 -3 -2 -1 o 1 2 3 4 5
Distance(krn)
Figure 3. Representative cross-shelf sections of dye
concentration cross he dye patch during the three surveys
showingBBL dye concentration s a functionof temperature
(top) and cross-shelfdistance bottom).
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HOUGHTON: LAGRANGIAN FLOW AT THE FOOT OF A SHELFBREAK FRONT 2037
Table 1. Evolution of dye patch
Time Time Temp x T x Tz ho Tt u
1•- øC km øC/km øC/m m 10-6øC/s rn/s
Injection 0 8.95 0
TR3 28 8.7 - 1.0 0.21 1.2 7
TR4 67 8.15 -3.45 0.28 0.9 5
TR5 90 7.85 -4.5 0.41 0.7 3.5
-3.9 -0.017
-3.6 -0.013
Dye patch ime from njection, emperature,ndpositionelative o the ront positive ffshore) efined
by thepeakdye concentrationor the hreesurveys: R3, TR4, andTR5. Temperatureradients ndBBL
thickness,o, aremeasuredt he ocationf thedye oncentrationeak. emperaturehangend ross-shelf
velocityare derived rom changes etweensuccessiveurveys.
gradient, t the opof theBBL, Tz, decreases,nd he hickness
of the BBL, ho, decreases. hese trends ndicate that the dye
patchhad been njectedon the seaward ideof the convergence
zone in the front instead of the shoreward side as intended.
These observations re used to construct schematicdiagram
(Fig. 4) illustrating he evolutionof the dye patchshown n the
BBL. Although he diagram s two-dimensionalt representshe
cross-shelf otionof a waterparcel hat s flowingnearly20 km
alongshore o the west. Thus, there is an implicit three-
dimensionality o the circulation.From its injectionpoint near
9øC the centerof massof the dye patchmovesonshore owards
the frontalconvergence oint as t broadens.Within the BBL the
dye was well mixed vertically. Traces of dye appeared o
penetratento hestratifiedayerabove heBBL as hr as he7øC
lO 8 6 4 2 o •
cross - shelf Distance (k•)
Figure 4. A schematic iagramof the evolutionof the dye patch
in the BBL at the foot of the shellbreak front. The cross-shelf
temperatureprofile is a mean derived from all sections aken
during he cruiseand s used o infer cross-shelf osition elative
to the front from temperaturemeasurements.he positionof the
dye concentrationpeak (dots) and approximateone standard
deviation width of the patch for each survey are shown along
with the time elapsed from the dye injection. The vertical
gradient above the BBL at x=0 is from the dye injection
measurements.he top of the BBL (dashedine) is definedby the
height of the maximum vertical temperaturegradient.Arrows
qualitatively epresenthe flow although nly the onshorelow is
actually measuredby the dye patch displacement.sothermsare
hand drawn to connect the mean BBL temperature with the
vertical stratification at x=0 and to represent the cross-shelf
variation in the vertical gradient. Between TR3 and TR4 the
entire rontalboundarywas displaced 2 to 15 km onshore.
isotherm. Here the decrease n dye concentrationwas abrupt
suggesting convergence n the center of the stratified layer
above he BBL as ndicatedby the arrows n Fig. 4. The thickness
of the BBL defined by the height of the maximum gradient
region diminished onshore so the dye patch thickness was
reduced as it moved onshore. The arrows pointing onshore
indicate aterlowdef:inedy thedyepatchmotion hile he
other arrows are a more speculativerepresentationof inferred
flow in the BBL at the fbot of the frontalboundary.
Discussion
There are several aspectsof theseobservationswhich at first
appearcontradictory.n particular,onshore nd westward low in
the BBL is not consistentwith Ekman dynamics.This apparent
contradictions resolved n model calculations y Chapmanand
Lentz [ 1994] where they consider frontogenesis on the shelf
driven by the BBL advection of buoyancy from an inshore
source.The offshoremigration of the front is arrestedwhen n the
BBL offshore flow of buoyant Shelf Water convergeswith an
onshore flow underneath the frontal boundary. This BBL
convergence zone is on the shoreward side of the frontal
boundary. The thermal wind vertical shear in response o the
increased cross-shelf density gradient reverses he alongshore
flow at the foot of the front. However, when an alongshore
pressure gradient is added to simulate the observed mean
southwestwardlow along the northeast ontinentalmargin there
is no reversal n the alongshore low in the BBL under the front
(see heir Fig. 13). Although he model s applied o an uniformly
slopingshelf while the front is actually situatedat the shellbreak,
the presentobservations ubstantiate everal mportant eaturesof
this frontogenesismodel.
Since the dye-tagged water was tbllowed in a Lagrangian
sense,heobservedooling, T/dt 4x10 6 øC/s,mustbe the
result of diffusive mixing. From the cross-shelf preadingof the
dyepatch cross-shelfiffusivityf K x - 10m2/s s estimated.
The cross-shelf arianceof the dye patch ncreases pproximately
as time squared indicating a major contribution from shear
dispersion.From measuredcross-shelf emperature radientsan
upper oundor Txx s - 0.1xl0-6øC/m, hencehecross-shelf
diffusive eat luxKxTxx lx10-6øC/s. incehis s onlyone
forthof the rateof the observed ye patchcooling, heremustbe
significant vertical heat flux through the top of the BBL to
achieveheat balance within the dye patch. An estimateof the
vertical diflhsivity Kz across he highly stratified op of the BBL
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2038 HOUGHTON: LAGRANGIAN FLOW AT THE FOOT OF A SHELFBREAK FRONT
isproblematical;oweveralue f Kz - 10 m2/s ields zTzz-
4x10-6øC/s, hich s approximatelyhe magnitudeequiredo
account for the cooling of the dye patch. Using the same
diffusivity results n a loss of approximately3 1 of dye which
when ubtractedrom he 16 1 nitially njectednto heBBL s
consistentwith the final dye inventory of 11.5 1. There is no
evidence hat double-diffusivemixing is a factor here. First, the
density atio,R = azXT/I3ASs approximately.4 andnot near
unity where doublediffusiveprocessesre more active.Second,
the T-S valuesof the water parcelevolve along he meanmixing
curve between Shelf and Slope Water properties with no
evidenceof a counterclockwise otation n T-S spaceas modeled
by Schmitt 1981 . When warranted y betterdyepatchsampling
in futureexperiments,hese lux calculations ill be repeated y
properly ntegrating ver he entirepatch ather hanusingmean
patch values.However, even thesecrude estimates mposean
upperboundon the diffusive lux through he highly stratified
boundary f the BBL near he foot of the front.
If to someextent the structuredepicted n Fig. 4 represents
steady-stateondition n the coastal egimewith no alongshore
variation, then both mass and heat balance must apply. Mass
balance s probablyachieved y an offshore low confined o the
stratified ayer at the top of the BBL. Houghtonet al. [1982]
estimate that during the summer the 'cold pool', shelf water
beneath he warm surfacemixed layer, warms at approximately
1øC/month. Approximating he cold pool as a wedge 100 km
wide and 60 m thick at the shelfbreak front this warming is
equivalento a heat luxof 4.9x10 W permeter f alongshelf
distance. When mixed to 6øC the onshore flow of 9øC water in
the BBL 6 m thick at the measured peedof 0.015 m/s represents
a flux of 1.1x106 W. Thus the heat flux associatedwith the
observed onshore flow in the BBL at the foot of the front could
contributesignificantly o the Shelf Water heat balanceand to
exchangeof Shelf and Slope Water propertiesvia diapycnal
mixing across he top of the BBL.
Conclusions
The results of this pilot cruise demonstratedhe utility of a
dye tracer o investigatemixing and circulationat the tbot of the
shelfbreak front in the Middle Atlantic Bight. It resolved water
displacementsf 3 to 4 km relative o the frontalboundary ver 3
days even when during the courseof the observation he front
was displaced12 to 15 km onshore. t has revealeda heretofore
undetectedonshore low responsible br convergencewithin the
frontal boundary. The reason that this onshore flow was not
detectedby mooredcurrentmeters s now clear. n the Chapman
and Lentz [ 1994] model the onshore low is weak and confined o
an approximately to 6 km interval at the tbot of the front while
onshore nd offshore not shown n Fig. 4) of this region he BBL
flow is offshore.Since the front undergoes ross-shelf xcursions
that exceed its width, any moored current meter will
predominantly ample he offshore low regime.
Details of the flow field suggestedn Fig. 4 requires urther
confirmation.A subsequent ruise s scheduledn 1997 nvolving
more controlleddye injection nto the BBL on both sidesof the
convergence one to refine the flow patterns nferred from this
pilot cruise.
These observations nd their apparentconfirmationof model
simulations by Chapman and Lentz [1994] indicate the
importanceof the BBL to both frontal dynamicsand to shelf-
slopeexchange rocesses.t is in the BBL at the foot of the front
where large T-S gradients mposedby the frontal boundaryand
turbulent nergyderived rom bottomboundary riction combine
to inducestrong'diapycnalmixing.
Acknowledgments. The success f this pilot cruise s due to
the skill and patienceof Captain Tyler and crew, especially he
winch operators, f the R/V ENDEAVOR. The dye injectionand
detection system was designed and constructed by Miguel
Maccio and Marcela Stern.Cheng Ho and JarvisBelinne assisted
in the data analysisand figure preparation.The technicaladvice
and encouragementby Jim Ledwell is especially appreciated.
This project is supportedby NSF grant OCE94-16074. Lamont
Doherty Earth ObservatorycontributionNo. 5693.
References
Aikman III, F., H.W. Ou, and R.W. Houghton,Currentvariability
across he New England Continental Shelf Break and Slope.
ContinentalShelfRes., 8, 625-651, 1988.
BeardsIcy,R.C., D.C. Chapman, K.H. Brink, S.R. Ramp and R.
Schlitz, The Nantucket Shoals Flux Experiment (NSFE 79).
Part I: A basic description of the current and temperature
variability.J. Phys.Oceanogr., 15, 713-748, 1985.
Butman,B., DownslopeEulerian mean flow associatedwith high
frequency current fluctuations observed on the outer
continental shelf and upper slope along the northeastern
United States continental margin: implications tbr sediment
transport.ContinentalShelfRes., 8, 811-840, 1988.
Chapman,D.C. and S.J. Lentz, Trappingof a coastaldensity ront
by the bottom boundary ayer. J. Phys. Oceanogr.,24, 1465-
1479, 1994.
Gawarkiewicz,G. and D.C. Chapman,The role of stratificationn
the tbrmation and maintenance f shelf break ronts. J. Phys.
Oceanogr.,22, 753-772, 1992.
Houghton, R.W., C.N. Flagg and L.J. Pietrafesa, Shelf slope
water frontal structure, motion, and eddy heat flux in the
Southern Middle Atlantic Bight. Deep Sea Res. part II:
Topical Studiesn Oceanography, ontinental helfRes..,41,
273-306, 1994.
Houghton,R.W., R.Schlitz, R.C. BeardsIcy,B. Butman and J.L.
Chamberlin,The Middle-Atlantic Bight cold pool: evolution
of the temperaturestructureduring summer 1979. J. Phys.
Oceanogr., 12, 1019-1029, 1982.
Schmitt, R. W., Form of the temperature-salinity elationship n
the Central Water: evidence for double diffusive mixing. J.
Phys.Oceanogr., 11, 1015-1026, 1981.
R. W. Houghton, Lamont Doherty Earth Observatory of
Columbia University, Palisades, NY 10964 (e-mail:
houghton@1deo. o umbia.edu)
(ReceivedApril 28, 1997; revisedJune 19, 1997;
accepted uly 8, 1997.)