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Theproblem:whatsetsthesizeoftheACC?Stommel1957,1962:EarlymodelsadaptSverdrupdynamicstotheACC,relaEngwindstresscurltotransport.MunkandPalmen,1951:Suchmodelsrequire‘uncomfortablylarge’valuesofeddyfricEoncoefficientstolimittheACCtransporttoreasonablevalues.Gill1968:LinearmodeloftheACCrequiresaboRomfricEoncoefficentof103cm2/salateralfricEoncoefficientof108cm2/s.
Theproblem:whatsetsthesizeoftheACC?Stommel1957,1962:EarlymodelsadaptSverdrupdynamicstotheACC,relaEngwindstresscurltotransport.MunkandPalmen,1951:Suchmodelsrequire‘uncomfortablylarge’valuesofeddyfricEoncoefficientstolimittheACCtransporttoreasonablevalues.Gill1968:LinearmodeloftheACCrequiresaboRomfricEoncoefficentof103cm2/salateralfricEoncoefficientof108cm2/s.Evenworse:howbig*is*theACC?ReidandNowlin,1971:Eastwardtransportof237SvthroughtheDrakePassageFoster,1972:Westwardtransportof15SvthroughtheDrakePassage(backwards!)InternaEonalSouthernOceanStudies(ISOS)programmeasuresDrakePassagetransport,structure,dynamics.NowlinandKlinck,1986:134Sv+-10%(eastward),withEmevariabilityof20%.
NowlinandKlinck,1986:134Sv+-10%(eastward),withEmevariabilityof20%.
ACCcharacterisEcs:- NOTanarrowjetorboundary
currentwithwithRo
- ThreenarrowfrontalregionsofwidthtwoorthreeEmestheRossbyradius
- ThecurrentpenetratesdowntotheboRomofthewatercolumn,withsubstanEalmeridionaldensitygradientsatdepth.
McWilliamsetal.,1978:A2-layer,eddy-resolvingQGmodeloftheACCwithvariousconfiguraEonsoftopographyandwindforcing.Inallmodelruns,eddiesplayedakeyroleintransporEngzonalmomentumdownward.Inmodelrunswithouttopography,fricEonwasonlystrongenoughtoholdmodeltransportvaluesaround400-600Sv.Inmodelrunswithtopography,topographicformdragwasstrongenoughtolimitthemodeltransportto100Sv.BoRomandsidewallfricEonisnotenough!Thus:
Steadystatezonalmomentumbalance:
NoEngthat:
Wecanwriteeqn(1)as
and
(eqn1)
TakingtheverEcalintegral:
TakingtheverEcalintegral:
InthecircumpolarregionoftheSouthernOcean,integratedzonalmomentumbalancebecomes:
Momentumsource:FricEonalwindstressatthesurfaceofthefluid
SOSE mean τx [N/m2]!
InthecircumpolarregionoftheSouthernOcean,integratedzonalmomentumbalancebecomes:
Momentumsource:FricEonalwindstressatthesurfaceofthefluidPotenEalmomentumsinks:1) FricEonalstressattheboRom;
SOSE mean τx [N/m2]!
InthecircumpolarregionoftheSouthernOcean,integratedzonalmomentumbalancebecomes:
Momentumsource:FricEonalwindstressatthesurfaceofthefluidPotenEalmomentumsinks:1) FricEonalstressattheboRom;2) FricEonalstressatthesidewalls,viameridionalmomentumfluxdivergence;
SOSE mean τx [N/m2]!
InthecircumpolarregionoftheSouthernOcean,integratedzonalmomentumbalancebecomes:
Momentumsource:FricEonalwindstressatthesurfaceofthefluidPotenEalmomentumsinks:1) FricEonalstressattheboRom;2) FricEonalstressatthesidewalls,viameridionalmomentumfluxdivergence;or3) Topographicformstress.
SOSE mean τx [N/m2]!
Topographicformstress
Howdoesmomentumtravelfromsurfacesourcetoseafloorsink?Interfacialformstress.
Howdoesmomentumtravelfromsurfacesourcetoseafloorsink?Interfacialformstress.
geostrophycontinuous stratification
and
⇣
0 = �T
0
✓z
1
⇢0
@p
0
@x
= fv
0
⇣
0 = �T
0
✓z
1
⇢0
@p
0
@x
= fv
0
Interfacialformstress:
VerEcalfluxofeastwardmomentumisproporEonaltoeddyheatflux.
Polewardheatfluxcorrespondstothedownwardfluxofeastward
momentum.
Givenafewnumbers…….thismodelcanbetestedobservaEonally.
1977DrakeClusterArrayFDRAKE75Mooring8
FDRAKE75Mooring10
ObservaEonsusedtotest
SOLIDLINE
Secondtest:Candown-gradienteddyheatfluxbeparameterizedintermsofEme-averagedbaroclinicfieldsalaGreen(1970)andStone(1972)?
ObservaEonsusedtotest
SOLIDLINE
DOTTEDLINE
EsEmaEngtransport
SOLIDLINE
DOTTEDLINE
EsEmaEngtransport:
=
SeqngeddyheatfluxesEmatesequaltoeachother:
AllowsustocalculateEmeaveragedACCverEcalshear:
FromwhichwecanesEmateanACCtransport:
.
Fordiscussion:theauthorsassumethattheRHSisjustasevenlydistributedastheLHS.IsthisareasonableassumpEon?
EKEfromsurfacealEmetry,2003-2013.Sheenetal.,2014.
Windstress(N/m2)fromNCEPreanalysis,1980-2000.MarshallandSpeer,2012.
ZoomintoDrakePassage:cDrakeExperiment,2007-2011.
1977DrakeClusterArrayFDRAKE75Mooring8
FDRAKE75Mooring10
Pressure (dbar)!
cDrakespaEalandtemporalvariability.
VerEcal,EmemeanIFS. TimemeanIFSprofiles.
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