gupea_2077_41805_2

gupea_2077_41805_2
THESISFORTHEDEGREEOFDOCTOROFPHILOSOPHY
EstimatingtheAir‐Water
GasTransferVelocityduring
LowWindConditions
SAMTOREFREDRIKSSON
FACULTYOFSCIENCE
DOCTORALTHESIS
UNIVERSITYOFGOTHENBURG
DEPARTMENTOFMARINESCIENCES
GOTHENBURG,SWEDEN2016
ISBN(Print):978‐91‐628‐9798‐7
ISBN(PDF):978‐91‐628‐9799‐4
SamToreFredriksson
EstimatingtheAir‐WaterGasTransferVelocityduringLowWindConditions
ISBN(Print):978‐91‐628‐9798‐7
ISBN(PDF):978‐91‐628‐9799‐4
Internet‐ID:http://hdl.handle.net/2077/41805
PrintedbyInekoAB
Copyright©SamT.Fredriksson,2016
Distribution:DepartmentofMarineSciences,UniversityofGothenburg,Sweden
II
Abstract
The abundances of atmospheric carbon dioxide, CO , and methane, CH , are increasing. These
increasesaffecte.g.,theglobalcarboncycleandtheclimatebothregionallyandglobally.Tobetter
understand the present and future atmospheric CO and CH concentrations and their climate
impact, the gas exchange between water and the atmosphere is important. This exchange can
occurintwodirections.OceanstakeupapproximatelyonethirdoftheanthropogenicCO release
(theoceancarbonsink).Atthesametimecoastalwatersandinlandwatersemitlargeamountsof
CO andCH ,altogethercorrespondingtoasimilaramountastheoceansink.
Theinterfacialgas‐fluxforCO andCH iscontrolledbythewater‐side.Thegas‐flux, ,isfor
where isthegastransfervelocity,
suchgasestypicallyestimatedas
and are the gas concentrations in the water bulk and in the air at the surface, and is the
dimensionlessOstwaldsolubilitycoefficient.Thesubjectofthisthesisistodescribeandestimate
for gases that have a water‐side controlled gas‐flux (e.g., CO , and CH ). Besides being
importantforthegeophysicalsciences, isalsousedtodesignandoptimizemanyapplications
ine.g.,chemicalandenvironmentalengineering.
The transfer velocity is influenced by interfacial shear stress from wind, natural convection
duetosurfaceheatflux,microscalebreakingwavesatmoderatewindspeeds,breakingwavesat
high wind speeds, bubbles, surfactants, and rain. This thesis focuses on the low wind condition
where the forcings due to shear stress, natural convection, and surfactants are important. The
relative importance of buoyancy and shear forcing is characterized via a Richardson number
⁄ ∗ . Here , , and ∗ are the buoyancy flux, kinematic viscosity, and friction velocity,
respectively. The thesis summarizes three papers where has been studied numerically with
directnumericalsimulations(DNS)andonepaperwherefieldobservationshavebeenused.
Theresultsfromthefieldmeasurementsshowcloserelationshipsforthemethodusing
flux‐chambers and the parameterization using the rate of turbulent kinetic energy dissi‐
pation, and the quantities surface rms velocity and the significant wave height. A para‐
meterizationofarea‐integratedvaluesof fromwavemeasurementswasproposed.
The DNS comprise flow conditions ranging from convection‐dominated to shear‐dominated
cases. The results are used to: (i) evaluate different parameterizations of the air‐water gas‐
exchange,(ii)determine,foragivenbuoyancyflux,thewindspeedatwhichgastransferbecomes
primarily shear driven, (iii) find an expression for the gas‐transfer velocity for flows driven by
both convection and shear, and (iv) investigate the influence of surfactants on gas transfer
velocity.
Parameterizations using either the rate of turbulent kinetic energy dissipation or the
horizontal surface flow‐divergence show a larger disadvantageous dependence on the type of
forcingthantheparameterizationusingthesurface‐normalheat‐flux.Twoparametrizationsusing
thewind‐speedabovethesurfacegivereasonableestimatesforthetransfer‐velocity,depending
however on the surface heat‐flux. The transition from convection‐ to shear‐dominated gas‐
transfer‐velocity is shown to be at
0.004. This means that buoyancy fluxes in natural
above approximately
conditions are not important for gas exchange at wind velocities
3
.Belowthiswindspeedthebuoyancyfluxesshouldbetakenintoaccount.
The transfer velocity is shown to be well represented by two different approaches:
⁄
⁄
1 ⁄
, where
is a
(i) Additive forcing as ,
∗
critical Richardson number, and (ii) either buoyancy or shear‐stress forcing that gives
⁄
for
and
for
. Here
0.4 and
∗
⁄ istheSchmidtnumber, isthegasdiffusivityinwater,and
0.1areconstants,
isanexponentthatdependsonthewater‐surfacecharacteristics.
Keywords: air‐sea gas exchange, turbulence, heat flux, natural convection, shear, direct numerical
simulations,gastransfervelocity,IR,flux‐chambers
III
Populärvetenskapligsammanfattning
Mängdenväxthusgasersåsomkoldioxidochmetanökariatmosfären.Ökningenpåverkarbland
annatvårtklimatsåvälglobaltsomregionaltochävenjordenskretsloppavkol.
Eftersomnaturensträvarefterjämviktlederskillnadenikoncentrationmellanhavochlufttill
en transport i riktning mot koncentrationsunderskottet. En ökning av koldioxidhalten i
atmosfärenlederalltsåtillenökningavmängdenkolijordensvattendragochviceversa.
Mängdenkolpåverkarisinturexempelvisvattnetssurhetvilketgörattlivetihavetförändras
ochpåverkardeorganismersomfinnsihavetochdessnärhet.
Förändringar i klimatet leder till förändrade temperaturer i hav och sjöar vilket i sin tur
växelverkarmedbådeklimatetochmedhursnabbtkoncentrationsutjämningenmellanatmosfär
ochhavsker.Dennaväxelverkanärkomplexochförattökaförståelsenförhurökadehalterav
växthusgaserpåverkarjordenärmodelleristorochlitenskalabrahjälpmedel.
För att ge trovärdiga och användbara resultat krävs att viktiga processer är modellerade så
korrekt som möjligt. En sådan viktig process är med vilken hastighet en ojämvikt i
koncentrationen mellan luft och vatten utjämnas. Denna hastighet beskrivs ofta som en
övergångshastighet för olika gaser. Denna avhandling handlar om att kunna beskriva och
modellera denna övergångshastighet (för vattenlösliga gaser för vilka gasflödet kontrolleras av
vattensidan,såsomkoldioxidochmetan)såkorrektsommöjligt.
Övergångenmellanvattenlöstkoldioxidochkoldioxidiluftenskergenommolekylärdiffusion
och kan beskrivas med hjälp av Ficks lag där flödet bestäms av gasens diffusionskoefficient
multipliceradmedgasenskoncentrationsgradientprecisundervattenytan.
Dådetgällerkoldioxidtransportgenomenvattenytaberorkoncentrationsgradiententillstor
delpåhureffektivtransportenavkoldioxidenärivattnet,vilketberorpåattkoldioxidblandarsig
mycketlångsammareivattenäniluft.Gasflödetsflaskhalsbliralltsåvattnet.
Gasens koncentrationsutjämning med hjälp av enbart diffusion, som kan ses som
koncentrationsutjämning i en helt stillastående vätska, är en mycket långsam process medan
koncentrationsutjämning med hjälp av rörelser (turbulens) i vattnet är betydligt snabbare.
Turbulensens intensitet påverkas av konvektion på grund av temperaturskillnader i vattnet,
vågor, hastighetsvariationer i vattnet på grund av vind, strömmar i vattnet, regn, bubblor,
bottenegenskaperocheventuellytfilmvilkenframföralltpåverkarvattnetsytspänning.
I detta arbete studerar vi övergångshastigheten som funktion av naturlig konvektion, vind
(vid relativt låga vindhastigheter), djup, ytfilm och vågor. Studien har utförts med hjälp av
fältmätningar vid Bornö forskningsstation i Gullmarsfjorden, men framförallt genom numerisk
modellering.
Resultaten kan sammanfattas i att övergångshastigheten vid låga vindhastigheter kan
beskrivas med hjälp av naturlig konvektion i vattnet och den skjuvkraft med vilken vinden
påverkarvattenytan.ResultatenvisarvidareattettRichardson‐talkananvändsförattbestämma
om det är drivningen från konvektion eller skjuvning som är dominerande för drivningen av
gasflödet.Konvektionenpåverkarövergångshastighetenupptillcirka3m/s.Resultatenbekräftar
ocksåetttydligtsambandmellanövergångshastigheten,gasensdiffusionshastighetivattnetoch
ytfilmensegenskaper.
IV
Preface
ThisthesisconsistsofasynthesisinPartAandfourappendedpublicationsinPartB.
ThepublicationsarereferredtointhetextbytheirRomannumbers.Thepublishedor
acceptedpublicationsarereprintedwithpermissionfromrespectivejournal.
I.
Fredriksson,S.T.,Handler,R.A.,Nilsson,H.,Zhang,Q.,andArneborg,L.(2016)
AnEvaluationofGasTransferVelocityParameterizationsDuringNatural
Convection using DNS. Journal of Geophysical Research: Oceans. doi:
10.1002/2015JC011112
Fredrikssonperformedthemodellingandalldataanalysis,hadaleadingrolein
writingthetextandpreparedallfigures.
II.
Zhang, Q., Handler, R.A., and Fredriksson, S.T. (2013) Direct numerical
simulation of turbulent free convection in the presence of a surfactant.
International Journal of Heat and Mass Transfer. doi: 10.1016/
j.ijheatmasstransfer.2013.01.031
Fredriksson had a minor role in writing, discussed the conclusions, and
commentedthetext
III.
Fredriksson, S.T., Handler, R.A., Nilsson, H., and Arneborg, L. (2016) Surface
Shear Stress Dependence of Gas Transfer Velocity Parameterizations
usingDNS.Submitted2016.
Fredrikssonperformedthemodellingandalldataanalysis,hadaleadingroleinwritingthetext
andpreparedallfigures.
IV.
Gålfalk, M., Bastviken, D., Fredriksson, S.T., and Arneborg, L. (2013)
Determination of the piston velocity for water‐air interfaces using flux
chambers, acoustic Doppler velocimetry, and IR imaging of the water
surface. Journal of Geophysical Research: Biogeosciences, doi:
10.1002/jgrg.20064
Fredrikssonhadaminorroleinwriting,discussedtheconclusions,andcommentedthetext
Peerreviewedpublicationsnotincludedinthisthesis:
Andric,J.,Fredriksson,S.T.,Lindstrom,S.B.,Sasic,S.,andNilsson,H.(2013)Astudyof
a flexible fiber model and its behavior in DNS of turbulent channel flow. Acta
Mechanica.doi:10.1007/s00707‐013‐0918‐y
Fredriksson, S.T., Arneborg, L., Nilsson H., and Handler, R.A. (2015). Near‐surface
physicsduringconvectionaffectingtheair‐watergastransfer.Proceedingsof7th
InternationalSymposiumonGasTransferatWaterSurfaces,Seattle,USA.
V
TABLEOFCONTENTS
PartA.Synthesis
1 INTRODUCTION................................................................................................................................1 1.1 1.2 1.3 1.4 Backgroundandthesismotivation...........................................................................2 Gasexchangeprinciples................................................................................................4 Forcingbywindandnaturalconvection...............................................................4 Gastransfervelocity........................................................................................................6 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 Estimationsof basedonwindspeed...........................................................7 Estimationsof basedonsurfaceheatflux................................................8 Estimationsof basedondissipation............................................................9 Estimationsof basedonsurfaceflowdivergence.................................9 Influenceofsurfactants............................................................................................9 2 METHODS.........................................................................................................................................10 2.1 2.2 Directnumericalsimulations...................................................................................10 Fieldmeasurements.....................................................................................................12 2.2.1 2.2.2 2.2.3 Fluxchambermethod............................................................................................13 Dissipationrateparameterization...................................................................14 SurfacedivergenceparameterizationviaIRandPIV..............................14 3 CONTRIBUTIONS...........................................................................................................................15 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Generalgas‐exchangecharacteristicsforbuoyancydrivenflow............15 Scaling.................................................................................................................................16 Influenceofnaturalconvectiveforcingandsurfacemixedlayer
thicknessongastransfervelocity..........................................................................18 Influenceofgasdiffusivityandsurfactantsonthegastransfer
velocity...............................................................................................................................20 Influenceofcombinedwindandbuoyancyforcingonthegastransfer
velocity...............................................................................................................................24 Observationalresultsathigherwindspeeds,andspeculations
abouttheinfluenceofwaves....................................................................................27 Parameterizationsofthegastransfervelocity................................................29 3.7.1 3.7.2 3.7.3 Basedondiffusivity,surfactants,andshear‐stressand
buoyancyforcing......................................................................................................29 Basedondissipation,divergence,orheatflux...........................................30 Basedonthemeanwindspeed .................................................................31 4 SUMMARYANDCONCLUSIONS..............................................................................................32 5 FUTUREPERSPECTIVES............................................................................................................34 ACKNOWLEDGEMENTS.....................................................................................................................35 REFERENCES..........................................................................................................................................36 PartB.PaperI‐IV
VI
PartA
Synthesis
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
1.INTRODUCTION
1 INTRODUCTION
The concentrations of atmospheric carbon dioxide (CO ) and methane (CH ) are
increasing.Thisaffectse.g.,theclimateoftheearthandresults,throughair‐watergas
exchange, also in an acidification of aquatic systems such as oceans, lakes, and
watercourses.Thegasconcentrationandthegasexchangevary,however,largelyboth
temporallyandspatially(Figure1)andanincreasedknowledgeofthetransportand
accumulationprocessesofCO andCH isincreasinglyimportantinordertobeableto
make more precise predictions of the future climate and the aquatic environment.
Recent research has e.g., updated the global carbon cycle estimates (Figure 2),
resultingintheinsightthatthegas‐exchangefrominlandwatersplaysamuchlarger
role than previously believed [Bastviken et al., 2011; Ciais et al., 2013; Tranvik et al.,
2009]. These predictions are often based on numerical global and regional models
wherethegasflux usuallyareestimatedasaproductofagastransfervelocity, ,
andthegasconcentrationdifferencebetweenthewaterandair.Theuncertaintyinthe
estimationsof isthoughstilllargeforlowwindconditions,typicallyfoundininland
watersandoccasionallyintheoceans.Typicalareaswithlowaveragewindspeedsin
the oceans are found e.g., along the equator [Monahan, 2006]). This thesis discusses
what affects during low wind conditions and presents new parameterizations
whichcanbeusedtoestimateit.
Figure1. Estimatedcarbondioxidefluxaveraged overyear2000. (Figure13in[Takahashiet
al.,2009])
The introduction will continue with a more thorough background description, and a
motivation for the need of further understanding of the gas‐exchange. Then the gas
transfervelocitywillbedefinedandtheprocessesthataffectitwillbediscussed.The
introduction is closed by presenting some of the parametrizations presently being
used. Section 2 describes the numerical and field‐measurement methods used in the
papersthatconstitutethisthesis.Themaincontributionsoftheworkarepresentedin
section3.Finally,theconclusionsandfutureperspectivesaregiveninsection4.
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Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
1.INTRODUCTION
1.1 Backgroundandthesismotivation
Figure3showsaclassicdiagraminthecontextofclimatechangeandtheabundance
of greenhouse gases. The measurements are carried out at Mauna Loa at Big Island,
Hawaii. It represents the longest continuous measurement series of the atmospheric
concentrationofCO anditshowsacontinuousincreaseoftheannualaveragesallthe
way from the beginning of the measurements. The black curve is the yearly mean
while the blue curve shows the yearly variation. Similarly, recordings of the
concentration ofatmosphericCH showasteadyincrease(approximately 10%since
1988). An increase of atmospheric CO affects the aquatic systems by changing the
balanceofdissolvedCO inthewater.Althoughtheincrease naturallyisaffectsland
basedprocessesaswell,thesearenotfurthertreatedinthisthesis.Furthermore,itis
affectingtheglobalclimate.Differentregionalandglobalmodelsareusedtoenhance
theknowledgeofhowthisincreaseaffectstheworldnowandinthefuture.Figures1
and 2 show two examples of results from global models where Figure 1 shows the
spatialdistributionofthemeancarbondioxidefluxfortheyear2000[Takahashietal.,
2009]andFigure2showsanestimateoftheglobalcarboncyclewheretheredarrows
manifest the anthropogenically changed carbon fluxes and reservoir masses [Ciais et
al.,2013].
Figure2.“Simplifiedschematicoftheglobalcarboncycle.Numbersrepresentreservoirmass,
alsocalled’carbonstocks’inPgC(1
10
)andannualcarbonexchangefluxes(in
).Blacknumbersandarrowsindicatereservoirmassandexchangefluxesestimated
forthetimepriortotheindustrialEra,about1750...Redarrowsandnumbersindicateannual
’anthropogenic’fluxesaveragedoverthe2000‐2009timeperiod…”(Figure6.1inIPCC2013
[Ciaisetal.,2013]).
2
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
1.INTRODUCTION
The work summarized in this thesis aims at improving: (i) numerical model
performance, (ii) monitoring of gas exchange in water bodies, and (iii) the
understanding of the processes involved in interfacial gas exchange. The common
methodtoestimatetheair‐watergas‐exchangeinbothregionalandglobalmodelsis
tomultiply agastransfervelocitywith the gasconcentrationdifference inthewater
and in the atmosphere. In turn, the gas transfer velocity is often estimated as a
function of the wind speed. Although the wind speed is important for the gas‐
exchange,itcannot,especiallyduringlowwindconditions,beusedalonetoestimate
the transfervelocitywithout missingoutotherimportant factors,suchaswater‐side
natural convection and surfactants. This is also manifested through a widely varying
magnitude of between different parameterizations [Bade, 2009; Takahashi et al.,
2009;Wanninkhofetal.,2009].Thefirstgoaloftheworksummarizedinthisthesisis
thereforetoprovideabetterparameterizationofthegastransfervelocitytoregional
andglobalmodels.
On a smaller scale, it is also important to be able to understand the processes in
smallerwaterbodiese.g.,lakes,streams,andcoastalwaters.Thegasfluxisdifficultto
measure directly, whereas measuring secondary quantities (to be used for the flux
estimation) such as the gas concentration in the water, surface heat flux, and wind
speedareeasier.Thesecondgoalisthereforetoimprovemethodsformonitoringand
estimating fluxes based on secondary quantities. These estimates can then beside
improvingtheunderstandingoftheactualwaterbodyalsobeusedtoaggregatebetter
estimates of the global gas‐exchange. It can e.g., be noted that the freshwater
outgassing that was not included in the previous assessment by IPCC is of the same
orderofmagnitudeasthenetoceangasflux(Figure2).
The third goal with this thesis is to enhance the understanding of the small‐scale
processespresentinthevicinityoftheair‐waterinterface.Thisunderstandingofair‐
watergastransfercanalsobeusedoutsidethegeophysicalsciences,e.g.,inchemical
andenvironmentalengineering[JahneandHaussecker,1998].
Figure 3. Recorded concentrations of atmospheric carbon dioxide from 1958 up to now at
Mauna Loa, Hawaii, USA. [Dr. Pieter Tans, NOAA/ESRL (www.esrl.noaa.gov
/gmd/ccgg/trends/) and Dr. Ralph Keeling, Scripps Institution of Oceanography
(scrippsco2.ucsd.edu/)]
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Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
1.INTRODUCTION
1.2 Gasexchangeprinciples
The factors that influence the gas exchange across an air‐water interface can be
divided into (i) physical factors, i.e., advective/turbulent and molecular transport
processesand(ii)biochemicalfactors(however,notconsideredinthisthesis)which
typicallyarebiochemicalorbiologicalprocessesthateitherproduceorconsumegas.
ThetransfervelocityforthetwogreenhousegasesCO andCH iscontrolled(limited)
by the water side meaning that the flux is mainly limited by physical transport
processes in the water [Jahne and Haussecker, 1998]. As a note it can be mentioned
that the transfer of many other common properties such as heat, momentum and
watervaporarecontrolledbytheairside.Thepresentworkdoesonlyconsiderwater‐
side‐controlled gases and hence only the transport processes at the water side. The
physical factors that influence the exchange of these gases (controlled by the water‐
side)comprisee.g.,interfacialshearduetowindforcing,microscalebreakingwavesat
moderate wind speeds, breaking waves at high wind speeds, bubbles, raindrops,
surfactants,andconvectionduetosurfaceheatloss[Macintyreetal.,2002].
The actual interfacial gas‐exchange is, neglecting the effects of bubbles or raindrops,
maintainedbypuremoleculardiffusiondrivenbythegasconcentrationgradientjust
belowtheair‐waterinterface.Adiffusiveboundarylayer(Figure4)isformedabovea
turbulent layer where the turbulent motions are attenuated due to viscous damping
and the presence of the surface. This diffusive gas exchange in this layer can be
estimatedbyFick’slaw
, (1)
where isthemoleculardiffusivityand ⁄ istheverticalconcentrationgradient
(Figure 4). Even though the gas exchange is a molecular diffusive process in the
diffusiveboundarylayer,themagnitudeofthediffusiveexchangeishighlydependent
on the turbulence below. This is since besides being the main transport agent in the
turbulent layer, the turbulence is also to a large degree influencing the molecular
diffusive transport by affecting the diffusive boundary layer thickness, . Intense
turbulenceandadvectivemotionsresultinathinner ,alargerconcentrationgradient
⁄ andhenceahighergasexchange.
1.3 Forcingbywindandnaturalconvection
In this thesis we focus on the forcing from interfacial shear due to wind shear and
naturalconvectionduetosurfaceheatlosssincetheyareimportantduringlowwind
conditions.AschematicoftheseforcingsisshowninFigure4.
The air‐water velocity difference causes a shear stress, , at the air‐water interface.
Thisshearstressresultsinamomentumexchangebetweentheairandwater,thereby
affecting the velocity and turbulence intensity in both. This exchange is in the
numericalsimulations modeledwithaconstantshearstressat thesurfaceboundary
assumingsteadywindconditionsandnowaves,spray,bubbles,orrain.
4
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
1.INTRODUCTION
Clouds
z
z
QR,SW
U10
Reflection
QR,LW
Air
ϑCab
Turbulent
layer
QS , QL
Diffusive
layers
ϑCas
Water
Cws
Turbulent
layer
Absorption
Cwb
Mixed layer
depth
Velocity
Gas conc.
Figure 4. Conceptual diagram of air and water velocity, heat fluxes, and mean gas
concentration in the air and water. Sensible heat flux, , latent heat flux, , and net
longwave radiation, , , originate from the water surface whereas the shortwave solar
isthewindspeed10 abovethewatersurface.
radiation, , ,penetratesthesurface.
,
,
, and
are the bulk and surface gas‐concentrations in the water and air,
respectively. is the dimensionless Ostwald solubility coefficient. Advective transport
dominates in the turbulent layers, whereas diffusive transport dominates in the very thin
diffusive boundary layers (note the different vertical scale for the velocity gradient and the
gasconcentrationrepresentedwithabroken ‐axisintheverticaldirection,e.g.,thediffusive
boundarylayerthicknessfor
and
inwateristypicallyoftheorderof1mmorless).
Thewindspeedisoftenreferredtoas whichisthewindspeedat10 abovethe
watersurface.Inordertoexpresstheapplied in ,theequation
∙ ∗
κ ln
5.7
(2)
∗
canbeusedforneutralconditions[Csanady,2001].Herethesubscript denotetheair
side, istheheightabovetheair‐waterinterface, isthevonKarmanconstant,and is the air‐side kinematic viscosity. The water‐side and air‐side friction velocity is
⁄ ⁄ where and are the densities of air and water. The
related as ∗ ∗
appliedshearstresses,
∗ ,intheDNScasesinthepresentworkcorrespondto
up to approximately 2
according to Equation (2). Without going into too
muchdetailitcanbesaidthatstableairconditions(meaninganegativebuoyancyflux
intheair,i.e.,decreasingdensitywithheight)decreasetheturbulenceintensityinthe
air,whileanunstableincreasesit.Thisresultsinthatahigher isrequiredinorder
to maintain the same ∗ for stable compared to neutral conditions [Csanady, 2001;
Garratt,1992].Similarlyalower isrequiredinordertomaintainthesame ∗ for
unstablecomparedtoneutralconditions.
5
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
1.INTRODUCTION
Thenetheatfluxattheair‐waterinterfacecanbewrittenas
, ,
(3)
where the sensible heat flux QS is driven by the temperature difference between the
waterandair,thelatentheatfluxQLbywaterevaporation,andtheradiativeheatflux
QR,LWbylongwaveradiativetransfer.Theradiativeheatfluxisheredecomposedinto
shortwave,QR,SW,originatingfromthesolarirradianceandlongwaveradiativefluxes,
QR,LW. QS, QL, and QR,LW originate from the uppermost molecular layers of the water
whereas QR,SW penetrates the surface. The penetration depth of QR,SW depends on the
radiative power, the wave length, and water characteristics OBS [Fairall et al., 1996;
Jerlov,1976;Ohlmannetal.,2000;Wicketal.,2005].
Apositivenetheatflux, ,isdefinedinthepositivedirectionofthe –axis(upwards
from the interface). QS can be either positive or negative whereas QL and QR,LW are
typically positive (upwards). is usually positive which results in a cooling of the
surface, especially during nighttime resulting in a so‐called cool skin at the surface
[Fairalletal.,1996;SolovievandSchlussel,1994].Theannualmeanisintherangeof
40
230
[Stewart,2008].Theshortwaveradiationcanespeciallyondays
without clouds, depending on the vertical distribution of the radiative absorption,
influence the buoyancy flux and thereby the cool skin. The heat flux condition in the
present work represents a situation with an even vertical distribution of the
absorptionofQR,SW.ThisconditionincludesthecasewithlimitedQR,SWasduringnight
time.Notealsothat thebuoyancyfluxin theatmosphericboundarylayerconsistsof
thesensibleandlatentheatfluxesonly,whichimpliesthatthebuoyancyfluxesabove
andbelowthesurfacearedifferent.
1.4 Gastransfervelocity
Equation (1) is difficult to use since it is difficult to measure the gas concentration
gradientintheverythindiffusiveboundarylayer,whichhasthickness intheorder
of 1 mm or less. For estimations of the air‐water gas exchange, equation (1) is
thereforeoftenrestatedinto
,
(4)
in order to be able to use the more easily measured bulk and air gas‐concentrations
instead.Here isthegastransfervelocity,
isthegasconcentrationinthewater
underthediffusiveboundarylayer, isthegasconcentrationintheairatthewater
surface, and is the dimensionless Ostwald solubility coefficient (Figure 5). Even
thoughitiseasiertouse
and insteadofmeasuringtheconcentrationgradient,
itisnowinsteadachallengetoestimate .
6
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
1.INTRODUCTION
Diffusive layer
thickness, δ
ϑCas
Turbulent layer
Water
Air
z
∆C
∆C
Cwb
Figure5.Aschematicsnapshotofthegasconcentration attwodifferentlocationsforagas
with a gas‐flux that is controlled by the water side. The gas concentration gradients are
assumed to be small in the air. The momentary gas concentration, , and the diffusive
boundarylayerthickness, ,aregiveninredwhilethemeanquantitiesaregiveningrey.
isthebulkgas‐concentrationinthewaterand isthesurfacegas‐concentrationintheair.
is the dimensionless Ostwald solubility coefficient. The water‐side gas concentration
gradient ⁄ variesduetothevaryingdiffusiveboundarylayerthickness.
In sections 1.4.1‐1.4.4 four commonly used parameterizations of estimating , are
described, i.e., (1) based on wind speed, (2) based on surfaceheat flux, (3) based on
rateofturbulentkineticenergydissipation,and(4)basedonsurfaceflowdivergence.
All these parameterizations have a term that takes the influence of the molecular
diffusivityandtheabundanceofsurfactantsatthesurfaceintoaccount.Thisinfluence
is therefore generally discussed in section 1.4.5. Although there are other processes
thatinfluencethegas‐exchange,suchaswhitecapping,seaspray,bubbles,rain,these
are not taken into account in this work since white capping, sea spray, and bubbles
from waves are not present during low wind conditions, and ebullition is not
controlledbythesurfacediffusiveboundary,andrainisdifficulttostudyinDNS.
1.4.1
Estimationsof
basedonwindspeed
There has been many attempts to estimate based on the wind speed 10 meters
above thesurface,referredtoas
[e.g.,Bade, 2009;Wanninkhofetal.,2009].Two
parameterizationsoftenusedare
0.215 .
2.07,
(5)
,
,
7
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
1.INTRODUCTION
presentedbyColeandCaraco[1998]forinlandwaters,and
0.1
0.064
0.011
3,
,
,
(6)
presentedbyWanninkhofetal.[2009]foroceanconditions.Herethetransfervelocity
is given in ( ) and the wind speed is given in (
). It can be seen that both
these equations have constants implying that there is a gas flux also for zero‐wind
conditions. This gas flux (and gas transfer velocity) must then be due to processes
enhanced by other means than wind speed, e.g., buoyancy flux. This is of course
problematicsincethevariationine.g.,thebuoyancyfluxisnotbedescribedinthese
equations.
Equations(5)and(6)aregivenforSchmidtnumbers
600and660representing
⁄ expresstheratio
at20°Cinfreshwaterandseawaterrespectively.Here
of the kinematic viscosity and molecular diffusivity. The relation between two
transfer velocities with different gas‐water properties are generally expressed via
theirdifferentSchmidtnumbersas
,
,
,
(7)
where is an exponent that depends on the surface characteristics. The exponent is
usually between 1⁄2 and 2⁄3 and represents the Schmidt number dependency and
therebythemoleculardiffusivitydependencyonthetransfervelocity.
1.4.2
Estimationsof
basedonsurfaceheatflux
The heat transfer velocity,
, and an expression for the conversion between heat
and gas through their and Prandtl number, , have been used [e.g., Frew et al.,
2004;Garbeetal.,2003;Hausseckeretal.,1998]toestimatethegastransfervelocity
as
,
,
.
(8)
⁄ istheSchmidtnumberforheatusingthethermaldiffusivity instead
Here
of the molecular diffusivity used in .
is a transfer velocity constant for the
parameterizationbasedonheatflux where isthespecificheatcapacity,and is
the surface skin‐bulk temperature difference across the thermal boundary layer.
Equation(8)isbasedontheassumptionthatthethermaldiffusiveboundarylayeris
controlled by the same processes as the gas diffusive boundary layers. There are,
however, three main differences: (i) Heat influences the buoyancy and thereby the
turbulentmotionsbelowthesurface,(ii)thesurfaceboundaryconditionsforgasand
heatdiffersbecausethetransportofgasiscontrolledbythewatersideandheatbythe
airside,and(iii)thediffusivitiescandifferbyordersofmagnitudewith
10 and
10 dependingonwhichgasitis.Inspiteofthesedifferences,e.g.,Jahne
etal.[1989]haveshownagoodagreementforoxygen(
10 )betweendirectly
measured transfer velocities and transfer velocities extrapolated from heat transfer
velocities.
8
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
1.INTRODUCTION
1.4.3
Estimationsof
basedondissipation
Theparameterizationusingtherateofturbulentkineticenergydissipationisbasedon
the theoretical framework of the eddy cell model [Fortescue and Pearson, 1967] but
withtheassumptionthatitratheristhesmallscaledissipativeeddiesthanthelarge
scaleeddiesthatarethemaintransportationagents[Banerjeeetal.,1968;Lamontand
Scott, 1970]. This assumption and the assumption that the turbulence can be
describedwithastandardturbulencespectrumyieldsthegastransfervelocityas
⁄
. (9)
,
Here
isatransfervelocityconstantforthedissipationparameterizationand is
therateofkineticenergydissipation.LamontandScott[1970]foundtheappropriate
valuestobe
1⁄2and2⁄3forfreefluidandsolidsurfacesrespectively.Inspiteof
some problems with the assumptions during natural conditions, the dissipation
parameterizationhasperformedwellinmanycasese.g.,PaperIV,Zappaetal.[2003],
andZappaetal.[2007].
1.4.4
Estimationsof
basedonsurfaceflowdivergence
The parameterization using the horizontal flow divergence,
thesurfaceisgivenby
⁄
,
⁄
⁄
, at
(10)
where
istheroot‐mean‐square,rms,ofthesurfaceflowdivergenceand and isatransfer
arethehorizontalvelocitiesinthe ‐and ‐directionsatthesurface.
velocityconstantfortheparameterizationbasedondivergence.Theparameterization
has been used in many studies [e.g., Banerjee et al., 2004; Calmet and Magnaudet,
1998;McKennaandMcGillis,2004]andtheoreticallyderivedbye.g.,Ledwell[1984].
1.4.5
Influenceofsurfactants
Surfactantsaresurface‐activechemicalagentsthatgenerallyreducegasexchange[e.g.,
Bade, 2009; McKenna and McGillis, 2004; Wanninkhof et al., 2009]. They are almost
always present in natural waters and occasionally the amount of surfactants even
forms a surface film and then requires an extra layer to represent the surfactants
when estimating the gas‐exchange. Also in smaller abundances, which is the usual
situation, they act to change the hydrodynamic conditions of the air‐water interface
[McKennaandMcGillis,2004].Theflowatthesurface,includingeddies,redistributes
the surfactant concentration and makes it patchy. A surfactant lowers the surface
tension,andsincethesurfactantconcentrationnowispatchy,thesurfacetensionwill
varyoverthesurface.Avaryingsurfacetensionresultsinelasticforcesthatattenuate
theturbulenteddies.Thisattenuationinfluencesthegasexchange,inparticularforthe
gases with thin diffusive boundary layers, i.e. those with high Schmidt numbers. The
surfactantinfluenceonthegas‐fluxanditsattenuationcanbediscussedinthelightof
thetheoreticalworkofLedwell[1984]wheretheinfluenceofmoleculardiffusivityon
the gas transfer velocity is studied and compared for both slip and no‐slip boundary
conditions.ThisgivesSchmidtnumberexponents
1⁄2foracleansurfaceand2⁄3
for a surface with surfactants, if a clean surface is represented by a slip boundary
condition (no attenuation of the horizontal components of the surface flow), and a
9
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
2.METHODS
surface with a large abundance of surfactants is represented by a no‐slip boundary
condition(horizontalcomponentsofthesurfaceflowiszero).
2 METHODS
2.1 Directnumericalsimulations
PaperI‐IIIusedirectnumericalsimulations,DNS,tostudyhowtheturbulenceandthe
heat‐andgas‐transportsdependondifferentflowconditions.Thegasismodeledasa
passivescalarwhichcanbeseenasaninertgas.Theflowconditionsarevariedvia(i)
different surface boundary conditions for the velocity (including shear and
surfactants) and the temperature (surface heat flux), (ii) different depths, and (iii)
differentmoleculardiffusivitiesforthescalar.
ThecomputationaldomaincanschematicallybeseeninFigure6.Thisschematicisin
general valid for the Papers I‐III. However, the horizontal plane in Paper I‐II is
quadratic since all the boundary conditions are identical in the spanwise and
streamwise directions in these papers (no surface shear‐stress). Furthermore, the ‐
and ‐directionsaredefinedintheverticalandthespanwisedirectionsinPaperII.
Figure 6. Computational domain for the cases with combined buoyancy and shear stress
0.1204 ,
3
and
inthedepth,
forcing.Thedomainsizeisgivenby
streamwise, and spanwise direction respectively. The surface is subject to a constant
outward‐going heat flux, , and a constant scalar concentration, , while the bottom is
subjecttozerofluxboundaryconditions.Thevelocityboundaryconditionsareeitherslip,no‐
slip or constant shear stress, , at the surface boundary and slip at the bottom boundary.
Periodic(cyclic)boundaryconditionsareusedforallvariablesinthehorizontal( ‐and ‐)
directions.Thetemperaturefieldisasnapshotfromcase240 ( ∗ 240withbuoyancy,
seesection3).(RedrawnfromFigure1inPaperIII).
10
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
2.METHODS
DNSimplythatthereisnoturbulencemodelthatmodelsorcreatesturbulenceinthe
computation. The turbulence is instead “naturally” invoked due to flow instabilities
thatariseduetotheflowforcing.TheDNSmethodisusedinordertobeabletostudy
theactualturbulenceanditsinfluenceonthegasexchangebysolvingthesmall‐scale
turbulent motions instead of using a turbulence model. The forcing is in Paper I‐III
eithernaturalconvection(buoyancy)orsurfaceshearstressoracombinationofboth.
The lack of a turbulence model sets very high requirements on the computational
mesh resolution since all the fluid motions and eddies must be resolved all the way
down to the sizes where the turbulence dissipates to heat. An extensive mesh
resolution and domain aspect‐ratio study was therefore performed in Paper I. The
resulting mesh resolution for Paper I and III can schematically be seen in the front
cornerofthedomaininFigure6.Hereonlyeveryfourthgridlineareplottedsincethe
mesh is very fine and the grid lines otherwise would be difficult to see. The mesh is
equidistant in the horizontal plane, and in Paper I and III densified towards the
surface. In Paper II the mesh is densified towards both the surface and bottom. The
verticalmeshspacingclosetothesurfaceis,though,thesameforthemeshesusedin
PaperI‐III.
InPaperIandIIIafinite‐volumemethodisusedwhereasapseudo‐spectralmethodis
used in Paper II. Please also refer to Paper I‐III where these methods as well as the
spaceandtimediscretizationsarediscussedinmoredetail.
InalltheDNS‐papers(I‐III)theNavier‐Stokesequations
U
k U∙ U
Π
U
(11)
and
∙U
0
(12)
using the Boussinesq approximation are solved in conjunction with the transport
equation
(13)
U∙
forthetemperature .InPaperIandIIIatransportequation
U∙ S
(14)
forapassivescalar issolvedaswell.HereU= , ,
isthefluidvelocitywherethe
components are given in ‐, ‐, and ‐directions respectively and is the time.
⁄
Π
, is the pressure, is a reference density, g is the acceleration of
gravity, k is a unit vector in the vertical direction, is the kinematic viscosity,
⁄
| isthethermalexpansioncoefficient, isthedensity, isthe
1⁄
temperature, isareferencetemperature, isthethermaldiffusivity, isthescalar
concentration, and is the molecular diffusivity of the scalar in water. In order to
sustainaconstantmeantemperatureinthedomainanevenlydistributedheatsource
isaddedtoequation(13)tobalancetheheatfluxthroughthesurface.Similarlyan
evenly distributed pressure gradient (not shown) is added to equation (11) in the
direction opposite to the surface shear stress cases in Paper III. The scalar source
⁄ isusedtoimposethescalarfluxthroughthesurfaceand isthearea‐
11
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
2.METHODS
averagedmeanscalarfluxoncesteady‐stateisachieved.Inthefollowing, , , , ,
and areusedtorepresentthefluctuatingpartsof , ,
, ,and respectively.
The surface boundary is flat, assuming that the surface deflection is negligible. The
surface boundary condition for the vertical velocity is therefore
0 for all cases.
The boundary conditions for the horizontal velocities are for the pure convection
⁄
drivencaseswithoutsurfactants(PaperI)eitheraslip( ⁄
0 orano‐
slip (
0 boundary condition. In Paper II the surfactant boundary conditions
⁄
⁄ and
⁄
⁄ where
for the horizontal velocities are
⁄
. The surface tension is a function of the surfactant concentration Γ
andislinearizedaroundtheinitialsurface‐tension .ForthecasesinPaperIIIdriven
by pure surface shear‐stress or by a combination of natural convection and surface
shear‐stress there is a slip boundary condition in the y‐direction and a shear‐stress
⁄ ). Here is the surface shear
boundary condition in the ‐direction ( ⁄
stress.Thebottomboundaryisassumedtobestress‐freeandismodelledwithaslip
boundaryconditionforallcases.
⁄ assuming a
The surface boundary condition for the temperature is ⁄
constant surface heat flux, [Soloviev and Schlussel, 1994]. Here λ is the thermal
conductivity. The surface boundary condition for the scalar is a constant scalar
concentration
assuming that the air‐water gas exchange is controlled by the
water‐side [Jahne and Haussecker, 1998]. The bottom boundary conditions for the
⁄
temperature and scalar are ⁄
0 assuming no heat or gas exchange
throughthatboundary.
Periodic (cyclic) boundary conditions are used for all variables in the horizontal ( ‐
and ‐)directions.
2.2 Fieldmeasurements
The field measurements reported in Paper IV were performed in order to compare
different methods of estimating in the field. These methods comprise (i) flux
chamber measurements, (ii) parameterization of as a function of the rate of
turbulent kinetic energy dissipation, and (iii) parameterization of as a function of
thesurfacedivergence.Herethesurfacedivergencewasestimatedviaparticleimage
velocimetry (PIV) of the surface temperature structures recorded by IR imagery. In
addition to these parameterizations a number of environmental parameters were
measured in an attempt to find other methods of estimating . These parameters
comprise e.g., bulk temperature (mean and rms), surface temperature (mean and
rms), IR surface velocity mapping (mean and rms), mean IR coherent structure size,
and wave height. The measurements were performed in August 17‐18 2010 in
Gullmarsfjord at the Bornö marine research station close to Lysekil, north‐west of
Gothenburg, Sweden. The measurement setup at the suspension bridge at Bornö,
where the depth is about 33 m, is sketched in Figure 7. The simultaneous
measurementswererecordedduringonediurnalcycle.
12
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
2.METHODS
Figure 7. Illustration of the instrument setup at the Bornö suspension bridge. Three
instruments were used simultaneously to measure : An IR camera, an ADV, and a flux
chamberwithtubesforcontinuousmeasurements.(Figure1inPaperIV).
2.2.1
Fluxchambermethod
Here wasestimatedbymeasurementsofthegasfluxacrosstheair‐waterinterface
and the gas concentration in the water and air inside the chamber. The gas flux was
estimated by measuring the concentration change ⁄ inside a round lightweight
chamber that was placed at the water surface. The concentration change was then
transformedintofluxusingthecommongaslaw,thevolumeofthechamber,andthe
surface water area covered by the chamber. The implicit assumption is that the
concentrationchangeiscausedbyfluxesthroughthesurface,andthatthefluxinside
the chamber is similar to that outside the chamber. The concentration at the surface
(
inequation(4))wasestimatedastheequilibriumconcentrationofthegasatthe
surfaceusingtheinitialgasconcentrationinthechamberandHenry’slaw.Here,the
assumption is that the gas concentration outside the chamber is equal to the initial
concentrationinthechamber.Thebulkgasconcentrationinthesurfacewater(
in
equation (4)) was measured at the start and end of each measurement period at a
depthofapproximately40cm.AlthoughfluxesofbothCO andCH weremeasured,
onlyCH ‐fluxeswereusedforestimating .Therationaleisthattherewasalwaysa
significant positive net flux of CH into the chamber while the fluxes of CO showed
more variation with both release from and uptake to the water with intermediate
periodsofnosignificantfluxduringthemeasurementperiod.Thetransfervelocityfor
accordingtoequation(7)with
1⁄2.
CH wastransformedinto
The edges of the chamber was submerged only 2.5 cm into the water due to the
lightweight chamber construction and the chamber was attached to the bridge with
13
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
2.METHODS
thin, slack strings enabling it to move with the water as freely as possible. This has
previouslybeenshowntobesuccessfulforchamberperformance[Coleetal.,2010].
2.2.2
Dissipationrateparameterization
The rate of the turbulent kinetic energy dissipation, , was estimated from the
turbulence spectra at approximately 0.3 m depth. The transfer velocity was then
calculated with equation (9) with
0.42 as found by Zappa et al. [2007]. The
spectra were calculated from 3D velocity vector time series recorded by the use of
acousticdopplervelocimetry(ADV).TheADVwasmountedlookingupwardsonataut
linehangingfromthebridge.AfinontheADVensuredthatthesensorwasupstream
oftheline(undisturbed).
2.2.3
SurfacedivergenceparameterizationviaIRandPIV
Ithasbeenshowninlaboratoryexperimentsthatparticleimagevelocimetry(PIV)can
be used to determine the surface divergence. Veron et al. [2008] extended this idea,
and used infrared (IR) imagery of the ocean surface to estimate surface velocity,
vorticity, and surface divergence. The idea is that the surface temperature (heat
pattern)measuredwithanIRcameracanbeusedasafluidflowtracer,seeFigure8.
This was in Paper IV also confirmed to be the case by comparing (directly in the IR
imagesequences)themotionofthebubblesandfoamatthesurfacewiththemotion
of the heat pattern. It should, however, be noted that thermal IR radiation has very
short transmission lengths in water (order of 1 100 , [e.g., Garbe, 2001]) which
meansthatPIVofheat‐patternsestimatesthevelocitiesintheverytopsurfacewater
(skin)whichinturnmaybedifferentfromthevelocitiesjustbelowthesurface[Volino
andSmith,1999].Theuseoftheheatpatternasafluidflowtracercanbeproblematic
for certain flow conditions, e.g., pure natural convection where there can be a
horizontal flow inside a more or less stationary plume as will be seen in section 3.1.
That type of flow would not be detected with IR/PIV, which only recognizes the
motionoftemperatureanomaliessuchasthestreaksofthecoldwaterenclosingthe
warm plume. This problem is decreasing for cases where there is more than pure
natural convection forcing. It should also be noted that the temporal and spatial
resolutionoftheIRimageryandthePIVmustbehighenoughtoestimatethesurface
divergenceproperly.
Figure 8. Example of a temperature field from an IR image. The average field of view is
95 88 .(PartofFigure4inPaperIV).
14
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
3.CONTRIBUTIONS
3 CONTRIBUTIONS
InPaperI‐IVavastamount ofresultsare presented,discussionsareperformed,and
conclusions are drawn. In this section of the thesis an effort to synthesize all this in
majorcontributionshasbeenmade.Inordertodosoanewnumberingsystemforall
the numerical cases could have been presented. This could, however, also lead to
misinterpretations since all the cases are more thoroughly described in each paper
thaninthissynthetizationoftheresults.Hencethecaseswerechosentobepresented
herewiththesamelabelingasinthepapersenclosed.
The cases in Paper I are named with (i) a letter for lip or for o‐slip surface
velocity boundary conditions, (ii) a number describing the computational domain
aspectratio,(iii)aletter or forthe asecaseora inemeshresolution,(iv)anda
letter or fora eepora hallowdomainor or fora owor ighsurfaceheat
flux.Thecasename 2 representsi.e.,acasewithaslipsurfacevelocityboundary
condition,adomainaspectratioof2,abasecasemeshresolution,andahighsurface
heatflux.
ThewindforcingisinPaperIIImodeledasafixedshearstress
∗ .Thecasesare
named with (i) a number for the shear‐based Reynolds number for ∗
∗ ⁄ ,
which describes the ratio between inertial and viscous forces, and (ii) a letter for
Buoyancy or letters
for No‐Buoyancy. In the no‐buoyancy cases the gravitational
acceleration was set to zero, so the temperature acted as a passive tracer only. The
domainaspectratio,domaindepth,andthemeshresolutionwasthesameforallcases.
Furthermore,thecase0 inPaperIIIisidenticalwiththecase 2 inPaperI.
Intheplotstocome, ̅and〈 〉denotevolumeandhorizontalareaensemblemeanof
anarbitraryvariable ,respectively.
3.1 Generalgas‐exchangecharacteristicsforbuoyancydrivenflow
InFigure9asnapshotofcase0 (slipboundaryconditionandbasecaseheatfluxand
meshresolution)ispresentedinordertogiveanintroductiontomanyoftheresults
presentedlaterinthissection.
The surface heat flux cools the surface water and thereby makes it denser. Due to
instabilitiesthisdenserwaterthenstartstodescendinthinplumessketchedasblue
arrows.Thedescendingplumessetupahorizontalflowsketchedwithyellowarrows
and an ascending flow of warmer water between the descending plumes. The
descending plumes are typically much thinner than the ascending warm water. The
horizontal and ascending flow typically stretch and squeeze the diffusive boundary
layer and thereby make it thinner. The patches with thin diffusive layer thicknesses
areherevisibleas“islands”penetratingthemeanthickness,separatedwithtrenches
oflimitedverticaldiffusivetransport.
15
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
3.CONTRIBUTIONS
a)
d)
F ⁄F
0
2
γ⁄γ
-2.5
c)
1
b)
̅
T
-4
T ⁄T
Depth mm
0.5
0
10
Figure 9. Snapshot for the case 0 (pure buoyancy forcing with slip surface boundary
⁄ and the surface water
condition). (a) The normalized temperature field
velocities. Blue and yellow arrows schematically represent the descending plumes and the
horizontalflowclosetothesurface.(b)Themeanandmomentarydiffusiveboundarylayer
thickness, ̅and ,wherethethicknessisdefinedaswhere5%ofthetotalverticaltransport
is diffusive. The iso‐surface of the momentary diffusive layer is colored by the actual layer
thicknesswherecoldercolormeanssmallerthicknesses.Theverticaldimensionintheplotis
scaledbyfiveforbettervisibility.(c)Thetemperaturefieldandcontoursofthenormalized
horizontal flow divergence, ⁄ , at the surface. (d) The surface‐normal scalar transport,
⁄ ,for
7acrossthesurface.
Figure5sketchesavaryingdiffusivelayerdepthsimilartowhatwouldbetheresultsif
Figure9bwasslicedwithaverticalplane.ItisseeninFigure5thatasmalllayerdepth
results in a higher concentration gradient, which in turn results in an increased
surface‐normal diffusive transport (Figure 9d). This increased gas flux can now in
Figure9dbeseentocoincidewiththe“islands”withthinboundarylayerthicknessin
Figure 9b. This is the reason for the good correlation between the temperature, and
horizontalflowdivergencefieldsthatcanbeseeninFigures9a,candeventuallyalso
between the momentary diffusive layer depth and surface‐normal scalar flux seen in
Figures9b,d.
3.2 Scaling
Nondimensional numbers and scales for e.g., length, time, velocity, temperature, and
scalar concentration can be used as tools to facilitate the understanding of which
processes and scales that are important in determining the transfer velocity. Paper I
presents scales that are appropriate for the analysis of flows driven by pure natural
convection(buoyancyforcing).Thesescales,presentedinTable1,aredividedininner
16
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
3.CONTRIBUTIONS
andouterscales.Theinnerscalesarebasedontheassumptionthatitistheprocesses
inthevicinityofthesurfacethatcontrolthegastransferwhereastheouterscalesare
based on the assumption that it is the whole domain (surface mixed layer) that
controlsthegastransfer.Theinnerscaleswillbeusedtodiscusstheresultsinsections
3.3 and 3.4 since these scales were found in Paper I to best scale the processes of
importanceforthegastransfervelocity.
Table1Scalingschemes
Scheme
Length, Velocity,
Time,
Temp.,
⁄
Inner
Outer
∗
/
∗
⁄
Scalar, ⁄
/
⁄
∗
∗
⁄
Div.,γ
/
∗
⁄
1⁄
1⁄ ∗ Themixinglayerdepthisinthesesimulationsassumedtobethedomaindepth .
Itismoreintriguingtofindsuitablescalesforthecaseswithcombinedforcing.Aflow
dominatedbybuoyancyforcingshouldusetheabovescaleswhileaflowdominatedby
shearforcingshouldusetheshearscalespresentedinPaperIII.Thesescalesandthe
transitionfromonesetofscalestotheotherarediscussedinmoredetailinPaperIII.
Furthermore,dimensionalanalysisinpaperIIIshowsthatthegastransfervelocityfor
acasewithcombinedforcingfrombothbuoyancyandshearstresscanbeexpressedin
non‐dimensionalrelationshipsaccordingto
, , ∗,
.
(15)
∗
where
havebeendefinedabove.TheReynoldsnumber
and
∗
∗
(16)
⁄ , represents the ratio between the inertial
based on the friction velocity, ∗
and the viscous forces. Here, , is the depth of the surface mixed‐layer (generally
considered as a quasi‐homogenous region in the upper ocean characterized of little
variation in density and temperature with depth [Kara et al., 2000]). It is here
assumedtoberepresentedbythecomputationaldomaindepth .Thevalidityofthis
assumption is discussed in section 3.3. The fourth variable is a Richardson number
definedas
,
(17)
∗
⁄ is
representingtheratiobetweenthebuoyancyandshearforcing.Here
thebuoyancyfluxjustbelowthesurface. willbeusedinsection3.5asameasureof
thetransitionfrombuoyancy‐toshear‐dominatedgastransfer.
17
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
3.CONTRIBUTIONS
3.3 Influenceofnaturalconvectiveforcingandsurfacemixedlayer
thicknessongastransfervelocity
The momentary temperature fields at the surface for three different surface heat
fluxes aregiveninFigure10.Theupper row(Figures10a‐c)showsthetemperature
variation in dimensional units (°C) whereas the temperature has been normalized
withtheinnertemperaturescale inthelowerrow(Figures10d‐f).Itcaninbeseen
thattheflowfeaturestypicallybecomesmallerforstrongernaturalconvectionforcing.
The temperature variation is increasing at the same time (i.e., a higher surface heat
flux gives higher buoyancy flux which results in smaller flow features and larger
temperature variation). The larger temperature variation is seen as an increasing
contrast in Figures 10a to 10c The strength and validation of the scaling practice is
showninFigures10d‐fwhereitisseenthatthetemperaturevariationscaleswellwith
⁄
theinnertemperaturescale
∝
(approximatelythesamecontrast,whichhere
representsthenormalizedtemperaturevariation).
Statistics for temperature and scalar concentrations for these cases with a heat flux
variationaswellasforthecaseswithadepthvariationarepresentedinFigure11.It
showsthehorizontallyaveragedrmsandmeanvaluesofthetemperatureandscalar
concentrations. The convective inner scales for length, temperature, and scalar
concentration have been used for the normalization. It can be seen that these scales
collapsetheresultsforboththetemperatureandscalarconcentrationverywell.This
isinterestingsincealloftheinnerscales( , ,and )thatareusedinFigure11,
arefunctionsofeithertheheatorscalarflux,and , , ,and butnotthevertical
dimensionofthecomputationaldomain.ThisisalsomanifestedinFigure9inPaperI
where the transfer velocity dependence of the buoyancy flux and domain depth is
presented.Thereisacleartransfervelocitydependenceofthebuoyancyflux ∝ ⁄ butonlyaverylimiteddependenceofthedomaindepth.Furthermore,itisshownin
PaperIthatouterscaling,thatincludesthedomaindepthforbuoyancydrivenflows,
doesnotscalethenear‐surfaceprocessesasaptastheinnerscaling.Thisimpliesthat,
(i) for large enough depths, the surface mixed layer thickness does not influence the
gas transfer velocity, (ii) the gas transfer velocity is a function of the buoyancy flux,
and(iii)thedomaindepthinthesimulationsislargeenoughtomodeltheprocessesin
thesurfacemixedlayerfornear‐surfaceprocessesastheinterfacialgas‐fluxprocesses.
18
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
3.CONTRIBUTIONS
a)
d)
T
T
b)
Q
50 Wm
c)
100 Wm
Q
Q
200 Wm
f)
e)
T
T ⁄T Figure10.Momentarytemperaturefieldsatthesurfaceforthreedifferentsurfaceheatfluxes
where
100
isthebasecaseheatflux.Theupperrow(a‐c)showsthetemperature
⁄ withacommon
andthelowerrow(d‐f)showsthenormalizedtemperature
⁄
is the convective inner
scale. is the domain mean temperature and
scale.Thesecasesarepresentedas 2 , 2 ,and 2 inPaperI.
Furthermore,Figure11showsthat
and
differclosetothesurfaceduetothe
twodifferentsurfaceboundaryconditionsforthetemperature(constantheatfluxi.e.
constanttemperaturegradient)andscalar(constantconcentration).Nevertheless,the
figurealsoshowsthatthemeangradientsareverysimilar.Thisisinterestingfroma
gas‐transfer‐velocity point of view, since the mean temperature magnitudes, as a
function of the depth, are used in the parameterization based on the heat flux
(equation (8)). This high similarity therefore gives reason to believe that the
parameterizationbasedontheheatfluxwillwork,asdiscussedfurtherinSection3.7.
19
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
3.CONTRIBUTIONS
0
0
−10
−2
−20
mean
rms
−4
−30
−6
z/L+
−40
−8
−50
−60
−10
−3
−2
−1
0
1
Base
−70
Low Q0
−80
High Q0
Shallow
−90
Deep
−100
−3
−2
〈T〉
T ⁄T , 〈s〉
−1
s̅ ⁄s , T
0
⁄T , s
⁄s 1
Figure 11. Mean and rms temperature (black) and scalar concentration (blue) normalized
withconvectiveinnerscales, and .Thedepthisnormalizedwith .Theinsetisazoom
ofthenear‐surfacearea.Thedifferentcasesaredifficulttodistinguishintheplotsincethe
normalizationcollapsetheresultsverywell.Thesecasesarepresentedas 2 , 2 , 2 ,
2 ,and 2 inPaperI.
3.4 Influenceofgasdiffusivityandsurfactantsonthegastransfer
velocity
TheinfluenceofgasdiffusivitywasstudiedinPaperIbymodelingscalarswith
7,
⁄ numberswerechosenas(i)oneequivalent
150,and600respectively.These
⁄ numberwhichcanbeseenasthe numberforheat,(ii)onethat
withthe
isequaltothe numberusuallyusedforCO infreshwater,and(iii)onein‐between.
AccordingtoFickslawgiveninequation(1),thediffusivegasfluxdependslinearlyon
thediffusivity.Thismeansingeneralthat,inordertomaintainthesamegasflux,the
gasconcentrationgradientmustbelargerforagaswithlowmoleculardiffusivitythan
for a gas with high molecular diffusivity. A larger concentration gradient can be
achieved by either a thinner boundary layer or a larger concentration difference
across the layer. It is shown in Figures 12a‐b to be both. Here both the diffusive
boundarylayerthickness,
,isthinnerandtheconcentrationdifferenceislargerfor
ascalar with
600thanforascalarwith
150andevenmoresofor
7.
This tendency can be seen to be amplified for the no‐slip condition (Figure 12b)
compared to the slip condition (Figure 12a). Both the changing boundary‐thickness
andconcentration‐differencescalewellwith and with
1⁄2and
2⁄3for
slipandno‐slip,respectively(Figures12c‐d).
20
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
3.CONTRIBUTIONS
0
−1
δ600
δ150
a)
b)
δ600
δ150
depth[mm]
−2
−3
−4
δ7
−5
−6
−7
−2
Sc = 7
Sc = 7
Sc = 150
Sc = 150
Sc = 600
Sc = 600
−1.5
−1
〈s〉
−0.5
0 −6
−5
−4
−3
〈s〉
s̅
δ7
−2
−1
0
s̅ 0
−1
c)
d)
−2
−3
−4
z/L
+
−5
−6
−7
δ600
Sc = 7
−8
−9
−10
−3
δ150
δ600
δ7
δ7
δ150
−2.5
Sc = 7
Sc = 150
Sc = 150
Sc = 600
Sc = 600
−2
−1.5
〈s〉
−1
s̅ ⁄s −0.5
0
−4
−3
−2
〈s〉
−1
0
s̅ ⁄s Figure12. Meanscalarconcentrationforslipandno‐slipboundaryconditions.Concentrations
andthesublayerthicknesses, ,aregivenforscalarswith numbersequalto7,150and600.
(a) Slip boundary conditions.The results for 2 (basecasemeshresolution)arepresented
withafulllinewhiletheresultsfor 2 (finehorizontalmeshresolution)arepresentedwitha
dash‐dottedline.Theresultsareverysimilarandthereforethefullanddash‐dottedlinesare
difficult to distinguish in the plot. (b) No‐slip boundary conditions, 2 . (c‐d) as (a‐b) but
scaled with inner scales and with
1⁄2 and
2⁄3 for slip and no‐slip boundary
conditions,respectively.(PartofFigure13inPaperI)
Ahigher number(i.e.lowerdiffusivity)requiresingeneralafinermeshresolution
inordertobefullyresolved.Theeffectofatoocoarsemeshcanbeseen(Figure12in
PaperI)asoscillationsintheconcentrationforthehigher numbers.Itis,however,
arguedwithsupportfromthemeshsensitivityanalysis,alsoperformedinPaperI,that
theuncertaintyintheresultsduetotoocoarsemeshresolutionisacceptableforthe
averagedflowquantitiesofinterestforthegas‐exchangeevaluation.Itcane.g.,beseen
21
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
3.CONTRIBUTIONS
inFigure12athatcase 2 and 2 givevirtuallythesamescalarmeanconcentration
although 2 hasafinermeshresolutionthanthebasecase 2 .
Theinfluenceoftheabundanceofsurfactantsforflowsdrivenbynaturalconvectionis
studiedinPaperII.Theresultsshowthatthesurfactantinfluencedependsbothonthe
meansurfactantabundanceatthesurfaceandontheturbulentconditionsintheflow
underneath the surface. Furthermore, it is possible to estimate this influence by a
turbulence‐surfactantparameter expressingtheratioofelastictoinertialforces.By
increasingthesurfactantabundanceitisalsofoundthatthereeventuallyisasaturated
surfactant abundance. At this abundance, the studied flow parameters (i.e. rms
velocity, rms and mean temperature, dissipation and mean absolute divergence) are
not affected further for an increased abundance. It is further shown that there is a
smoothtransitionfortheseflowparametersfromthecleantothesaturatedsurfactant
condition(Figure4inPaperI).
InPaperItheresultsfromPaperIIarecomparedtotheresultswithaslipandano‐
slip boundary condition. This is done in order to find out if the less resource‐
demanding no‐slip boundary condition can be used to study flow conditions with
surfactants. It is shown that the results for the no‐slip boundary conditions are very
similartothesaturatedsurfactantcaseexceptforthermshorizontalvelocitycloseto
thesurface.Thisiszeroforno‐slipandnon‐zeroforsurfactantboundaryconditions.
Atafirstglance,itissurprisingthattheflowdivergence(whichisimportantforgas‐
exchange) can have a similar behavior for the two different boundary conditions
althoughthermshorizontalvelocitiesdifferclosetothesurface.Thesimilarityinflow
divergence can be explained by a decomposition of the horizontal flow into a
solenoidal and an irrotational component (see Figure 13) [Hasegawa and Kasagi,
2008]. Asurfactant boundarycondition mainlydampenstheirrotationalcomponent,
which is the dominating contributor to the horizontal flow divergence while the
solenoidal component is less dampened and still contributes to the rms horizontal
velocity. To summarize, it is therefore found that a slip and a no‐slip boundary
condition can be used to model a clean and a saturated surfactant condition,
respectively,whenstudyinggastransfer.
Figure 13. Decomposition of the interfacial velocity vector into (a) solenoidal and (b)
irrotationalcomponents.(Figure4inHasegawaandKasagi[2008])
The resulting transfer velocities, , for slip and no‐slip boundary conditions for
scalars with
7,
150, and
600 are shown in Figure 14. The transfer
velocity decreases by a factor of approximately 3 for a no‐slip (surfactant‐saturated)
comparedtoaslip(clean)boundaryconditions,whichmatcheslaboratoryresultsfor
gas transfer velocities for clean and contaminated surfaces [McKenna and McGillis,
22
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
3.CONTRIBUTIONS
2004]. The difference is decreasing with decreasing and is approximately 1.5 for
7.
Furthermore, it is seen that the results for the gas transfer dependence of the numbers closely follow theoretical derivations [e.g., Ledwell, 1984]. The DNS give
⁄600 with
0.521and 0.668,whilst
1⁄2and
2⁄3inthe
theoreticalderivationforslipandno‐slip,respectively.Thisisthefirsttimetothebest
of our knowledge that this Sc dependency has been confirmed with DNS. The close
agreementwiththeresultofthetheoreticalderivationisinterestingsinceitisbased
onthe
inthevicinityofthesurface,andtheassumptionthat
∝ fora
∝ for a surface with surfactants (no‐slip). This
clean surface (slip) and
assumption is as shown in Paper I only valid for the innermost part of the diffusive
boundarylayerfor
7,whichinturn,impliesthatitactuallyistheprocessesinthe
very vicinity of the water surface that controls the gas exchange during natural
convection.
−2
10
n = 1/2
n = 2/3
k s2F
k s2B
k n2B
−3
10
ks ms-1
s2F
n7−600 = 0.519
s2B
n7−600 = 0.521
−4
10
−5
10
n2B
n7−600 = 0.668
−6
10
0
1
10
2
10
10
Sc
3
10 Figure14. Scalartransfervelocityforcases 2 , 2 (bothslip,clean surface)and 2 (no‐
slip,saturatedsurfactant)forthreepassivescalarswithSchmidtnumber
7,
150,
and
600, respectively. The results for thebasecase 2 andthecasewithfinermesh
resolution, 2 , are difficult to distinguish since they are very similar. Dashed and dotted
linescorrespondto
1⁄2and
2⁄3andoriginatefrom , fortheslipandno‐slip
boundaryconditioncaserespectively.
23
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
3.CONTRIBUTIONS
Heretheparameterizationofthetransfervelocityforpurenaturalconvection
⁄
,
(18)
canbepresentedbeforetheresultsforthecaseswithcombinedbuoyancyandshear‐
0.4isatransfervelocity
stressforcingarepresentedinthesectiontocome.
coefficientand
1⁄2forslip(clean)and
2⁄3forno‐slip(saturatedsurfactant)
boundaryconditionsatthesurface.
3.5 Influenceofcombinedwindandbuoyancyforcingonthegas
transfervelocity
One of the major contributions of this thesis is to find at which conditions the
buoyancy‐ and wind‐forcing dominate the gas transfer velocity. The results for low
wind speed conditions (
2
) from the numerical study in Paper III are
discussedinthissectionwhiletheresultsforintermediatewindspeedfromthefield
measurementspresentedinPaperIVwillbediscussedinsection3.6.
Inordertohelpthereaderwerepeatthatthecasesarenamedwith(i)anumberfor
the shear‐based Reynolds number ∗
∗ ⁄ , which describes the ratio between
inertialandviscousforces,and(ii)a forBuoyancyor forNo‐Buoyancy.Thecase
0 inPaperIIIisidenticalwiththecase 2 inPaperI.
The flow pattern for buoyancy driven flows is characterized by thin descending
plumesofcolddensewater,warmwiderascendingplumes,andoccasionallysurface‐
normalvortices.Thesurfacenormalscalarfluxfollowthispattern(Figures9aandd).
Figure 15 shows snapshots of the surface normal scalar flux fields at the surface for
the case 0 (pure convective forcing) and the cases with combined and pure shear
forcing.Itisseenthatoncetheshearstressisappliedtothesurface(inthe ‐direction
towardsrightinthefigures),thepatternandvorticesstarttobebendedandstretched
andafish‐scalepatternbecomesvisible.
Wall‐bounded flows have been shown to typically create streaky structures in the
vicinityofthewallwithaspanwisespacingofabout100 ∗ [e.g.,KimandMoin,1989;
Kim et al., 1987]. Later it was shown to be valid for temperature fields and slip
boundary conditions as well [e.g., Handler et al., 2001]. It can now be seen that the
coherent structures in the fish‐scale patterns follows this streak spacing length scale
well for cases driven by pure shear‐stress (120 and 180 in Figure 15). It can,
however, also be seen that these coherent structures typically are finer with than
without buoyancy comparing 120 with 120 and 180 with 180 . The scalar
fluxvariationisincreasingwithincreasingshearforcingandthevariationishigherfor
pure shear forcing than for combined forcing. These difference between cases with
pure shear and combined forcing decrease with increasing shear‐stress (increasing
),indicatingthatthebuoyancyforcingbecomeslessimportant.Itisinthefollowing
shown that this transition in the scalar flux pattern (decreasing difference) is
accompaniedbytransitionsinmanyotherflowcharacteristicsandeventuallythegas
transfervelocity.
24
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
3.CONTRIBUTIONS
Increasing shear forcing
Buoyancy and shear forcing
Pure shear forcing
0 60 100 ∗ 120 120
100 ∗ 100 ∗ 180 180
100 ∗ 100 ∗ 240 2
100 ∗ 0
F ⁄F 4
5
Figure 15. Normalized surface‐normal scalar flux fields. The cases are named as the
for o‐ uoyancy.Thesamescalingisusedforall
∗
∗ ⁄ and for ouyancyand
⁄ ∗ ,isindicatedinthesubplotsforcaseswith
subplots.Thelengthscale100 ∗ ,where ∗
0. Case 60B is not shown in Paper III since it needs further sampling time before
∗
statisticalpostprocessing.Thesimulationhas,however,reacheditssteadystateconditionso
thatasnapshotcanbeusedasisdoneinthisfigure.
Figure16showsthesurface‐normalscalarfluxatthesurface,thescalarconcentration
intheinteriorandiso‐surfacesofthepositiveandnegativestreamwisevorticityΩ .By
comparing Figure 9 with Figure 16, the transition from buoyancy to shear stress
dominatedflowcanbeseenwithintheinterioroftheflowaswell.Itisshownthatthe
vorticity cores are more elongated and surface‐centered for increasing shear‐stress.
Furthermore,itcanbeseenthatthevariationofthenormalizedsurface‐normalfluxis
increasing (note the different scales) with streaks of intense flux (red) as the shear
stress is increased. The zoomed square shows the interplay of streamwise vorticity,
scalarconcentrationandsurface‐normalscalarfluxclearer.Hereitisseenthatwater
with low scalar concentration is drawn downwards (downwelling) between the
vorticity‐cores shifting from positive to negative in the ‐direction (diagonally from
thelefttotheright).Thisphenomenonissimilartothethinplumesofdensewaterin
the case with no shear shown in Figure 9. Concurrently, areas of thin diffusive
boundary‐layersareformedbetweenthevorticity‐coreschangingsignfromnegative
to positive, and these areas then coincide as expected with areas of high surface‐
normalscalar‐flux(upwelling).
25
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
3.CONTRIBUTIONS
60 240 F ⁄F F ⁄F 0
s⁄F ∙ 10 sm
0
2.5
0
4
s⁄F ∙ 10 sm
0
1.8
1.5
Figure16.Snapshotsforcase60 (lowleft)and240 (lowright)andablow‐upfromcase
240 .Surface‐normalscalarflux ⁄ atthesurfaceandscalarconcentration ⁄ inthe
interiorofthedomain.Isosurfacesofnormalizedstreamwisevorticity ⁄ ∗ ⁄ equal0.25
and 0.25coloredredandblue,respectively.(Figure3inPaperIII).
Thescalartransfervelocities , increaselinearlywith ∗ forcaseswithpureshear‐
stress forcing (Figure 17a). These results are close to the measurements of gas
transfervelocitiesinawindtank[Jahneetal.,1987]
,
8.9 ,
(19)
∗
given in the same figure. Combined forcing gives on the other hand a more or less
constant , for low ∗ , and then , seems to connect to the linear trend as ∗ increases.AnotherwayofexpressingthiscanbeseeninFigure17bwhere , ⁄ ∗ asa
functionof ispresentedfollowingequation(15).Here , ⁄ ∗ isdecliningdowntoa
limiting magnitude for decreasing Ri. This limiting magnitude is set by the no‐
buoyancy cases. A Richardson number
0.004 is found to express the conditions
whenthescalartransferstartstochangefrombeingdominatedbybuoyancyforcing
toshear‐stressforcingwhichisrelevantfordeterminingthebuoyancyinfluence[e.g.,
Macintyreetal.,2002;Readetal.,2012;RutgerssonandSmedman,2010].
26
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
3.CONTRIBUTIONS
−4
a)
1
b)
x 10
0.08
B
0.9
0.07
0.8
0.06
0.6
ks,7/u*
ks,7 ms-1
0.7
0.5
0.4
B
0.3
NB
0.05
0.04
kg,W2009
0.2
0.03
kg,CC1998
0.1
0
180NB
kg,J1987
0
0.5
1
1.5
u∗ ∙ 10 ms
2
0.02
−3
10
2.5
−2
10
−1
10 Ri
Figure 17. (a) The scalar transfer velocity ,
. Circles denote cases with
, ⁄
buoyancy and squares denote no‐buoyancy cases. The dashed and dash‐dotted lines denote
the wind parameterizations with
1⁄2 according to equations (5) and (6) respectively.
The solid line denotes a linear increase of the transfer velocity as a function of the friction
velocity[Jahneetal.,1987].(b)Transfervelocityconstant , ⁄ ∗ accordingtoequation(15)
asafunctionof .(Figure6and7binPaperIII)
3.6 Observationalresultsathigherwindspeeds,andspeculations
abouttheinfluenceofwaves
The transfer velocity estimations based on the flux‐chamber and dissipation
parameterization, and the quantities significant wave height ( ), and IR surface
) show a close relationship (Figure 18). The uncertainty in the
velocity (
dissipation parameterization, however, increased for low dissipation rates since the
turbulencesignalthenwasdominatedbywavesandinstrumentnoise.Hence,transfer
arenot
velocitiesusingthedissipationparameterizationthatarebelow2 ∙ 10 presented in Figure 18. Nevertheless, a significant linear relationship was found
betweenthetransfervelocityestimationsbytheflux‐chambermethodanddissipation
parameterizationsandthesignificantwaveheight.Alinearfitgave
1.95 ∙ 10
4.9 ∙ 10
4.9 ∙ 10
1.5 ∙ 10 . (20)
,
,
Nolocalwindmeasurementswereavailablefromtheexperiment,butitisreasonable
to assume that the wave heights can be related to the wind speed and fetch, [e.g.,
Hasselmannetal.,1976].Forafetchofabout3km,whichisreasonablefortheBornö
siteatthegivenwinddirection,thisequationcanbetransformedinto
5.4 ∙ 10
3.7 ∙ 10
4.8 ∙ 10
1.5 ∙ 10 . (21)
,
,
27
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
3.CONTRIBUTIONS
Figure 18. Comparison of transfer velocities using the flux‐chamber method (filled circles),
dissipation parameterization (plus signs), significant wave height (diamonds), and IR rms
surfacevelocity(filledtriangles).(Figure7inPaperIV).
Theslopeofequation(21)isclosetotheslopeof ,
for
1⁄2andratherclose
tothetransfervelocityforcedbyshearstressonly,seesection3.7.3.Itcantherefore
bearguedthatitactuallyistheshearstressratherthanthewavesthatenhancethegas
transfervelocity(elaboratedinPaperIII).Ifso,thesignificantwaveheightcanstillbe
agoodproxyfortheintegratedeffectoftheshearstress,andtherebythegasflux,over
theareaofinterest.Inordertomakeequation(21)moregeneral,theequationcanbe
transformedtoincludethesignificantwaveheightandfetch(seePaperIV).
There was also a good correlation between the transfer velocity and the rms
horizontal surface velocity estimated from PIV (from IR images). This can be
expressedas
, ,
∙
(22)
where
and
areconstants.Thiscloserelationshipfor
isunexpectedsince
there is no direct relation between the rms horizontal surface velocity and the rms
near‐surfaceverticalvelocitywhichmaybeexpectedtobeimportantforgasexchange
(see the discussion regarding solenoidal and irrotational components in section 3.4
and Figure 13). A reasonable explanation for the close
relationship may be
found in the close relationship between the significant wave height and the transfer
velocity, since estimated rms wave orbital velocities agree fairly well with
from
theIR/PIV‐measurements.Inthatcase,eventhiscorrelationiscausedbytheinfluence
ofwindstressonbothgastransferandwaves.
One example of the temperature field used for PIV is shown in Figure 8 (from IR
images).Itshowsasimilartemperaturepatternasthelowshear‐stresscasesshownin
Figure 15. Even though the DNS results show that the surface divergence
28
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
3.CONTRIBUTIONS
parameterization works well, the transfer velocity estimation using the surface
divergence from the IR/PIV‐measurement failed to give good correlation with the
results from the other estimation methods. This is, however, most likely not due to
problemswiththedivergenceparameterizationbutrathertheresultofaneedoffiner
spatialresolutionofthevelocityfieldintheIR/PIVmethod.Otherwise,theimportant
small‐scaledivergenceisnotproperlytakenintoaccountintheestimationofthetotal
divergence.
3.7 Parameterizationsofthegastransfervelocity
3.7.1 Basedondiffusivity,surfactants,andshear‐stressandbuoyancy
forcing
PaperIshowsthatthetransfervelocityforpurebuoyancyforcingiswellrepresented
byequation(18).Itishereinterestingtoseetheevidentrelationshiptothebuoyancy
fluxandthatthereisnoinfluenceofthedepthforlargeenoughdepths.Itcanalsobe
seenthattheSchmidtexponentcloselyfollowsthetheoreticalderivationforslipand
no‐slip wall conditions. It should, though, be noted that the kinematic viscosity is
included into equation (18) from dimensional considerations only and has not been
alteredintheanalysis.
Theparameterizationforthecombinedforcingismorecomplextakingboththeshear‐
stress and the buoyancy forcing into account. Paper III presents three different
parameterizations.Therationaleforthreeparameterizationsis(i)thattheusersofthe
parameterizationsmighthavespecificneedsfortheirimplementationand(ii)thatthe
parameterizations represent different ways of interpreting the physics. The first
parameterizationisbasedonahypothesisthattheforcingsfrombuoyancyandshear
stressareadditiveresultingin
k ,
A
u∗ Ri⁄Ri
1 ⁄ Sc ,
(23)
⁄
where Ri
is a critical Richardson number and
0.1 is the
transfer velocity coefficient for shear‐stress forcing. It is based on the dissipation
parameterization (equation (9)) and makes use of the fact that the forcings from
buoyancy and shear scale as and ∗ ⁄ , respectively. This parameterization
(equation(23))isfor
50, 100,and200
drawningreeninFigure19.
The other two parameterizations are based on the hypothesis that the transfer
velocitycanbeseentobeintwodifferentstates.Thefirststateisbuoyancydrivenand
the second state is shear‐stress driven. The transition from one state to another is
defined by a critical Richardson number. These two parameterizations either use an
errorfunctionas
,
⁄
∗
,
1
29
,
(24)
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
3.CONTRIBUTIONS
orapiecewiselinearfunctionas
⁄
,
,
∗
.
(25)
50, 100,and200
inredwith ,
0.01and
Equation(24)isdrawnfor
100 in yellow in Figure 19. All three
equation (25) is drawn for
parameterizations(23)‐(25)convergeathighaswellaslow .
x 10
−4
1.2
1
k7 ms-1
0.8
0.6
B
NB
0.4
kg,W2009
kg,CC1998
kg,J1987
kg,sum
kg,erf
0.2
kg,tres
0
0
1
2
u∗ ∙ 10
ms
3
Figure 19. The gas transfer velocity constant , according to equations (23) in green and
50, 100,and200
.Thescalartransfervelocitiesforpurebuoyancy
(24)inredfor
50and200
aremarkedwithfilledmarkersandwerepresentedin
forcingwith
PaperI.Thetransfervelocitiesforthepurebuoyancyandshearforcing(equation(25))are
indicatedinyellow.(Figure9inPaperIII)
3.7.2
Basedondissipation,divergence,orheatflux
It was found in Paper I that the three parameterizations based on heat flux,
dissipation,ordivergence(equations(8)‐(10))giveverygoodestimatesofthetransfer
velocity for pure buoyancy forcing while varying the surface heat flux and domain
depth. The values of the related transfer velocity coefficients are
0.45,
0.57,and
0.90.
30
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
3.CONTRIBUTIONS
The results for the parameterizations for the combined forcing in Paper III are,
however,notasconvincingastheresultsforbuoyancyforcingonly.Thisgivesreason
tobecautiousinusingthedissipationasaunifyingquantity(proxy)thatcanbeused
to add different forcings into a total gas transfer parameterization. The relative
⁄
variation
is here used to rank the different parameterizations.
Thevariationisforthecases0 to240 foundtobeapproximately10%,15%,and
more than 35% for the heat, divergence, and the dissipation parameterizations
respectively.
3.7.3
Basedonthemeanwindspeed
Figure 20 shows a number of parameterizations as functions of
. The
parameterizationinequation(23)ishereplottedforsurfaceheatfluxesintherangeof
0
400
. The buoyancy flux influences the gas‐transfer velocity up to
accordingtoadditiveparameterization,k , .
approximately2‐4
Furthermore,itisshownin Figures19and20 that thetwoparameterizations based
on the mean wind speed (equation (5) and (6)) give reasonable predictions of the
transfer velocity for both the cases with pure natural convection and the combined
forcingforacleansurface(slip).Itcanbeseenthatoneparameterization[Wanninkhof
et al., 2009] overestimates and the other parameterization [Cole and Caraco, 1998]
underestimates the transfer velocity compared to the base case with a surface heat
. Congruent transfer velocities using equations (5) and (18) would
flux of 100
imply a surface heat flux of approximately 35
, whilst equations (6) and (18)
.Thesurfaceheatfluxis,however,inequations
wouldimplyapproximately200
(5)and(6)notexplicitlyaccountedforsincethetransfervelocityisafunctionof
only. For low wind conditions, it is therefore advisable to use any of equations (23)‐
(25)inordertohaveaparameterizationthattakesthebuoyancyfluxintoaccount.It
can further be seen that the two parameterizations (19) from wind tunnel tank test
and equation (21) from field measurements give transfer velocities in the same
magnitude.
Figure20alsoshowsthelargeinfluenceofthesurfactantsonthegasflux.Thereisa
factor of approximately 3 between the transfer velocity for a clean surface (slip,
1⁄2) and for a surface that is saturated with surfactants (no‐slip,
2⁄3) for
600.
Previous research has found that microscale breaking waves significantly contribute
tothemeansquareslopeofwaves,whichinturncanbecorrelatedtothegastransfer
velocity [Zappa et al., 2002; 2004]. The gas transfer was found to be enhanced by a
factor 3.5 comparing background levels and areas with microscale breakers.
Furthermore, it is inferred that the microscale breaking may be the mechanism that
enhances heat and mass transfer. The close agreement between the slopes in the
parameterizations originating from wind tunnel tank measurements ( ,
), using
significant wave height ( ,
), ,
and ,
, and equation (23) for clean
conditions(
1⁄2)and
0
(
0)isthereforeinterestinginaspectsof
how large enhancement of the transfer‐velocity waves and microscale breakers may
givecomparedtopureshear‐stressforcing,andisrelevanttonoticeforfuturework
31
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
4.SUMMARYANDCONCLUSIONS
−5
2.5
x 10
kg,sum
n=1/2
n=2/3
kg,sum
kg,J1987 n=1/2
kg,W2009
kg,CC1998
kg,G2013
k600 ms-1
2
1.5
1
0.5
0
0
1
2
3
U ms
4
5
Figure 20. Transfer velocity constant ,
according to equation (23) in green for
0, 50, 100,200and400
and
1⁄2(clean)anddottedline
2⁄3(saturated
surfactant).Theparametrizationsinequations(5‐6),(19),and(21)aregivenforreference.
The transfer velocity estimated with equation (6) is transformed into
600 using
equation(7)and
1⁄2.
4 SUMMARYANDCONCLUSIONS
There is a growing need to determine the air‐water gas exchange accurately during
lowwindconditionssince(i)thereisageneralincreaseoftheconcentrationandthe
interest in greenhouse gases e.g., CO and CH in the atmosphere, (ii) it has become
evident that the gas fluxes from fresh‐water bodies (where the wind speed often is
low) play an important role in the global carbon cycle, and (iii) often used
parameterizations based only on the wind speed cannot take other forcings as e.g.,
buoyancyintoaccount.
Newparameterizationsfor gastransfervelocityestimationshave been developedby
use of numerical simulations and field measurements in the ocean. The numerical
simulations are performed as direct numerical simulations of fully developed
turbulent flow for pure natural convective forcing, and combined convection and
wind‐shear forcing. The influence of surface heat flux, mixed layer depth, Schmidt
number, and surfactants are evaluated. The field measurements comprise gas flux
measurements by gas‐flux chamber, IR/PIV‐recording (e.g., surface flow divergence,
rmssurfacevelocity),andrateofturbulentkineticenergydissipationinthewaterby
acousticdopplervelocimetry.
The temperature and the surface‐normal scalar flux fields at the surface show
elongatedstreaksofwarmandcoldwater(highandlimitedscalarflux)forthecases
withpureshearstressforcing.Thestreakspacingisoftheorderof100 ⁄ ∗ (forpure
32
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
4.SUMMARYANDCONCLUSIONS
shearstressforcing)whichpreviouslyhasbeenseenforshear‐stressdrivenflows,for
both slip and no‐slip surface boundary conditions. The temperature and the surface‐
normalscalar fluxfieldare morecomplexforthecombinedforcedcases.Asshearis
“added”toapurenatural‐convectionconditiontheplumesstartstobeelongatedand
eventuallyastheshearstressisincreasedthestreaksshowalargersimilaritywiththe
pure shear‐driven cases. This and the averaged statistics for all quantities studied
indicate a transition from natural‐convection (buoyancy) to shear‐stress dominated
flow at
4 ∙ 10 , which means that buoyancy fluxes are not important for gas
.
exchangeatwindvelocities above3
Parameterizationsusingtherateofturbulentkineticenergydissipation,surfaceflow
divergence, and heat flux, estimate the transfer velocity well for the cases with pure
natural‐convection, while varying the surface heat flux, domain depth, and Schmidt
number. These parameterizations, however, experience some problems for the cases
with combined convective and shear stress forcings. The relative variations in the
transfervelocityarelargestfortheparameterizationbasedonthedissipationrateand
smallest for the parameterization based on the heat flux. The two parameterizations
based on wind speed estimate the transfer velocities reasonable well, depending,
however, on the surface heat flux. One parameterization [Cole and Caraco, 1998]
correspondstoaheatfluxofapproximately35
whiletheother[Wanninkhofet
al.,2009]correspondstoaheatfluxofapproximately200
.Furthermore,there
isnoincreaseoftransfervelocityasfunctionofincreasingdomaindepth(studiedfor
pureconvectionforcedcaseonly).
Theproposednewgastransferparameterizationsrepresenttwodifferenthypotheses.
Thefirstoneassumesthattheforcingfrombuoyancyandshearstressareadditive.It
usestheframeworkofthedissipationparameterizationandsumsthetwodissipation
scales for buoyancy and shear stress which results in the expression
⁄
where the critical Richardson number
1 ⁄
,
∗
⁄
4 ∙ 10 .
The second one assumes that the forcing is either from the buoyancy or the shear
stress.Herethetransfervelocityiseithermodelledwithacontinuouserror‐function
,
⁄
,
∗
,
where
,
0.01.
orwithapiecewiselinearfunction,thathasaconstanttransfervelocitythatequalsthe
⁄
, for
whereafter the
transfer due to buoyancy ,
is
transfer velocity due to shear according to the expression ,
∗
used. The gas flux is to some extent overestimated by , and underestimated by
and , .Themaximumerrorsforthefirsttwoparameterizationsarelessthan
,
10% and for the latter approximately 20%. The critical Richardson number in these
parameterizations can be seen to express the transition point where the gas‐flux
forcingshiftsfrom beingdominated byeither buoyancy orshear‐stress.Thisimplies
that the buoyancy flux influence the gas transfer velocity up to approximately
3
fornaturalconditions.
33
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
5.FUTUREPERSPECTIVES
The results from the field measurements show close relationships for the method
using flux‐chambers and the parameterization using the rate of turbulent kinetic
energy dissipation, and the quantities surface rms velocity and the significant wave
height.Theserelationshipscanallbeexpressedas ∝
withaslopeclosetothe
resultsintheDNSforpureshearstressforcingandtestsinawindtank[Jahneetal.,
1987].
5 FUTUREPERSPECTIVES
Thepresentworkprovidesafirmgroundfortheunderstandingofgasfluxacrossthe
air‐waterinterfaceduringlowwindspeedconditions.Thereare,though,stillneedsfor
futureworkforhighSchmidtnumbersand higherwindspeeds.Althoughtheresults
for high Schmidt number gases in Paper I are consistent regarding the gas transfer
velocity,isstillremainstobeconfirmedthatthesearevalidforacomputationalmesh
with higher resolution as well. This can be achieved in a similar way as Herlina and
Wissink [2014] who used two different meshes with different mesh resolutions for
solvingtheflowfieldandthescalarfield.
It would also be fruitful to continue the work towards more accurate gas transfer
estimationsforhigherwindspeeds.Thenextstepisthentoperformdirectnumerical
simulations in order to study the mechanisms of e.g., microscale‐breaking and
breaking waves. This has to some extent been done [e.g., Lin et al., 2008; Tsai and
Hung, 2007] but there is still a need for a comprehensive parameter study including
theinfluenceofsurfactants.
Furthermoreitwouldbeinterestingtostudyhowtheconceptofturbulence‐surfactant
parameter can be used in field work and how the surfactant concentration and the
surfaceelasticitycanbeestimated?
Eventually it would be worthwhile to study whether the temperature field recorded
withanIRcameracanobtainhighenoughresolutiontocapturetheimportantsmall‐
scaledivergenceatthesurface.
34
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
ACKNOWLEDGEMENTS
ACKNOWLEDGEMENTS
NowIwouldliketotaketheopportunitytoacknowledgemysupervisors,colleagues,
friendsandfamily,whohavesupportedmeduringmystudiesandthisPhDproject.
First, I would like to express my sincere gratitude to my supervisor, Lars Arneborg,
andco‐supervisor,DavidBastviken.Ihavealwaysfeltaverysupportiveattitudefrom
them,andbeenencouraged bytheircompetenceandeagerness tolearnandexplore
new things. I would also like to express my sincere gratitude to Robert Handler and
Håkan Nilsson who both have been very encouraging during the work leading up to
this thesis. The meetings with Robert (by wire, in Texas, or in Gothenburg) have
alwaysbeenasourceoflargeinspirationtome.Håkanhasbeenaveryvaluableguide
duringmyexplorationandeventuallyprogrammingofOpenFOAM.Iwouldalsoliketo
expressmyappreciationtotheremainingco‐authorsofjointlywrittenpapersduring
mystudies.Ithase.g.,beeninspiringtoseethefascinatingIR‐imagesbyoneoftheco‐
authors, Magnus Gålfalk. Many thanks also to the group of gas‐flux researchers from
theUppsalaUniversityfornicefieldworkandfruitfuldiscussions.
I would also like to thank Ola Kalen, a companion at several conferences who I have
sharedofficewithforseveralyears.Besidetheworkithasbeeninspiringtotalkabout
ourcommoninterestsoutsidetheacademia.Thanksalso;toArdoRobijnforbeingmy
fellow researcher at the expeditions to the areas at and around Svalbard, to Anna
Wåhlin for making our participating in that research project (PREPARED) possible,
andtoallofthemembersofthesememorableresearchcruises.Thelistofcolleagues
tothankcouldbeaslongasamoviecredit.However,duetospacelimits,letmejust
send my general and genuine thanks to all the colleagues at GU not mentioned here
butstillrememberedandallofyouwhohavebecomedearfriendsofmineduringmy
studies.
Agoodlifeoutsidetheofficeisofgreatimportanceformeandforthesuccessofmy
work,andIamluckytohavemanywonderfulpeoplearoundme.FirstIwouldliketo
thank Anna for her support, joy, and ultimately even some help with the final
formatting of this thesis. I would then like to give my wholehearted thanks; to mom
and dad for their caring and unconditional support to me and the family, and to my
brotherformanygoodtimestogether.GreatthankstoKristinaandAndersforalltheir
journeys to Gothenburg during these years. I am also very grateful for the large and
caringringoffriendsthatbringmesomuchfriendshipandenjoyment.
EventuallyIwouldliketosendaheapofhugstomylovelychildrenSara,Martin,and
Emil.Youhavebeenverypatientduringthisspringandyoualwaysbringmesomuch
joy!
I would also like to acknowledge Semcon who gave me study leave to fulfil this PhD
project. The computations were performed on resources provided by the Swedish
National Infrastructure for Computing (SNIC) at C3SE (Chalmers Centre for
Computational Science and Engineering) computing resources. My supervisor Lars
ArneborgwassupportedbytheSwedishResearchCouncil.
35
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
REFERENCES
REFERENCES
Bade, D. L. (2009), Gas Exchange at the Air–Water Interface, in Encyclopedia of Inland
Waters, edited by G. E. Likens, pp. 70‐78, Academic Press,
Oxford,http://dx.doi.org/10.1016/B978‐012370626‐3.00213‐1.
Banerjee,S.,D.S.Scott,andE.Rhodes(1968),MassTransfertoFallingWavyLiquidFilms
inTurbulentFlow,IndEngChemFund,7(1),22‐&,Doi10.1021/I160025a004.
Banerjee, S., D. Lakehal, and M. Fulgosi (2004), Surface divergence models for scalar
exchangebetweenturbulentstreams,IntJMultiphasFlow,30(7‐8),963‐977,DOI
10.1016/j.imultiphase.2004.05.004.
Bastviken,D.,L.J.Tranvik,J.A.Downing,P.M.Crill,andA.Enrich‐Prast(2011),Freshwater
Methane Emissions Offset the Continental Carbon Sink, Science, 331(6013), 50‐
50,DOI10.1126/science.1196808.
Calmet,I.,andJ.Magnaudet(1998),High‐Schmidtnumbermasstransferthroughturbulent
gas‐liquid interfaces, Int J Heat Fluid Fl, 19(5), 522‐532,Doi 10.1016/S0142‐
727x(98)10017‐6.
Ciais,P.,etal.(2013),CarbonandOtherBiogeochemicalCycles.In:ClimateChange2013:
The Physical Science Basis. Contribution of Working Group I to the Fifth
AssessmentReportoftheIntergovernmentalPanelonClimateChangeRep.,465–
570pp,CambridgeUniversityPress,Cambridge,UnitedKingdomandNewYork,
NY,USA,10.1017/CBO9781107415324.015.
Cole,J.J.,andN.F.Caraco(1998),Atmosphericexchangeofcarbondioxideinalow‐wind
oligotrophiclakemeasuredbytheadditionofSF6,LimnolOceanogr, 43(4),647‐
656
Cole, J. J., D. L. Bade, D. Bastviken, M. L. Pace, and M. Van de Bogert (2010), Multiple
approaches to estimating air‐water gas exchange in small lakes, Limnology and
Oceanography:Methods,8(6),285‐293,10.4319/lom.2010.8.285.
Csanady,G.T.(2001),Air‐seainteraction:lawsandmechanisms,vii,239p.pp.,Cambridge
UniversityPress,Cambridge;NewYork
Fairall,C.W.,E.F.Bradley,J.S.Godfrey,G.A.Wick,J.B.Edson,andG.S.Young(1996),Cool‐
skin and warm‐layer effects on sea surface temperature, J Geophys Res‐Oceans,
101(C1),1295‐1308,Doi10.1029/95jc03190.
Fortescue, G. E., and J. R. A. Pearson (1967), On Gas Absorption into a Turbulent Liquid,
ChemEngSci,22(9),1163‐&,Doi10.1016/0009‐2509(67)80183‐0.
Frew,N.M.,etal.(2004),Air‐seagastransfer:Itsdependenceonwindstress,small‐scale
roughness, and surface films, J Geophys Res‐Oceans, 109(C8),Artn C08s17,Doi
10.1029/2003jc002131.
Garbe, C. S. (2001), Measuring heat exchange processes at the air‐water interface from
thermographic image sequence analysis, 232 pp, Rupertus Carola University of
Heidelberg,Heidelberg
Garbe,C.S.,H.Spies,andB.Jahne(2003),Estimationofsurfaceflowandnetheatfluxfrom
infrared image sequences, J Math Imaging Vis, 19(3), 159‐174,Doi
10.1023/A:1026233919766.
Garratt,J.R.(1992),Theatmosphericboundarylayer,CambridgeUniversityPress
Handler,R.A.,G.B.Smith,andR.I.Leighton(2001),Thethermalstructureofanair‐water
interfaceatlowwindspeeds,TellusA,53(2),233‐244
Hasegawa,Y.,andN.Kasagi(2008),SystematicanalysisofhighSchmidtnumberturbulent
masstransferacrossclean,contaminatedandsolidinterfaces,IntJHeatFluidFl,
29(3),765‐773,DOI10.1016/j.ijheatfluidflow.2008.03.002.
Hasselmann, K., W. Sell, D. B. Ross, and P. Müller (1976), A Parametric Wave Prediction
Model, J Phys Oceanogr, 6(2), 200‐228,10.1175/1520‐0485(1976)006<0200:
APWPM>2.0.CO;2.
36
SamT.Fredriksson
Estimatingtheair‐watergastransfervelocity
REFERENCES
Haussecker,H.,U.Schimpf,andB.Jahne(1998),Measurementsoftheair‐seagastransfer
and its mechanisms by active and passive thermography, Igarss '98 ‐ 1998
International Geoscience and Remote Sensing Symposium, Proceedings Vols 1‐5,
484‐486,Doi10.1109/Igarss.1998.702947.
Herlina, H., and J. G. Wissink (2014), Direct numerical simulation of turbulent scalar
transport across a flat surface, J Fluid Mech, 744, 217‐249,Doi
10.1017/Jfm.2014.68.
Jahne,B.,andH.Haussecker(1998),Air‐watergasexchange,AnnuRevFluidMech,30,443‐
468
Jahne, B., P. Libner, R. Fischer, T. Billen, and E. J. Plate (1989), Investigating the transfer
processesacrossthe free aqueousviscousboundarylayerbythecontrolledflux
method,TellusB,41(2),177‐195,DOI10.1111/j.1600‐0889.1989.tb00135.x.
Jahne, B., K. O. Munnich, R. Bosinger, A. Dutzi, W. Huber, and P. Libner (1987), On the
Parameters Influencing Air‐Water Gas‐Exchange, J Geophys Res‐Oceans, 92(C2),
1937‐1949
Jerlov,N.G.(1976),MarineOptics,ElsevierScience
Kara,A.B.,P.A.Rochford,andH.E.Hurlburt(2000),Anoptimaldefinitionforoceanmixed
layer depth, Journal of Geophysical Research: Oceans, 105(C7), 16803‐
16821,10.1029/2000JC900072.
Kim, J., and P. Moin (1989), Transport of Passive Scalars in a Turbulent Channel Flow, in
TurbulentShearFlows6,editedbyJ.‐C.André,J.Cousteix,F.Durst,B.Launder,F.
Schmidt and J. Whitelaw, pp. 85‐96, Springer Berlin Heidelberg,10.1007/978‐3‐
642‐73948‐4_9.
Kim, J., P. Moin, and R. Moser (1987), Turbulence Statistics in Fully‐Developed Channel
Flow at Low Reynolds‐Number, J Fluid Mech, 177, 133‐166,Doi 10.1017/
S0022112087000892.
Lamont,J.C.,andD.S.Scott(1970),AnEddyCellModelofMassTransferintoSurfaceofa
TurbulentLiquid,AicheJ,16(4),513‐&
Ledwell,J.J.(1984),TheVariationoftheGasTransferCoefficientwithMolecularDiffusity,
inGasTransferatWaterSurfaces,editedbyW.BrutsaertandG.H.Jirka,pp.293‐
302,SpringerNetherlands,Dordrecht,10.1007/978‐94‐017‐1660‐4_27.
Lin,M.Y.,C.H.Moeng,W.T.Tsai,P.P.Sullivan,andS.E.Belcher(2008),Directnumerical
simulation of wind‐wave generation processes, J Fluid Mech, 616, 1‐30,Doi
10.1017/S0022112008004060.
Macintyre,S.,W.Eugster,andG.W.Kling(2002),TheCriticalImportanceofBuoyancyFlux
for Gas Flux Across the Air‐Water Interface, in Gas Transfer at Water Surfaces,
edited,pp.135‐139,AmericanGeophysicalUnion,10.1029/GM127p0135.
McKenna, S. P., and W. R. McGillis (2004), The role of free‐surface turbulence and
surfactants in air‐water gas transfer, Int J Heat Mass Tran, 47(3), 539‐553,DOI
10.1016/j.ijheatmasstransfer.2003.06.001.
Monahan, A. H. (2006), The probability distribution of sea surface wind speeds. Part 1:
Theory and SeaWinds observations, J Climate, 19(4), 497‐520,Doi 10.1175/
Jcli3640.1.
Ohlmann,J.C.,D.A.Siegel,andC.D.Mobley(2000),Oceanradiantheating.PartI:Optical
influences, J Phys Oceanogr, 30(8), 1833‐1848,Doi 10.1175/1520‐0485(2000)
030<1833:Orhpio>2.0.Co;2.
Read,J.S.,etal.(2012),Lake‐sizedependencyofwindshearandconvectionascontrolson
gasexchange,GeophysResLett,39,ArtnL09405,Doi10.1029/2012gl051886.
Rutgersson,A.,andA.Smedman(2010),Enhancedair‐seaCO2transferduetowater‐side
convection,JMarineSyst,80(1‐2),125‐134,DOI10.1016/j.jmarsys.2009.11.004.
Soloviev,A.X.,andP.Schlussel(1994),ParameterizationoftheCoolSkinoftheOceanand
of the Air Ocean Gas Transfer on the Basis of Modeling Surface Renewal, J Phys
Oceanogr,24(6),1339‐1346
37
Estimatingtheair‐watergastransfervelocity
SamT.Fredriksson
REFERENCES
Stewart,R.W.(2008),Introductiontophysicaloceanography,September2008ed.
Takahashi,T.,etal.(2009),ClimatologicalmeananddecadalchangeinsurfaceoceanpCO2,
andnetsea–airCO2fluxovertheglobaloceans,DeepSeaResearchPartII:Topical
Studies in Oceanography, 56(8–10), 554‐577,http://dx.doi.org/10.1016/
j.dsr2.2008.12.009.
Tranvik,L.J.,etal.(2009),Lakesandreservoirsasregulatorsofcarboncyclingandclimate,
LimnolOceanogr,54(6),2298‐2314,DOI10.4319/lo.2009.54.6_part_2.2298.
Tsai,W.T.,andL.P.Hung(2007),Three‐dimensionalmodelingofsmall‐scaleprocessesin
the upper boundary layer bounded by a dynamic ocean surface, J Geophys Res‐
Oceans,112(C2),ArtnC02019,Doi10.1029/2006jc003686.
Wanninkhof,R.,W.E.Asher,D.T.Ho,C.Sweeney,andW.R.McGillis(2009),Advancesin
QuantifyingAir‐SeaGasExchangeandEnvironmentalForcing,AnnuRevMarSci,
1,213‐244,DOI10.1146/annurev.marine.010908.163742.
Veron, F., W. K. Melville, and L. Lenain (2008), Infrared techniques for measuring ocean
surface processes, J Atmos Ocean Tech, 25(2), 307‐326,Doi 10.1175/
2007jtech0524.1.
Wick,G.A.,J.C.Ohlmann,C.W.Fairall,andA.T.Jessup(2005),ImprovedOceanicCool‐Skin
Corrections Using a Refined Solar Penetration Model, J Phys Oceanogr, 35(11),
1986‐1996,10.1175/JPO2803.1.
Volino,R.J.,andG.B.Smith(1999),UseofsimultaneousIRtemperaturemeasurementsand
DPIVtoinvestigatethermalplumesinathicklayercooledfromabove,ExpFluids,
27(1),70‐78
Zappa, C. J., P. A. Raymond, E. A. Terray, and W. R. McGillis (2003), Variation in surface
turbulenceandthegastransfervelocityoveratidalcycleinamacro‐tidalestuary,
Estuaries,26(6),1401‐1415,Doi10.1007/Bf02803649.
Zappa,C.J.,W.E.Asher,A.T. Jessup,J.Klinke,andS.R.Long(2002),EffectofMicroscale
Wave Breaking on Air‐Water Gas Transfer, in Gas Transfer at Water Surfaces,
edited,pp.23‐29,AmericanGeophysicalUnion,10.1029/GM127p0023.
Zappa,C.J.,W.E.Asher,A.T.Jessup,J.Klinke,andS.R.Long(2004),Microbreakingandthe
enhancement of air‐water transfer velocity, J Geophys Res‐Oceans, 109(C8),Artn
C08s16,Doi10.1029/2003jc001897.
Zappa,C.J.,W.R.McGillis,P.A.Raymond,J.B.Edson,E.J.Hintsa,H.J.Zemmelink,J.W.H.
Dacey,andD.T.Ho(2007),Environmentalturbulentmixingcontrolsonair‐water
gas exchange in marine and aquatic systems, Geophys Res Lett, 34(10),Artn
L10601,Doi10.1029/2006gl028790.
38
PartB
PapersI–IV
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