JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 106, NO. C2, PAGES 2477-2497, FEBRUARY
15, 2001
Turbulence Beneath Sea Ice and Leads: A coupled Sea Ice/LargeEddy Simulation Study
Eric D. Skyllingstad
Collegeof OceanicandAtmosphericSciences,OregonStateUniversity,Corvallis,Oregon
Donald
W. Denbo
JointInstitutefor the Studyof the AtmosphereandOcean,Universityof Washington,Seattle,Washington
Abstract. The importanceof leads,seaice motion,andfrazil ice on the wintertimeocean
boundarylayerwasexaminedby usinga large-eddysimulationturbulencemodelcoupledto a
thermodynamic
slabice model.Couplingwasachievedthroughexchangecoefficientsthat
accountedfor the differing diffusionratesof heat and salinity.Frazil ice concentrations
were
modeledby usingan ice crystalparameterization
with constantcrystalsizeandshape.
Stationaryice withoutleadsproducedcellularstructuressimilarto atmosphericconvection
withoutwinds.Ice motioncausedthis patternto breakdowninto a seriesof streaksaligned
with the flow.Eddy fluxeswere stronglyaffectedby ice motionwith relativelylarger
entrainmentfluxesat the mixed layerbaseundermovingice, whereasstationaryice produced
largerfluxesnearthetop of theboundarylayer.Openingof leadscausedsignificantchangesin
the turbulentstructureof the boundarylayer.Leadsin stationaryice producedconcentrated
plumesof higher-salinitywaterbeneaththe lead.Ice motioncausedthe leadconvection
to
follow preexistingconvectiverolls,enhancingthe roll circulationsalinityandverticalvelocity
underthelead.Comparisonof modeltime seriesdatawith observations
from theArcticLeads
Experimentshowedgeneralagreementfor bothpackice andleadconditions.Simulatedheat
flux carriedby frazil ice had a prominentrole in the upperboundarylayer,suggesting
that
frazil ice is importantin the heatbudgetof ice-coveredoceans.
1. Introduction
and freezing leads [McPhee 1992; McPhee and Stanton,
1996, hereinafter MS; Morison and McPhee, 1998] that have
Climate studiesconsistentlypoint out the importanceof
polar sea ice as a componentin the global heat budget.
Major factorsthatgovernice propertiesincludedynamicprocesses,which distort the ice causingcracks or leads, and
thermodynamic
processes,
which controlfreezingand thawing of the ice pack. Becauseof theseprocesses,significant
changesin the heat, salinity,and momentumcontentof the
ocean boundary layer (OBL) are produced as water is
exposedin leadsor insulatedbeneathmultiyearice. During
provideda view of the turbulence
structureandfluxesin the
OBL. By usingtheseobservations
alongwith high-resolution
model results,we presenta detailedpicture of turbulence
underleadsandseaice with varyingice velocity.
A schematicshowingthe dominantfluxesthat controlthe
ice, heat,andsalinitybudgetsof theupperpolaroceanis presentedin Figure 1. The mostsignificantdriversof the system
are the surfaceheat and momentumfluxes. Open water in
leads and areasof thin ice have the highestupward heat
the winter, leads are a main conduit for ocean heat loss via
radiative, latent and sensible heat fluxes. In the summer, the fluxes,which are forcedby extremelycold Arctic air masses
low albedoof leadsallowsfor significantsolar energyflux thatare commonoverthepackice in winter.Thesefluxesare
by increasedlongwaveradiationflux generated
into the OBL, whichforcesice meltingat the lead edgeand compounded
beneaththe ice pack. A key parameterin theseprocesses
is by therelativelywarmseawaterexposedin the lead.In comthe turbulent heat transfer between the ice and OBL. This
parison,heattransferthroughthick ice is greatlylimitedby
of the ice andoverlyingsnowcover,
transferhas a dominantrole in controllingthe sea ice mass the insulatingproperties
which causerelatively low surfacetemperaturesand small
budget.
The presentstudyexamineshow turbulenceinteractswith values for the latent and sensible heat flux. Because of these
ice processes
and upper ocean fluxes in the polar ocean. factors, fluxes at leads constitute about 1/3 of the total surface
Using a large-eddysimulation(LES) turbulencemodel cou- heatflux of theArctic ocean,eventhoughtheir surfacecoverpledwith a thermodynamic
seaice model,we focuson freez- age is limited to only a few percentof the ocean [Maykut,
ing conditionsunder pack ice and leads. Our work is 1978].
When the motion of sea ice relative to the OBL is small,
motivatedby recentturbulencemeasurements
beneathseaice
Papernumber1999JC000091.
turbulencebeneathleadsis forcedmainly by convectionproducedby brinerejectionduringfreezing.Dependingon lead
size and coolingrates,convectioncan causecoherentcirculationsthatare linkedwith the leadgeometry,andcantransport
water directly to the mixed layer base over limited areas
0148-0227/01/1999JC000091
[Morison et al., 1992; Morison and McPhee, 1998].
Copyright2001 by the AmericanGeophysicalUnion.
$09.00
2477
Leads
2478
SKYLLINGSTAD
AND DENBO: TURBULENCE
Latent and Sensible
(a)
Radiative
Heat Fluxes
Flux
ent.•.•Flux
BENEATH
SEA ICE AND LEADS
Accurate representationof leads in climate models
requiresanunderstanding
of howfluxesaredistributed
laterally beneathleadsand seaice. For example,can leadsbe
parameterized
by a mean flux, or do turbulentprocesses
beneathleadsrequirea moresophisticated
approach?
Critical
parametersthat controlmixing beneathleads are the ice
motion and the surfaceheat flux. Recent measurementsby
Morison and McPhee [1998] and MS demonstratethat the
Salt
Flux
Uice
Heat Flux
motionof the ice cancausesignificantvariationsin the convectivecirculationbeneaththe lead and in the salinityflux at
the downstreamedge of the lead. Two-dimensional
turbulence closuremodelingstudiesof mixing processes
under
leadssupporttheseresults,showingepisodicplumeevents
• Turbulent
Fluxes
Entrainment
downstream from the lead in caseswith ice motion [Kantha,
1995; Smith and Morison, 1993, 1998]. While these results
areencouraging,
theyprovideonlya smallsampleof theconditions that force turbulence beneath Arctic leads and are
unableto yield a detailedthree-dimensional
analysisof the
turbulentprocesses
that occurbeneathand downstreamfrom
leads.
To extendtheseresults,our approachis to apply a threedimensional LES model to the problem of convection
beneathleadsand seaice. The LES modelis coupledwith a
detailedice model so that interactionsbetweenupperocean
turbulenceand seaice can be directly examined.Our goal is
to examinethe boundarylayer structurecreatedbeneathsea
ice and leadsand determinehow ice processesaffect turbulence and turbulentfluxes in the under-iceOBL. Using the
LE,Stechnique,we are able to examinethe OBL underslab
ice at near-equilibriumconditions.This is not the casewith
leads,wherewe canonly examinethe short-terminfluenceof
the lead circulationbecauseof the closedperiodicboundaries
(b)
z=h+H
Snow
inherent with LES models.
ß
z=0
_
The paperis organizedas follows.A descriptionof the
coupledLES-icemodelis presented
in section2 alongwith
the experimental
designin section3. Two mainexperiments
areperformedby usingthe model:packice anda leadwith
ice motion.The objectivein performingtheseexperiments
is
to better understand the basic structure and influence of tur-
bulentprocessesactiveunder sea ice and leads.Key processesthat are examined include mixing produced by
roughness
ontheicepackbase,frazil ice,theroleof saltflux
from ice formation in both leads and under pack ice, and
Figure 1. Schematicof the fluxesaffecting(a) the ice-cov- entrainmentacrossthe haloclineat the mixed layer bottom.
ered oceanmixed layer and (b) the ice model.Symbolsare Resultsfrom theseexperimentsare presentedin section4
includingcomparisons
with flux measurements
takenas part
defined in the text.
of the Arctic LeadsExperiment(LEADEX) in spring1992.
The conclusions
of thepaperarepresented
in section5.
(w'T')
may alsocauseenhancedupperoceanmixingbecauseof dif- 2. LES-Ice
ferentialmomentumflux createdaswindsimpartmomentum
Model
to the exposedseasurfacein the leadand,for largerleads, Mostexistingice modelsfocuson theprediction
of longbecauseof Langmuircirculations
generated
by wave-current termice behaviorappropriate
for climatesimulationmodels.
interactions.
In contrast
to the uniqueturbulence
signature
of Emphasis
hasbeenplacedon accuratepredictionof ice proAs a
leads,mixing beneathpack ice is more like an aerodynami- cesseshavingtimescalesrangingfrom daysto seasons.
havingvery shorttimescales
andspatial
cally roughwall layer flow. Featuresin the ice, suchas com- result,ice processes
Thesemodelsincludepropressionridges, create a turbulentboundarylayer that is scalesare usuallyparameterized.
dependenton the roughnessof the ice, oceancurrentveloci- cesses,suchas heatdiffusionthroughthick ice, that are very
ties, and the motion of the ice surface. Fluxes of heat and slow in comparison
with the timescalessimulatedby using
salinitybeneathpack ice are muchlessthanthe correspond- LES (typically0.5-1 day). One exceptionis the coupledice/
ing fluxes under leads becauseof the reducedsurfaceheat LES model presentedby Kiimpf and Backhaus[1999] and
flux and correspondingice bottom freezing rate and do not Backhausand Kiimpf [1999], which focuseson sea ice in
typicallyinfluenceturbulenceas muchas the bottomrough- open oceanconditionsover scalesconsiderablylargerthan
ness [McPhee, 1992; MS].
the currentapplication.
SKYLLINGSTAD
AND DENBO' TURBULENCE
BENEATH
SEA ICE AND LEADS
2479
Becauseof the limitationsof existingmodels,we decided scalemomentumflux at the modeltop. We apply a Moninto build a new ice model based on features from the model of
Obukhov similarity profile in estimatingthe under-ice
Coxand Weeks[ 1988] andMaykut[ 1978] with parameteriza-
momentum
flux:
tions of ice-water interfaces[McPhee et al., 1987] and frazil
ice production[Ornstedtand $vensson,1984; Jenkinsand
( I,littl,13
tt) '- CDAl,
li ,
(3)
Bornbosch,
1995]. Our goalwasto producean ice modelthat
wouldaccuratelypredictfluxesof heatand saltbetweenthe where
oceanand ice during either freezingor thawing conditions
with anexistingice packandnewice in leads.
Couplingof the LES modelwith the slab and frazil ice
model is accomplished
by the additionof ice-relatedflux Arti = ttice
- tti(Zl),•SZ= 1/2Az,Azis thegridspacing,
• is von
termsto theLES equations.
Scalarquantitiesin theLES were Kfi•fin's constant, Zo is the ice bottom aerodynamic
roughness,
andz• is the depthof the centerof the grid box
modeledby using
adjacentm the ice. By using(3), we areimplicitlyassuminga
constantflux over the first grid box in contactwith the ice
Co= ln(•/Zo)'
Oq•_
Oq•
bottom. For cases initialized
•}G
----Uigx
i •X-•
'(uittq))
+G,
with constant ice thickness and
no leads, the bottom of the ice slab was assumedto be at the
Oq•
whereq• is temperatureT or salinity$; xi are the Cartesian
coordinateswith i = 1 and 2 denotingthe horizontalx and y
axis,respectively,
and3 denotingtheverticalz axis;ui arethe
Cartesianvelocity components;t is time; double primes
denotesubgridscalequantitiesthatarenot explicitlyresolved
in the flow field; Kh is the scalareddydiffusivitycalculated
model top so that z• = 1/2• (at the first momentumgrid
point on the staggered•akawa C grid). This assumptionis
valid for short simulationperiods when the ice growth is
relativelyminor in comparisonwith the grid spacing.Leads
were geated in the samemanner,basicallyplacing the thin
lead ice as an upper bound• condition and ignoring
dynamiceffectsassociatedwith the leadedge.
The prima• surfacefluxes simulatedin the surfaceice/
snowmodel are shown schematicallyin Figure lb. For the
fromthesubgrid
scaleparameterization;
andG• representssnow-coveredice surface, we follow
fluxesfrom frazil ice processes.
At the top model grid point
adjacentto the ice, the subgridscalescalarflux, (ui"•), is
replacedby the ice bottomtemperatureand salinity fluxes,
Cox and Weeks [1988]
andMaykut [1978] andcalculatethe surfacetemperature,To,
at each horizontal grid point location by solving an energy
balance
FT,s,calculated
byusingtheicemodeldescribed
below.
F r + F l - Fœ+ F s+ F e+ F c = 0,
The equationsof motionin the LES modelare modifiedto
includethe effect of surfaceice slabmovementand the presence of frazil ice in the water column,
Oui
Oui
i)t
Ox•
-
where
(u,uj>- •xi+eijkujf
k,
•
a,gE+
c(Pø-P')I
+•a':ui
Po
(4)
(2)
Fr incomingshortwaveradiation;
Fl incominglongwaveradiation;
FE emittedlongwaveradiation;
Fs sensibleheatflux;
Fe latentheatflux;
Fc conductive
heatflux.
All fluxeshave units of watts per squaremeter. At the ice
surface,we prescribeFr, Fl, and Fe. Emitted longwave
radiationis definedby usingthe Stefan-Boltzmanlaw,
where
•= P+
Fœ= •OT4o
(5)
po 5q;
p' andPo represent
the densityperturbation
from the initial
state and the initial state domain averaged density,
respectively;
Pi is thedensityof ice;C is theconcentration
of
frazil ice;f• represents
thecomponents
of theCorioliste•; g
is gravity;P is the pressure;
• is a filter factor(appliedeve•
20th time stepto removehorizontal2• noise);Km is the
subgridscaleeddy viscosity;and q representssubgridScale
turbulencekinetic energy(which is combinedwith pressure
and is not explicitly calculated).Frazil ice affects the
buoyancyof the water colurn in the fifth te• of the
equation.A sugary of the LES and ice model constants
is
presentedin Table 1. For a more detaileddescriptionof the
wheree is the emissivityof ice [Ebert and Curry, 1993] and
o is the Stefan-Boltzman
constant. Sensible heat flux is
parameterized
by usinga bulkaerodynamic
formula:
Fs =PaC. C•V(Ta- To),
(6)
wherePais thedensity
of air, Cpis thespecific
heatat
constantpressure,Cs is the sensibleheat bulk transfer
coefficient,V is the wind speed,andTa is the air temperature.
The conductiveheat flux is definedby assuminga linear
temperature
profilethroughthe ice yielding
kski
F c = •(rw-ro),
(7)
LES model, we refer the readerto Skyllingstadet al. [1999]
hk•+Hk i
andDenboand Skyllingstad[1996].
The effectsof seaice roughness
on the oceancu•ent struc- where
ki (Wm-1K-1)isthethermal
conductivity
oftheice
ture are parameterizedby substituting
the under-icesubgrid [Maykut, 1978] definedas
2480
SKYLLINGSTAD
Table
AND DENBO:
1. Model
TURBULENCE
BENEATH
Constants
Value
Constant
numerical filter factor
gravity
Pi
icedensity
•:
920
kgm-3
0.03
emissivityof ice
m
0.99
Stefan-Boltzman
constant
5.67x 10-8
W m-2K-1
1.4
kgm-3
specific
heatofwater 4.217x 103
J(kgøC)-I
density
ofair
0.003
sensible heat transfer coefficient
0.31
thermalconductivityof snowcover
kS
ms
0.4
ice aerodynamic
roughness
length
Pa
-2
9.81
yon Kfirmfin's constant
•
Unit
0.5
g
Zo
SEA ICE AND LEADS
W m-• K-•
3.34x 105
Jkg-•
kinematic viscosityof seawater
1.4x 10-6
m2 s-•
•T
molecularthermaldiffusivity of seawater
1.4 x 10-7
m2 s-1
•S
molecularhaline diffusivity of seawater
7.4 x 10-•ø
m2 s-•
L
latent heat of fusion
1.0
Nusselt number
Nu
0.564
frazil crystalthermalconductivity
kW
W m-• øC-•
QL = L/(CpPo), whereL is the latentheatof fusion.
Si
Scaling
(8)and(9)withthefriction
velocity
u, = (Z/po)
ki = 2.03
+0.117•o,
Si is the ice salinity,ks is the thermalconductivityof snow
cover,h is the ice thickness,H is the snowthickness,
andTw
andintegratingverticallyyield
T(z)-Tw
is the temperatureof the water at the ice-water interface
[Maykut, 1978]. The experimentsperformedin this paper
(WiceQ
L + F•.)/u,
= •r
(10)
examined
S(z)-Sw
= •s,
Wice(Sw
-- Si)/ll ,
(11)
conditions
with
water
near
or at the seawater
freezing point, thereforeTw was prescribedto the freezing
temperature,Tw = -mSw,where rn = 0.054 [UnitedNations
where'r is thestressimpartedby theice roughness
(from(3))
and Sw is the salinityof the water verticallyadjacentto the and T(z) and S(z) are the temperatureand salinity at the
ice. Equations (4)-(7) were solved by using a Newton- nearestmodelgrid pointin the verticaldirection(locatedat
Raphsontechnique
to obtainTo, Fs, FE, andFc.
Knowingu,, T(z), and S(z) and replacingTw with -rnS•,,
McPhee et al. [1987] developeda setof surfacelayer flux
equationsbasedon a steadystatebalancebetweenice melt- (10)-(11) describea quadraticequationfor the solutionof $w:
ing/freezingand diffusionof heat and salinity.We modified
theseequationsin the presentmodel to includethe effectsof
ec,
Educational, Scientific, and Cultural Organization, 1981],
WiceQ
L = (Woro)- F c
(8)
Wice(Sw-Si) = (WoSo),
(9)
i+ dP
mS2w
+ r(z)_dPrF_•__•
u, _mS
sJSw
-
Si +
IT(z)S i- •rFc
•;sQ•S(z)l
O,
(12)
lt,
where Wic
e -- -pi/Po d represents
the verticalvelocityof the which can thenbe usedto solvefor the ice growthvelocity
ice surface(negativewith ice growth);(Woro) and (woSo)
u,[S(z)-Sw]
representthe heatandsalinityflux into the oceanjust beneath
(13)
Wice =
•s(Sw-S•)
the ice, respectively;d is the ice growth rate; and
SKYLLINGSTAD
AND DENBO:
TURBULENCE
BENEATH
McPhee et al. [1987] point out the significanteffect that
moleculardiffusionhasin controllingseaice meltingrates.
Becauseof thesepossibleeffects,we implementedthe flux
model describedby McPhee et al. [1987]. Nondimensional
SEA ICE AND LEADS
(Ti-T)
q = Nu kw• d
2481
,
functions,(I:)r and (I)S, were prescribed
on the basisof the whereNu is a Nusseltnumber;kw is the thermalconductivity
modelof YaglomandKader[1974]asmodifiedby McPhee of the ice crystals;Ti is the ice temperatureadjacentto the
water,takenas the local freezingtemperatureof the seawater,
et al. [1987]for themolecular
transition
sublayer
1
=
+
Tf =-0.054S-7.53x 10-4z;
T is thelocalseawater
2
temperature;and d is the crystal disc thicknessdefined as
• v
(14)
0.01Ri.At the ice slabbase,frazil ice is deposited
according
to the rise velocityflux, wrC. We assumethat the subgrid
scaleflux of frazil ice is equivalentto other scalars,which is
reasonableas long as the crystalsdo not overly affect the
(I)turb
-' •ln
local subgridturbulentvelocityfield. Freezingandmeltingof
frazil ice affect the temperatureand salinity of the water
wherev isthemolecular
viscosity
andCtr,
Sarethemolecular through
diffusivitiesof heatand salt,respectively.
We follow Mellor
et al. [1986] in calculatingthe heatandsalinityflux from the
ice interfacemodel.Usingthisapproach,fluxesfor heatand
GT= 2Cq, Gs= 2SCq
RiPoCp
salinityare defined:
RiLPo
'
F T = F c+ WiceQ
L
respectively.As a simplification,we ignorethe influenceof
molecularprocesseson exchangeratesbetweenthe crystals
(15)
F s = -Wice(Si-S(z)).
and surroundingwater.
Our choiceof Ri was determinedthroughtrial-and-error
As was shown by Mellor et al., the effects of advection applicationsof the ice model usingobservedturbulentheat
producedby Wic
e on the heat exchangeare negligiblein andsaltfluxesas a basisfor validation.DecreasingRi created
comparisonwith turbulentwall layer fluxes.
greaterproductionof frazil ice but reducedthe depositionof
ObservedLEADEX upperoceantemperatures
were rarely frazil on the slab ice via wr becausethe rise velocity is proabovefreezingduringthe nighttime[seeLevineet al., 1993] portional to Ri [see Jenkinsand Bombosch,1995]. As a
andaswasshownby MS, turbulentheatfluxesat nightwere result, for small Ri, frazil producednear the ice bottom
usuallyupward,implyingthattheseawateradjacentto the ice meltedwithin 2- to 3-m depthbecauseof the pressuredepenwas supercooled.
Supercooled
water typically causesfrazil dence
of Tf(ourinitialtemperature
profilewasassumed
conice to form, whichreleaseslatentheat,therebyreducingthe stantat the under-icefreezing temperature).Melting of frazil
levelof supercooling.
We foundthatapplying(13)-(15) with- producedsalt fluxesthat were lower than the observations.In
out accountingfor frazil ice formation producedturbulent contrast,increasingRi reducedthe productionof frazil but
heat fluxesnear the ice bottomthat were much greaterthan increasedthe removalof frazil as wr increased.On the basis
thoseobservedduringLEADEX, indicatingthe need for a of thesetestcases,we foundthat Ri = 0.001 m gaveresults
frazil ice parameterization.
A modifiedversionof the Omst- consistent with the observed heat and salt flux behavior
edt and Svensson[1984] (hereinafter OS) frazil ice model observedby MS.
wasemployedfor thispurpose.The originalOS model simuWe want to emphasizethat the frazil ice model employed
latesthe effectsof frazil ice by assuminga concentration
of in theseexperimentshasnot been validatedagainstobservasphericalice crystalshavinga constant,prescribedradiusand tionsof frazil ice. Many simplificationsare containedin this
rise velocity.Here we modify the OS model by assuming model,suchas uniformcrystalsize, shape,and growthrates.
disc-shapedcrystals and apply exchangecoefficientsas Becauseof these assumptions,adjustmentsin the crystal
definedby JenkinsandBombosch[1995]. This modification radiusand rise velocity were necessaryso that the modeled
is moreconsistent
with observedcrystalshapes;however,as fluxeswould matchthe observedturbulentfluxes.Clearly, a
waspointedout by OS, frazil ice cantake manyformsrang- morecompletefrazil ice modelwouldbe preferred,for examing from hexagonalstarsto flat discs.
ple, with ice crystal distributionsand accurate exchange
The modified OS model simulatesthe growth of frazil rates.However,observationsof crystalsize and shapedistrithrougha concentrationequationbasedon the LES scalar butionsare neededbeforesucha modelcan be developed.It
equationpresentedin (1):
is also possiblethat unforeseenice processes(e.g., slushy
ice) at theice slabbasealtertheexchangecoefficientsdefined
in (14), therebypreventingsupercooling
andfrazil formation.
Growth and advectionof the ice slab were predictedby
3t
OXi
using the ice growth and rise velocity and prescribedice
advectivevelocityfield,Uiceand
Vice:
+2Cq(RiLP
i)-•
---•(tliC
)4•x•i
Kh•ii)
i)C•
•x3(WrC),
(16)
whereC is the frazil ice concentration,
Ri is the prescribed
crystalradius,wr is theice crystalrisevelocitycalculatedby
3h
Oh
Oh
Po
3t ----Uice•-•
--Vice•y•//Wice
4-WrC'
(17)
following
Jenkins
andBombosch
[1995•'
andq isthesourceThroughoutour simulations,Uice was held constantand Vice
termfor freezingandmelting.The sourceterm is definedas
was set to zero. Leads were initialized with an existing ice
2482
SKYLLINGSTAD
I
AND DENBO: TURBULENCE
I
I
I
10-
10--
•
20
BENEATH SEA ICE AND LEADS
20-
--
30-
40-
40-
50
- 1.70
I
I
- 1.50
I
I
- 1.30
50
I
30.0
Temperature(øC)
I
I
30.•,
I
I
30.8
I
I
.31.2
Salinity(psu)
Figure2. Initial potentialtemperature
andsalinityprofilesrepresenting
conditions
duringLEADEX.
coverof 0.08 m, to avoidshort-termprocesses
involvingthe
transportandraftingof greaseice acrossthe lead.
havethisrestrictionbecauseturbulence
is completelyparameterizedand is not resolvedas it is in LES. For boundarylayers with homogeneous
forcing(for example,a uniformice
3. Experimental Design
However,with leads,circulationssetup by the lead surface
The main focus of the LES experimentswas to quantify
the influenceof ice motion,brine rejection,andfrazil ice on
the upper ocean mixed layer. Initial conditionswere prescribedby usingan idealizedneutralboundarylayer profile
representative
of conditionsmeasuredduringLEADEX (Figure 2). Initial ice thicknesswas set to 1 m with a snowdepth
of 0.25 m for pack ice; leadswere initially assumedto have
ice coverageof 0.08 m without snowcover.Other external
forcingwill causechangesin the boundarylayer structure
thatcanultimatelyaffectthe turbulence
signature
produced
by the lead.To avoidthis interaction,
the durationof lead
forcing
parameters
wereset
asfollows:
Fs= 0 W m-2,Fe=1
2
2
o
100 W m-,F l = 80 W m- , Ta = -25 C, and V= 7.4 m sN m-2) representingconditions
for midwinterat the LEADEX location.Ice salt content,Si,
was setto 4 practicalsalinityunits(psu)for packice and 16
psu for thin lead ice, reflectingobservations
of ice salinity
duringrapid freezing [Eickenet al., 1998]. Pack ice experimentswithoutleadswere performedby usinga domainsize
a wind stressof-0.1
(giving
field),periodicboundaries
donotposea significant
problem.
simulationswas limited so that the lead did not significantly
changethe overallboundarylayer structure.The use of
periodboundaries
imposesa significant
constraint
on the
lengthof leadsimulations,
limitingourinvestigation
to a few
hoursfollowingthe initial leadopening.We cannotrealistically examinethe longtime periodresponse
of the OBL to
leadsby usingthe LES method,exceptfor caseswith lead
coverageequivalentto the experimentalsetup(-21%), which
is considerably
higherthan observedwintertimelead coverage (-5%) duringstorms.Instead,we focuson the turbulent
structurenear the lead and make comparisonswith similar
observations.
Resolution in the lead simulations
was reduced so that the
modeldomaincouldbe increased,therebypermittinglonger
with a grid spacingof 0.75 m (256 x 256 x 64 grid points). simulations.Reduced resolution decreasesthe accuracyof
For caseswith leads, a domain size of 720 m x 720 m in the the resolvededdystructurenear the upperboundaryadjacent
horizontaland 48 m in the vertical was chosenwith a grid to the ice slab,whichmay causea problemin comparingour
spacingof 1.5 m (480 x 480 x 32 gridpoints).A small(10%) results with turbulence observations taken beneath the ice
randomvariability was added to the ice stressand salinity duringLEADEX. Thesemeasurements
were typicallytaken
flux duringthe initial simulatedhour to promotethe forma- at •-4 m belowtheice, whichis only •-3 gridpointsin thelead
tion of turbulenteddies.Simulationswithoutleadswere per- simulations.However,for the heat and salinity flux, most of
formedfor 12 hours,which is •-6 large-eddyturnovertimes, the vertical transportis achievedthrougheddiesthat scale
to allow for the developmentof a nearsteadystateboundary with themixedlayerdepth(-32 m), sothat subgridfluxesare
layerturbulentstructure.Simulationswith leadswererun for still smallin comparison
with theresolvededdyfluxes(thisis
10 hoursbeforeinitializingthe lead.
shownin our analysis).Nevertheless,
detailsof the turbulent
Periodiclateral boundaryconditionswere appliedwith an structureadjacentto the ice are necessarilylackingbecause
openradiativeboundaryconditionfrom Klemp and Durran the flow is dominatedby shearandthe verticaleddystructure
[1983] at the modelbase.LES modelsalmostalwaysemploy is limitedby the grid resolution.
periodic horizontal boundariesto avoid having to define
Two methodswere consideredfor simulatingice motion.
three-dimensional
turbulencevelocity and scalarfields out- In the first method,motionwas modeledby holdingthe lead
constant
a(the centerof themodeldomain
and
sideof the modeldomain.Higher-orderclosuremodelssuch position
asthoseusedby Kantha [1995] or Mellor et al. [1986] do not imposinga constantadvectivevelocity for the entire water
of 192 m x 192 m in the horizontal and 48 m in the vertical
SKYLLINGSTAD
AND DENBO:
TURBULENCE
BENEATH
SEA ICE AND LEADS
2483
Table 2. ExperimentalParameters
Experiment
No-lead
Simulations
150-m lead simulations
Ice Velocity
Ice Thicknessh
Uic
e= 0.0,0.03,0.09,0.12ms-1
1m
Uic
e= 0.0,0.03,0.09ms-1
pack, 1 m; lead, 0.08 m
column [e.g., Kantha, 1995]. The secondmethod held the
modeldomainat a constantpositionand movedthe surface
ice field [e.g., Smithand Morison, 1998]. Both casesare fundamentallythe samebecauseof theperiodicboundaries
(we
are essentiallyperforminga Galileantransformation).
How-
ever,in thefirstmethod,changing
theaveragewatervelocity
generatesincreasednumericalsmoothingthat is inherent
with the flux conservingfinite differencemethodsusedto
advectscalarquantities.
Movingthewateralsoposesa more
stringentcriterionon the maximumadvectivetime step
because
thebackground
watervelocityis thespeedof theice
ratherthanzero.To avoidtheseproblems,we choseto move
theiceandinitializethewatervelocityat zero.
Leadcaseswereinitializedaftera 1O-hourspinup period
by reducingthe ice thickness
overa rectangular
regioncenteredon thex axisandextendingin they directionacrossthe
domainwithconstant
widthof 150m. Simulations
wereperformedfor 2 hoursafter lead initialization, which is aboutthe
timeit takes
forthefastest-moving
leadcase(0.09m s-1)to
advanceacrossthe x axis periodicboundary,reenterthe
domainon the oppositeside,andmovebackto aboutthe center of the domain.
boundaryduring the winter months. Thus turbulent fluxes
producedunderpack ice are an importantpart of the overall
Arctic oceansalinityand heatbudget.
The salinity structurenear the top of the OBL is shownin
Figure 3 for eachof the pack ice velocityscenarios(Table 2)
after 12 hours.The ice growthwas nearly constantfor each
caseat -0.0037 m per day from directfreezingand -0.001 m
per day from frazil ice deposition.As new ice forms beneath
stationaryseaice (Figure3a), rejectedbrine providesthe primary forcing for turbulence.Under the ice, convectivecells
are producedwith scales(-50 to 75 m) that are about twice
the mixed layer depth.Coherentstructures(as shownby animations)appearas narrowdownwellingplumessurrounded
by broadregionsof upwelling,consistentwith previousstudies of planetary boundarylayer convection[Moeng, 1984;
Mason, 1989]. With ice motion,the cellularcoherentpatterns
quickly form into streakystructuresthat are aligned in the
direction of the ice motion (Figures 3b-3c), much like the
coherent turbulent structurein the atmosphericboundary
layer [seeMoeng and Sullivan, 1994]. Scale and separation
between streaksappearto increaseslightly with increasing
ice velocity.
Resultsfrom the SurfaceHeat Budgetof the ArcticOcean
Vertical
cross
sections
fromcases
withUice
= 0.0ms-1and
4 show
theeffect
thaticemotion
hason
(SHEBA)experiment
suggest
thatthe oceanboundarylayer 0.12m s-1inFigure
andicemoveasessentially
oneunit,rotatingwith an inertial the transportof salt from the ice baseto the upperhalocline.
frequency
in response
to windforcing(M. McPhee,personal When
Uice
= 0.0ms-1,plumes
transport
saltdownward
with
communication, 1999). Because of this observation, we
weak lateralmixing (e.g., x = -80 m). Settingthe ice velocity
chose an inertial reference frame for the simulations as was
to0.12m s-1disrupts
thecoherence
of thesaltplumes
and
done by Skyllingstadet al. [2000]. In this referenceframe,
the verticalcomponentof the Coriolis term is set to zero,
avoiding the inertial rotation of the ice and mean current
generatesmore concentratedburststhat mix downward in
responseto local regions of momentum flux from the ice.
Plumesactively transporthorizontalmomentumcreatedby
structure.
the motionof the surfaceice field as shownby the relatively
strongpositivezonal velocityperturbationin the plumeat x =
-10 m. These plumes of enhanced momentum cause
4. Results
increasedmixing of halocline water near the mixed layer
A seriesof sevenexperiments
wereperformedas outlined base, for example, as demonstratedby the detrainmentof
in Table 2. A range of ice velocitieswere considered,with saltierwater at x = -130, z = 30. The correspondence
of high
maximum
values chosen to match observed ice velocities
salinitywith highmomentumflux in the streakswhen Uice =
duringselected
casesfromLEADEX. We beginouranalysis 0.12ms-1isconsistent
withatmospheric
results
fromMoeng
with an overviewof theturbulence
structure
beneathpackice and Sullivan [1994] and Khanna and Brasseur [1998], who
without leads.
4.1. No-Lead Simulations:Turbulence Structure,
Transport, and Energetics
The firstsetof simulations
represent
conditionsthatmight
be expectedin regionsof uniform first-yearice coverage
without leads and with minimal dynamic effects such as
ridgesandkeels.Undertheseconditions,
mixingin theupper
water columnis generatedmostlyby ice bottomroughness
and convectionforcedby salinityflux as new ice freezeson
the bottomof the ice pack.Althoughthe upperoceanfluxes
of heatandsalinitywithoutleadsarerelativelysmall,a large
portionof the Arcticoceanhastheseconditionsas an upper
indicatethatboundarystreaksareregionsof highmomentum
and scalarflux. Overall, the averagesalinityin Figures3 and
4 increases
slightly
when
going
fromUice
= 0.0ms-1toUice
1
= 0.12 ms-. Analysis of the turbulentfluxes (presented
below) indicatesthat entrainmentat the mixed layer base
causes this increase.
Becauseof therole convection
may havein controllingsalt
and heatflux at the baseof the Arctic oceanboundarylayer,
we are particularlyinterestedin the verticalpenetrationof
eddiesproducedat the ice-water interface.One measureof
eddy strengthis the magnitudeof the horizontallyaveraged
eddysaltandheatfluxes,w'S', w'T', whicharekey termsin
the budgetsof the horizontallyaveragedheatandsalt:
2484
SKYLLINGSTAD AND DENBO: TURBULENCE BENEATH SEA ICE AND LEADS
(a)
(b)
-1
Uic
e -- 0.0 m s-1
Uice -- 0.03 m s
7C''i•:11;•;:•.•,:•;:':?;•:;
L•::
•'•'•:::.... :•/' •....•-'.-•.-•:•.:•
,•.. ' ' :'..:
:'.,.•:.•
' • '•.•-•;•.L
150
E lOO
50
o
0
50
1 O0
150
o
5o
1oo
150
x(m)
Ice Motion
(c)
(d)
-1
Uice
Uice - 0.09 rn s
150
-1
-0.12ms
150
30.003
E lOO
•'•
•o
CL
loo
30.002CU
30.001
50
1 O0
150
Figure3. Salinity(psu)at a depthof 4.1 m after12 hoursfor icevelocities
of (a) 0.0, (b) 0.03,(c)
0.09,and(d)0.12m s-1.
•---•
=- O•-(z
w'S'
+Kn••)
+•s
igt =- •zz
+Kh
0__•
0TM
'T----;
• •) +•r.
•}t
boundarylayer, the salt fluxes for each case have similar
profileswith a peakdownwardfluxjustbelowtheice at -2.5
m. Nearthebottomof theboundary
layer,theUice = 0.12m
s-1saltfluxincreases
more
rapidly
sothattheupward
fluxat
(18) -30
m is -50% higherthanthe stationary
case,indicating
greater entrainment of halocline water. This result is
Primesin theseequations
denoteperturbations
aboutthe consistent
with the highmomentum
pulsesnotedin Figure
horizontalmeanandrepresent
theturbulenteddies,whereas 4b, which sweephaloclinewater upwardinto the mixed
overbars
denotehorizontal
averages
or meanprofilevalues. layer.With ice motion,turbulence
at themixedlayerbaseis
Eddy salt and heat fluxes for the four ice velocities are generatedvia increasedmean current shear. Stronger
presented
in Figure5. Alsoshownarethesubgrid
scaleheat turbulenceproducesa greaterlocal flux as saltierhalocline
flux, demonstrating
that the resolvededdy fluxes are water is transported
upward.When the ice is stationary,
dominant
except
for verynearthesurface
andin theupper convective
cells transportsalt directlyto the mixed layer
pycnocline
at themixedlayerbase.Throughout
mostof the base;however,thisgenerates
lessmixingof waterfrom the
SKYLLINGSTAD AND DENBO: TURBULENCE BENEATH SEA ICE AND LEADS
248:5
(a)Uic
e= 0.0rns-1
"-
005
ms
0
-1
50
1 O0
150
x
Ice Motion
(b)Uic
e= 0.12rns-1
.--•
........
•• i":!'
';'"
'i."•
......
'?'•
"•
A
E 10
"-
20
30
lOO
150
x
ß ......
,
30.001
,
,
;50.002
,
,
;50.003
Salinity (psu)
Figure4. Verticalcrosssections
of perturbation
velocityvectorandsalinity(psu)at hour12from(a)
Uice
= 0.0ms-] and(b)Uice
= 0.12ms-].Cross
sections
aretaken
from(a)y = 165mand(b)y = 5
m. Vectorsare plottedfor everyothergrid point.
againdenote
theresolved
eddyfieldor
upper halocline in comparison with shear-generated andprimedquantities
turbulence. Plots of the turbulent heat flux also demonstrate
departure
from
thehorizontal
mean,
E= (1/2pu'i2).
Terms
the effectof shear-induced
entrainment,althoughin the case
of heat, the flux divergenceis reversedfrom the salt flux
becausethe ice heatflux is positive.
The evolutionof turbulencecanbe quantifiedthroughthe
budgetequationfor horizontallyaveragedturbulencekinetic
in the E budgetequationare referredto as (I) shear
production,
(II) buoyantproduction,
(III) dissipation,
and
(IV) total verticaltransportby resolvededdies,subgrid
turbulence,
andpressure,
respectively.
Plotsof thedominant
energy,
presented
above.With stationary
ice,E is produced
mainly
by buoyancy
assalineplumesaccelerate
awayfromtheice.
Interestingly,
frazilformation
justbelowthepackicecauses
a
negative
buoyancy
termbecause
of stratification
produced
by
thelower-density
frazil.A portionof theturbulence
produced
•---•
-'--11
i 113
•X-X3
113'
g•oq-{tl"ill"3)
OXj
I
II
OX
3
III
' " 3+/'t
'3P)
IV
(19)
termsin areshownin Figure6 for thefouricevelocitycases
neartheice bottomis transported
downward
by pressure
and
advective
transport,
sothatdissipation
rates-5 m beneath
the
ice are somewhatsmallerthan the buoyancyterm. At the
mixedlayerbase,the transported
E performs
work against
the stable stratificationof the halocline, as shown by the
where
.,
/Ou
i
illj,)----gmL•x
jq-a.x;i,
J
negativebuoyancyproductionterm. Dissipationratesare
very uniformwith depthshowingthat the transportand
buoyancy
termstendto counteract
eachother.
2486
SKYLLINGSTAD
(a)
I
I
AND DENBO: TURBULENCE
_
4.2.
lO
O.12
ms-•
O0
e- 20
.09
ms-•
0.03
rns-1/
I'•'•,N,",,,
30
35
40
-1.0 x10 -$
0.0 x10ø
SEA ICE AND LEADS
at the mixed layer baseas shownby the increasedbuoyancy
term at 30-35 m in Figure 6d.
I
15
BENEATH
1.0 x10 -e
Salt flux (psu m s-•)
(b)
Comparison With LEADEX Data: No Lead.
Measurementsof turbulenceparametersduringLEADEX
providea uniquedatasetfor testingthe LES modelin simulating under-iceturbulence.Under-icemeasurements
can be
acquiredwith lessdifficultyin comparisonwith open-water
measurements
becauseof the relativelystableplatformprovidedby the ice sheet.Time seriescomparisonsare madeby
usingfive modelprofilesthat are movingwith the ice sheet
velocity,representingstationsanchoredto the ice surface.
Initial positionsof themodelprofilesweretakenfrom a depth
of-2.6 m at the x = 1.5 m boundaryand for five y positions
rangingevery22.5 m startingat y = 1.5 m. Becausethe flow
is turbulent,we cannotexpectto duplicatethe exact conditions that were encounteredduring LEADEX, but we can
makequalitativecomparisons
andestablishif the LES model
reproduces
statisticalvariabilityconsistent
with observedturbulence.
Time seriesplotsof the perturbation
temperature,
salinity,
zonal velocity,vertical velocity, eddy heat, and eddy salt
fluxesfrom a 1-hourperiod on LEADEX day 85.122 (Runway experiment,MS) are shownin Figure7 alongwith simulationresultsfrom hour 12 at y = 24 m. Perturbations
in these
plots are calculatedby subtractinga linear trend from each
time series(this is denotedby the circumflexin the figure)
and are thereforeslightly different from the perturbation
quantitiescalculated by subtractingthe horizontal mean.
0[ I..i•subgrid••••••,••
i I I I• •I
5
0.0,5 m s-•
lO
/
..-.
•5
0.0
ms-1
-,•,/,•,,/'
•//••,:,,
• 20
I'
o.o ,- ,Y/
J.:
Modelresults
aretakenfromtheUic
e = 0.12m s-1 case,
whichis very closeto the observedice velocityof 0.118 m s-
1.Because
theobservations
weremade
atnight(around
midnight,localtime), we assumethatsurfaceforcingwas similar
to the idealized simulationvalues, althoughdaytime solar
heatingand a diurnal cycle in the mixed layer fluxesmay
haveproduceda laggedsignalin thetemperature
(seeMS for
details). The largest qualitative differences between the
observations
and modelresultsare, for the mostpart,related
to the smoother model time series. Model
35
•o'•"X
o.o •.o •o' •.o
Heat flux (Wm -2)
Figure 5. Horizontally averaged(a) salinityflux and (b) heat
flux from under-ice simulations with ice velocities of 0.0,
0.06,and0.12m s-1.
Ice motioncausessignificantchangesfrom the stationary
E budget,particularlyin theuppersectionof theprofile.Current sheargeneratedby the ice createsa shearproduction
term that has two main effectsnear the ice base.First, the dis-
sipationrateincreases
sothata largeportionof theshearproductionterm is immediatelycanceledthroughthe subgrid
model.The secondmajoreffectof the shearis to decreasethe
relativeimportanceof thebuoyancyandadvectivetermsnear
thesurface.Deeperin thewatercolumn,however,shearproductionandthe transportof E beginto havea dominantrole
asicevelocity
isincreased.
WhenUic
e= 0.12ms-1,boththe
transportand shearproductioncausesignificantentrainment
time series are ill-
teredby the combinationof a 4-s model time step,versus
1.5 s for the observations,and temporal averagingof the
third-orderAdams-Bashforthtime-differencingscheme.The
LES modelfieldsarealsofilteredby thesubgridscaleparameterizationso that the smallestresolvededdies (~2Ax) have
very little energy.In effect,the LES modelcannotaccurately
simulateturbulencewith length scalesmuch smaller than
4Ax.
Plotsof theeddyfluxesalsoshowtheeffectsof smoothing,
with measureddata having more pronouncedpeaksin the
fluxes.On average,however,modeledfluxesarewithin -20%
of the observations,
mostlybecausethe large-scaleeddiesare
responsible
for the bulk of the scalartransport.Someof this
agreement
is basedon our choiceof thefrazil ice crystalsize,
which was selectedto yield a heat flux matchwith the nolead, Runwayexperimentdata, thus fitting the model to the
observations.Many factors could explain the differences
betweenthe modeland observations,
but overallthe qualitative comparisonis encouraging,especiallygiven that our
forcingis only an approximationof the actualdata.
A morequantitativecomparisonof the modelandobservationscanbe madeby usingensemble-averaged
spectra.We
computedthe ensemble-averaged,
observedspectralenergy,
SKYLLINGSTAD
AND DENBO: TURBULENCE
BENEATH
SEA ICE AND LEADS
2487
(b)
(a)
Uic
e = 0.0 rn s-1
Uic
e - 0.05 rn $-t
i
___>
Transport
'
Buoyancy
Shear
•i•
•',1
Shear
15
15
'11
Dissipafiøn
•ii !•
Dissipation
•i
',1
•,,j Transparr
30
,/I
40
40
-5.0
xl 0 -a
0.0 x10 ø
5.0 x10 -a
-5.0
,
x10 -a
5.0 x10 -•
0.0 x10 ø
Energy(W kg-•)
Energy(W kg-1)
(d)
(c)
-1
Uic
e - 0.12 m s-1
Uice = 0.09 m s
Buoyancy
Shear
Shear
15
15
Dissipation
' /I• Transport
Transport
Dissipation
•
I
!
!
40
-5.0 x10-•
Buoyancy
40
0.0 x10 ø
5.0 x10 -•
Energy(W kg-1)
-5.0 x10 -B
0.0 x10 ø
5.0 x10 -a
Energy(W kg-•)
Figure 6. Verticalprofilesof the horizontallyaveragedturbulencekinetic energybudgettermsof
equation(19) for shearproduction
(I), buoyancy
production
(II), dissipation
rate(III), andtotaltrans1
1
1
port(IV)foricevelocities
of(a)0.0ms-, (b)0.03ms-, (c)0.09ms-, and(d)0.12ms-].
S(j), wheref = 2re/T,and T is the period,usingdatafrom five
individual hours ranging over day 85.122 to 85.289 of
LEADEX, taken from the "Runway" experiment(Figure 8).
The five time periodswere selectedon the basisof the condition that the net salt flux was negative,indicatingfreezing
conditionsat the ice base.Averageice velocitiesduring the
time of these measurements were between 0.115 and 0.13 m
s-1.Averages
fromthemodel
werecreated
byusing
thefive
time seriesdescribedabove.Model spectraare limited by the
gridresolutionto a maximumfrequency(1/2 theNyquistfrequency)e ual to rcU/2Ax,where U = Uice- u(z-- 3.4 m)=
sured and model data is consistent with observations of wall-
boundedflow reportedby Katul and Parlange[1995]. Kader
and Yaglom[1991] refer to this range of frequencies(or
wavenumbers)as the "productionrange," where energyis
injectedinto the turbulencefield from the meanshear.
At higherfrequencies,
the observedspectrafollow a -5/3
powerlaw indicatingan inertialsubrangethatextendsto the
instrumentresolution.Turbulenceenergyat thesefrequencies
is gainedor lostprimarilythroughinteractions
with otherturbulent eddies,with little injectionof energyfrom the mean
flow. SimulatedSww(J)
and Sss(f)havea more limited-5/3
-0.08
ms-ct
isthe
ice
relative
average
horizontal
velocity
atz regionin comparisonwith thedatabecauseof the modelres-
= 2.6-m depth. As Figure 8 shows,the model compares
favorablywith the low-frequencyflow featuresandis ableto
duplicatethe-1 spectralbehaviorthat is evidentin the measureddata.The presenceof a-1 spectralregionin the mea-
olutionbut are in goodagreementat the resolvedfrequency.
The agreementbetweenthe model and observedspectrato
just beyondthe observedtransitionbetweenthe -1 and-5/3
regionsindicatesthatthe modelresolutionis likely sufficient
2488
SKYLLINGSTADAND DENBO:TURBULENCEBENEATHSEAICE AND LEADS
(b) Model Results
(a) Observations
0.002
0.002
o,.,o.ooo 4,-,,,-.x?.•-.•.-,,.-.
•.,,'•-,•,•..• .t•.;w.•,..•-•.',•-,,_w-,-•-•-o,.,o.ooo
-0.002
-0.002
0.003
o.
•
.A•, .• •..•'•1,,, h,,,,, ,t
0.000
•'
0.003
"'"'"'•....
•'•"'•"•' 't •o.ooo
-0.003
-0.003
0.025
0.025
7
E o.ooo
E o.ooo
-0.025
-0.025
0.025
0.025
E o.ooo
E o.ooo
I
<•:
-0.025
0
10
20
30
40
50
-0.025o
60
1o
20
30
40
50
Time (mln)
Time (rain)
..-. o.ool
i
E o.ooo
............................
•--.ds,,
0.000
-o.ool
,•,0.002
E
1.....J..,d,,
•
,
,
,
,
...•,,-•
..........
•
,
• • 0.002
,..,
E
<•
<•
< • -0.002
0
<• -0.002
10
20
30
Time (rain)
40
50
60
0
10
20
30
40
50
60
Time (rain)
Figure 7. Time seriesof (a) observed
and(b) modeledperturbation
temperature,
perturbation
salinity,
perturbation
zonalvelocity,verticalvelocity,heatflux, andsaltflux.Observations
aretakenstartingat
day 85.122 of LEADEX from a depthof 3.0 m below the ice. Model resultsare from y= 24 m
betweenhours11 and 12 at a depthof 2.625 m. The averageobservedheatandsalinityfluxesare2.81
x 10-7 K m-2(1.14W m-2)and-1.63x 10-6psums-],where
theaverage
modeled
heatandsalinity
fluxes
are2.0x 10-7K m-2(0.8W m-2)and-1.11x 10-6psums-](fromfivetimeseries
adjusted
to3m depth).
for thecurrentapplication.
Furtherconfidence
is providedby tion,centeredon thex axis(seethe Uice= 0.0 casein Figure9
the spatialspectra,takenas the x axis ensembleaverageof for the approximateinitial location).We chosethis initializathey axisspectra,whichindicatea broader-5/3 regionin the tion procedureso that turbulencein the boundarylayer would
modelspectra.
be fully developed,simulatingupperoceanconditionsafter a
sustainedperiodunderuniformlyroughice beforeencountering the lead. Initial ice thicknessof the lead was set to 0.08
4.3. Lead Simulations:TurbulenceStructure,Transport,
m, which yieldeda nearlyconstantice growthrate of-0.028
and Energetics
rn/d over the lead duringthe 2-hour simulationperiod.
The leadexperiments
focuson threedifferentice velocity
Horizontal cross-sectionplots of the salinity for the lead
cases,eachhavingidenticalforcing as the no-leadcasesbut casesare shownin Figure9 from a depthof 3.8 m at hour 12
with different surface ice velocities as shown in Table 1. Lead
or 2 hoursafter initializing the lead. As in the no-leadcases,
simulationsare performedby initializingthe flow fieldsasin ice motionhasa profoundeffect on the strengthand organithe uniform ice simulations discussed above and then at hour
zation of turbulencein the boundarylayer. When ice is sta10 openinga 150-m-widelead extendingacrossthe y direc- tionary,plumesare producedat the lead edge that quickly
SKYLLINGSTAD
AND DENBO: TURBULENCE
BENEATH SEA ICE AND LEADS
2489
of downward
motion,ratherthana singleplume
removethe moresalinewaterproducedduringfreezingat the tworegions
lead surfaceand transportit to the mixed layer base.The centeredon the leadaxis.This is shownmoreclearlyin a verplot (Figure 10a), wheretwo regionsof
structureof turbulencein this case is almost completely tical cross-section
-50 m apartin thecenter
determined
by theleadcoolingrateandleadwidth,with con- strongverticalmotionareindicated
vectiveplumesactingasa conduitfor the verticaltransport
of of the lead.
Ice motionbreaksthesymmetryof theleadconvective
cirsalt and heat.Becausethe lead is considerablywider thanthe
by disconnecting
thesurface
forcingfromtherestof
mixedlayerdepth,the patternof convectionis dominatedby culation
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•
_
_
-
_
_
10-14
-
I
10-3
I
I
I
I
I I I I
10 -2
I
I
I
I
I
I I I I
10 -1
I
I
I
I
I
I I I
10ø
Figure 8. Time seriesspectraof (a) w and(b) S fromLEADEX observations
on day 85.122(black)
andmodel
hour11-12(gray).
Alsoshown
arethek-5/3andk-1spectral
curves
representing
theinertial
subrange
andproduction
rangeof turbulence
and,in Figure8a,themodelx axisensemble
averaged
y
axisspectracalculated
from hour 12 (labeled"spatialtransform").
2490
SKYLLINGSTAD
AND
DENBO:
TURBULENCE
BENEATH
SEA ICE AND
LEADS
(Iv) Uic
e = 0.0;5m s-1
(a)
600
40O
200
400
2OO
600
x(m)
(c)
Uice
0
200
0.09
m
s
600
x(n,)
Ice Motion
=
400
-1
600
50.007
4OO
,..,,
v
50.005
>'
200
30.003
30.001
0
200
400
600
Figure 9. Salinity (psu)at a depthof 3.8 m below the pack ice after 12 hoursfor ice velocitiesof (a)
0.0ms-], (b)0.03ms-],and(c)0.09ms-1andaninitialleadwidthof 150m.These
plots
are2 hours
afteropening
thelead.
NotethatwithUic
e= 0.09ms-1theleadbegins
atthecenter
ofthedomain,
as
in Figure9a, andadvectsthroughthe right-handsideperiodicboundary,reappearing
on the leviathan
sideandadvectingbackto almostthe middleof the domain,centeredat x = -288 m.
the lead circulationas shownin Figures9b-9c and 10b. This
tendsto smooththe effectsof leadconvectionby separating
convectiveelementsfrom the surfaceforcing and by introducing a diffusive turbulentflux from ice roughnessand
shearproduction.The importanceof under-iceshearproduction is made clear by the coherentstructureof turbulence
the enhancedsalinityflux at the leadcausesa gradualdeepeningof the salineplumesdownstream
from the lead.With
eachplumeis a tendencyfor positivemomentumtransportas
shownby the vectororientationwithinthe plumes.Thusthe
plumesactto transportmeanmomentumgeneratedby the ice
motiondownwardinto the mixed layer.
within the lead circulation,which is setmostlyby streaksthat
Visual inspectionof the crosssectionsshownin Figures9
arepresentunderthe packice. Thesevorticesare enhancedat and 10 suggests
that the verticalsalt and heat fluxesbeneath
the lead by increasedsalinity flux but in general remain leadsare greatly affectedby increasingice motion. This is
coherentas the lead passesoverhead.As Figure 10b shows, verified by plotting the averagesalt and heat flux for each
SKYLLINGSTAD
AND DENBO: TURBULENCE
case at hour 12 (Figure 11). In thesecases,increasingice
motionforcesweakerturbulentheatflux but strongerentrainmentat the mixing layerbaseasindicatedby the salinityflux.
The depthof the maximumheat flux increaseswith decreasing ice velocitybecauseindividualplumesare able to extend
deeperinto the boundarylayer with lesscurrentshear.All of
the flux profileswith leadshadmaximathatwere deeperthan
the no-leadsimulations.Plots of the E budgetprofiles(not
presented)are similar to plots for the pack ice simulations
shownin Figure7 but with a strongerbuoyancyterm because
of the increased surface salt flux at the lead.
The relative importanceof turbulencegeneratedby ice
motion versusbuoyancyforcing can be estimatedby using
the ratio of the mixed layer depthandMonin-Obukhovlength
scale defined as
BENEATH
SEA ICE AND LEADS
2491
pack ice region, respectively.Similar nondimensional
numbersare given by Morison et al. [1992] and Kantha
[1995].
Values
forLorange
from-1forUic
e= 0.09m s-1,
indicatinga mixedforcedandfreeconvection
regime,to -15
forUice
= 0.03m s-1,implying
a freeconvective
scenario.
Thesevaluesare consistentwith thosereportedby Morison
and McPhee [1998] for leads3 and 4 of LEADEX, which
hadicevelocities
of-0.09and-0.03ms-1,respectively.
4.4. ComparisonWith LEADEX Data From Lead 3
Comparisonbetween LEADEX observationsand the
modelwere madeby usingdatafrom lead 3 takenbetween
day98.427and98.594at a depthof 4.3 m. At thetimeof the
observations,lead 3 was --1 km wide, coveredwith -8 cm of
ice,andhadanicemotion
of 0.092m s-1.Timeseries
plots
are presented
in Figure 12 comparing
the observedturbu-
,
Lo= gd(w'O') lead
(20)
lencecharacteristics
with the modeloutputfrom the Uice=
0.09 rn s-I case.Thesetime seriesweretakenfrom the downwhere d = 32 m is the mixed layer depthand the buoyancy streamleadedgeat y = 46.5 m andat a modeldepthof 3.8 m,
and momentumfluxesare estimatesover the lead region or usingthe samex positions
astheno-leadcase.As in the no-
p(UtW
t) ice
(a)Uic
e= 0.0rns-1
o
.
..
ElO
•':i•::
•i"
.....
.I"'•-•-•ma'""••-•'•••••"'•••••""
'•--'
"j "• ••r
0.20
-==?•==---=='=•-=---'
............
'•"•"'"
•"='""
................................
?•:'="•';.--:'
•'•'"-:
..-L"=•t
-' "'•'"
50
225
325
275
375
425
475
x (•)
Ice Motion
(b)Uic
e- 0.09rns'1
o
E10
.c 20
•, 30
40
75
175
125
225
275
325
375
x (m)
0.05 rn s-]
30.001
30.003
30.005
30.007
Salinity (psu)
Figure10. Cross-section
plotsof salinityandperturbation
velocityvectorfor leadsimulations
with
(a)Uice
= 0.0ms-1and(b)Uice
= 0.09ms-1.Sections
aretaken
fromy = 200athour12.Leadposition is indicatedby the thick line abovethe plots.
2492
SKYLLINGSTAD
AND DENBO' TURBULENCE
(a)
'\ •
'• "•,,•
lO
15
0.0m 1
/
0.03
.s: 20
o.o
,-,
30
35
40
-1.2
x10 -6
, i •/Ji
-6.0 xl 0 -7
0.0 xl 0ø
6.0 x 0 -7
Salt flux (ps• m s-'•)
(b)
o
i
i
i
i
5
lO
0.09ms
,
15
E
.c:
2o
0.03
ms-'"•.•'//
/
/7
25
3o
35
•.•
BENEATH
SEA ICE AND LEADS
resemblesimilar structuresobservedin the atmosphereand
OBL, as was notedby Thorpe[1985].
Overall, the range of simulatedsalinity is relatively close
to the observations,
althoughtemperaturevariationsappearto
be greaterin the LEADEX data.Heat and salinityflux values
showgoodagreement;however,as Figure 11 shows,vertical
turbulentflux gradientsvary rapidly near the ice bottom.
Thusrelativelyminorverticalaveragingcouldleadto significant changesin the heat and salinityflux estimates.Plots of
the ensembleaveragedspectratakenfrom the five time series
cases (Figure 13) also show reasonablecorrespondence,
althoughthe agreementis not a goodasthe higher-resolution
no-leadcase(Figure8). Nevertheless,
the spatialspectrastill
show a region of-5/3 drop-off indicatingthat the model is
simulatinga portion of the inertial subrange.The vertical
velocity spectraare again in betteragreementthan the salinity spectra,which showsa "flatter"profile at large scalesin
comparisonwith the observations.
The relativelygoodagreementbetweenthe simulatedand
observedtime seriesand fluxesis somewhatsurprisinggiven
the much greater lead width for lead 3 versusthe model
(•-1000 m versus150 m). This can be explainedby considering the relatively shallow time seriesdepth relative to the
boundarylayer changesbroughton by the lead surfacefluxes.
As waterpassesunderthe lead,it developsan internalboundary layerforcedby the leadsurfacefluxes.In the time it takes
the lead to traverse150 m, this boundarylayer grows to
almostthe haloclinedepth at 32 m. Thus the lead internal
boundarylayer has almost reachedthe preexistingOBL
depthby the time the data are collected.This growthis consistentwith Morison and McPhee [ 1998], who used an autonomous
underwater
vehicle
to
examine
the
horizontal
turbulentstructurebeneathlead 3 at 15-m depth,They found
that fluxeswere relativelyuniformacrossthe lead,indicating
thatthe lead-inducedboundarylayerrapidlyreachedan equilibrium downstreamfrom the leadedge.
5. Frazil
Ice Effects
Althoughmostof theheatlostthroughtheice goestoward
new ice growthat the ice base,a significantfractionof the
4o
heatlossactsto coolthe oceanjust beneaththe ice. During
0.0
LEADEX, theboundarylayertemperature
structure
wastypHeat flux (W m-2)
ically very nearfreezingso that heat flux from the water to
the ice producedsupercoolingand formationof frazil ice.
Figure 11. Horizontally averaged(a) salinity flux and (b) Using optical techniques,Pegauet al. [1996] observedthat
heat flux from 150-m lead simulations with ice velocities of
mostof the frazil ice formedby surfacecoolingwasconfined
0.0,0.03,and0.09m s-1.
to the upper2-3 m of the watercolumn.This was alsotrue in
our simulations,as is shownby a plot of the y axis averaged
frazil icefor the Uice = 0.09 m s-1 leadcase(Figure14). Modleadcase,smoothing
in themodelcauses
thegreatest
qualita- eled concentrations
are similarto the observations
(-0.05 kg
tive difference between the simulation and measurements.
m-3)withthehighest
concentrations
located
justbeneath
the
Nonetheless,
the modelduplicates
the generalpatternof
surfaceand a strongreductionin concentrationbelow -5 m.
strongdownwardmoving salineplumesas shownin the Observations
of the frazil verticalstructureshowa sharpcutLEADEX data. The effect of the lead in these time series is off of measurable
concentrations
between3- and4- m depth,
mostnotablebythemuchlargertemperature
andsalinityper- whereas in the model, the concentrationdrops off more
turbations
in comparison
with the no-leadcase(Figure7; smoothly.The frazil modelusedin theLES only considereda
notethe changein axisscales).We alsonotethatperturba- singlecrystalsize and did not simulatethe effectsof crystal
tionstendto havelongertimescales
in theleadcase,suggest- growth.The lack of theseprocesses,
along with the coarse
ingmorecoherent
plumes
of downward
movingsalinewater. gridresolution,couldhavecontributedto the relativelylarger
There is an indicationof ramp-likestructures
in the time concentration
in the simulatedfrazil ice andthe greaterdepth
series,withsalinityincreasing
relativelyslowlybeforedrop- of frazil transport(crystalswould have grown and moved
ping rapidlyas plumespassthe measurement
site.They upward because of buoyancy). Nevertheless,the simple
SKYLLINGSTAD
AND DENBO: TURBULENCE
SEA ICE AND LEADS
2493
(b) Model Results
(a) Observations
•
BENEATH
•
o.ooo
o.ooo
0.006
•- 0.000
0.000
-0.006
-0.006
0.025
•,. 0.025
T
0.000
E o.ooo
-0.025
-0.025
0.025
0.025
E o.ooo
E o.ooo
-0.025
10
20
50
40
50
10
20
•,.
50
40
50
40
50
Time (rain)
Time (min)
0.005
0.005
• 0.000
o
-0.005
,•.
0.010
0.010
T
E
0.000
-0.010
0
c•-0.010
10
20
,50
Time(rain)
40
50
60
0
10
20
,50
60
Time(rain)
Figure 12. Time seriesof (a) observedand (b) modeledperturbationtemperature,salinity,zonal
velocity,verticalvelocity,heatflux, and saltflux. Observations
are takenfrom 4.3 m belowthe ice
startingat day 98.51 of LEADEX. Model resultsaretakenbetweenhours11 and 12 from a depthof
3.8 m on thedownstream
leadedgeat y = 46.5 m. The meanobservedheatandsalinityfluxesare3.54
x 10-6øCm-2(-14W m-2)and-1.54x 10-5psums-], whereas
themean
modeled
heatandsalinity
fluxes
are-2.5x 10-6øCm-2(-10 W m-2)and- -1.2x 10-5psum s-] (based
onfivetimeseries
adjustedto 4.3 m).
modelemployedhereproducedgoodresultsfor the short pressure
effecton freezingpoint).Melting coolsthe water
timeperiodsimulations.
column;however,thisis offsetby turbulentheattransportso
Without frazil ice, the heat budgetof the ice-coveredthatthe localtemperature
changeis minor.Frazil concentraboundary
layeris incomplete.
Thisis clearlyshownby com- tionfallsto nearzerobelow-10 m, andtemperature
changes
paringtheboundary
layerturbulent
heatbudgetwiththefra- in the lowerhalf of the boundarylayerare dominatedby
zil sourcetermfrom as presented
in Figure15. Heat flux coolingfrom turbulenttransport.
Continuous
coolingof the
fromtheoceanintothe-0.08-m-thickiceovertheleadis -35 middepthboundarylayerby frazil meltingwouldeventually
W m-2inthesimulation.
Mostofthisfluxisremoved
viafra- cause
thelocaltemperature
todecrease
tothefreezing
point.
zil production
in theupper5 m of thewatercolumnasshown However,duringLEADEX, daytimesolarradiationheated
bythesignificant
heating
generated
byfrazilproduction.
A thewater
below
theleadwitha fluxofupto-100W m-2,
largeportionof the frazil ice risesto the ice bottomandis compensating
for the nighttimecoolingfromfrazil ice melt-
incorporated
into the ice sheet,effectivelydecreasing
the heat ing.
flux outof the upperocean.Below-5-m depth,frazil transWe notethata similarverticalheatingprofileis produced
porteddownwardby turbulence
startsto meltastheseawater by frazil icein thepackicesimulations
discussed
in section1
temperaturerises slightly abovefreezing (becauseof the (notshown).However,in caseswith 1-m-thickpackice, the
2494
SKYLLINGSTAD
AND DENBO: TURBULENCE
I
10-4
I
I
I i I I [
•
10 -5 _
10-s
I
]
I
BENEATH
I
I
SEA ICE AND LEADS
I I ill
I
t
I
I
Model
I I I I
(a)
..........
'...........................
'"•,,•
....
--.'",,,/•
.,•,..,..:•, Observations
_
•: 10-7
Spatial
Spectra
10-•
'^
10-9 --=
_
_
_
_
_
_
_
10-m
[
!
[
10-3
t
10 -5
•
t
t
• tt,I
]
,
,
i
i
i
[
[
!
i
i
i
Model
10-6
10 -7
_
"•'"'"•...x,,.
'//!
......
...••
10-9
Observations
10-•o
[
]
[
!
'
[ ' I
10-2
!
!
'
[
!
[ [ [ [
1O-•
[
[
[ [ !
10ø
Figure13. Timeseries
spectra
of (a) w and(b)S fromLEADEXobservations
onday98.51(black)
andmodel
hour11-12
(gray)
fromtheUic
e= 0.09ms-1leadsimulation.
Thek-5/3andk-1spectral
curvesarealsoshown,
representing
theinertialsubrange
andproduction
rangeof turbulence,
andthe
spatial
y axisspectra
ensemble
averaged
in thex direction
forsalinity
fromz = 3.8m (offset
bya factorof0.01).Because
thefrequency
spectra
aretaken
fromtheleadcirculation,
theyhavemoreenergy
thanthe spatiallyaveragedspectra.
oceancooling rates are much smaller,so that frazil concen- (Figure16). Beneaththelead,heatflux is relativelysmall,as
trationsare very small. In addition,mostof the frazil ice is mostof the surfaceheatlossgoestowardfrazil ice formation.
deposited
on thebaseof thepackice beforeit canbe trans- As the frazil ice meltsand plumevelocitiesincreasedownportedto significantdepthsand melted.Frazil ice in these stream from the lead, the turbulent heat flux increases to a
casesis, in effect,equivalent
to an increase
in thepackice maximum-25-50 m downstream
from the leadedge.The
freezingrate,whichcauses
lessoceancoolinganda greater localmaximumin heatflux decreases
to nearbackground
under-ice salt flux.
A plotof theturbulent
heatflux,w'T', averaged
alongthe
y axis providesa clearer view of the local effect of the lead
values -200 m downstream from the lead.
The verticalprofileof heatflux in Figure16 at the downstreamleadedgeis consistentwith LEADEX measurements,
SKYLLINGSTAD
AND DENBO:
TURBULENCE
BENEATH
SEA ICE AND LEADS
2495
Ice Motion
Lead Location
IIIIIII III I IIIII
-'.-'"--'-'".
....::(:i:i:•
•' •:!•:':;':•'•J•i,..•'..,.
....
•.
........•:•.i•..•::':."
'O.O1 ' '- '-. .........
2O
o
,oo
Figure14.Cross
section
ofy axisaveraged
fraziliceconcentration
inkgm-3athour12fortheUic
e=
0.09 m s-] leadsimulation.
showing
anincrease
from~6W m-2at4-mdepth
to~30W
m-2at10-m
depth
reported
inMS.Without
frazilice,it isdif-
mum in turbulentheatflux just belowthe surfaceanda nearlinear decreasein heat flux with depth[seeSkyllingstadand
ficult to explain how heat flux would increasewith depth Denbo, 1995]. One alternativeexplanationfor the heat flux
below
theleadatnight.
Typical
boundary
layer
'heat
fluxpro- maximummightbe the entrainmentof relativelywarm water
files for a cooledconvectiveboundarylayer showa maxi- from the pycnocline(sincewater temperatureincreaseswith
increasingdepth).This is evidentin Figure 16, asis shownby
the higher heat flux at ~30 m. However, fluxes related to
entrainmentcovera smallerregion and are physicallysepaI
I
I
I
rate from the maximum
heat flux in the middle of the bound-
ary layer downstreamfrom the lead. Becausemost of the
/
downward shift in heat flux is due to frazil ice effects, we
Frazil
believetherole of frazil ice may be criticalin determiningthe
polaroceanheatbudget,especiallyunderleads.
/
/ •'• Turbulenf
6. Conclusions
10
Tofol
e-
A large-eddysimulationof turbulenceunderfreezing sea
ice andleadswasperformedfor a rangeof ice velocitiesand
comparedwith observedturbulenceparameters.Stationary
ice withoutleadsproducedturbulentstructures
that exhibited
a cellularpatternsimilar to atmosphericboundarylayer convectionnotedin previousLES studies.Ice motioncausedthis
patternto break down rapidly, with ice velocitiesas low as
T
15
2O
0.03m s-] promoting
theformation
of streak-like
structures
25
3O
I
o.oo
I
I
O. lO
Heating (øC per day)
0.20
alignedwith the ice motion.With increasingice velocity,the
horizontal separationbetween the streaksgrew, and they
becameless distinct becauseof more vigoroussmall-scale
turbulence.Analysisof the heat and salinityfluxesshowed
that slow-moving ice caused a decreasein the relative
strengthof the heatflux just underthe ice relativeto stationary ice, but with faster velocity, the flux again increased.
Entrainment at the mixed layer base also increased in
response
to sheargenerated
by moreboundary
layermomen-
tum. Analysisof the TKE budgetfor eachcasedemonstrated
shear production from strong ice velocities overlation along with turbulentflux and frazil heatingrates whelmedentrainmentfrom negativelybuoyantplumesin the
averagedbetweenhours10 and 12. Note that mostof the fra- stationarycase.
zil heatingabove~ 4 m is accounted
for by deposition
of
Openingof leadscausedsignificantchangesin the turbufrazil ice on the bottom of the surface ice slab.
lent structureof the mixed layer,particularlywhenice veloc-
Figure
15.Total
heating
rateforUice
= 0.09ms-I leadsimu- how
2496
SKYLLINGSTAD
AND DENBO: TURBULENCE
BENEATH
SEA ICE AND LEADS
Ice Motion
Lead
Location
lO
3o
4o
o
1 oo
2oo
5oo
400
X(m)
Figure16. Cross
section
ofturbulent
heatflux( pCvw'T') fromtheUice= 0.09leadcase
athour7.
Theheatfluxis averaged
alongthey axis.Thicklineabovethegraphsignifies
theapproximate
location of the lead.
ity was small.A 150-m lead in stationaryice generatedtwo
downwellingregionswith spacingof-50 m, centeredin the
middle of the lead. Ice motion caused a much different struc-
ture, with preexistingcoherentstreakstructures
definingthe
main plumesof higher-salinitywaterbeneaththe lead.Traveling leadsproduceda trailing plume of enhancedsalinity
anddownwarddirectedvelocitythatlengthened
with increasing ice velocity.In comparisonwith the pack ice simulations,
heat flux peakedat greaterdepthsbecauseof the higherconcentrationof frazil ice andrelatedheat transport.
Model time seriesdatatakenfrom a pointmovingwith the
ice showedgoodcomparisonwith LEADEX datafrom under
pack ice and the edgeof a 1-km-widelead.Qualitativecomparisonshowedthatthe modelwas able to duplicatelow-frequency flow features,such as plume structures,with good
accuracy. Comparisonof modeled and measuredvertical
velocity and salinityspectrashowedgood agreementat low
frequenciescoveringa portion of the productionrange and
inertial subrange.
Fluxes were also modeledaccurately;however,this good
agreementwas partly a resultof the ice crystalsize selection
boundarylayer.In comparison,
typicalconvectiveboundary
layershavea maximumturbulentfluxjust belowthe cooled
surface[e.g.,Skyllingstad
andDenbo,1995].A possibleconsequenceof this result is that accuratemeasurements
of
under-ice heat flux may require turbulencemeasurements
away from the ice bottomto avoid errorsassociated
with
latentheatcontainedin transported
frazil ice.
Simulationresultsimply that the effect of leadson the
upperoceanheatandsalinitybudgetsmay needspecialized
parameterization
in modelsof thepolaroceans.Forexample,
our resultsindicatethat frazil ice underleadscan carry a sig-
nificant
heatflux(i.e.,--10-30
W m-2)andneeds
toberepresentedin the upperoceanheatbudget.Most thermodynamic
seaice modelssimplyconvertall heatinto new ice whenthe
oceantemperature
reachesthefreezingpoint.LEADEX measurementsand our resultsindicatethat a significantfraction
of the outgoingheatflux cancool the oceanboundarylayer
while ice is forming.We planto furtherexplorethishypothesis in future researchby usingdata from the SurfaceHeat
Budgetin the Arctic(SHEBA) experiment.
in the frazil ice model. Nevertheless, the constant frazil ice
Acknowledgments.The authorswould like to thank the three
anonymous
reviewersandWilliam Smythand ClaytonPaulson
scenarios(i.e., under 1-m-thick ice versus0.08-m lead ice), for veryusefulcomments.
Specialgratitudeis extendedto Miles
indicatingthat the modelis robustand shouldbe applicable McPhee for kindly supplyingturbulencedata from LEADEX.
over a rangeof conditions.Transportof heat by frazil ice in We would also like to acknowledgethe supercomputertime
the boundarylayer was found to have a significantrole in providedby theNationalCenterfor Atmospheric
Research.
This
determiningthe overall flux of heat into the upper ocean. work was supported
as partof the SHEBA projectby National
Near the ice bottom, most of the heat transferred to the water
ScienceFoundationgrantOCE-97-03539.
was usedto form frazil ice, which was then depositedunder
the ice and mixed downwardby turbulence.Melting of the
References
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increasein the local turbulentheat Backhaus,J. O., and J. Kampf, Simulationsof sub-mesoscale
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AND DENBO:
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Omstedt,A., and U. Svensson,
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Jenkins,A., andA. Bombosch,Modelingthe effectsof frazil ice
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(ReceivedOctober11, 1999;revisedMay 26, 2000;
acceptedOctober 10, 2000.)