JOURNALOF GEOPHYSICALRESEARCH,VOL. 98,NO. D10,PAGES18,589-18,595,
OCTOBER20, 1993
ChaoticAdvectionin the StratosphereImplicationsfor the Dispersal
of Chemically Perturbed Air From the Polar Vortex
R. BRADLEY PIERCE
Atmospheric
Sciences
Division,NASALangleyResearchCenter,Hampton,Virginia
T. DUNC^N A. FAi}•LIE
Scienceand Technology
Corporation,
Hampton,Virginia
The Lagrangianevolutionof materiallines within the northernhemispherewinter stratospheric
vortex is determinedusing isentropicwinds and diabaticheatingrates obtainedfrom the NASA
LangleyResearchCenter(LaRC) atmospheric
circulationmodel.Transient,subtropical
anticyclones
lead to deformationof the materiallinesnear the edgeof the polar vortexwhich then rapidly evolve
into elongatedfilamentsas material is drawn aroundthe anticyclones.The rate of stretchingof the
materiallinesis shownto be exponential,with typicale-foldingtimesof the orderof 4 to 8 days. These
resultsprovideevidencefor "chaoticadvection"nearthe edgeof the stratospheric
polarvortex which
leads to rapid mixing of vortex air with tropical and midlatitudeair. The characteristictimescalesof
thesemixingprocessesand the extentto whichthe mixingpenetratesthe polar vortex have important
implications for the dispersal of chemically perturbed air from the polar vortex throughout the
northern hemisphereand attendant ozone depletion.
INTRODUCTION
al., 1987]. The stratosphericwinds and heating rates axe
representedusingsphericalharmonic expansionin the horThe observed 2-6% reductions in middle- and high- izontal (triangular truncation to wave number 16) and a
latitudetotal ozone in the northern hemisphere stratosphere vertical resolution of 3 km. The use of realistic large-scale
windsandradiativeheatingdistributionsin this
overthe last 10 years [Stolarskiet al., 1991]have been linked stratospheric
toprocessing
of stratosphericair within the polarvortex. An investigationallows us to assessthe impact of large-scale
on the dispersalof polar air in the lower
understanding
of the processesthat are responsiblefor the transportprocesses
transportof processedair out of the vortex and subsequent stratosphere.
Plate 1 shows streamlines of the circulation on the 425 K
mixingwith midlatitudeand subtropicalair is fundamentalto
a completeunderstandingof the ozonedepletionproblem.A surface for December ! of the LaRC model simulation. The
numberof outstandingissuesremain. What are the charac- map shows a large circumpolarcyclonic vortex with a
teristictimescalesfor the dispersalof air from the polar counterclockwise circulation and smaller transient anticyvortex? How far into the polar vortex does the mixing cloneswhich are locatedin subtropicallatitudes.This patof the large-scaleflow during
processextend?To what extent doeslow-latitude air pene- tern is fairly representative
midwinter in the lower stratosphereof the northern hemitrate the vortex?
larger
In this paper we addresstheseissuesby investigatingthe sphere,althoughthe simulatedvortex is considerably
in Plate
behaviorof material lines located within the polar vortex in than is typicallyobserved.The coloredstreamlines
thelowerstratosphere.
We considerthe behaviorof material ! reflectstreamlinesalongwhichair parcelsorbit within and
linesthat are initially located on the 425 K surface of around the edge of the polar vortex. During the model
potentialtemperature(0). Within the isentropicframework, simulationthe anticyclonesmove eastwardaroundthe polar
0isusedas a vertical coordinate.Quasi-horizontaldistortion vortex and the closed streamlines within the vortex deform,
regionsof increased
curvaturebetweenthe antiof material lines which are initially located on isentropic developing
surfaces
is causedby transientadiabaticdisturbances,while cyclones.Rossbywave breaking[Mcintyre and Palmer,
diabatic
heatingandcoolingleadsto verticaldisplacement
of
the materiallines. The 425 K isentropic surface, which lies
near70 mbar in the lower stratosphere,correspondsto the
regionwherethe potentialfor chemicalprocessing
of stratosphericair and the attendant ozone losses are likely to be
1983]mayoccurnearsuchregionsresultingin theejectionof
filamentsof vortex materialinto subtropicallatitudes[Polvani and Plumb, 1992].In this paper we will investigatethe
evolutionand morphology
of materiallineswhich are ini-
tially coincident
with the instantaneous
streamlines
within
largestdue to cold temperatureswhich favor the formation the polarvortexon DecemberI of the modelsimulation.
of polarstratospheric
clouds(PSCs).
We have conductednumerical computationsusing full
LAGRANG!AN
EVOLUTIONOF VORTEXMATERIALLINES
three-dimensional distributions of horizontal winds and ra-
The differentialadvectionof material elementsby a three-
diativeheatingrates from the NASA Langley Research
dimensional,time-dependent
circulationcanbe investigated
Center(LaRC)atmospheric
circulationmodel[Blackshear
et
by computing
the Lagrangian
evolutionof a matehalline
Copyright1993by the AmericanGeophysicalUnion.
which is composedof an ensembleof parcels.The LagranPapernumber93JD01619.
0148-0227/93/93
JD-01619505.00
gian representation
of three-dimensional
advectionof a
materialline composed
of (n) parcelsin isentropiccoordi!8,589
180
Northern
Hemisphere
i
90W
90E
425K StreamlinesDay 0
GM
Plate 1. Polar stereographicplot of streamlinesshowingthe northern hemisphere stratosphericcirculation on the
425 K isentropic surfacefor December 1 of the LaRC model simulation. Arrows indicate the direction of the circulation.
The closedlines within the interior of the circumpolarcyclonicvortex indicatethe initial locationof material lines which
are coincident
with the vortex
D__ Day0
streamlines.
E•Day10
F
'".,•'""',,•'",.,•.'
•-' ' '.,.
' '":,,
x
(
,
GM
Day20
•'••---.m-•.,--.--?
',, ,
GM
GM
Plate 2. Polarstereographic
plotsof thehorizontalprojectionof the materiallinesduringthe Lagrangianintegration
for (a) day 0, (b) day 10, and (c) day 20. Colors indicatethe flow regimeof the material lines; red denotesinterior
material lines, white the separatingmaterialline, and yellow the edge material lines. The 425 K potential vorticity
distributions
are shownin thebottompanels
for (d) day0, (e) day 10,and(f) day20. Contourintervalsare I x 10-6
Km 2 s -1 kg
.
PIERCEAND FAIRLIE:CHAOTICADVECTION
IN THE STRATOSPHERE
18,59!
nates
is equivalent
to the simultaneous
solutionof 3n ordi- thepolar vortexandotherpartsof the materiallinesstretch
into longfilamentsleadingto the dispersalof air throughout
narydifferential
equations
tropicaland subtropicallatitudes.The developmentof filaJJi'- U(Xi, Yi, 0i, t), i = 1, n
(la)
mentary structuresnear the edge of the polar vortex by
large-scaleadvective processesis likely to enhancethe
(lb)
•i-' V(Xi, Yi, Oi, t), i-- 1, I•
efficiencyof small-scalemixing of vortex edge air with
tropical
and midlatitudeair by increasingthe interfacial
(lc)
bi = Q(xi, yi, Oi, t), i= 1, n
surfacearea of the boundarybetweentheseair masses.The
whereu and v are the x and y componentsof the velocity large-scalefeaturesof the material lines are evident in the
fieldevaluatedon an isentropicsurface 0 and Q is the computedpotentialvorticity distributions(Plates2d-2f).
diabatic
heatingrate associated
with departuresof the strato- The white materialline, whichseparatesthe two regionsin
spheric
temperatures
fromradiative
equilibrium
values.
The the Lagrangiansimulation,lies nearthe largestmeridional
numerical
calculationsof the Lagrangianevolutionof vortex gradientsin PV. The PV distributionshowsevidenceof the
materiallines involve quasi-isentropictrajectory computa- foldingbehaviorfound for the interior materiallines near
tionsperformed
in an off-linemode[MahlmanandMoxim, 225ø on day 20. There is no evidenceof the longfilaments
1978].Winds and diabaticheatingrates from the LaRC which characterize the material lines at the edge of the
atmospheric
circulationmodelare storedat 3-hourincre- vortex.
Plates3a-3c showmefidionalprojectionsof the material
mentsfor the trajectory calculations.An implicit integration
scheme[Austin and Tuck, 1985] was used to integrate linesfor days0, 10,and20 of the Lagrangiansimulation.The
equations
(1a)-(1 c), withwindsandheatingrateswhichare material lines are initialized on the 425 K surface. However,
asthe Lagrangiansimulationproceeds,the materiallinesare
linearlyinterpolatedin time.
which
Differenttechniqueshave been developedfor Lagrangian displacedin the verticaldue to diabaticprocesses
materialline simulations. A "contour surgery" technique result in cross isentropicmovement of air parcels. The
of the materiallines duringthe simuwasdeveloped
by Dritschel[1988]for usein contourdynam- verticaldisplacement
ics. Contour surgeryinvolves the continualadjustmentof lation is small since the 425 K isentropic surface is well
the number of parcels used to define the material line. below the level of maximum radiative heatingin the middle
WaughandPlumb[1993]haveshownthat contoursurgery
accuratelypredictsthe evolutionof material lines for a
varietyof modeledand observedstratospheric
flows.This
technique
has alsobeenusedby Norton [1993]in shallow
stratosphere.
However, there is a systematiclatitudinal
differencebetweenthe verticaldisplacement
of the material
lines.Radiativecoolingdueto CO2 emissionleadsto a slow
descent of the material lines within the interior of the vortex.
The largestdiabaticdescentoccursnear 45øNdue to enhancedradiativecoolingof adiabaticallywarmedair parcels
parcels
to accuratelypredictthe evolutionof the material in the regionbetweenthe vortex and the transientanticymateriallinelieswithinthisregionof
linesoverthe periodwe are simulating.For theseexperi- clones.The separating
watersimulations.Here, we chosea differentapproach.We
initializethe material lines with a sufficientlylargenumberof
diabaticdescent.Subtropical
latitudesare sunlit
ments,over 150,000individualparcel trajectorieswere com- strongest
Ultravioletabsorption
by
putedfor a periodof 20 days.The initial densityof the duringearly andmid-December.
ozone
leads
to
weak
radiative
heating
in
these
latitudes
ensemble
of parcelsalongthe instantaneous
streamline
determines
the lengthof time that the deformationof the whichresultsin the very slowascentof the vortexfilaments
Radiativecoolingrates
material
line canbe accuratelycomputed.This techniqueis astheyextendintotropicallatitudes.
simulation
notascomputationally
efficient
ascontoursurgery,
although neartheedgeofthevortexduringtheLagrangian
largerlocal
it doesprovidea meansof accuratelyresolvingthe initial rangefrom 1ø to 2øK per day. Significantly
with high,cold
development
of vortexfilaments,
whichbeginassmall-scalecoolingrates(5-!0 K per day) associated
folds in the material
lines.
cirrus clouds have been found near the edge of the polar
vortex [Tuck et al., 1992].In the real atmosphere,local
during
the 20-dayintegration.Plates2a-2c depictthe hori- diabatic descent associated with these cloud decks may
affectthe Lagrangianbehaviorof the vortex
zontaldistributionof the materiallinesfor days0, 10, and 20 significantly
oftheLagrangian
simulation.
Plates2d-2f showthe distri- filaments.
Plate 2 shows the evolution of the vortex material lines
bution
of potential
vorticity(PV) onthe 425K surface
for
thesedays.By day !0, materiallinesnearthe edgeof the
polarvortex(yellowmateriallines)have developed
long
filaments
extending
from the vortexedgeintothe tropics.
CHARACTERISTIC
TIMESCALES
OF THE MATERIALLINE
DEFORMATION
(la)-(lc) is formally
Materiallinesin theinteriorof thepolarvortex(redmaterial The systemdefinedby equations
to a nonautonomous
dynamical
system
andlends
lines)
havea verydifferent
morphology.
Thesemateriallines equivalent
typically
developintrusions
whichextendpoleward,
then itselfnaturallyto the applicationof the conceptsof dynamsimilaritybetween
fold onto themselves.The white material line deformsin a ical systemstheory.The mathematical
evolutionequations
andthenonautonomous
quasi-periodic
mannerwithverylitfienetchange
throughout theLagrangian
introduces
the possibility
of chaotic
the 20-day simulation.This material line separatestwo dynamicalsystems
parcel
trajectories.
Aref
[!984]
investigated
the
Lagrangian
regions
of distinctlydifferentLagrangian
behavior.This
(Q
materialline will be referredto as the separatingmaterial evolutionof an ensembleof parcelsin a two-dimensional
= 0), incompressible,
laminar
flow.He foundthattheparcel
Withinthe vortex, materiallines characteristically
de- motionwas stochasticandtermed this stochasticresponseto
line.
velop
multiple
foldswithminimal
stretching.
Nearthevor- deterministicflow "chaotic advection." Khakhar eta!.
thatthepresence
of chaotic
advection
is
texedge,partsofthematerial
linesremain
associated
with [1986]haveshown
A
450
Day 0
B
440
E 430.
Day10
C
450 ............
450
440
440
430
Day 20
E 430
..,..,
'-o
•'
• 420
420.
420
410
4!0
410
400
90 60 30 0
Latitude
400
90 60 30 0
Latitude
400
90 60 30
Latitude
,
•
,
0
Plate3. Meridional
projections
ofthematerial
lines
during
theLagrangian
integration
for(a)day0,(b)day10,and
(c) day 20.
color scale
16
18
20
22
24
26
28
30
PV units
180
90W
'"--,....
•'
Northern
Hemisphere
& ' r .--
,•
-,-,'i .....
: .......
• 90E
Plate
4. Polar
stereographic
plotofisentropic
potential
vorticity
forDecember
24,1988,
onthe425K isentropic
surface.
Potential
vorticity
datawere
provided
byTerryDavies
andwere
obtained
fi'om
European
Centre
forMedium
Range
Weather
Forecasting
(ECMWF)
operational
analyses.
Potential
vorticity
greater
than16isentropic
potential
vorticity
(IPV)units
isconsidered
"vortex
debris"
andisshaded.
Potential
vorticity
lessthan16IPVunits
iscontoured
with an intervalof threepotentialvorticity(,PV)units.
PIERCEANDFAIRLIE:CHAOTICADVECTION
IN THESTRATOSPHERE
related
to theefficiency
of mixingprocesses.
In theirsimulations,
simpletime-dependent
flowswere ableto deform
material
linesto scaleswhichweremuchsmallerthanthe
length
scaleof theflowitself,therebyleading
to efficient
mixing.The materiallineswere foundto stretchat an
exponential
ratein theregions
of theflowwherechaotic
advection
was occurring.Liapunovexponents
providean
invariant
measureof the characteristic
timescales
of a dynamical
system.For chaoticadvectionthe Liapunovexponentis directlyrelatedto the long-timeaverageof the
"specific
stretching
rate"of matehal
lines[Khakhar
et al.,
18,593
Characteristic
exponent
andzonalmeanPV gradient
1.0000 •
.1.0
.....
-0.8
o.1ooo•
ß
:
•
'•,
:0.6 =
o.0oo
0.0010
•
'0.2>•
0.0001
60
' 0.0
50
40
3O
20
Latitude
1986].
If materiallinesdeformat an exponential
rate,then
therateconstantof the deformationis equalto the specific
stretching
rate of the materiallines.
We monitoredthe lengthof the vortex materiallinesover
the20-daysimulationto determinewhetherchaoticadvectionwasoccurring
in theLagrangian
simulation
of thevortex
materialline deformation.Figure 1 showsthe computed
Fig. 2. Thecharacteristic
timescales
for thematerial
linedeformationduringtheLagrangian
simulation
(solidline)computed
from
the e-foldingtimesof the least squaresexponential
fits of the
materialline deformationshownin Plate 3. The meridionalgradient
of the initialzonalmeanpotentialvorticityis alsoshown(dashed
line).Characteristic
timescales
arerelatedto latitudeby the injtia.
l
mean location of the material lines. The zonal mean pote.ntial
is computed
at theGaussian
latitudepointsof theLaRC
length
ofthematerial
linesnormalized
bytheirinitiallengths vorticity
model.
as a function of time. Material lines are designatedby
numbers
which increasewith the distancefrom the vortex
center.Linear and exponentialbest fits to the computed
curvesare also shown. Material lines 1-4 (red in Plate 2) initial locationof the material line. An additionalsimulation
toexamine
thissensitivity.
Sixmaterial
lines,
stretch
by 2 to 4 timestheir initiallengthover the 20-day wasperformed
simulation.
Matehallines6 and7 (yellowin Figure2) stretch three on each side of the separatingmaterialline at 1ø
from1 and2 ordersof magnitudeduringthe simulation.The latitudinalincrements,were initialized to investigatethe
separating
materiallineis number
5 anddoesnotshowany characteristicsof the transitionzone betweenlinear and
stretching
rateregimes.
Thethreematerial
lines
net stretchingduring the 20-day simulation.Root-mean- exponential
of theseparating
materiallineshowed
square
(rms)errorsfor linearandexponential
leastsquares whichwerepoleward
initiallybutthenbeganstretching
nearday
fitsto the curvesindicatethat the stretchingrate of the two nonetstretching
The
materiallinesclosestto the edgeof the vortex(materiallines 15asthe materiallinesbeganfoldingin on themselves.
6 and7) are best characterized
as exponential.The rms
errorsin linear and exponentialleast squaresfits for the
interiormateriallines (matehallines 1-4) are so closethat
bothprovidea goodfit, although
the exponential
rateconstant
isquitesmall.Theseparating
materiallineliesbetween
thelinearandthe exponentialstretchingrate regions.
threematerial
lineswhichwereequatorward
of thesepa,[a•7
ingmateriallineshowedmorestretching,
extending
equatorwardwithintheenvelope
formedby material
lines5 •r!'.d
6. The materiallinewhichwasinitialized3øequatorward
qt[
theseparating
material
linestretched
5 timesitsinitiallength
and extendedwell into the tropicsby day 20.
The accuracy
of our stretching
rate calculations
in the
region
which
is
characterized
by
exponential
stretching
rates
separating
material
lineis likelyto be quitesensitive
to the
was also investigated
with a high-resolution
Lagrangian
The evolutionof material lines in the neighborhoodof the
simulation.We initializeda high-resolution
materialline on
materialline 7 which had the largeststretchingrate in the
Streamline1
Streamline2
Streamline 3
Streamline4
4,
4
4
4'
i
•
e,21
el2
'• I
0•
'
I
0 ......
•
"
•
;
--
'
2
1
0t
'
original
simulation.
The initialparceldensity
of thisnew
materialline was 10 times greater than in the original
simulation.The deformationrate of the high-resolution
materialline wasvirtuallyidenticalto the originalmaterial
line.Thecomputed
e-folding
timesdiffered
bylessthan1%
0 5 101520
0 5 101520
0 5 101520
0 5 101520
whichindicatesthat we haveinitializeda sufficientnumber
Time(days)
Time(days)
Time(days)
Time(days)
ofparcels
toadequately
describe
thematerial
linedeforma-
Streamline5
2.0i ' '
i
Streamline6
15•
Streamline7
•
150; ........
tion duringthis period.
Figure
2 shows
thecharacteristic
exponents
oftheoriginal
sevenmateriallines(stars),materiallinesin the neighbor-
3 0.5•
0.0.
i el 5
,
0
•, 50
0 5 101'52'0 0 5 101520
0
0 5 101520
hoodof the separating
materialline (triangles),
andhighresolution
material
line(square)
plottedasa function
of the
initial mean latitudeof the materiallines. The exponents
characterize
thedeformation
rate of the materiallinesand
aredetermined
fromthe leastsquaresexponential
fit to the
Fig.1. Computed
length
ofthematerial
linesversus
timeduring materialline deformation
(cf. Figure1). The characteristic
theLagrangian
integration.
Streamlines
arenumbered
fromthe
Time(days)
Time(days)
Time(days)
is equal
to thetime-averaged
specific
stretching
interior
ofthevortexoutward.
Squares
indicate
thecomputed
length exponent
ofthematerial
line.Thesolidlinesindicatetheleastsquares
bestfit rate of the materiallinesand thereforeprovidesa crude
tothedataassuming
an exponential
stretching
rate.Thedashed estimate
of theLiapunov
exponent
whichcharacterizes
the
lines
indicate
theleastsquares
bestfit tothedataassuming
a linear Lagrangian
behavior
of
the
material
lines.
The
zonal
mean
stretching
rate.Thelengths
arenormalized
bytheinitiallength
of
the material lines.
potential
vorticity
gradient
onthe425K surface
is also
!8,594
PIERCE AND FAIRLIE: CHAOTICADVECTION IN THE STRATOSPHERE
shown.The maximumgradientin potentialvorticity, which
is generallycoincidentwith the zonal jet maximumand is
often usedto define the edgeof the polar vortex, is located
near 40øN. The maximum PV gradient is typically observed
near 60øNat this level in the Arctic stratosphere[Tuck eta!.,
1992]. The difference reflectsan inability of the LaRC model
to adequately represent the polar night jet in the lower
stratosphere.
The characteristic
timescale
of the material
lines outside
the vortex is of the order of 4 to 8 days. Within the vortex
(north of 40øN) the characteristic timescale is of the order of
15 to 30 days. Between these regimes lies a narrow zone
approximately 5ø wide with much longer characteristictimescales.This zone acts as an effective barrier to large-scale
horizontal transport of material from within the vortex
during the simulation. Similar zones have been found in
idealized models of chaotic mixing [Khakar et al., 1986;
Behringer et al., 1991]. In two-dimensional flows they are
composed of "KAM curves" [Guckenheimer and Holmes,
1983] which enclose an "island" of fluid with regular,
quasi-periodic behavior that does not mix with the surrounding fluid. The length of time that an island of fluid remains
isolated is determined by the survival of the outermost KAM
curves. In the stratosphere the survival of the separating
material line is sensitive to the amplitude of the transient
waves and to the frequency of rotation of the trajectories
about the polar vortex. It is likely that the separating
material line would eventually succumb to changes in the
shear deformation and begin stretching.The evolution of the
material lines in the neighborhoodof the separatingmaterial
line supportsthis hypothesis.
These calculationsestablishthat positive Liapunov exponents exist for the stratosphericcirculation. Unfortunately, a
robust quantitative estimate of the Liapunov exponent cannot be obtained using these techniques due to the relatively
short period of time over which the averaging occurs.
Long-term Lagrangian simulations are not feasible because
of numerical errors in the computation of the individual
parcel trajectories which also grow at an exponential rate in
the regions of chaotic advection [Franjione and Ottino,
1987]. However, the existence of positive Liapunov exponents indicates that chaotic advection is occum'ng near the
edge of the polar vortex in this model simulation of the
northern hemispherelower stratosphere.The chaotic advection is characterized by the development of filaments of
vortex material which extend well into the tropics on timescales of 4 to 8 days.
DISCUSSION
Our simulations indicate that a significant amount of the
air near the edge of the polar vortex may be drawn into thin
filaments through chaotic advective processes.The development of filamentary structures in constituent distributions
can drastically increase the efficiencyof mixing by increasing the interfacialsurfacearea betweendifferentair masses.
Prather and Jaffe [1990] investigatedthe impact of stretching, moleculardiffusion, and photochemistryon chemically
perturbed air parcels embeddedin a homogeneouslyturbulent circulation. They found that the evolution of chemically
perturbed air parcels in the lower stratosphere was controlled by stretching until scales became small enough for
molecular diffusion to become important. They predicted
that chemicallyperturbedair parcelswouldremainisolated
for 7-20 days assuminga random strain rate of 10-s s-•
They notedthatthe primaryuncertaintyin their calculations
is the strain rate used in their model. For homogeneous
turbulencethe specificstretchingrate of a materiallineis
equal to the Lagrangian-averagedstrain rate of the flow
[Batchelor, 1952]. The computed specificstretchingrates
due to chaotic advection suggestthat the actual strainrate
near the outer edge of the vortex is of the order of 2 x 10-6
s-1, whichwouldresultin evenlongerisolationtimes.The
dominanceof stretching over diffusive and photochemical
processes in determining the evolution of exvortex air
massesindicatesthat chaoticadvectioncouldhave a significant impact on the distribution of trace constituentsin the
lower stratosphere.
Our simulations also suggestthat the large-scale horizon-
tal exchangeof vortex material is restricted by a zone near
the edge of the vortex which acts as an effective barrierto
large-scalemixing.We are left with an apparentdichotomy.
Material slightly poleward of the separating material line is
highly isolatedfrom the surroundingcirculation, yet material
slightly equatorward of the separating material line mixes
very effectively with the middle latitude and tropical air
masses.High-resolution assimilated stratosphericdata sets
may provide insight into the effectiveness of this barrier in
the real atmosphere.
Plate 4 showsa map of isentropic potential vorticity (IPV)
on the 425 K isentropic surface for December 24, 1988,just
prior to the first Airborne Arctic Stratospheric Expedition
(AASE). The IPV map was provided by Terry Davies of the
European Centre for Medium Range Weather Forecasting
(ECMWF) and was produced at a triangular 63 spectral
resolution. High values of IPV, which are typical of vortex
air, are dispersed throughout middle and subtropical latitudes. Large amounts of such "vortex debris" were foundin
ECMWF IPV analysis throughout the AASE mission [Tuck
et al., 1992]. The interpretation of these small-scale features
in stratospheric IPV analyses is admittedly plagued with
uncertainties.
If one assumes that the vortex debris reflects
the signatureof the vortex filaments, then clearly there is a
significantpotential for aliasingof these narrow features.In
a spectral model this aliasing could result in the bloblike
appearanceand lack of continuitywhich is often associated
with the small-scale features in the IPV distribution.
Alter-
natively, the small-scalefeatures may reflect the impactof
noisegeneratedduringthe assimilationprocess.In spiteof
theseuncertaintiesthe assimilatedIPV distributionsprovide
us with a dynamicallyconsistentdepiction of the quasihorizontaltransportin the lower stratosphere.The relatively
highpotentialvorticity valuesof someof the debrisindicates
that this air came from well within the polar vortex. The
presenceof air with potentialvorticity characteristic
of the
interiorof the vortex suggests
that exchangeprocessesother
than large-scalechaoticadvectionplay an importantrole
near the vortex edge.
Danielsen eta!. [!991] have shown that cross-jettransport
of traceconstituents
in thelower stratosphere
is dominated
by low-frequency
inertial-gravitywaves. Quasi-isentropic
transportby thesesmall-scale
wavesleadsto pronounced
laminae in the vertical distribution of ozone near the north-
ern hemisphere
polar vortex edge[Danielsonet al., 1991;
Reid and Vaughhan,1991;Browell et al., 1990].The large
amounts
of relativelyhighpotential
vorticityair outside
of
PIERCEAND FAIRLIE: CHAOTICADVECTIONIN THE STRATOSPHERE
18,595
thepolarvortexmayreflecttransport
across
thepolarjet by Khakhar, D. V., H. Rising,and J. M. Ottino, Analysisof chaotic
mixingin two modelsystems,J. Fluid Mech., 172,419-451, 1986.
small-scale
inertia-gravitywaves,followedby dispersalof
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(Received January 5, 1993;
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acceptedJune 9, 1993.)