JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 104, NO. Cll, PAGES 25,833-25,851, NOVEMBER
15, 1999
A case study of air-sea interaction during swell conditions
A. Smedman,U. H6gstr6m, H. Bergstr6m,and A. Rutgersson
Department of Earth Sciences,Meteorology,Universityof Uppsala, Uppsala, Sweden
K. K. Kahma
and H. Pettersson
Finnish Institute of Marine Research, Helsinki
Abstract. Air-sea interaction data from a situationwith pronouncedunidirectionalswell
havebeen analyzed.Measurementsof turbulenceat three levels(t0, 18, and 26 rn above
meansealevel)togetherwithdirectional
wavebuoydatafromthe siteOstergarnsholm
in
the Baltic Sea were used.The situation,which lastedfor --•48hours,appearedin the
aftermathof a gale. The wind directionduring the swellsituationturned slowlywithin a
90ø sector.Both duringthe gale phaseand the swellphasethe over-waterfetch was >150
km.Thewindspeedduringtheswellphasewastypically
4 rn s-•. Duringtheswellphase
a wind maximumnear or below the lowestwind speedmeasuringlevel t0 rn was observed.
The netmomentum
fluxwasverysmall,resulting
in Cz>values--•0.7x 10-3. Throughout
the lowest26 m, coveredby the tower measurements,turbulenceintensitiesin all three
componentsremainedhigh despitethe low value of the kinematic momentumflux -u'w',
resultingin a reductionof the correlationcoefficientfor the longitudinaland vertical
velocityfrom its typicalvalue around -0.35 to between-0.2 and 0 (and with some
positivevaluesat the highermeasuringlevels),appearingabruptlyat waveageco/Uwequal to
1.2. Turbulencespectraof the horizontalcomponentswere shownnot to scalewith height
abovethe water surface,in contrastto vertical velocityspectrafor which sucha variation
was observedin the low-frequencyrange. In addition, spectralpeaksin the horizontal
windspectra
werefoundat a frequency
aslowas10-3 Hz. Froma comparison
with
resultsfrom a previousstudyit was concludedthat this turbulenceis of the "inactive"
kind, beingbroughtdown from the upper parts of the boundarylayer by pressure
transport.
1.
Introduction
face shearingstressat a site in the Baltic Sea. The near-surface
atmosphericcharacteristics
in the STH (1994) studywere very
muchthe sameasthosereportedin the above-citedreferences.
The air-sea interaction regime characterizedby the dominatingwavestravelingfasterthan the wind (swell)is muchless No wave measurements were available, but as the situation
well studied and understood
than the situation with a wind
appeared in the aftermath of a gale, it was conjecturedthat
speedhigherthan the dominantwavespeed.In view of obvious "swell conditions,"here defined as conditionswith co/U•o >applicationsthe interest in situationswith growingwaves is 1.2, prevailed.
natural. Nevertheless,as pointed out alreadyby Kitaigorodskii
The basicconceptualideafor air-seainteractionduringswell
[1973],possiblewidespreadoccurrenceof "supersmoothflow" conditionsis that the surfacewavestransportmomentumup[Donelan,1990]overthe oceancouldbe of considerableinter- ward into the atmosphere,with the aid of pressurefluctuations
est from a global climatologicalviewpoint. Observationsof inducedby the waves.That this actuallyoccurs,at least during
situationswith very low surfacefriction and even, sometimes, idealized laboratory conditionsover mechanicallygenerated
momentum
flux directed from the water surface to the atmomonochromaticwaves,has been convincinglydemonstratedin
sphereduringconditionswith co/U > 1, where Cois the speed several studies [Harris, 1966; Lai and Shemdin, 1971]. The
of the dominatingwavesand U is the wind speedat somelow depth of the atmosphericlayer affectedby this energytransfer
height abovethe water surface(typically10 m), were made was found by Lai and Shemdin[1971] to be appreciableand
ch•rino qovor•l rn•rine Rc•viet exnediticm•q in the 1970s [Volkov.
muchdeeperthan the corresponding
depth affectedin the case
1970;Makova, 1975;Benilovet al., 1974]. Similar resultswere of developingwaves (when there is a pressuretransport of
reportedfrom measurements
over Lake Michiganby Davidson energyin the oppositedirection,i.e., from the atmosphereto
and Frank [1973]and from watersoutsidethe Australiancoast thewatersurface).The fieldstudiesreportedbyMakova[1975]
by Antonia and Chambers[1980] and Chambersand Antonia seem,in fact, to indicatethat surfacewave-inducedsignatures
[1981].Smedmanet al. [1994] (hereinafterreferred to as STH can be traced to appreciableheightsin those conditions.
The laboratory studies cited above were conducted over
(1994)) carried out an intensivestudyof the entire marine
monochromaticwaves, giving rise to a well-defined peak in
boundarylayer with the aid of an instrumentedaircraft and
spectraof the wind componentsat the samefrequency.With a
tower-mountedinstrumentationduringa situationwith no surnatural oceanicwave spectrum,wave forcing occursover a
Copyright1999by the AmericanGeophysicalUnion.
continuumin frequency.Benilov et al. [1974] carried out a
theoretical
analysisbased on a simplifiedassumptionof the
Paper number 1999JC900213.
0148-0227/99/1999 JC900213 $09.00
interaction
25,833
of turbulence
in the airflow with the wave-induced
25,834
SMEDMAN
ET AL.: AIR-SEA
INTERACTION
DURING
SWELL
OSTERGARNSH
TOWER
GOTLAND
0
f!6 ø
18ø
5 km
20ø
Figure1. Map of theBalticSea,witha close-up
of thesiteOstergarnsholm.
Thewavebuoyis mooredin
36m deepwater--•4kmto theESEof thetowersiteonOstergarnsholm,
having
roughly
thesamesectorof
>150
km unobstructed
over-water
fetch as the tower site.
perturbationsand arrived at spectraltransferfunctionsthat
resultin appreciableinfluencesover a broadbandof frequencies,particularlyso for the swellcaseand for the spectrumof
vertical velocity.Although Belcherand Hunt [1993] convincingly show that the key assumptionmade by Benilovet al.
[1974], i.e., that the "basic"turbulent fluctuationsof the airflow over the wavesare passivelyadvectedalongwavytrajectories,is fundamentallywrongfor the caseof stronglydeveloping waves,the situationrelated to swellconditionsin this
respectis not known.
In spring 1995 an air-sea interaction researchfacility for
long-term measurementsof turbulent fluxes at three levels
above the water surface and simultaneous
sectorfrom NE to SW in the clockwisesense.The seafloorup
to 500 m from the peninsulahasan approximateslopeof 1:30,
varyingsomewhatin different directions.About 10 km from
the peninsula,the depthis 50 m, reachingbelow 100 m farther
out. In section3 the possibleinfluenceof limited depthon the
wave field is discussed.
The data from a wave rider buoy (run and ownedby the
FinnishInstitutefor Marine Research)mooredat 36 m depth
---4km from the tower in the direction115ørepresentthe wave
conditionsin the upwind fetch. During the swell period the
buoyis exposedto nearlythe samegeneralwaveconditionsas
the flux measurements.
surface wave mea-
The 30 m tower is instrumentedwith slow-response
("profile") sensorsof in-housedesignfor temperature[H6gstr6m,
Ostergarnsholm.
Themeasurements
andthesitearedescribed 1988]and for wind speedand direction[Lundinet al., 1990]at
in section 2. From the data set available from this site so far, a
the followingheightsabovethe tower base:7, 11.5, 14, 20, and
particularsituation,occurringon September18-19, 1995,has 28 m. In addition, humidity was measuredat 7 m above the
been chosenfor an analysisof the air-sea interaction mecha- tower base. Turbulent fluctuations were recorded with SOnism during swell conditions.As describedin section3, this
LENT 1012R2sonicanemometers(Gill Instruments,Lymingsituation occurredduring a period immediatelyfollowing a
ton, United Kingdom)at the heightsof 9, 17, and 25 m above
gale,which culminatedduringSeptember15 and 16, resulting
the towerbase.The sonicswere calibratedindividuallyin a big
in low windsand swell,so that co/U•o -> 1.2. In section4 the
wind tunnelprior to beinginstalledon the tower.The calibraturbulencestructureis presented.In section5 the findingsare
tion procedureusedis similarto that describedby Grelleand
discussed
with referenceto previousfindingsin generaland
Lindroth
[1994],givinga matrix of calibrationconstantswhich
thosereportedby STH (1994) in particular.
surements
was established
at a site in the Baltic
Sea called
correct for flow distortion caused by the instrument itself.
From the sonicsignalsthe three orthogonalcomponents
of the
2.
Site and Measurements
wind and virtual temperature(the measuredtemperaturesigThemainmeasuring
siteistheislandC)stergarnsholm,
situ- nal agreesto within0.20% with thevirtualtemperature[Depuis
ated •4 km eastof the big islandof Gotland in the Baltic Sea, et al., 1997]) are obtained.
Both profile and turbulencedata are 1 hour averages.In
Figure1. C)stergarnsholm
is a lowislandwithnotrees.The 1
km long peninsulain the southeasternpart of the islandrises order to removepossibletrends,a high-passfilter basedon a
10 min running averagewas applied to the turbulencetime
to no more than a coupleof metersabovemean sea level. A
30 m tower has been erected at the southernmosttip of this seriesprior to calculatingmoments(variancesand covaripeninsula.The baseof the tower is situatedat just about 1 m ances).This procedureamountsto applyinga high-passfilter
above mean
sea level. The
distance
from
the tower
to the
shorelinein calm conditionsis only a few tensof metersin the
witha cutofffrequency
at --•10-3 Hz. A wayto checkthatthis
proceduredoes not mean reducingthe measuredvariances
SMEDMAN
ET AL.' AIR-SEA
INTERACTION
and covariancesis to produce so-calledogive curves,i.e., to
integrate measuredcospectra(derived from the unfiltered
time series)from the high-frequency
end(in thiscase10 Hz) to
successively
lower frequenciesn and plot this integral as a
functionof n. The resultis a curvewhich normallyrisesmonotonicallywith decreasing
frequencyandwhichfinallylevelsout
asymptotically.
This asymptotegivesthe total covariance.For
the swellcasesof this studyit is found that the ogivesattain a
plateauat a frequency
somewhere
in the range2 x 10-3 <
Ft< 10--2Hz andthenriseto a finalasymptote
at n • 10-3
Hz. These two plateausare likely to representdifferent transport mechanisms. Nevertheless, we have used the lowfrequencyplateauthroughoutto obtainan estimateof the total
flux.This meansthat our 10 min runningmean proceduregives
accuraterepresentationof the covariancesand hence of the
correspondingfluxes.
As discussedin section 5, the low-frequencypart of the
turbulenceduring swell is likely to be highly influenced by
so-called "inactive" turbulence, brought down by pressure
transportfrom the upper layersof the boundarylayer to the
layersnear the surface.This turbulencedoesnot contributeto
the momentumflux but causesrandom variability in the lowfrequencypart of the u, w cospectrum,where u and w are the
longitudinaland vertical components,respectively.This is the
causeof the large scatterin the plots involvingthe kinematic
momentum
flux - u ' w '.
The measurementsrun continuously,with a samplingfrequencyof 1 Hz for the meteorologicalslow-response
(profile)
sensorsand 20 Hz for the turbulence signals.Wave data is
recordedonce an hour. The directionalspectrumis calculated
from 1600 s of data onboard the buoy. The spectrumhas 64
frequencybands(0.025-0.58Hz). The significant
waveheight
DURING
SWELL
25,835
speedof dominantwavesin the footprint, calculatedover the
flux footprintof the 10 m measurements
(circles)(seeappendicesA andB) and the 26 m measurements
(crosses),
with the
limited depth being accountedfor.
From Figure 2c we can see that {Co) for the footprint of
turbulentflux measuredat 26 m height(the crosses)
doesnot
differ noticeablyfrom the deep-waterphasespeed(the stars),
except during a short time at the very peak of the gale. As
shownin the so-calledfootprint analysisin appendixA, during
typicalconditions,90% of the turbulentflux measuredat 26 m
height originatesfrom distances>770 m away from the tower.
At lower levelsthe footprint of the turbulentflux lies closerto
the tower and partly in shallowerwater. Still, Figure 2c shows
that duringthe swellperiod, {Co), over all the footprintscorrespondingto the measurementheights10 m and 26 m, is very
closeto the deep-watervalue of Co. This appliesalso to the
period before the gale.
Using the results of Anctil and Donelan [1996], we have
estimatedin appendixB that the reductionin {co) (compared
with the deep-watervalue) shouldbe larger than that seenin
Figure 2c before shoalingwave effectsmanifestthemselvesin
the airflow. This result is confirmedin the analysisof turbulencemomentspresentedin section4.2, where no distinctionis
found in the plots for caseswhere (Co) is very closeto the
deep-watervalue. It is also shownthat the resultsof the analysisare, in effect,independentof measuringheightand thusof
differencesin footprint.
Our conclusion,therefore, is that during the swellperiod it
is very unlikely that the turbulent flux measurementsat any of
the three levels are influenced by effects of limited water
depth. During the gale these effects seem small, and they
cannot alter the significantdifferencesobservedbetween the
swellperiod and the pre-swellperiod.
While multiple peaks are common in wave spectrain the
Baltic Sea, especiallyduringswell,the wave spectraduringthe
study period exhibit only one well-defined peak. A typical
exampleof a measuredspectrumis presentedin Figure 3 (the
top curve).Also shownin Figure 3 is the corresponding
Pierson-Moskowitzspectrum[Piersonand Moskowitz,1964] calcu-
is calculatedby trapezoidmethodfrom frequencybands0.050.58 Hz, and the peak frequencyis determinedby a parabolic
fit. The meteorologicalmeasurementshavebeen runningsemicontinuouslyfrom May 1995. Wave data have been recorded
semi-continuously
duringthe sameperiod but with breaksduring wintertime periodswith risk for ice damage.
For the present analysisof swell, data have been chosen
from one particular situation, September 18-19, 1995, with lated for the samewind speed,4 m s-•, as that measured
due referencealsoto the high-windperiod precedingthe swell locally. Figure 3 showsthat swell energy dominatesthe specsituation itself, as described in detail in section 3.
trum, and up to 0.6 Hz, the wave spectrumis higher than the
maximum spectrumthat can be generatedby the local wind.
The swellhasbeen generatedseveralhoursearlier -100 km to
3.
General Characteristics
the southby the higherwind that was blowingat that time. By
of the Measuring Situation
the time the wavesarrivedat the measuringpoint the wind had
Figure 2a shows,for the time periodSeptember14-19, 1995, decayed,and the waveshad turned into swell.The shorterlocal
the variationof the wind speed(starsand left-handscale)and waves(the shadedspectrumin Figure3) were generatedby the
significant
waveheight(circlesandright-handscale),Figure2b weaker local wind from the SE. The directional spreading
presentswind directionand dominantwavedirection,and Fig- between0.27 and 0.5 Hz is therefore higherthan normal. This
ure 2c eives the vhase sveed of the dominatin•
wave. The wind
confirms that at those frequencies the spectrum is the sum of
increased
at firstto a maximum
of- 16m s- • onSeptember
15, the two wave systems:the fully developedlocalwavesand the
followedby a decrease
to -4 m s-• on September
18 and19. superimposedswell.During September18 and 19 there were
The wind direction(Figure 2b, stars)duringthe period Sep- periodswhenwind andwavedirectionswereveryclose(Figure
tember 14-17 was -90 ø, turning to between 110ø and 200ø
during the last two daysof the period. With referenceto the
descriptionof the site in section2 it is clear that the wind was
from the sectorwhere the upwindfetch was over 150 km. As
previouslystated,the presentstudywill concentrateon results
from the last 2 days.The phasespeedplot, Figure 2c, shows
boththe phasespeedof dominantwavesin deepwater (stars),
which is expected to equal the deep-water value, and a
weightedmean phasespeed(Co) that representsthe phase
2b) but also periodswith deviationsas large as 60ø. In the
analysespresentedin section4.2, data from this period have
been dividedinto two groupsaccordingto whether the deviation between wind and wave direction is less than or larger
than 30 ø.
Figure 4 showsthe wind gradientevaluatedat 10 m (in the
followingtext, "height" alwaysrefersto height abovemean sea
level)for the entireperiodSeptember14-19. The gradientwas
derived at the lowest turbulence level, 10 m, from a best fit
25,836
SMEDMAN
ET AL.' AIR-SEA
INTERACTION
DURING
SWELL
20
It
4.5
18
16
-4
14-
-3.5
•%
12-
•
•
0(9
.%
o
-3
o
E
•E1o
•o o
•o
-2
o
6
-1.5
o
**'-1
2
0
14
15
16
17
18
19
0
20
September 1995
350
-
b
300
-
250
-
200
15O -
o
IO0
©
o
o
o©
o
o
14
15
16
17
18
19
September 1995
Figure 2. (a) HourlymeanwindspeedU at 10 m abovemeansealevel,denotedby stars,and significant
waveheightH s, denotedbycircles,duringthetimeperiodSeptember
14-19, 1995.(b) Winddirectionat 10m,
denotedby stars,anddominantwavedirection,denotedby circles,duringthe sametimeperiodasin Figure
2a. (c) Phasespeedof dominantwavesco. Deep-watervaluesaredenotedbystars,andweightedmeanvalues
overthe fluxfootprintare denotedfor the 10 m measurements
by circlesandfor the 26 m measurements
by
crosses
(seeappendixB for details).
log-lin plot of wind speedmeasuredat the five heightsmenThe kinematicmomentumflux - u' w' dropsto very small
tioned in section2. Note that the gradientis negativefor most values
(aroundor below0.01m2 s-2) at -2000 localstandard
of the time duringSeptember18-19. This meansthat the wind time (LST) on September17 andstaysat that low levelfor the
profile has a maximumat a heightbelow 10 m. It is natural to remainingperiod.As noted above,the wind gradientbecomes
interpretthis localwind speedincreaseas the effectof a "wave- negativeor very smallat the sametime as the momentumflux
drivenwind";comparethe laboratoryresultof Harris[1966]and dropsto valuesnear zero.
the field resultfrom Lake Ontarioof Donelan[1990].
Stabilitywas closeto neutral duringthe high-windperiod
SMEDMAN
ET AL.: AIR-SEA INTERACTION
DURING
SWELL
25,837
13
12
11
xx xX
x•%
e' xxx
4
x
x
ß
ooo
x
0
0 xXX
0
C•oO
0
o
o
-
o
o
o
I
6
14
I
I
I
I
16
17
18
19
20
September 1995
Figure 2. (continued)
/•
N
(September 14-17). During September 18-19 the sensible
heat flux was positivebut numericallysmall. As discussedin
section5, it is doubtful whether it is meaningfulto attempt a
stabilitycorrectionduringthoseconditions.Calculationof
Hs
=0.7
rn
for the swellperiodgivesa meanof --•0.7x 10-3, withlarge
E 0.25-
•no-H•z
0.19
scatter. Here Cr, is defined in the usual manner as Cr, =
(u./U•o) 2, whereU•o iswindspeedat 10m.
ß• 0.20-
In Figure 5, hourlymeanvaluesof the verticalwind gradient
at 10 m (derivedfrom 5 levelsof wind speedmeasurements)
have been plotted as a function of wind speedfor the same
height for the entire time period of wind increaseand subsequent decrease(compareFigure 2). The curveswith arrows
drawnby handto fit the data indicatethe directionof evolution
with time. A pronouncedhysteresis
effect is found.Thus dur-
'- 0.15-
0.10 -
ing the stageof increasing
wind a wind speedof 7 m s-•
corresponds
to a windgradient
of --•0.05s-•, ascompared
to a
valueof just0.01s- • for thesamewindspeedduringdecreasing wind conditions.Again, it is seenin thisplot that the wind
gradientbecomesnegativefor most of the time during September
18 and 19.
1130
4.
Turbulence
Characteristics
4.1. Turbulence Kinetic Energy Budget
In stationaryand horizontallyhomogeneousconditionsthe
25
turbulence
kineticenergybudget(theTKE budget)attainsthe
0
0.0
I
I
0.2
0.4
form [Moninand Yaglom,1971]:
0.6
Frequency n (Hz)
Figure 3. An exampleof wavespectrumwith meandirection
and spreadingversusfrequencyduringthe swellperiod. The
smaller shadedspectrumis the Pierson-Moskowitzspectrum
[Pierson
andMoskowitz,1964]for fully developedwavesat 4 m
OU
g
0 w' e'2
1 0
u'w'Oz ToW'O'
v+ Oz 2 + po•p 'w' + õ O,
P
B
Tt
Tp
(1)
•
where
e2/2= •(u2 + v2 + w2) istheturbulent
kinetic
s- • windspeed,thelocalwindspeedduringthemeasurement.energy,-u'w'
is the kinematicmomentumflux, w' O'vis the
25,838
SMEDMAN
ET AL.: AIR-SEA
INTERACTION
DURING
SWELL
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
-O.O2
-0 O4
,
14
15
16
17
18
-19
September 1995
Figure 4. Wind gradient at 10 m, derivedfrom cup anemometermeasurementsat five levelsfor the time
period September14-19, 1995.Note that negativegradientsprevailduringmostof the swellperiod,September
18-19.
kinematicheat flux, or, more precisely,the flux of virtual po- (B < 0) or destruction(B > 0) of TKE by buoyancy;Tt,
tential temperature.To, mean temperature(in Kelvin) of the turbulenttransport
of TKE; Tp, pressure
transport
of TKE;
surfacelayer; #, accelerationdue to gravity;9o, air densityat and 5, molecularrate of dissipationof TKE.
temperature T O. The physical interpretation of the various
Figure 6 showsthe terms of the TKE budgetfor the time
terms in (1) is as follows:P, mechanicalproductionof TKE periodwith swell,September18-19, 1995.The termsP and B
from the mean flow; B = -(#/To)(w'O'•, ), production were evaluated from the turbulence measurements at 10 m and
0.16
,
,
,
4
6
•
8
0.14
0.12
0.1
0.08
0.06
0 04
o o2
-0.02
-004
2
•
•0
1
•2
1
•
14
•
16
18
U (m/s)
Figure 5. Estimatedvaluesof hourlymeanwindspeedgradientat 10 m (determinedfrom cupanemometer
measurements
at fivelevels)for the entiretime periodSeptember14-19, 1995,plottedasa time sequence
in
the directionindicatedby the arrowsand as a functionof wind speedat 10 m. Stars,September14; phis,
September15; crosses,
September16; pluses,September17; solidcircles,September18; and opencircles,
September19.
SMEDMAN
ET AL.: AIR-SEA
INTERACTION
DURING
SWELL
25,839
X 10'3
18
19
September 1995
Figure 6. Turbulence energybudget at 10 m for the time period with swell, September 18-19, 1995. B,
buoyancy
production;
P, mechanical
production;
e, dissipation;
Tp, pressure
transport
term;andTt, turbulent
transport
term.Valuesareto the 10-3 power.
co/U•o < 1.2 the correlation coefficient has its usual value
found in near-neutral atmosphericsurface layers over land,
18 m. The dissipationterm e was obtainedfrom inertial sub- -0.35 _ 0.05. For swell conditionsof the last two days,ruw
range levelsof longitudinalvelocityspectra,assuminga value attainsvaluesbetween -0.20 and 0. Note the rapid transition
of 0.52 for the Kolmogoroff spectralconstanta [HOgstrOm, in the value of ruw at co/U•o = 1.2, the wave age at which the
1990].The pressure
transporttermTp wasassumed
to equal wavesbecomefully developedaccordingto Piersonand Mosthe imbalance.This is a reasonableassumption,considering kowitz [1964]. As illustratedby the mean valuespresentedin
that changesin the turbulenceenergywere sometimespositive Table 1, the situationis exactlythe sameat 18 and at 26 m; see
and sometimesnegative,with no indication of a systematic also Figure 7b, which showsthe situation for the 26 m level.
time rate of changeduring the time period of swell studied The observedtrend of ruw with wave age is in agreementwith
here; nor were any systematicadvectivechangesobserved. earlier findings,i.e., Kitaigorodskii[1973] and Makova [1975].
Concerninginterpretation of the pressuretransport term, see Most previousstudiesof this quantitywere, however,made at
section 5.
a fairly low height abovethe water surface.Note that there is
From Figure 6 it is first of all seenthat mechanicalproduc- no significantdifference between the two groups during the
tion of turbulent kinetic energy is close to zero during the swell period representingsmall and large deviation between
entire period.The two dominatingsourcetermsare buoyancy wind and wave direction, nor do the data points representing
production
B andpressure
transportTp. The followingmean "pregaleconditions"(circles)standout amongthe other data
values are obtained for the entire swell period, September for "youngwave conditions."The reasonfor the drop of -ruw
18-19,1995:
P = 0.08x 10-3 m2s-3, Tp= -0.47 x 10-3 with wave age is very probably the dominance of so-called
m2 s-3, Tt = -0.10 x 10-3 m2 s-3,B = -0.62 x 10-3 m2 inactive turbulenceduring swell, as discussedin detail in sec-
from mean wind profile fits. The turbulencetransportterm T t
was derived from measurements of w'e '2 at the levels 10 and
s-3, and e = 1.11 x 10-3 m2 s-3.
4.2.
Turbulence
The correlation
tion 5.
Moments
coefficient
between
u and w is defined
r•w= u'w'/rruO'w,
(2)
where - u'w' = u,2, the kinematicmomentumflux;o-u, the
standard deviation of the longitudinalwind component;and
O-w,the standarddeviation of the vertical wind component.
Figure 7a shows,for 10 m, ruw plotted againstwave age
co/U•o (actually,(co/U•o), where anglebracketsdenotethe
weightedmean, but for conveniencewe drop the anglebrackets from here on). During the period September14-17 when
Figure 8 shows,for 10 m, rrw/U, as a function ofco/U•o. As
illustratedby the mean valuespresentedin Table 2, the result
is very much the samefor the other two measuringheights,18
and 26 m. This quantityhasits normalneutralvalueof --1.2 for
co/U•o < 1.2 and valuesabout double that for swellconditions.Again, note the rapid transitionat the fully developed
wave age co/U•o = 1.2. Also, in this plot there is no systematic differencebetween swell caseswith small and large deviation betweenwind and wave direction or for the pregale data
during the phasewith co/U•o < 1.2. Exactlysimilarincreases
asfor rrw/U, are found for the normalizedstandarddeviations
of the two horizontal components,rr•,/u, and rr•,/u, (not
25,840
SMEDMAN
ET AL.: AIR-SEA INTERACTION
DURING
SWELL
ruw
0
i
I
i
+
-0.05
i
x
i
+
x
x
x
-0.1
x
x
+
XX
-0.15
young waves
+
+
Xx
swell
+
x
x
x
+
x
x
-0.2
+
x
x
-0.25
-0.3
-0.35
-0.4
-0.45
0.5
•
•5
1
•
1.
2
•
•
2.5
3
3.5
2.5
3
3.5
co/U10
ruw
0.2
i
0.1
0
young waves
-0.1
swell
_
-0.2
-
-0.3
)I•
•
-0.4
-0.5
0.5
1
1.5
2
co/U10
Figure 7. (a) Correlationcoefficientr•,w = u'w'/(%,trw) for 10 m plotted as a functionof the waveage
parameterco/U•o (whereCohasbeencalculatedasweightedmeansoverthe fluxfootprintfor the 10 m level,
seeappendixB). Circles,data from the pregaleperiod duringSeptember14; stars,data from the galeperiod
September14-17; pluses,data from September18 and 19, with wind-waveangle difference<30ø; crosses,
sameas pluses,but with wind-waveangledifferencebetween30ø and 60ø. (b) Sameas Figure7a but from
measurements
at 26 m and with Cocalculatedas weightedmeansover the flux footprintfor this level. Note
that here no distinctionis made betweenthe three data categoriesof Figure 7a.
shownhere). Thusthe normalizedturbulenceenergyincreases 4.3. Spectral Characteristics
In a near-neutralsurfacelayer over land, spectraof atmoby a factor of 3 to 4 for co/U•o > 1.2 comparedto its normal
value. In section5 it is explainedhow this result is a conse- sphericvariablesscalelinearlywith the heightabovethe surquenceof the flow being dominatedby inactiveturbulence.
face [Kaimalet al., 1972].During the period of increasingwind
SMEDMAN ET AL.: AIR-SEA INTERACTION
DURING SWELL
25,841
Table 1. Mean Values and StandardDeviationsfor the Correlationruw for the Three
MeasuringHeightsand for Young Waves(co/U•o < 1.2) and Swell(co/U•o > 1.2)
10 m
co/U•o < 1.2
co/U•o > 1.2
18 m
26 m
ruw
s.d.
N
ruw
s.d.
N
r,w
s.d.
N
-0.34
-0.14
0.04
0.07
57
33
-0.38
-0.17
0.05
0.07
57
33
-0.34
-0.10
0.05
0.11
57
33
N, numberof measuringhoursfor eachcategory.
in September 1995 this was also found to be the case for
Twenty-fourhour mean u, v, and w spectraare shownin
spectra
measured
at Ostergarnsholm
(notshown
here).Such Figure 11. Possibleweak wave influencesmay be noted. Thus
scalingis not obtainedduringthe swellperiod. Figure 9 shows
an exampleof the longitudinalvelocity spectrumnSu(n),
wheren is frequency,plottedagainstn for the threemeasuring
heights10, 18, and 26 m. It is clearthat the spectraare virtually
independentof height (the pointsrepresentingthe two lowest
frequenciesbeingvery uncertain,for statisticalreasons).An
exactly similar picture is obtained for the spectrumof the
lateralcomponent
nSv(n) (not shownhere). The spectrumfor
the vertical componentnSw(n) differs in a systematicway
from this picture,as shownin Figure 10. For this component
the high-frequency
part of the spectrum(aboven • 0.1 Hz)
is also independentof height. The spectrallevel of the lowfrequencypart varies,however,systematically
with height.The
presentresultfor the horizontalandverticalvelocityspectrais
in total agreement with the findings from measurements
throughoutthe boundarylayerin the studyby STH (1994), as
discussed in detail in section 5.
the vertical velocity spectrumhas a wide plateau, and the
horizontalvelocityspectrahavean inflectionor evena "bump"
near the peak wave frequencyno, as indicatedin Figure 11.
4.4.
Quadrant Analysis
Quadrantanalysisis a conditionalsamplingtechniqueoriginally developedfor turbulent laboratory flows by Lu and
Willmarth[1973].It separatesthe fluxesinto four categories,
accordingto the signof the two fluctuatingcomponents.Thus,
with the two componentsdenotedx andy and numberingthe
quadrantsaccordingto mathematicalconvention,we have for
the x-y plane:
quadrant I
x > 0, y > 0
quadrant II
x < 0, y > 0
quadrant III
x < 0, y < 0
Ow/U.
3.5
x
2.5 _ young waves
swell
x
x
+ Xx
XxX++X
x
1.5
x
++
xx
x +
1I
o
0.5
1
1.
2
215
3
co/U1o
Figure 8. NormalizedverticalvelocitystandarddeviationCrw/U.for 10 m plotted as a functionof the wave
ageparameterco/U•o (whereco hasbeencalculatedasweightedmeansoverthe flux footprintfor the 10 m
level,seeappendixB). Circles,datafrom the pregaleperiodduringSeptember14; stars,datafrom the gale
period September14-17; pluses,data from September18 and 19, with wind-waveangle difference-<30ø;
crosses,sameas for crosses,but with wind-waveangledifferencebetween30ø and 60ø. Note that the data set
includesthree additionaldatapointswith co/U•o valuesbetween2 and 3 and Crw/U.between5 and 6, i.e., out
of range of the plot.
25,842
SMEDMAN ET AL.: AIR-SEA INTERACTION
DURING
SWELL
Table 2. Mean Values and StandardDeviationsfor rrw/u, for the Three Measuring
Heightsand for Young Waves(co/U•o < 1.2) and Swell(co/U•o > 1.2)
10 m
co/U•o < 1.2
co/U•o > 1.2
18 m
26 m
rrw/U,
s.d.
N
rrw/U,
s.d.
N
rrw/U,
s.d.
N
1.16
2.15
0.04
1.02
57
33
1.18
1.91
0.09
0.52
57
33
1.28
2.84
0.13
1.42
57
33
N, number of measuringhoursfor each category.
quadrant IV
regionin the quadrantanalysis.By progressively
increasingthe
magnitudeof H the importanceof eventsexhibitingincreas-
x > 0, y < 0,
wherey = w andx = u, or 0 (0v, actually,but for the present inglylargevaluesof Ix'y'l can be determined
within each
purposethe distinctionis of little relevance)in our case.Pos- quadrant.
itive contributions to the kinematic momentum flux - u' w' are
FollowingRaupach [1981], a flux fraction Sir•, where subobtained for quadrant II events(ejections,i.e., momentum scripti refersto the quadrantnumber,is definedas
deficitbeingtransportedupward)and for quadrantIV events
s,,, = [ x 'y ' ] i,,/x'y ' ,
(4)
(sweeps,i.e., momentumexcess
beingtransporteddownward),
whereasthere are negativecontributionsfor quadrantI (out- where the bracketssignifya conditionalaverage.This condiward interaction)and quadrantIII (wallwardinteraction).For tionalaverageis formallydefinedusinga conditioningfunction
the heatflux,w' O'v
quadrantsI andIII givepositivecontributions. IiH which obeys
The importanceof relativelyshort-livedlargevaluesof the
IiH =
momentsx'y' may be seen by estimatingthe importanceof
these eventsto the total flux and by comparingthis with the
fractionof time theselargevaluesoccur.This is accomplished
0, otherwise.
by determiningthe cumulativefrequencydistributionsof the
Then,
the conditionallyaveragedstressbecomes
fluxeswhen keepingvalueslargerthan somegivenfractionof
the averageflux. This is equivalentto usingthe hyperbolic
hole, introducedby Willmarthand Lu [1974].The sizeH of the
[x'y']iH
= liminf7 x'y'(t)I,H(t)
dt.
(5)
1,ifthe
point
(x',
y')
lies
in
the
ith
quadrant
and
•c'y'
I->
H•c'y'
hole is defined
as
S:
Ix'y' I/Ix'y'l,
(3)
Sincethe stressfractionsare normalizedquantities,it is clearthat
where the point (x', y') lies on the hyperbolawhichbounds
the wholeregionin thex-y plane.The hyperbolichole is shown
as the hatched area in Figure 12 and becomesan excluded
4
• Si,0= 1.
26 rn
18m
c- 0'2
lorn
lO•
10-4
i
10'3
i
10ø2
I
-1 10-'•
, i ...... 1
10ø
n(s )
Figure 9. Exampleof longitudinalvelocityspectra,nSu(n) from 10 m (stars),18 m (circles),and 26 m
(crosses)
for a particular30 min period(September18 around0100localstandardtime (LST)) plottedon a
logarithmicscaleagainstlog n, wheren is frequency(Hz).
(6)
SMEDMAN ET AL.' AIR-SEA INTERACTION DURING SWELL
25,843
10-2
26
18m
10-3-
10m
10-4
10-4
10
-3
10
-2 n(•1) 10
'• I
no
t0ø
10•
Figure 10. Exampleofverticalvelocityspectra,
nSw(n) from10m (stars),18m (circles),and26 m (crosses),
for a particular30 min period(September18 around0100LST) plottedon a logarithmicscaleagainstlogn,
wheren is frequency(Hz). The no indicatesthe frequencyof the peak in the wavespectrum.
Figures13a-13d showexamplesof cumulativedistributions
in the four quadrantsfor -u'w' (Figures13aand 13b)andfor
w' O'v(Figures13c and 13d) at the lowestmeasuringheight,
10 m. Note thatH, by definition,is alwayspositive.Thishasthe
consequence
for the compositequadrantplots of Figure 13a13d that H increasesfrom the centerline towardthe right for
quadrantsI andIV and towardthe left for quadrantsII and III.
Note alsothat the stressfractionsSill (Figures13a and 13b)
are positivefor quadrantsII andIV but negativefor quadrants
I and III. For the heat flux plots, Figures 13c and 13d, the
corresponding
heat flux fractionis positivefor quadrantsI and
III and negativefor quadrantsII and IV.
To exemplify,take Figure 13a,which showsthe momentum
flux analysisfor youngwaves,and extract first the stressfrac-
l
100
2
EJECTION
x
10-1
OR BURST
I
OUTWARD
INTERACTION
lu'w'l- H lu'w'l
10-2
o
o o
o o o o o •o•
• •I
l
o
o o
10-•
10-4
I
•o'•
I
INWARD
I
•c/•
•c; I
n(s-1)
•oø
no
Figure 11. The 24 hour mean (from September18, 1995)
INTERACTION
3
SWEEP
OR GUST
4
velocityspectra,nS..... (n) for the horizontalcomponents
u
(closedcircles)and v (crosses)
andfor theverticalcomponent Figure 12. Longitudinaland verticalvelocityfluctuationdow (opencircles)for 10 m plottedon a logarithmicscaleagainst main showingthe quadrantsand the hyperbolicexcludedrelog n. Also indicatedin Figure 11 is the peak wavefrequency gion(hatchedarea).H, sizeof the hyperbolichole.After Shaw
no during the measurementperiod.
et al. [1983].
25,844
SMEDMAN ET AL.' AIR-SEA INTERACTION
1.0
-1.0
0.8
-0.8
S 2H
2nd qu.
81H
1stqu.
o
0.6
-0.6
oO
c0.4
/
.o
-0.4
• i.2.___.._
E
++
•
-0.4
S 3H
0.2
+
+
+
3d qu.
04
+
-0.6
S4H
4thqu
+
06
+
-0.8
•
-1.0
30
0.8
10
20
10
Figures13a and 13c are from September15, when the wind
was increasingand co/U1o = 0.90; Figures13b and 13d are
from September 18, with co/U1o = 3.33. For young wave
conditionsthe plot for -u'w' (Figure 13a) hasrelativelylarge
contributionsfrom the ejectionand sweepquadrantsII and IV,
respectively,comparedwith the much smaller contributions
from the interactionquadrantsI and III, in generalagreement
with what is typicallyfound overland. For swellconditionsthe
- u'w' plot (Figure 13b) differs strikinglyfrom the correspondingplot for co/U1o = 0.90 (Figure 13a). Thus the interactionquadrantsare almostaslarge as the sweepand ejection quadrants.This result is in general agreementwith the
findingsof ChambersandAntonia [1981].In addition,all four
curvesof Figure 13b are much spread out, indicating that
infrequentbut intenseeventsof fluxesof both signsplay a big
role in the transportprocess,resultingin nearlyzero net flux.
The corresponding
plots for the heat flux, Figures13c and
13d, are also different from each other, but here a strong
relative accentuationof the role of quadrantI resultswhen the
-0.2
2
•
0
10
Hole s•ze, H
20
30
Hole size, H
2.5
-1.0
1.0
-0.8
0.8
-2.5
82H
2ndqu.
1.5
DURING SWELL
o
SIH
1st qu.
-0.6
-1.5
x
.o¸
x
x
o
SIH
S 2H
x
x
1
ooOøø
0.5
2ndqu'
-0.4
x
•
-0.5
-0.2
xx
1stqu.
•x.
....
0.4
0.2
.
x
XXXXXxxxx
x
x
--= o
-r'
-0.5
0.2
+++--0.5
-0.4
0.4
+*
S4H
S 3H
S3H
*+*
•+
-1.5
-0.6
1.5
+++++*
-0.8
0.8
-2..0_
30
4th qu
3d qu.
0.6
S4H
4thqu.
2.0
20
10
Hole s•ze, H
0
10
20
30
1.0
30
Hole size, H
20
d
1.0
the flux occursin eventsmore than 10 times the averageflux
and that out of this, 0.2/0.28 •- 70% occursin ejections,i.e.,
quadrant II events.
0.8
-0.8
-0.6
2nd qu.
•<
1stqu.
x
8 2H
0.6
SIH
x
x
-0.4
0.4
x
0.2
-0.2
XXXXxv
)+++;
',',•',',i',',I',','•
:•I,::
0
tion values for the various quadrantsfor hole size H = 0.
Figure13agives,approximately,
S•,o = -0.17, S2,o= 0.65,
S3,o = -0.38, andS4,o= 0.90, the sumof whichis 1.0,as
statedby (6). For H = 10 the corresponding
approximate
flux
fractionsare S•,•o = -0.02, S2,o= 0.20, S3,o = -0.02,
andS4,o= 0.12. Thesumof thisis0.28,meaning
that28%of
3O
Hole s•ze, H
Hole s•ze, H
Figure 13. Examplesof quadrantanalysisfor 10 m (a) and
(c) from an hourwith youngwaves,co/U•o = 0.90 (September 15, 1500 LST) and (b) and (d) from an hour with swell,
co/U•o -- 3.33 (September18, 2000 LST). Figures13a and
13b refer to the momentumflux and Figures13c and 13d refer
to the kinematicheat flux. Figures13a-13d giveflux fractions
SiN, equation(4), in the four quadrantsi againsthole sizeH,
equation(3). Note that H, by definition,is positivefor all
quadrantsand that in the momentumflux plots,Figures13a
and 13b,the signof Si• is positivefor quadrantsII and IV and
negativefor quadrantsI and III and that the corresponding
signsare reversedin the heat flux plots,Figures13c and 13d.
-1.0
10
10
0.2
-0.2
0.4
-0.4
84H
S 3H
0.6
4th qu
3d qu.
-0.8
0.8
1.0
30
-0.6
2'0
1'0
Hole size, H
1'0
2'0
Hole size, H
Figure 13. (continued)
-1.0
3O
SMEDMAN ET AL.: AIR-SEA INTERACTION
Table 3. Ratiosfor MomentumFlux [(II + IV)/(I + III)]Hm
and for Heat Flux [(I + III)/(II + IV)]Hh for 10 and 26 m
and For Young Wave (co/U•o = 0.89) and Swell
(co/U•o = 2.04) Conditions
co/U•o
DURING SWELL
25,845
of -0.35 to a value between0.2 and 0. (3) Most of the time
there is a wind speedmaximumbelow a heightof 10 m above
the mean water level, a phenomenoninterpretedas a wavedrivenwind speedincrease.(4) The characteristicchangesto
the turbulence
structure
mentioned
under feature
2 are ob-
served equally clearly at 10 and at 18 and 26 m. (5) The
Sea Level, m
H
0.89
2.04
turbulenceenergybudget at 10 m is dominatedby two gain
terms of approximatelyequal magnitude,pressuretransport,
Momentum Flux
and buoyancy,whereasthe local mechanicalproductionand
10
0
3.1 _+ 0.4
1.5 _+ 0.3
turbulent transport terms are very small numerically.(6)
5
7.9 _+ 2.5
1.7 +_ 0.5
10
17.6 +_ 7.7
2.0 _+ 0.9
Wave-relatedsignaturesin energyspectraand cospectraare
26
0
2.8 _+ 0.7
1.5 +_ 0.5
not verypronouncedat anyof the measuringlevels.(7) Quad5
6.6 _+ 3.2
1.6 _+ 0.5
rant analysisof the momentum flux showsthat flux contribu10
14.6 _+ 8.3
2.0 _+ 1.0
tionsfrom the interactionquadrantsbecomealmostas big as
Heat Flux
the sumof sweepsand ejectionsfor high-waveageconditions,
10
0
3.3 _+ 0.8
8.1 _+ 0.6
makingthe net flux numericallysmall;no suchcorresponding
5
9.3 _+5.6
o•
effect is observedin quadrantanalysisof the heat flux. In that
10
19 +_ 12
o•
26
0
3.3 _+ 0.5
6.0 _+ 2.6
case,instead,the relative contributionof quadrantI to the
5
9.4 +_ 4.0
29 _+ 14
transportprocessincreasesdramatically.
10
24 +_ 13
o•
The above picture for the momentum flux is in general
agreement
with previousfindingsin similarsituations[Volkov,
The figuresare meanvalues,derivedfrom hourlymeansfor periods
Height Above
'
of -48 hours duration each, with standard deviations. Roman numer-
1970; Makova, 1975; Antonia and Chambers, 1980; Chambers
als denote quadrantnumber, and H is hole size.
andAntonia, 1981].As noted in section4, previousmeasurementswere mainlyconfinedto relativelylow heightsabovethe
water surface, and in none of these studies were there simul-
wave age increases.Chambersand Antonia [1981] observeno
changein the form of their heat flux quadrantplotswhentheir
c/u, increasesfrom -•40 to 80, but their analysisis basedon
just a few cases.The pattern illustratedin Figures13a-13d is
very persistentin the present data set. This is illustrated by
the analysis
presentedin Table 3. Shownin Table 3 are the ratios
[(II + IV)/(I + III)]Hm for--u'w' and [(I + IXI)/(II + IV)]nh
for w' O'v,whereromannumeralsdenotequadrantnumbers,H
is hole size, and m and h denote momentum and heat flux,
taneous
measurements
of turbulent
characteristics
at several
levels.Thus it is a new findingof this studythat the turbulence
"anomalies"during swell (compared to young wave conditions)are actuallyobservedto occurin a layerextendingto at
least 26 m. In fact, there are no indications in the data of a
gradualdecreaseof the "degreeof anomaly"within this layer.
5.2. PossibleLinks to Processesin the Deep
Boundary Layer
respectively.All data from September14 and 15 have been
As mentionedin section1, the meteorologicalregime studtaken togetherin one group,havinga meanvaluefor co/U•o of ied by STH (1994) had all the characteristics
of previousstud0.89, and all data from September18 and 19 are in another iesduringswellconditions.There were,unfortunately,no wave
groupwith a mean co/U•o of 2.04. Resultsare given for three measurements
to confirmthat, actually,co/U > 1.2. The fact
hole sizesH - 0, 5, and 10.
For the momentum flux, Table 3 shows that for 10 m and
co/U•o = 0.89 the ratio increasesfrom -•3 to -•18 when the
that the situationoccurredin the aftermathof a galeis, how-
hole size increasesfrom 0 to 10, whereasit is in the range
between 1.5 and 2 for co/U•o = 2.04, thus showingthe
stronglyincreasinginfluenceof the interactionquadrantswith
increasingwave age and increasinghole size. The pattern is
verymuchthe samefor 26 m. For the heat flux the ratio [(I +
III)/(II + IV)]nh changesfrom 3 to 20 whenH increasesfrom
0 to 10 for the youngwave case.For the swellcasethe ratio is
between6 and 8 for H - 0 andvery largefor H -> 5. Also for
the heat flux the pattern remains largely unchangedwith
the occurrence of simultaneous
height.
5.
5.1.
Discussion
Summary of Results
ever,strong
indirectevidence
thatthiswasactually
thecase.
The uniquefeatureof the studydescribed
by STH (1994)is
airborne and tower-mounted
measurements.During a period of-•5 hours the momentum
flux was observedto be slightlypositivenot only in the tower
measurementsat a height of 22 m but throughoutthe lowest
100-200 m layerof the atmosphere,asrevealedfrom flightlegs
at 30, 60, 90, 150, and 200 m above the water surface. Wind
speedwasbetween
2 and3 m s- • throughout
thelowest500m.
In spiteof thisvirtual absenceof shearingstressat the surface,
turbulenceintensitywas high, giving,in fact, almostconstant
rate of dissipationthroughoutthe bulk of the boundarylayer
or, more precisely,up to a height of 700 m.
Figure 14, whichis reproducedfrom STH (1994), presents
the terms of the turbulence energy budget for the entire
boundarylayer. Figure 14a showsthe mechanicalproduction
term P, dissipation•, turbulenttransportterm Tt, and the
buoyancyproductionterm B, whereasFigure 14b showsthe
imbalanceterm (solid curve in the right-handpart of the
The most strikingfeaturesof the presentstudyare the following:(1) For valueslargerthan 1.2 for the waveageparameter co/U•o the shearingstressat and near the surface becomesstronglysuppressed,-u'w' taking on values smaller graph),interpreted
as pressure
transportTp. Note that all
than0.01m2 s-2, thecorresponding
average
Co valuebeing terms,includingthe pressuretransportterm derivedfrom the
-•0.7 x 10-3. (2) Theturbulent
intensities
of allthreevelocity airbornemeasurements,
extrapolatenicelyto the independent
componentsremain high, so that the modulusof the correla- tower measurements at 22 m.
tion coefficientfor u andw dropsfromitstypicalnormalvalue
The
relative
role of the various
terms of the turbulence
25,846
SMEDMAN ET AL.: AIR-SEA INTERACTION
DURING
SWELL
z/z i 1.0
(a)
0.8
0.6
O.4
0.2
I
5
&
13,
3
2
LOSS
I O
13
•,
1
0
-1
I
I
I
-2
-3
-½
GA!N (m2- s-3)
.
-5 .10-•
zlz i
1.0
(b)
0.8
0.6
0.4
0.2
o0
•
' nce
•
I
I
2
4
6
!
U(ms'1)
•
0
-1
!o
-2
GAIN
I
!
-4
-3
(m25'3 )
-5 lO-;
Figure 14. Turbulenceenergybudgetestimatesfrom the studyof STH (1994). (a) Mean profilesof the
varioustermsof the turbulenceenergybudgetthat were directlyderivedfrom airborneslantprofiles(curves)
and mast measurements(circles).(b) Right-handpart: imbalanceobtainedwhen summingup the directly
measuredtermsfrom slantprofiles(solidcurve),horizontalflightlegs(dashedcurvewith crosses),
and mast
measurements
(circle).Dashedcurvewith trianglesis the time rate of changeterm derivedfrom profilesat
0900 and 1130LST. Left-handpart: Mean wind profile.Samenotationsasin Figure6; zi denotesthe height
of the mixed layer. After Smedmanet al. [1994].
energybudgetfor the layerscloseto the surfacegivenby STH
(1994) are very much the same as observedin the present
study:Mechanicalproductionis closeto zero,whichis alsothe
casefor turbulent transport.The pressuretransportterm and
buoyancyproductionthus make up most of the energygain,
being balancedby dissipation.In Figure 14 it is clearly seen
that the net sourceof turbulentenergyis mechanicalproduction in the upperhalf of the boundarylayer;buoyancy
production, which is a gain near the surface,beinga lossthroughout
the bulk of the boundarylayer.
The turbulencecharacteristics
of the boundarylayerstudied
by STH (1994) bear all the characteristics
of a convectively
mixedboundarylayer [Kaimalet al., 1976].However,the similarity is only formal, with the height of the boundarylayerzi
being the characteristiclength scale.It was shownthat this
boundary layer is not driven by thermal convectionbut by
large-scale
turbulencethat wasproducedin the upperlayersin
the boundarylayer and broughtdownto lower heightsby the
pressuretransportmechanism.
It wasarguedthat thisphenomenon must be identical to inactive turbulence, which was first
identifiedby Townsend[1961] and Bradshaw[1967] in laboratory flow. H6gstr6m[1990] showedthat inactiveturbulenceis
likely to be universallypresent in near-neutral atmospheric
boundarylayer flow (explaining,e.g.,why the correlationcoefficient between u and w in the near-neutral atmospheric
surfacelayeris about -0.35 rather than -0.5 astypicallyfound
in turbulentlaboratoryboundarylayer flow).
As the conceptof activeand inactiveturbulenceis crucialto
the interpretationof the presentflow regime,a brief summary
of the general characteristicsof these phenomenais given
SMEDMAN
ET AL.: AIR-SEA
INTERACTION
here. Townsend[1961,p. 116] introducedthe conceptof active
and inactiveturbulencein a boundarylayer thus:"(i) Active
turbulencewhich is responsiblefor the turbulent transfer and
determinedby the stressdistributionand (ii) an inactivecomponentwhich doesnot transfermomentumor interactwith the
universalcomponent."Inactive turbulenceis characterizedby
the following:(1) It doesnot interactwith the activeturbulence in the inner layer (the surfacelayer). (2) It does not
contributeto the shearingstress.(3) It arisesin the upperpart
of the boundarylayer.(4) It is of relativelylargescale.(5) It is
partly due to the irrotational field created by pressurefluctuationsin the boundarylayer and partly due to the large-scale
vorticity field of the outer layer seen as an unsteadyexternal
stream.
Note
that in a flow situation
where
inactive
turbulence
be-
comesof major importancethe surfacemomentum flux drops
while turbulence intensity remains high. This will result in
reduction
of the correlation
coefficient
between
the u and w
component,-ruw, as observed(Figure 7), and an increaseof
normalizedvelocity standarddeviations,as illustrated in Figure 8 for rr,•/u, but also noted for the two normalized horizontal wind components.
The followingmain conclusionwas drawn by STH (1994)
concerningthe mechanism of inactive turbulence: The net
energyexchangeat the surfaceis suchthat the surfaceshearing
stressis closeto zero. In keepingwith the conclusionfrom the
community-wide evaluation of turbulent boundary layers
[KlineandRobinson,1989]that turbulenceproductioncloseto
the surfaceis an autonomousprocessthat takes place largely
independentof large-scaleprocessesin the outer layer it was
argued that the turbulenceobservednear the surfacewas in
fact just inactiveturbulence,"imported"from aboveby pressuretransport.As a contrast,the "traditionalview," expressed,
e.g., by Kitaigorodskii[1973] aswell as by Antonia and Chambers [1980] concerningthe observedcombinationof numericallyvery smallvaluesof momentumflux and relativelylarge
values of the turbulent fluctuations, is that this state of affairs
is brought about by pressuretransportof momentum upward
from the wavesto the atmosphere.Below, an attempt will be
made to reconcilethesetwo seeminglycontrastingviewsof the
turbulence mechanism above a surface with waves traveling
DURING
SWELL
25,847
Figure 10 showsan exampleof simultaneousw spectraat the
three measuringheightsof the presentstudy.As noticed earlier, the spectralcurvescollapsein the high-frequencyrange
but diverge in the low-frequencyrange, with spectrallevels
increasingwith height. Comparisonwith the correspondingw
spectrafrom STH (1994, Figure 5c) showsexactlyanalogous
behaviorthroughoutthe lowest300 m. The frequencyof the
spectral peak at the lowest measuring height in that study,
22 m, correspondsquite well with that observedat 26 m in the
present study. In fact, the above spectralbehavior is exactly
what is expectedfor a boundary layer dominated by inactive
turbulence,which, in turn, bears striking resemblanceto a
convectiveboundarylayer.Thus, as explainedby STH (1994),
the spectraof the horizontal componentsremain largely the
same over a large portion of the boundarylayer whereasthe
spectra of the vertical component changesystematicallywith
height in sucha manner that the spectralmaximum shiftsto
progressively
lower frequencieswith height.Note that the similarity with a convectiveboundarylayer is only formal, as discussed below.
In the discussionof the turbulenceenergybudget at 10 m in
section4 it was noted that buoyancyproductionwas of the
same magnitude as the pressuretransport gain. Thus it is a
relevant questionwhether the boundarylayer of the present
studyis in fact dominatedby buoyancyinsteadof, as suggested,
by inactiveturbulence.Also, in the caseof STH (1994), buoyancyproductionoccurredin the layersnear the surface(Figure
14a). This term changessign alreadyat --•200m, and it was
shownby STH (1994) that spectralscalingwas not in agreement with the idea of mixedlayer scaling.Thus observationsof
Kaimal et al. [1976] showthat the ratio of dissipationto buoyancy production is constant with height in the convective
boundarylayer: ß = •/[(#/To)(w'O')o] • 0.6. For the
presentstudy,ß • 1.7,which is not far from the value reported
by STH (1994, p. 3405), "around2." This analysisshowsconclusivelythat mixed layer scalingis not applicablehere. Another consequenceis also evident: As the boundary layer is
controlledby an entirely different turbulencemechanismthan
is usuallythe case,we cannot expectMonin-Obukhov scaling
to be valid.
The result shownin Figure 13d for the heat flux during swell
is in remarkable agreement with the large eddy simulations
(LES) of KhannaandBrasseur[1998]of the expectedvaluesof
5.3. A Conceptual Model of the Turbulence Regime
w' O' conditionedon w' for the simulatedconvectiveboundary
Above a Surface With Waves Travelling Faster
layer [Khannaand Brasseur,1998,Figures26 and 28]. Khanna
Than the Wind
and Brasseurfind both for the very unstablecase(characterReturn to the spectralgraphsof the longitudinalwind com- ized by zi/L = - 730, where zi is the height of the convective
ponentand note the following:(1) From the individualexam- boundarylayer and L is the Monin-Obukhovlength) and the
ples of simultaneousspectraat 10, 18, and 26 m in Figure 9 it slightly unstable case (zi/L = -8) that the heat flux is
is clear that these spectrado not scalewith height. The same stronglydominatedby upward directed motions,at least for
resultwasobtainedthroughoutthe swellperiod. (2) From the heights>0.1 z i. Again we see striking similarity between the
24 hour mean u spectrumdisplayedin Figure 11 it is clear that swell boundary layer, which is controlled by inactive turbuthe peakis foundat a frequency
as low as 10-3 Hz. This lence, and the ordinary convectiveboundarylayer.
To conclude,in the lowestlayersof the near-neutral marine
contrastssharplywith the wave spectrumpeak which is found
around0.2 Hz. In fact, the shapeof the u spectrumin Figure atmospheric boundary layer during swell conditions, both
11 is very similarto that observedby STH (1994) throughout buoyancyand shear production are small, leaving pressure
the lowest300 m (STH, 1994,Figure5a), the main difference transportas the dominantsourceof turbulent energy.This
being the slight bulge noticeable in the 10 m spectrum in energyis fed into the vertical componentand redistributedto
Figure 11 near the peak wavefrequency.Spectraof the lateral the horizontalcomponentsby pressure-velocity
derivativecorcomponenthave the same characteristicsas the u spectrum: relations.This meansthat the "swellboundarylayer" has cerindependenceof height and with a peak frequency around tain characteristics in common with a free-convection bound10-3 Hz aswell asstrikingsimilarity
withcorresponding
spec- ary layer, becauseshearingstressis quite small and the energy
input is in the vertical component.
tra observedby STH (1994,Figure5b).
faster than the wind.
25,848
SMEDMAN
ET AL.: AIR-SEA INTERACTION
DURING
SWELL
X 10'3
-1
10'4
10
'3
10
'2n (s' 1) 10
'•
10
ø
101
10'3
10'2
10ø
10'•
9O
80-
70-
60-
5O
40
302O
10
0
10'4
'
n (s'l)
10'•
Figure 15. (a) Mean u, w cospectra(curveswith circles)and quadraturespectra(curveswith stars)for
September18, 1995, 10 m, and (b) the corresponding
phaseangle 4• as functionof frequency.
Figure 15a showsmean cospectraand quadrature spectra
COuw
(n) and Quw(n), respectively,calculatedfor the entire
September18, and Figure 15b showsthe corresponding
phase
angle4>for the sameperiod,determinedfrom the relation[see,
e.g.,Lumleyand Panofsky,1964]
tan 4)= Q,w(n)/Co,w(n).
(7)
completelyout of phase, giving zero contributionto the cospectrumand thusto the momentumflux, in exactagreement
with the predictionfor inactiveturbulence,whichwe expectto
find at theselow frequencies.Note that the phaseangleis ->60ø
for frequencies
below---10-2 Hz. Thisis an indication
thatin
thefrequency
range10-3 < n < 10-2 thereis a mixtureof
truly inactiveturbulence,which has a phaseangle of 90ø, and
activeturbulencewith phaseanglezero. Analysisof cospectra
andquadraturespectraandthe corresponding
phaseanglefor
vertical velocityand temperature (not shownhere) for the
zerophaseanglefor frequencies
below---10-2 Hz (notshown sametime period (September18) revealsan entirelydifferent
here). It is notablethat the phaseanglein Figure 15b comes behavior,i.e., a phaseangle that fluctuatesrandomlyaround
closeto 90øfor the lowestfrequencies;that is, u and w become zero over the entire frequencydomain encountered.
The systematicincreaseof phase angle with decreasingfrequencydisplayedin Figure 15b is in strikingcontrastto the
correspondingplots for the pre-swelldayswhich shownear-
SMEDMAN
ET AL.' AIR-SEA
INTERACTION
DURING
SWELL
25,849
From comparisonof spectra from the present study and therewasa windspeeddropfrom -15 m s-• to 4 m s-• over
those from STH (1994) the following conclusionscan be a period of about a day; during a period of 48 hoursafter this
drawn: (1) It is quite reasonableto assumethat the same wind speeddrop occurred,the wind directionfluctuatedwithin
mechanism
created the observed turbulence
features in the
a _+50ø sector, and the wind speed was rather constant;the
two studies.(2) It is highlyunlikely that this turbulencehas wave spectrum had a single peak, and the direction of the
been producedby influencefrom the waves.Instead,it is very waveswas roughlythe same as that of the wind; and the swell
probable that inactive turbulence produced aloft has been originated from an area with stronger winds located in the
brought down to near the surfaceby pressuretransport.The southernmostpart of the Baltic Sea. From the information
crucial questionthen becomesthe following: How does the available for the caseswith strong frictional decouplingreair-seainteractionprocesscome into the picture?
ported in section1 it appearsthat similar conditionsprevailed
It is reasonableto assumethat in a shallowlayer just above in these casesas well. As revealed by Figures 7a and 8, no
the undulatingwater surfacethere is, in the terminologyof systematicdifferenceswere found in statisticsderived sepaBelcherand Hunt [1993], an inner surfacelayer, which is gov- rately for periodswhen wind and wave directionswere within
ernedby localmomentumtransferin the directionfrom the air 30ø of each other and when they differed by between 30ø and
to the sea.In this layer it is alsoreasonableto assumethat the 60ø, respectively.
It is interesting to ask what the requirements are for a
ordinarywall layer turbulenceproductionmechanismis active
[Klineand Robinson,1989].At the sametime, the longerwaves situationsimilar to this to occur,in terms of wind speeddrop,
(whichtravelfasterthan the wind) producemomentumtrans- alignmentof wave propagationand wind, and, not the least,
port by pressurefluctuationsin the oppositedirection. That timescaleof the drivingforcesproducingthis situation.To be
suchtransportactuallytakesplaceis clearly demonstratedby more precise' Does a similar reduction of stressas that obthe quadrant analysis,which showsthat for the momentum servedhere occur as soon as there is an appreciabledrop in
transportthe interactionquadrantsbecomeof increasingim- wind speed;doesit occurin a situationwith a multipeakwave
portancewith increasingwave age;that is, excessmomentumis spectrum?At presentthere appearsto be no informationavailbeing transported upward and deficit momentum is being able to answer these and related questionsconcerningthe
transporteddownward.At the sametime, the heat flux is not at generality of the results discussedhere. One may speculate
all affected in this way. Thus momentum must be transported
upwardfrom the surfaceby a mechanismwhichincludespressure-velocitycorrelations.Sucha mechanismis not possiblefor
transport of a scalar, such as virtual potential temperature,
that effects of this kind occurringduring lesswell pronounced
conditionscould temporarily reduce the stressand thus contribute to the inevitablescatterof Co plots(a hysteresiseffect
similarto that displayedin Figure 5 for the wind gradient).It
is alsorelevant to askwhat the requirementsare for frictional
This situation creates a net momentum transport that is reductionto occurin open oceanareas;is the situationoccurclose to zero. This in turn means that there can be little local
ring as regularly as there are appreciablewind speed drops
mechanicalproduction of turbulence (because mechanical after the passageof storms, or does omnidirectional swell
productionis equal to the productbetweenthe kinematicmo- changethe situation to a considerabledegree?
mentumfluxandthe localwindgradient).The net resultof this
which is studied here.
state of affairs is that, in fact, there will be little active turbu-
lence in the boundarylayer, exceptin a shallowinner surface
layer near the undulatingwater surface,leavingprimarily the
inactivekind of turbulence,whichis likely to originate,primarily, highup in the boundarylayer.It is worth notingthat during
the presentsituationwith swell,the number of individual60
min periodswith negativenet momentum flux (upward directedflux)increases
with height,beingzero at 10 m, 3 at 18 m,
and 6 at 26 m. In the casestudiedby STH (1994) the net
momentumflux wasfound to be slightlynegativein the lowest
200 m during a period of severalhours.
The abovesketchdoesnot answerthe questionof how deep
the zone of direct wave influenceis and how deep the inner
surfacelayer is. The measurementsof this studydo not give
very clear surfacewave signaturesin the spectraduring the
swellperiod:At the mostthere is a bulgeand a plateauin the
mean u and w spectradisplayedin Figure 11. At the same
time, as shownin Figure 4, there is a wind maximum present
somewherebelow the lowestmeasuringpoint, 10 m, for most
of the time during the swellperiod. From that it can be concludedthat the inner surfacelayer is certainly<10 m deep.A
way of describingthe situationwouldbe to saythat the bulk of
the boundarylayeris floatingwith verylittle frictionon top of a
layerlimitedin depthby thiswindmaximumcloseto the surface.
5.4.
Generality of the Present Results
The situationthat hasbeen the subjectof the presentstudy
is very well defined:It occurredin the aftermath of a gale, so
6.
Conclusions
A casehas been studiedwhich is characterizedby the dominant waves traveling faster than the wind. It has been demonstratedthat at the same time as momentum is transported
from the atmosphereto the ocean surface by the ordinary
turbulent mechanism, momentum is also transferred from the
wavesto the atmosphereby the pressuretransportterm, producinga wave-drivenwind increaseat low height(a consistent
wind speedmaximumbelow 10 m) and very low net surface
shearing stress.It was observedthat turbulence intensities
were neverthelessquite high at 10, 18, and 26 m above the
surface,givinga u, w correlationcoefficientwith a modulusin
the range 0 to 0.2. Direct wave signaturesin the wind spectra
are quite weak. It is concluded that mechanical turbulence
productionin the layer coveredby the observationsis virtually
zero. Instead, the turbulenceenergy must have been brought
downby pressuretransportfrom layersin the upper parts of
the boundarylayer, so-calledinactiveturbulence.Analysesof
turbulencecharacteristicsreveal that a systematicchange occurs at wave age co/U•o = 1.2, indicatingan almost discontinuouschangeof regime.
Appendix A: Determination of Flux Footprint
for the Eddy Correlation Measurements
at Ostergarnsholm
The turbulentfluxmeasured
at someheighton the Ostergarnsholmtower originatesfrom an upwindarea at somedis-
25,850
SMEDMAN
ET AL.' AIR-SEA
INTERACTION
tance from the tower. It is the purposeof appendixA to show
how the locationof this area, "the flux footprint,"for the three
measuringheights10, 18, and 26 m abovemean sea level was
determined.
DURING
SWELL
tion from a strip of width Ax situatedbetweenx and x + Ax.
By accumulatingflux contributions/SF(x) from x = 0 to
increasingdistancesin the wind directionit is possibleto calculatethe relativerole of upwindareasat differentdistancesin
It is assumedthat the flux originatesat the surfacefrom a the total measured flux.
It is found from such calculations that for the 10 m level,
row of infinitely wide line sourcesoriented perpendicularto
the mean wind direction during a particular run. The source 90% of the measuredflux originatesfrom areasbeyond250 m
strengthis assumed
to equalQ(x) with unitskg m-2 s-•. and 50% originatesfrom beyond670 m and that 70% of the
Assumingstationaryconditionsand that the flux gradientre- flux comes from areas between 250 and 1700 m. For 18 m the
lationshipholds,the diffusionequation takesthe form:
correspondingfiguresare 450 m, 1250 m, and 450 and 3200 m,
respectively.For 26 m, finally, the correspondingfigures are
770 m, 1980 m, and 770 and 5300 m.
The abovecalculationsrefer to an ordinaryneutral surface
Here K z is the exchangecoefficient,• is the mean concentra- layer. In this study,particularinterestis focusedon the swell
tion, and u is the mean wind speed. For neutral conditions, situation.As discussed
in this paper, the turbulencestructure
Kz •- u,kz and g = u,/k ln z/zo, and (A1)cannot be solved in this case differs from that of the ordinary case. At this
analytically.An approximate solution of this equation was, moment there is hardly enoughinformation to tailor the foothowever,obtainedby van Ulden [1978]. Gryninget al. [1983] print equationsto fit exactlythis kind of situation.Generally
carried out numerical solutions, which were found to be in
speaking,Co wasfound to be reducedcomparedto the ordiclose agreementwith those of van Ulden [1978] and in very nary caseduringswell.This meansthat the effectiveroughness
good agreement with measurementsfrom Project Prairie lengthz 0 is likely to be appreciablysmallerthan assumedin the
Grass. Gryning et al. find that the solutioncan be approxi- abovecalculations
(1.5 x 10-4 m). This,in turn,is likelyto
have the effect on the footprint that it becomesremovedeven
mated with the followingexpression:
farther from the shore comparedto what was obtained from
Q
exp {-[z/B'
•(X,Z)= At(s)btpxO.z
(s)(rz]s},
(A2)
the detailed
calculations.
whereUpxisthemeanwindspeed
attheheight
0.6;•, where Appendix B: Determination of the Effects
Z(x) is the heightof the plumecenterline, crz • 1.35 Z, for
neutral conditionsand s is a parameter which can take on
valuesbetween0.5 and ---2.7 dependingon stabilityand distance from the source.For neutral stratification,Gryninget al.
[1983] found that s •- 1.25. For this value,van Ulden[1978]
findsA'
= 0.902
and B'
-- 0.968.
of Water Depth in the Footprint for the
Eddy Correlation Measurements
at 0stergarnsholm
To quantifythe influenceof shallowwater, we have defined
a weightedmean phasespeed
van Ulden[1978]presentsthe followingexpression
for neutral conditions'
(Co}=
=
X/Zo
K2ZoIn
0.6
.
F(x, Z)Co(X) dx
(A3)
over the footprint. The weightingfunction is the vertical flux
Takingz0 = 1.5 x 10-4 m asa typicalvaluefor the rough- densityF(x, z) givenby (A7) in appendixA, normalizedso
that
nesslengthoversea,x canbe computed
asa functionof •.
Plotting the result in a log-log representationshowsthat the
data fall closelyon a straightline, which correspondsto
2 = 2.22 x 10-2(x0'94)
Jo
©
F(x,
z)dx
=1.
(A4)
From van Ulden[1978]it alsofollowsthat for neutralconditions The phase speed has been calculated using the dispersion
relation
•:(x, O)u,/Q •- 1.54/x.
(A5)
CO---
The verticalflux at the point (x, z) is
F(x, z) = -rz(o•/Oz)(x,
z) • -kzu(O•/Oz)(x,
z)
(A6)
The derivative O•/Oz is obtained after differentiation of
(A2). Insertingthe ensuingexpression
in (A6), togetherwith
(A3) and (A4) andthe valuesfor s, A ', andB' outlinedabove
givesthe followingapproximateexpression
for neutralconditions:
0.674
I3.0X10-2(X
z 0'94)
exp{
[3.0
x10_2(x0.94)
11'25}.
F(x,z)/Q= x
z
ß
-
(A7)
The totalverticalfluxat (x, z) is the integralofF(x, z) over
x from zero to infinity.By numericalcalculationwith (A7) it is
simpleto obtain an approximateestimateof the flux contribu-
# tanh
6O0
,
where6o0is the frequencyof dominatingwaves(the peakof the
wave spectrum)and h is the depth.The resultsare shownin
Figure 2c for the flux footprint for 10 m (circles)and 26 m
(crosses),
togetherwith the phasespeedin deepwater (stars).
Thesevaluescan be comparedwith the resultsof Anctil and
Donelan [1996],who have measuredthe effectsin turbulent
fluxesinducedby shoalingwaves.From their run 166,in which
no shoalingeffectscan be seenin the wave heightor the drag
coefficient,we calculatedc0 overthe footprintto varybetween
79 and 91% of the deep-watervalue.
In our data, duringthe swellperiod the valueswere consistently closer to the deep-waterphase speed over all three
footprints.Over the footprintcorresponding
to the lowest10 m
elevation,Co varied between92 and 99% of the deep-water
SMEDMAN
ET AL.: AIR-SEA
INTERACTION
value (Figure 2c). Over the footprint correspondingto 26 m,
Coledeep
wasbetween
99 and100%.
During Anctil and Donelan's[1996] run 166 the peak wave
period T Owas5.7-6.1 s, and the significantwaveheightH swas
0.8 m, which are comparableto our values;The ratio Hs/Xo
(where Xois the wavelengthof waveshavingperiod To) was
higher in their data than in our data.
In our data the valuesof H• and H•/X o over different parts
of the footprint were consistentlysmaller.Therefore no shallow-watereffectscan be expectedto be seen in our flux data
from the swell period.
On the other hand, duringthe galebefore the swellperiod a
significantportion of the flux at 10 m height originatesfrom
the part of the footprintwhere the principalwave components
are influencedby the bottom. The weightedmean Coover the
footprint correspondingto the lowest 10 m level varied between77 and 94% of the deep-watervalue (Figure 2c). Since
this is only slightly less than the range 79-91%, where no
effectswere found by Anctil and Donelan [1996], and significantlyabovethe range 69-89%, where clear shoalingeffects
were measuredboth in wavesteepness
and in drag coefficient,
we do not expectthe shallow-watereffectsat our lowestlevel
to be as strongas thoseobservedby Anctil and Donelan. Our
higher levelsshouldbe free from shallow-watereffects:The
corresponding
rangeof Coledeep
is 86--97%at 18 m leveland
90-99%
DURING
SWELL
25,851
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Harris, D. L., The wave-driven wind, J. Atmos. Sci., 23, 688-693, 1966.
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with a modified similarityformulation for near neutral conditions,J.
Atmos. Sci., 47, 1949-1972, 1990.
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characteristics
of surfacelayer turbulence,Q. J. R. Meteorol.Soc.,98,
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S. J. Caughey, and C. J. Readings, Turbulence structure in the
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summaryof the data, in Zoran Zaric MemorialInternationalSeminar
on Near-Wall Turbulence,Dubrovnik,Croatia,pp. 200-217, Hemisphere,New York, 1989.
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at 26 m level.
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Beforethe gale,Coledeep
wasashighas 94-95% overthe
481-511, 1973.
footprint correspondingto the lowestlevel, and therefore the
fluxesduring that time shouldnot be influencedby shallow Lumley, J. L., and H. A. Panofsky,The Structureof AtmosphericTurbulence,239 pp., Wiley-Interscience,New York, 1964.
water effects.Thesepoints(circles)canhardlybe distinguished Lundin, K., A. Smedman, and U. H6gstr6m, A systemfor wind and
from the other tightly clusteredpre-swellvaluesin Figures7a
turbulencemeasurementsin a wind farm, paper presentedat Euro-
and 8. Therefore, even during the gale, the shallow-watereffects seem small at all elevations.
pean Community Wind Energy Conference,Madrid, September
10-14, 1990.
Makova, V. I., Features of the dynamicsof turbulencein the marine
atmosphericsurfacelayer at variousstagesin the developmentof
waves,Izv. Acad. Sci. USSRAtmos. OceanicPhys.,Engl. Transl., 11,
Acknowledgments.
The costsfor establishing
the Ostergarnsholm 177-182, 1975.
field station were defrayed by grants from the Natural ScienceResearchCouncil (NFR) contractG-AA/GU 03556-313and from the
SwedishNational EnergyAdministration,grant506 226-4.The work of
the first author was made possibleby a grant from NFR contract
S-AA/FO
03556-314.
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