JOURNALOFGEOPHYSICALRESEARCH,VOL.87, NO.CI, PAGES595-600,JANUARY20.1982
Low-Frequencywaves in the Ligurian SeaDuring December 1977
M. Cnnpou
Laboratoire d'OcéanographiePhysique,Musëum Nationald'Histoire Naturelle,43 rue Cuvier,75005Paris, France
L. Wlrn e.uo J. M. MoucBr
Centre de Télédétectionet d'Analyse des Milieux Natur.els,Ecole Nationale Supérieuredes Mines de paris
Sophia-Antipolis, 06560Valbonne, France
Observationsoflow-frequency wavesin the Ligurian Seain December 1977are presented.From
time seriesof thermalinfraredimagesobtainedby satelliteNOAA 5, the meanwaveiengthandphase
velocity are estimated.They are, respectively,38 km and 18cm s-r. Thesewaves are analyzèdas
large-amplitudebaroclinic waves.Fairly goodagreementis found with a twoJayer model.
IN:rLopuc'ttoN
The northwesternMediterraneanbasinis characterizedat.
all seasonsby a largecyclonic circulation of surfacewater.
This is shown in Figures I and2, which showthe dynamic
contours and the velocitiescalculatedat the surfacefrom a
hydrological cruise done by Tchernia in February-March,
1960(H. LacombeandP.Tchernia,unpublisheddata,1965).
This large-scalemotionis mainly dueto theinflow of surface
water comingfrom the Atlantic Oceanthroughthe Straitsof
Gibraltar, which compensatesfor the waterlost by evapora-
tion. In winter, strong convective motions occur in the
center of the gyre, and deep water massesare formed by
mixing over the whole depth [Gascard, 1978].
The Ligurian Seais the easternpart of that region.It has
been studied by many authors lLacombe and Tchernia,
1972;Gostan, 1967a,b; HeIa, 1963;Trotti, 1953;Tchernia
and Saint-Guily,1959;Dahme et al., l97l; Stocchinoand
Testoni, 1977,19781.Three different massesof water are.
found. In December,a surfacelayer of some100m in depth
is observed.Its temperatureis between13.50and 14'C,its
salinity is between38.05and38.207oo,andits density(oe)is
between 28.50 and 28.95. Between 100 and 650 m an
intermediate water type of levantine origin is found. Its
temperatureis about 13.25'C,its salinity is about 38.52%a,
and its potential density (o) is about 29.08.Below this, a
deep water type is found with a potential temperatureof
12.70"C,a salinityof 38.41%o,anda density(oe)of 29.11.A
typical density profile is shownin Figure 3.
The horizontal velocities extend from the surfaceto at
least 500-600 m. The deep water is nearly quiescent. A
vertical section of the velocities on the line Nice-Calvi in
October 1963is presentedin Figure 4 (H. Lacombe andP.
Tchernia, unpublisheddata, 1965).The velocitiesarecalcu-
latedby thedynamicmethodfrom hydrologicaldata.Veloci-
ties up to 50 cm s-r are ençounteredat the surface.These
velocities are smallerthan thosemeasuredduring the same
period with a GEK (Figure 5). This could be due to the
existenceof a cyclonic barotropic current of afew centime-
terss-1.
From the aboveconsiderations,it appearsthatthe Liguri-
anbasincanbe modeledasatwo-layeroceanwith a surface
layer of a thicknessH1 of 200m, a Brunt-Vâisâlâfrequency
N1 of 4 ' l0-3 s-1, and aninternal radiusof deformationR1
: Nflrtf : 8km overlying adeeplayer of athicknessI/2 of
Copyright@1982bytheAmericanGeophysicalUnion.
Papernumber lcl439.
ot48-0227l82lNl C-I439$01.00
20(X)m, a Brunt-VâisâlâfrequencyNz of 0.4 . 10-3s-r, and
aninternal radiusof deformationR2alsoof 8km (Figure3).
The generalcyclonic motion suggestsçool water in the
interior with warmer water at the periphe-y of the sea.In
between, there is a thermal front with a variation of a few
tenths of a degreeacrossthe front. This feature is clearly
visibleonthethermalinfraredimagerygivenby theradiome-
ter VHRR of the satelliteNOAA 5 (Fieure 6).
The aim of this noteis twofold. First, we presentobserva-
tions of low-frequency waves propagatingin the Ligurian
Seamadeby satelliteNOAA 5duringDecember1977.From
these observations,someparametersspecificto wave mo-
tion areestimated.Secondly,we examinethewavephenom-
enon in terms of the baroclinic instability mechanismand
çomparethe observationswith the rotatingtank experiment
of Saunders[1973]and with the modelof TanSU9751.lt is
found that the Ligurian Seamay be baroclinically unstable
andthat thewavelengthspredictedby thebaroclinicinstabil-
ity theory of Tang [1975]are in generalagreementwith our
calculations.
OssBnvarroNs
ln December 1977,the meteorologicalsituationover the
Ligurian Seawas atypical. From DecemberI to December
20 the northern part of the Ligurian Sea was calm, but
easterlywinds wereblowing continuouslyover the southern
part. Their velscities were largerthan 8 m s-l on December
1,2,4, 15,16,19.
Seven clouô-free thermal infrared imageswere obtained
during that period. The NOAA 5 satellite data were proc-
essed by the Centre de Télédétection et dlAnalyse des
Milieux Naturels (CTAMN). This included the following:
computation of equivalent tempelatures; smoothing by a
two-dimensionalspatialfilter contrastenhancement;plotting
of full thermal resolution maps; and, finally, a geometric
correction for the earth's spin and the curvature of its
surface.
The absolutevaluesof temperatureprovided by the radi-
ometer are not very accurate,but seasurfacetemperatures
(SST) may be determinedwith an açcuracyof 0.5.C at a 3-
km resolutionin this arealAlbuissonet aI., 1979;Wald and
Nihous, 19801.In order to make the imagessuperposable
(-r 1km2),they mustbegeometricallycorrectedonthebasis
of known landmarks.
Oneof the sevenimagesof December1977is presentedin

llÂtrfi iÆro{AtDHtsIoRtr{AILnEtrE
OûIÂIffiIËilEPHEUI
SCALE0
6r ,,,+#Éh
Fig' l. Dynamic contoursin centimetersat the surfacein f"U-a.y-fvfarctr, tX0. The zero-vel..ity d"pth ir;00 *
ilr$u{ uno|A D'Hslontuluntut
DOGÂITGRÂPIIIIPHNUf,
SCALE
Fig. 2. Surfacevelocity in February-March, 1960.

f.
28.60 28.90 nN 2e.10
CnBpoll ET AL.: Bnrer Rsponr 597
Fig. 3. Typical density profile in December 1960(after Gostan
Il967al) (solid line) and its schematic representation (dotted line),
fitting the Tang model.
Figure 6. The sevenimagesexhibit large meandersof the
thermalfront. ThehorizontalSSTgradientsarethe strongest
we haveever seenon satelliteimagesin this region;they are
of the order of 0.05'C/km. Observationsof the wavemotion
over 24-hour sequencesare possiblefor December3 and 4
andDecember17,18,19,and20, 1977.Meandersmayalso
be followed, but lessclearly, on the imagesof January5, 6,
and7. 1978.
In Figure 7 we presentmeandersof two frontal isotherms
(solid and dotted lines) on December3 (thick lines) and 4
(thin lines). Wavesapparentlypropagatearoundthe central
eddy in the cyclonic direction. At any particular time the
meanders are of different shapesalong the front, but a
particular meanderkeepsthe sameshapeduringits propaga-
tion. This shapepreservationallowsmeasurementsof wave-
lengthsand phasespeeds.
The mean values of wavelength and of phase speed,
computedfrom 30 measurements,are, respectively, 38km
and 18cm s-1,with rms valuesof 10km and2 cm s-1.The
phasespeedis in the samedirectionas,but smallerthan,the
meancurrent of Nice, which is about50çm s-t. Theperiod
is 2.5daysandis greaterthan the inertial period 2zlf (about
17.30 hours). These quantities axe remarkably constant
during the period of observation.
We have examinedthe possibility that the phasevelocity
was due to the stroboscopic effect. This mechanismgave
unrealistic valuesfor the phasespeed,and hencethis was
not consideredfurther.
Five similar meanderswere also observedbetweenNice
andMarseille on oneimagefrom NOAA 6 on November26,
1979.The distancebetweentwo adjacentcrestsrangedfrom
30to 70km. The lack of additionalinformationpreventedus
from combining the observationsof December1977and of
VERT|CALPROFIIESOF CURRENTSONTHELINE NICE-CALVI
ocroB ER 1963
017"
q.,.*,
l1000décibors
1 Knof
Frg. 4' Velocity profilescalculatedby the Helland-Hansenmethodon the line Nice-Calvi in October 1963.

598 Cnrpon ET AL.: Bruer REponr
Fig. 5. Velocities at the surfacecalculatedwith the GEK in October 1963.
November 1979.Infact, it seemsthat theLigurian currentis
particularly unstableat the endof Novemberandin Decem-
ber. Unfortunately, this period is the worst for satellite
infrared imagerybecauseoffrequent cloud coverage.
DrscussroN
The shapeof thethermalfront presentedin Figures6and7
looks very muchlike thatof theSaunders[1973]experiment,
which dealswith the instability of a baroclinic vortex in a
rotating tank. Using dimensionalanalysis,hefound that the
instability occurs when
| >> R2lD2
where R is the internal radius of deformationandD is the
width of the current. By substitutingthe valuesof R andD
computedfor the Ligurian basin(R : 8 km, D : û km). we
find that this instability criterion is satisfiedandthatthis area
maybebaroclinicallyinstable.A relationbetweenR andthe
number meanderslqtcan be found:
m: 1.8DIR
where an z is an integer.
For the Ligurian basin,we find ltt : 13,which is in rough
agreementwith the ninemeandersobservedin Figure6 and
7.
The explanation of the above-mentionedphenomenon
o Sonm
\
I T A L Y
Copruio
0
Fig. 6. Satelliteinfrared thermal imageof the Ligurian Seaon
December4, 1980,at 0900UT. The warmesttemperaturescorre-
spondto the darkesttonesfor the sea.The meandersin the frontal
zone are clearly visible.
Fig. 7. Meanders of two isotherms ? (dotted lines) and T *
0.5'C(solidlines)on December3 (thicklines)and4 (thinlines).Let
us notice that the two thick lines (solid anddotred)of December3
are transformed into the two thin ones of December 4 through a
cyclonic rotation. This allowsus to estimatethe phasespeedof the
waveJike motion.

-H2
F!e, 8. Schematicrepresentationof thevelocityprofileof the
model:layerwith constantshearon top of quiescênilayer(after
Tang).
maybe soughtthroughtheoriesof large-amplitudebaroclinic
waves and, in particular, of baroclinic instability. These
baroclinic waves could have been initiated by the wind
blowing in the southernpart of the region,which generated
cross-cuffent perturbations. Among the baroclinic models
fitting geographicaland observationalconditions, the two-
layer model of Tang t19751is pertinent to this study. This
analytical model dealswith small perturbationsof a mean
current. A similar model was successfullyemployed by
Gascard [1978] in the Medoc area, where Mediterranean
deepwater formation ocçurs.
The linearizedversionsof the quasi-geostrophicvorticity
equation and of the continuity equationfor smallperturba_
tions are
la _ a\a,r, ô{r,ôu Nz
l - + 1 7 : - l _ - r - - * - _ w , : 0 ( Z )
\ôr ôxl ôz ôx ôz f
where ry''denotestheperturbationof the streamfunction, w'
denotesthe perturbation of the vertical velocity, N is.the
Brunt-Vâisâlâfrequency (assumedto be constant).andfi is
the meanzonal velocity in the x direction.
Let us assumethe solutionto be of the form
l*'\
r ' -r
I
'.l:R.l V.*,"-")sin/yl
frl
\.'l lw
"l
where Re denotesthe 'real part of,' û(z) and w(z) are the
complex Fourier coefficients, k = 2rlL (where I is the
wavelength in the r direction), I : nlD (where D is the
distancebetweenthe nodalsurfacesin they direction)andc
is the complex phasespeed.
Let us consider the twoJayer fluid mentioned in the
introduc.tion.Let us assumethat u is uniform with y, varies
linearly with z in the upperlayer (i.e., ù = u at z = Hr andù
59
: 0 at z: 0), andis equalto zeroin the lower layer (Figure
8).
Equations (1) and (2) are applied to each layer. The
generalsolution is
tt : At exp(KtlH) * 81 exp (-K*lHr)
in the upperlayer and
th. : Az exp (K2zlH) + 82 exp (-KzzlHz)
inthelowerlayer,whereK1: p,H1Nrlf,Kz: p,H2N2lf,and,
p: (l* + P)tt2.By usingtheabovedefiniti,onôf Hr, Hr, Nr,
andN2, the following dimensionlesspaxametersarecomput-
ed.
K : tanh K2ltanhK1 M : N1lN2
a : 2[(Ktl2) - tanh(Krlz)ll(Kr - tanhK1)
b : 2l(Kl2) - coth (Ktlz)ll(Kt - tanh K1)
Then, the phasevelocity is written in the form
c : c r * i c ; c ; ) 0
The solutionof (1),(2)with theboundaryconditionsat the
surface(rigid lid), at theinterface(continuity ofthe motion),
and at the bottom (vertical velocity equalto zero) leadsto
[TanS, 1975]
u f MK ÂnhK,l
c,:11 I _ _______-j_t (+)
- L Kt(t+ Mnl
u Kr- tanhKr_
,,:
rffi l.-(MK+ a)(MK+ b)ltt2 (5)
Thecutof wavelengthseparatingthe shortstableandlong
unstablewavesis readily obtainedby settingMK + b : 0 in
(5). With the actual valuesof the physical parameters,one
finds ,I,. = 48 km. The growth ratekc;is drawn in Figure 9.
Its maximumis obtainedat Kt = 0.78,which correspondsto
the most unstable wave whose wavelength is 56 km. By
substitutingthe numericalvaluesin (4)andassumingthat a
: 50 cm s-r, it is foundthat the velocitj,c,:6 cm s-1.
Thesevaluesareroughly comparableto the observedwave-
length of 38 km and velocity of 18 cm s-r. It shouldbe
emphasizedthat the theoreticalvaluesarevery sensitiveto
the physical parametersand to the model. Moreover. the
CnnpoN ET AL.: Bnrer Reponr
l a ô \ ^ a
[;+, ^ lV'.lt':f-w
\or dxl dz\ /
(l)
Fig. 9. Nondimensionalgrowth rute Kç;lu with respectto K1 for
H,IH,: 1120.
KlCi/u

600 CnBpox ET AL.: Bnrep Rrronr
baroclinic waves are really three-dimensionaldisturbances,
whereasthe observationsare only the surfacesignature.
An explanationof the wave motion could be soughtfrom
theories of barotropic unstability and of shelf waves. The
width of the Ligurian current of Nice is about 60 km
fGostan, l967bl. Becausethis width is muchgreaterthanthe
internal radius of deformation(8 km), the observedmotion
cannot be barotropically unstable fStern, 19751pedtosky,
19791.Shelf waves are
motion, since the shelf
generatesuchwaves.
an explanation of the wave
too narrow and too steep to
CoNcrusroNs
Observationsfrom NOAA 5 have suggestedlong waves
propagatingin the Ligurian SeaduringDecember 1977. The
estimatedvaluesofthe wavelength,thephasespeed,andthe
period are, respectively,38 km, 18cm s-1, and 2.5 days.
Hydrological data taken in that region during the month of
Decemberby previousauthorsshowthatbaroclinicunstable
waves can develop.The observedwavelengthwas, howev-
er, smallerthanthe theoreticalones.
This paperindicatesthe strengthandweaknessof satellite
thermalimagesfor quasi-instantaneoussurveyofvast areas.
However, only relative values of superficialtemperatures
are obtained. Furthermore, our interpretation ignores the
interior dynamics. Nevertheless,it is remarkableto obtain
from a routine satellite survey quantities associatedwith
wave propagation.
Acknowledgments.Wearegratefulto H. Lacombe,E. Salusti,
and J. C. Gascardfor fruitful discussionsandto R. Lasbleiz,
Directorof theCentredeMétéorologieSpatiale,forkindlyprovid-
inguswiththesatellitedata.-ThisworkwassupportedbytheCNEXO(CentreNationalpour
l'ExploitationdesOcéans)andtheCNRS(CentreNationaldela
RechercheScientifique).
RBnsRENcns
Albuisson,M., L. Pontier,andL. Wald.A comparisonbetweensea-
surfacetemperaturemeasurementsfrom satelliteNOAA 4 and
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within the first 150m ofdepth ofthe Ligurian Seàandits seasonal
variationsduringthe years1960-1967, Tech.Memo. 165,Saclant
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instability and oceanic eddies,Oceanol.Acta,1(3), 315-330,
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-J., Geophysical Fluid Dynamics, 624 pp., Springer-
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not
is
(ReceivedJuly 7, 1980;
revisedSeptemberll, 1981;
acceptedSeptember15,1981.)