～40inagreementwithaccelerationmea-surementsin[10].
10
L
q
D10
10
DL
10
FIG.5:ESSplotsofthestructurefunctionvariation(indou-blelogcoordinates).Thesolidcurvesarebestlinear tswith
slopesequaltoξL
q=0.56±0.01,1.34±0.02,1.56±0.06,1.8±0.2forp=1,3,4,5fromtoptobottom.Coordinatesinarbitraryunits.
Moregenerally,onecanchoosetodescribetheevolu-tionofthePDFsbythebehavioroftheirmoments(or
‘structurefunctions’)DL
changeofq(τ)= |δτv|q .Indeed,acon-sequenceoftheshapeofthePDFswithscaleisthattheirmoments,asthe atnessfactorabove,varywithscale.ClassicallyintheEulerianpicture,oneex-pectsscalingintheinertialrange,DE
q(r)∝rζq,atleastinthelimitofverylargeReynoldsnumbers.Atthe -niteReynoldsnumberwheremostexperimentsaremade,thelackofatrueinertialrangeisusuallycompensatedbystudyingtherelativescalingofthestructurefunc-tions–theESSansatz[16].Weusethesecondorderstructurefunctionasareference.Indeedthedimensional
estimationofDL2(asthatofDE
3)dependslinearlyontheincrementandonthedissipation.Fig.5showsthat,asintheEulerianframe,arelativescalingisobservedfortheLagrangianstructurefunctionsoforders1to5,DLq(τ)∝DL2(τ)ξq.Weobservethattherelativeexpo-nentsfollowasequencecloseto,butmoreintermittentthanthecorrespondingEulerianquantity.Indeed,we
obtain:ξLL
L/ξLξ1/ξ3=0.42,ξ3=0.75,ξL/ξLL3=1.17,5
/ξL
2
43=1.28tobecomparedtothecommonlyac-4
ceptedEulerianvalues[17]ξEξ1/ξE3=0.36,ξE2/ξE
3=0.70,E4/ξE3=1.28,ξE5/ξE
3=1.53.
Inconclusion,usinganewexperimentaltechnique,wehaveobtainedaLagrangianvelocitymeasurementthatcoverstheinertialrangeofscales.OurresultsareconsistentwithKolmogorov-likedimensionalpredictionsforsecondorderstatisticalquantities.Athigherorders,theobservedintermittencyisverystrong.HowtheLagrangianintermittencyisrelatedtothestatisticalpropertiesoftheenergytransfersisanopenquestion.Fromadynamicalpointofview,theNavier-StokesequationinLagrangiancoordinatescouldbemodeledusingstochasticequations.WorkiscurrentlyunderwaytocomparethedynamicsoftheLagrangianvelocitytopredictionsofLangevin-likemodels.
acknowledgements:WethankBernardCastaingforinterestingdiscussionsandVermonCorporationforthedesignoftheultrasonictransducers.Thisworkissup-portedbygrantACINo.2226fromtheFrenchMinist`eredelaRecherche.
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