Sound-Flow Interactions

TheCarg`eseSummerSchool“Sound–?owinteractions”washeldinthe- stitutd’EtudesScienti?quesdeCarg`eseinCorsica,Francefrom19thJune to1stJuly,2000. Theunderstandingofsoundand?owinteractionshasmadesomerema- ableprogresssincethepioneeringworksoftheRussianandBritishschools, inthe1950s. Inaddition,thegrowingavailabilityduringthepast10years ofsophisticatedcomputer/electronics/materialstechniquesallowsforthe- velopmentofagrowingnumberofapplicationsaswellasthepossibilityof addressingnewfundamentalproblems. Thecouplingbetweenacousticwaves and?owmotionisbasicallynonlinear,sothatthesoundpropagationand generationismodi?edbythe?owandthe?owcanalsobemodi?edbythe sound. Asaresult,thisproblemisinvestigatedinmanydi?erentscienti?c communities,suchasappliedmathematics,acousticsand?uidmechanics, amongothers. Inouropinion,thetimehadcometotrytogatherthe- searchersinthedi?erentcommunitiestogetherinatutorialenvironemnt. So, thisschoolbroughttogetherworldwidespecialistsinordertopresentvarious aspectsofsound–?owinteractions,andshareexpertiseandmethodologiesso astopromotecross-fertilisation. ThebasicknowledgeintheareaisintroducedbyA. HirschbergandC. Schram. Hepresentstheaeroacousticsofinternal?owinaverylivelyway withalotofillustrationdevices. Heintroducesaeroacousticanalogiesand applicationslikemusicalinstruments,theRijketube,speechproductionetc. M. S. Howeintroducesthetheoryofvortexsoundinaverydidacticway. From Lighthill’sacousticanalogy,heshowshowvorticityandentropy?uctuations canbeseenassourcesofsound. Then,usingthecompactGreen’sfunctions, heshowshowtocomputethevortexsound. Asanexampleofthemethod presented,heappliesthistheorytopressuretransientsgeneratedbyhi- speedtrains. F. Lundgivesthebasicequationsofsound–?owinteractions. Thenheintroducesveryclearlythescatteringofsoundbecauseofvorticity andgivesthemostrecentresultsonultrasoundpropagationthroughadis- dered?ow. V. Ostashevpresentsgeometricalacousticsinmovingmediaand theimportantpracticalproblemofsoundpropagationinturbulence(at- sphere,ocean). A. Fabrikantexaminestheplasma–hydrodynamicsanalogies includingtheresonantwave-?owinteractioninshear?ows,wavesofnegative VI Preface energyandover-re?ectionandacousticoscillatorsin?uid?ows. P. J. Mor- sondescribesthedynamicsofthecontinuousspectrumwhichoccursinshear ?ow. Theresultsareinterpretedinthecontextofin?nitedimensionalHam- toniansystemstheory. G. Chagelishvilipresentsnewlinearmechanismsof acousticwavegenerationinsmoothshear?owsusinganon-modalstudy. N. Peakepresents?uid–structureinteractionsinthepresenceofmean?ows, includingtheproblemsofinstabilityandcausality. Finally,W. Lauterborn presentsnonlinearacousticswithapplicationstosonoluminescenceandto acousticchaos. InthisCarg`eseSummerSchool,54studentsfrom12nations,and11l- turersfrom7nationsparticipated. Aknowledgements. TheSummerSchoolandthispublicationwouldnot havebeenpossiblewithout: •?nancialsupportfromtheEuropeanUnion,theCentreNationaldela RechercheScienti?que,theMinist`eredesA?airesEtrang`eres,theM- ist`eredel’EducationNationale,delaRechercheetdelaTechnologieand theGroupementdeRecherche“Turbulence”; •the guidance of Elisabeth Dubois–Violette, director of the Institut d’EtudesScienti?quesdeCarg`ese; •thehelpofChantalAriano,NathalieBedjai,BrigitteCassegrain,Pierre- EricGrossiandthewholeteaminpreparingandhostingofthisschool. Finally,wewishtothankthelecturersforgivingsomuchtimeinprep- ingthelecturesandwritingthemup,aswellasmakingthemselvesavailable fordiscussionsduringtheschool. 1 LeMans,Paris,Lyon YvesAur´egan , 2 September2001 Agn`esMaurel , 1 VincentPagneux , 3 Jean-Fran¸coisPinton . 1 Laboratoired’Acoustiquedel’Universit´eduMaine,UMRCNRS6613, Av. OMessiaen,72085LeMansCedex9,France 2 LaboratoireOndesetAcoustique,UMRCNRS7587, ESPCI,10rueVauquelin,75005Paris,France 3 LaboratoiredePhysique,UMRCNRS1325, EcoleNormaleSup´erieuredeLyon,46all´eed’Italie,69007Lyon,France Preface VII SomeofthelecturersoftheCarg`eseSchool,fromlefttoright:M. S. Howe,A. Hirschberg,P. Morrison,W. Lauterborn,V. Ostashev,A. Fabrikant,N. Peake, T. Colonius(PhotoC. Schram) SomeoftheparticipantsoftheCarg`eseSchool(PhotoC. Schram) TableofContents APrimitiveApproachtoAeroacoustics AvrahamHirschberg,ChristopheSchram. . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 FluidDynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 Lighthill’sAnalogy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 JetNoise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5 Thermo-Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 6 AcousticalEnergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 7 Rijke-Tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 8 Vortex-SoundTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 9 ChoiceoftheGreen’sFunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 10 Howe’sEnergyCorollary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 11 TheOpenPipeTerminationofanUn?angedPipe . . . . . . . . . . . . . . 21 12 Whistler-NozzleandHumanWhistling . . . . . . . . . . . . . . . . . . . . . . . . 25 13 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 LecturesontheTheoryofVortex–Sound MichaelS. Howe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1 AerodynamicSound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1. 1 Lighthill’sAcousticAnalogy(1952). . . . . . . . . . . . . . . . . . . . . . . 31 1. 2 AerodynamicSoundfromLow-Mach-NumberTurbulence ofUniformMeanDensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1. 3 AerodynamicSoundfromLow-Mach-NumberTurbulence ofVariableMeanDensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2 VorticityandEntropyFluctuations asSourcesofSound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2. 1 TheRˆoleofVorticityinLighthill’sTheory. . . . . . . . . . . . . . . . . 37 2. 2 AcousticAnalogyinTermsoftheTotalEnthalpy. . . . . . . . . . . 39 2. 3 VorticityandEntropySources. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3 FundamentalSolutionsoftheWaveEquation. . . . . . . . . . . . . . . . . . . 43 3. 1 TheHelmholtzEquation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3. 2 TheWaveEquation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4 GeneralSolutionoftheInhomogeneousWaveEquation. . . . . . . . . . 47 4. 1 GeneralSolutionintheFrequency-Domain. . . . . . . . . . . . . . . . . 47 X TableofContents 4. 2 GeneralSolutionintheTime-Domain. . . . . . . . . . . . . . . . . . . . . 49 5 CompactGreen’sFunctions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .