About the Book
TheCargeseSummerSchool Sound ?owinteractions washeldinthe- stitutd EtudesScienti?quesdeCargeseinCorsica, 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. InthisCargeseSummerSchool,54studentsfrom12nations, and11l- turersfrom7nationsparticipated. Aknowledgements. TheSummerSchoolandthispublicationwouldnot havebeenpossiblewithout: nancialsupportfromtheEuropeanUnion, theCentreNationaldela RechercheScienti?que, theMinisteredesA?airesEtrangeres, theM- isteredel EducationNationale, delaRechercheetdelaTechnologieand theGroupementdeRecherche Turbulence; the guidance of Elisabeth Dubois Violette, director of the Institut d EtudesScienti?quesdeCargese; thehelpofChantalAriano, NathalieBedjai, BrigitteCassegrain, Pierre- EricGrossiandthewholeteaminpreparingandhostingofthisschool. Finally, wewishtothankthelecturersforgivingsomuchtimeinprep- ingthelecturesandwritingthemup, aswellasmakingthemselvesavailable fordiscussionsduringtheschool. 1 LeMans, Paris, Lyon YvesAuregan, 2 September2001 AgnesMaurel, 1 VincentPagneux, 3 Jean-Fran, coisPinton . 1 Laboratoired Acoustiquedel UniversiteduMaine, UMRCNRS6613, Av. OMessiaen,72085LeMansCedex9, France 2 LaboratoireOndesetAcoustique, UMRCNRS7587, ESPCI,10rueVauquelin,75005Paris, France 3 LaboratoiredePhysique, UMRCNRS1325, EcoleNormaleSuperieuredeLyon,46alleed Italie,69007Lyon, France Preface VII SomeofthelecturersoftheCargeseSchool, fromlefttoright: M. S. Howe, A. Hirschberg, P. Morrison, W. Lauterborn, V. Ostashev, A. Fabrikant, N. Peake, T. Colonius(PhotoC. Schram) SomeoftheparticipantsoftheCargeseSchool(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 TheR oleofVorticityinLighthill 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ."
