Sound-Flow Interactions (Lecture Notes in Physics, 586)

✍ Scribed by Y. Auregan (editor), A. Maurel (editor), V. Pagneux (editor), J.-F. Pinton (editor)

• Publisher: Springer
• Year: 2002
• Tongue: English
• Leaves: 284
• Edition: 2002
• Category: Library

✦ Synopsis

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 YvesAur´egan , 2 September2001 AgnesMaurel , 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 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. .

✦ Table of Contents

Chapter 1
1 Introduction
2 Fluid Dynamics
3 Lighthill's Analogy
4 Jet Noise
5 Thermo-Acoustics
6 Acoustical Energy
7 Rijke-Tube
8 Vortex-Sound Theory
9 Choice of the Green's Function
10 Howe's Energy Corollary
11 The Open Pipe Termination of an Unflanged Pipe
12 Whistler-Nozzle and Human Whistling
13 Conclusion
References
Chapter 2
1 Aerodynamic Sound
1.1 Lighthill’s Acoustic Analogy (1952)
1.2 Aerodynamic Sound from Low-Mach-Number Turbulence of Uniform Mean Density
1.3 Aerodynamic Sound from Low-Mach-Number Turbulence of Variable Mean Density
2 Vorticity and Entropy Fluctuations as Sources of Sound
2.1 The Role of Vorticity in Lighthill’s Theory
2.2 Acoustic Analogy in Terms ofthe Total Enthalpy
2.3 Vorticity and Entropy Sources
3 Fundamental Solutions of the Wave Equation
3.1 The Helmholtz Equation
3.2 The Wave Equation
4 General Solution of the Inhomogeneous Wave Equation
4.1 General Solution in the Frequency-Domain
4.2 General Solution in the Time-Domain
5 Compact Green’s Functions
5.1 Time-Harmonic Problems
5.2 Time-Domain Problems
6 Influence of Solid Bodies on the Generation of Aerodynamic Sound
6.1 Integral Representation of Aerodynamic Sound
6.2 Curle’s Theory Applied to Compact Bodies
6.3 Vortex Sound
6.4 Influence of Vortex Shedding
7 Vortex-Airfoil Interaction Noise
7.1 Blade-Vortex Interactions in Two-Dimensions
7.2 Three-Dimensional Interactions
7.3 Blade-Vortex Interactions in Three Dimensions
8 Vorticity Production by Sound
8.1 Interaction of Sound with a Solid Surface
8.2 Interactions at a Trailing Edge
8.3 Leading Edge Interactions
8.4 Application to Resonant Oscillations
9 Perforated Screens
9.1 Rayleigh Conductivity
9.2 The Bias Flow Aperture
9.3 Reflection and Transmission of Sound by a Perforated Screen
10 Compression Wave Generated when a Train Enters a Tunnel
10.1 The Governing Equations
10.2 Linear Theory
10.3 Contribution from the Surface Dipoles
10.4 Contribution from the Exit Flow Vorticity
11 The Flared Portal
11.1 Suppression of the Micro-pressure Wave
11.2 The Function varphi^*
11.3 Optimal Flaring
11.4 Comparison with Measurements
References
Chapter 3
1 Introduction
2 The Basics – Vortex Sound
2.1 Incompressible Flow
2.2 Slightly Compressible Flow
2.3 Incompressible Vortex Dynamics
2.4 Vortex Sound
2.5 Bibliographical Notes
3 Scattering of Sound by Vorticity
3.1 Kelvin’s Theorem
3.2 Scattering to Order M
3.3 Bibliographical Notes
4 Two Dimensions
4.1 Vanishing Circulation
4.2 Surface Waves
4.3 Shallow Water
4.4 Deeper Water
4.5Exp erimental Results
4.6 Bibliographical Notes
5 Multiple Scattering
5.1 Equations to Order M^2
5.2 Appendix
5.3 Example: a “Gas” of Vortices
5.4 Two Dimensions
5.5 Three Dimensions
5.6 Bibliographical Notes
6 Loose Ends
6.1 Optical Theorem
6.2 Validity of the Born Approximation
Acknowledgements
Chapter 4
1 Introduction
2 Linearized Equations of Fluid Dynamics
3 Solution of Linearized Equations of Fluid Dynamics
3.1 Debye Series
3.2 Eikonal Equation
3.3 Dispersion Equation
3.4 Transport Equation
3.5 Conservation of Acoustic Energy
4 Geometrical Acoustics in a Three-Dimensional Inhomogeneous Medium
4.1 Group and Phase Velocities
4.2 Ray Path
4.3 Eikonal and Time of Sound Propagation
4.4 Amplitude of the Sound Pressure
5 Geometrical Acoustics in a Stratifed Medium
5.1 Refraction Law for the Unit Vector n
5.2 Refraction Law for the Unit Vector s
5.3 The Ray Path
5.4 Eikonal
References
Chapter 5
1 Introduction
2 Equations for a Sound Wave in a Random Moving Medium
2.1 Helmholtz-Type Equation
2.2 Parabolic Equation
2.3 Parabolic Equation in a Refractive Medium
3 Statistical Description of Random Inhomogeneities
3.1 Correlation Functions and Spectral Densities
3.2 Energy, Inertial, and Dissipation Subranges
3.3 Kolmogorov Spectrum
3.4 Gaussian Spectrum
3.5 von Karman Spectrum
4 Scattering of Sound
4.1 Sound Scattering Cross-Section
4.2 von Karman Spectrum
5 Line-of-Sigh Sound Propagation in a Random Moving Medium
5.1 Statistical Moments of a Sound Field
5.2 E.ective Correlation Function and Spectral Density
5.3 Markov Approximation
5.4 Rytov Method
5.5 Formulas for Statistical Moments of a Sound Field
5.6 Coherence Function
6 Interference of the Direct and Ground-Reflected Waves
6.1 Mean Squared Sound Pressure
6.2 Comparison with Experimental Data
7 Sound Propagation Near Impedance Ground in a Refractive, Turbulent Atmosphere
7.1 Mean Sound Field
7.2 Coherence Function
References
Chapter 6
1 Research Philosophy
2 Resonant Wave-Flow Interactions
3 Negative Wave Energy and Over-Reflection
4 Acoustic Analogues of Microwave Devices: Monotron and Klystron
5 Wave-Vortex Interactions
6 Analogies Table
Chapter 7
1 Introduction
1.1 Basic Problems in Shear Flows
1.2 Essence of the Diffculties of the Modal Approach
1.3 Onto Nonmodal Approach
2 Mathematics of the Study
2.1 Types of Disturbances
2.2 Onto the Value of Shear Rate
3 The Dynamics of SFH of Acoustic Waves
3.1 Velocity Field of SFH of Acoustic Waves
3.2 The Dynamics of SFH of Acoustic Waves: Low Shear Rates
3.3 The Dynamics of SFH of Acoustic Waves: Moderate Shear Rates
4 The Dynamics of the SFH of Vortices
4.1 Conversion of Vortices to Waves
4.2 The Nature of the Conversion Phenomenon
4.3 Onto the Amplitude of the Generated Wave SFH at Conversion
4.4 Demonstration of the Conversion Phenomenon by Direct Numerical Calculation
4.5 Onto the Vortex-Wave Interaction
5 Mutual Transformation of Waves
5.1 Mechanical Analogy
5.2 Qualitative Description of the Resonance Transformation of Waves
6 Conclusion
Acknowledgments
References
Chapter 8
1 Introduction
2 Shear Flow
2.1 Equilibrium and Linearization
2.2 Singular Eigenmodes and the Continuous Spectrum
3 The Integral Transform–Coordinate Change
3.1 Integral Transform Pair
3.2 Solution
4 Hamiltonian Interpretation
References
Chapter 9
1 Basic Problem
2 Solution Technique
3 Solution for Fluid-Loaded Plate with Mean Flow
3.1 Wave Energy
4 Modifications to the Basic Model
4.1 Plate Curvature
4.2 Nonlinear Motion
4.3 Effects of a Boundary Layer
5 Conclusion
References
Chapter 10
1 Introduction
2 Origin of Nonlinearity
3 Equation of State
4 Simple Nonlinear Waves
5 Shock Waves
6 Sonoluminescence
7 Chaos Physics
8 Acoustic Chaos
Acknowledgment
References