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Aerodynamic Sound Emission as a Singular Perturbation Problem

 

作者: S. C. Crow,  

 

期刊: Studies in Applied Mathematics  (WILEY Available online 1970)
卷期: Volume 49, issue 1  

页码: 21-46

 

ISSN:0022-2526

 

年代: 1970

 

DOI:10.1002/sapm197049121

 

数据来源: WILEY

 

摘要:

Sound emission from an eddy region involves three length scales: the eddy sizeI, wavelengthλof the sound, and a dimensionLofthe region. They are related by the Mach numberM = l/λ, small for nearly incompressible eddies, and a parameter Λ =L/λwhich plays no apparent role in current theories of aerodynamic sound. The theories of Lighthill and Ribner are examined in the caseM≪ 1, Λ ˜ 1. Ribner's result is found to contain an unacceptable improper integral. The utility of Lighthill's solution is found to depend on properties of the quadrupole momentTijthat can be established only by studying the flow in more detail than Lighthill's theory allows. The general problem is posed in the form: given the body forcefand vorticityωfind the densityρand potentialφof the velocityu= ∇ × ψ{ω} + ∇φThe problem is solved forM≪ 1, Λ ˜ 1 by matching a compressible eddy core scaled onIto a surrounding acoustic field scaled onλ. Lighthill's solution forρis shown to be adequate in both regions ifTijis approximated byρ0υiυj, withv= ∇ × ψ. The situationM≪ 1, Λ ≫ 1 is studied, and the conclusion is reached that sound emission from large bodies of turbulence is an open problem

 

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