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Sound Radiation from High Reynolds Number Turbulence

 

作者: Robert H. Kraichnan,  

 

期刊: The Journal of the Acoustical Society of America  (AIP Available online 1958)
卷期: Volume 30, issue 7  

页码: 675-676

 

ISSN:0001-4966

 

年代: 1958

 

DOI:10.1121/1.1929970

 

出版商: Acoustical Society of America

 

数据来源: AIP

 

摘要:

It has been found, on the basis of a recent, anticipatedly exact theory of homogeneous turbulence, that the acoustic power radiated at high Reynolds numbers and low Mach numbers is dominated by the high‐frequency contributions from the inertial wave‐number range. The inertial range pressure wave‐number spectrum in the isotropic case has been found to beP(k) = aρ2εv0k−2, where ρ is density, ε is the dissipation rate by viscosity, per unit mass, andv0is the rms turbulent velocity in any direction. The universal numberais determined by the theory. The power spectrum of the inertial range radiation per unit mass has been found to beW(ω) = AM5εω−1, whereMis the Mach numberv0/cand the universal numberAis determined by the theory. The total inertial range radiation power is of orderAM5εlnR02/3, whereR0is the Reynolds numberv04/εν(ν = kinematic viscosity) which characterizes the turbulent macrostructure. In the present paper, an attempt will be made to give an elementary physical interpretation of these results in terms of the dynamical interaction of the sharply defined shear fronts and vortex filaments which make up high Reynolds number turbulence. Some implications for radiation from jets, wakes, and boundary layers will be discussed briefly. (The research described was supported by the Mechanics Branch, Office of Naval Research.)

 

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