The interpretation of unsteady surface shear stresses as dipole sound sources is discussed. Provided ωv/c2 « 1, it is legitimate to calculate the radiated pressure using viscous surface dipoles in combination with an inviscid-medium Green function. This is demonstrated via comparisons of acoustic-analogy predictions with exact solutions, for two plane-boundary problems. A Green function that is tailored to the linear relation between pressure and normal velocity on the boundary, as used by Powell [J. Acoust. Soc. Am. Vol. 32, 1960, pp. 982–990], highlights the role of viscous stresses in aeroacoustic calculations.
References
1.
PowellA., “Aerodynamic noise and the plane boundary,”Journal of the Acoustical Society of America, Vol. 32, No. 8, 1960, pp. 982–990.
2.
PowellA., “Three-sound-pressures theorem, and its application, in aerodynamically generated sound,”Journal of the Acoustical Society of America, Vol. 34, No. 7, 1962, pp. 902–906.
3.
CurleN., “The influence of solid boundaries upon aerodynamic sound,”Proceedings of the Royal Society of London, A, Vol. 231, 1955, pp. 505–514.
4.
WilliamsFfowcs J.E. and HawkingsD.L., “Sound generation by turbulence and surfaces in arbitrary motion,”Philosophical Transactions of the Royal Society of London, A, Vol. 264, 1969, pp. 321–342.
5.
KambeT., “Influence of viscosity on aerodynamic sound emission in free space,”Journal of Sound and Vibration, Vol. 95, 1984, pp. 351–360.
6.
KambeT., and MinotaT., “Acoustic wave radiated by head-on collision of two vortex rings,”Proceedings of the Royal Society of London, A, Vol. 386, 1983, pp. 277–308.
7.
ObermeierF., “Aerodynamic sound generation caused by viscous processes,”Journal of Sound and Vibration, Vol. 99, No. 1, 1985, pp. 111–120.
8.
DaviesH.G., “The radiated fields of multipole point sources near a solid spherical surface,”Journal of Fluid Mechanics, Vol. 43, 1970, pp. 597–606.
9.
CrightonD.G., “Basic principles of aerodynamic noise generation,”Progress in Aerospace Sciences, Vol. 16, No. 1, 1975, pp. 31–96.
10.
CrightonD.G. and LeppingtonF.G., “On the scattering of aerodynamic noise,”Journal of Fluid Mechanics, Vol. 46, 1971, pp. 577–597.
11.
HoweM.S., Acoustics of Fluid-Structure Interactions, Cambridge University Press, Cambridge, UK, 1998.
12.
WilliamsFfowcs J.E. and HallL.H., “Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane,”Journal of Fluid Mechanics, Vol. 40, 1970, pp. 657–670.
13.
PierceA.D., Acoustics: An introduction to its physical principles and applications, Acoustical Society of America, Woodbury, NY, 1989, Section 10–3.
14.
MiklowitzJ., The Theory of Elastic Waves and Waveguides, North-Holland, Amsterdam, NL, 1978.
15.
DanilovS.D. and MironovM.A., “Conversion of transverse into longitudinal waves at an interface and the problem of sound generation by wall turbulence,”Soviet Physics Acoustics, Vol. 31, No. 4, 1985, pp. 314–315.
16.
RybakS.A., “The relation between the tangential stresses on a rigid wall and the pressure fluctuations generated in a turbulent boundary layer,”Acoustical Physics, Vol. 47, No. 5, 2001, pp. 629–631.
17.
PhillipsO.M., “On the aerodynamic surface sound from a plane turbulent boundary layer,”Proceedings of the Royal Society of London, A, Vol. 234, 1956, pp. 327–335.
18.
HoweM.S., “A note on the Kraichnan-Phillips theorem,”Journal of Fluid Mechanics, Vol. 234, 1992, pp. 443–448.
19.
ChaseD.M., “Fluctuations in wall-shear stress and pressure at low streamwise wavenumbers in turbulent boundary-layer flow,”Journal of Fluid Mechanics, Vol. 225, 1991, pp. 545–555.
20.
HuZ.W.MorfeyC.L. and SandhamN.D., “Aeroacoustics of wall-bounded turbulent flows,”AIAA Journal, Vol. 40, No. 3, 2002, pp. 465–473.
21.
HuZ.W.MorfeyC.L. and SandhamN.D., “Sound radiation in turbulent channel flows,”Journal of Fluid Mechanics, Vol. 475, 2003, pp. 269–302.
22.
LandahlM.T., “Wave mechanics of boundary layer turbulence and noise,”Journal of the Acoustical Society of America, Vol. 57, No. 4, 1975, pp. 824–831.
23.
EfimtsovB.M.ZosimovV.V.RomashovA.V. and RybakS.A., “Correlation of pressure fluctuations with tangential stresses in a turbulent boundary layer,”Acoustical Physics, Vol. 49, No. 1, 2003, pp. 113–115.
24.
HoweM.S., “The role of surface shear stress fluctuations in the generation of boundary layer noise,”Journal of Sound and Vibration, Vol. 69, 1979, pp. 159–164.
25.
Naugol'nykhK.A. and RybakS.A.“Sound radiation from a turbulent boundary layer,”, [in Russian] Trudy Akusticheskogo Instituta Akademii Nauk SSSR, Issue 16, 1971, pp. 129–135.
26.
Naugol'nykhK.A. and RybakS.A., “Sound radiation from a turbulent boundary layer,”Soviet Physics Acoustics, Vol. 26, No. 6, 1980, pp. 502–504.
27.
ChaseD.M., “Fluctuating wall-shear stress and pressure at low streamwise wavenumbers in turbulent boundary-layer flow at low Mach numbers,”Journal of Fluids and Structures, Vol. 6, 1992, pp. 395–413.
28.
LeleS.K., “Computational aeroacoustics: A review,”AIAA 1997–0018 (invited paper presented at 35th Aerospace Sciences Meeting, Reno, 6–9 Jan), 1997, pp. 1–15.
29.
WangM.LeleS.K. and MoinP., “Sound radiation during local laminar breakdown in a low-Mach-number boundary layer,”J. Fluid Mech., Vol. 319, 1996, pp. 197–218.
