We saw in Chapter 11 that Lighthill’s theory of aerodynamic sound identifies the quadrupole term T ij = ρu i u j + p ij − c 2ρ′δ ij as the source of sound in an unboundedfluid in nonlinear motion, ρ is the density, u the particle velocity p ij the compressive stress tensor and c the speed of sound in the distant linearly disturbed fluid. The mean density is denoted by ρ0, and ρ′ = ρ − ρ0 is the density perturbation. It is sometimes convenient to rewrite this quadrupole source in a way which emphasises the dependence of the noise-producing elements of T ij on local vorticity. One advantage of doing this is that vortical regions of the flow are often much more concentrated than the hydrodynamic region over which T ij is nonzero. Moreover, the development of the vorticity field can be described by simple kinematics.
KeywordsGreen Function Vortex Ring Line Vortex Density Perturbation Sound Field
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- Batchelor, G.K. (1967). An Introduction to Fluid Mechanics. Cambridge University Press.Google Scholar
- Kambe, T. & Minota, T. (1981). Sound radiation from vortex systems. J. Sound.Google Scholar
- Kambe, T., Minota, T. & Ikushima, Y. (1986). Acoustic waves emitted by vortex-body interaction. Proc. IUTAM Symposium on Aero-and Hydro-Acoustics. Springer-Verlag, pp.21–28.Google Scholar
- Lamb, H. (1932). Hydrodynamics. Cambridge University Press.Google Scholar