Vortex Sound

  • D. G. Crighton
  • A. P. Dowling
  • J. E. Ffowcs Williams
  • M. Heckl
  • F. G. Leppington


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.


Green Function Vortex Ring Line Vortex Density Perturbation Sound Field 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • D. G. Crighton
    • 1
  • A. P. Dowling
    • 2
  • J. E. Ffowcs Williams
    • 2
  • M. Heckl
    • 3
  • F. G. Leppington
    • 4
  1. 1.University of CambridgeUK
  2. 2.Department of EngineeringUniversity of CambridgeUK
  3. 3.Technische Universität BerlinGermany
  4. 4.The Imperial College of Science and TechnologyLondonUK

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