Theoretical background: Aeroacoustics

Owing to the nonlinearity of the governing equations it is very difficult to predict the sound production of fluid flows. This sound production occurs typically at high-speed flows, for which nonlinear inertial terms in the equation of motion are much larger than the viscous terms (high Reynolds numbers). Because sound production represents only a minute fraction of the energy in the flow, the direct prediction of sound generation is very difficult. This is particularly dramatic in free space and at low subsonic speeds. The fact that the sound field is in some sense a small perturbation of the flow can, however, be used to obtain approximate solutions.

Aeroacoustics provides such approximations and at the same time a definition of the acoustical field as an extrapolation of an ideal reference flow. The difference between the actual flow and the reference flow is identified as a source of sound. This idea was introduced by Lighthill (1952, 1954), who called this an analogy. A second key idea of Lighthill's (1954) is the use of integral equations as a formal solution. The sound field is obtained as a convolution of the Green's function and the sound source. The Green's function is the linear response of the reference flow, used to define the acoustical field, to an impulsive point source. A great advantage of this formulation is that random errors in the sound source are averaged out by the integration.