COMPUTATIONAL AEROACOUSTICS EXAMPLES SHOWING THE FAILURE OF THE ACOUSTIC ANALOGY THEORY TO IDENTIFY THE CORRECT NOISE SOURCES

Lighthill's Acoustic Analogy has been the dominant theory of aeroacoustics, especially jet aeroacoustics for almost fifty years. As yet, except for the u⁸ scaling law, which was derived by dimensional analysis, jet noise prediction based on the Acoustic Analogy approach has not been particularly successful. This paper examines some of the weaknesses and ambiguities in the formulation of the Acoustic Analogy theories. It is concluded that if the analogy is carried out completely, in the sense that the full wave propagation terms are retained in the propagation part of the equations of the analogy, then the theory offers no sensible noise source terms. To demonstrate that the Acoustic Analogy can fail to identify the correct noise sources, four examples are considered. They include an initial value problem, a boundary problem, the problem of weak solution and the problem of sound generation by instability waves in jets and mixing layers. These examples show clearly how, in each case, the Acoustic Analogy theory identifies the wrong noise source. Indeed, the Acoustic Analogy could provide, if not careful, misleading interpretation of the physics of sound generation.

This paper is dedicated to Professor David G. Crighton, outstanding applied mathematician, world famous acoustician and a much respected friend.