Near-field scattering by the method of locally subsonic waves
John Chapman (Keele)
A technique is developed for determining the sound field scattered by a compact body when it is close enough to an acoustic source to be in its near field. In this case, the field incident on the compact body (`the scatterer') cannot be well approximated by an ordinary plane wave, so that many formulae of Rayleigh scattering do not apply. Our technique is based on the observation that many near fields can, nevertheless, be well approximated at each point in space by a subsonic plane wave (also called an inhomogeneous plane wave), defined by two properties: in one direction the wave propagates, but with a phase speed which is subsonic; whereas in a perpendicular direction the amplitude of the wave varies exponentially with position. Hence by defining a new canonical problem, compact scattering of a subsonic plane wave, and solving it, we give a unified analytical treatment of many near-field scattering problems. This offers a new approach to many applied problems, especially in aeroacoustics. A key role is played in our approach by Debye's approximation to Bessel functions, in the regime `argument less than order'.
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