Using a partial-wave method for sound–mean-flow scattering problems

Abstract : We present a semianalytical method, based on a partial-wave expansion and valid in the short wavelength limit for small Mach number flows, to analyze sound–vortical-flow interactions. It is more powerful than ray-tracing methods because it gives both amplitude and phase of the sound wave, and because it is less restrictive on the smallness of the wavelength. In contrast with the Born approximation approach, this method allows the computation of the sound field in the whole interaction domain including the near field , and preserves energy conservation. Vortical flows with finite circulation are amenable to our analysis, which gives a satisfactory description of wave front dislocation by vorticity, in good agreement with direct numerical simulations. We extend previous versions of this method to the case of smooth vorticity profiles which are observed in aeroacoustics experiments.
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Remy Berthet, Christophe Coste. Using a partial-wave method for sound–mean-flow scattering problems. Physical Review E , American Physical Society (APS), 2003. ⟨hal-01406762⟩

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