SIMILARITY VARIABLES FOR SOUND RADIATION IN A UNIFORM FLOW

Abstract This paper derives a parametric family of similarity variables for describing sound radiation in a uniform flow. The variables, based on a Lorentz-type transformation between the wave equation and the convected wave equation, contain Doppler factors and generalize the Prandtl–Glauert variables used in aerodynamics. The parameter specifying the family may be chosen to match the frequency dependence of the sound on the Mach number of the flow in problem being solved. The variables are used to derive a “fundamental rule” for obtaining a solution of the convected wave equation from a solution of the unconvected wave equation; the rule does not correspond to a Galilean transformation. The method of the paper is applied to several examples from aeroacoustics, including a thickness-noise acoustic source modelled by the Ffowcs Williams–Hawkings equation; a point-force acoustic source; a spatially extended time-harmonic source; a duct mode; and the sound radiated during blade–vortex interaction.

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