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An acoustic spacetime and the Lorentz transformation in aeroacoustics

Gregory, AL and Sinayoko, S and Agarwal, A and Lasenby, J (2014) An acoustic spacetime and the Lorentz transformation in aeroacoustics.

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Abstract

This paper introduces acoustic space-time and Geometric Algebra as a new theoretical framework for modelling aeroacoustic phenomena. This new framework is applied to sound propagation in uniform flows. The problem is modelled by means of transformations that turn the convected wave equation into an ordinary wave equation, in either time-space coordinates or frequency-wavenumber coordinates. The transformations are shown to combine a Galilean transformation with a Lorentz transformation and geometrical and physical interpretations are provided. The Lorentzian frame is the natural frame for describing acoustic waves in uniform flow. A key feature of this frame is that it combines space and time in a way that is best described using a hyperbolic geometry. The power of this new theoretical framework is illustrated by providing simple derivations for two classical aeroacoustic problems: the free-field Greens function for the convected wave equation and the Doppler shift for a stationary observer and a source in uniform rectilinear motion in a uniform flow. This new framework will help tackle the fundamental problem of sound propagation in non-uniform flows.

Item Type: Article
Uncontrolled Keywords: physics.flu-dyn physics.flu-dyn
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 07 Apr 2014 01:10
Last Modified: 08 Apr 2014 19:18
DOI: