Sound Produced by a Vortex Ring Interacting with an Aperture of Variable Radius

Abstract

An analysis is made of the sound generated when a vortex ring approaches an aperture of time dependent radius in a thin rigid wall. This is possibly the simplest model problem for elucidating the acoustic significance of glottis oscillations in the production of voiced speech. The aperture is acoustically equivalent to a monopole source whose strength is determined by the unsteady volume flux induced by the vortex. The unsteady working of suction forces at the edge of a contracting aperture in an ideal fluid transforms the transmitted, positive acoustic pressure pulse predicted for a constant radius aperture into a large amplitude expansion wave. The suppression of large suction forces in a real fluid by viscosity is examined by the imposition of a Kutta condition, leading to vortex shedding and ‘jetting’ from the aperture. The shed vorticity is found to increase further the resistance of the closing aperture to the induced flux, and results in an expansion wave of greatly increased amplitude.

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