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Acoustic emission of a vortex ring near a porous edge. Part 1: theory
Published online by Cambridge University Press: 27 April 2022
Abstract
The sound of a vortex ring passing near a semi-infinite porous edge is investigated analytically. A Green's function approach solves the associated vortex sound problem and determines the time-dependent pressure signal and its directivity in the acoustic far field as a function of a single dimensionless porosity parameter. At large values of this parameter, the radiated acoustic power scales on the vortex ring speed $U$ and the nearest distance between the edge and the vortex ring
$L$ as
$U^6 L^{-5}$, in contrast to the
$U^5 L^{-4}$ scaling recovered in the impermeable edge limit. Results for the vortex ring configuration in a quiescent fluid furnish an analogue to scaling results from standard turbulence noise generation analyses, and permit a direct comparison to experiments described in Part 2 that circumvent contamination of the weak sound from porous edges by background noise sources that exist as a result of a mean flow.
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- © The Author(s), 2022. Published by Cambridge University Press.
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