Acoustic emission of a vortex ring near a porous edge. Part 1: theory

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.