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. Author manuscript; available in PMC: 2019 Jul 11.
Published in final edited form as: J Acoust Soc Am. 2005 Jul;118(1):410–427. doi: 10.1121/1.1862251

FIG. 8.

FIG. 8

Aeroacoustic source expressed as a convolution of W(t) and I(t). W(t) is the spectrum of a unit-circulation vortex ring passing through the constriction at speed Uj, reflecting the shape of the duct and the path of the vortex. I(t) is a circulation-weighted function indicating the arrival in the source region of a vortex ring. (a) Single vortex ring. (b) Many vortex rings. The broadband behavior of S(t) arises due to the random phase of the time of arrival of each successive vortex ring into the source region.