Spectral analysis of the air flow pattern near the labium of a recorder

Navier-Stokes-based simulations of the air flow through a recorder allow detailed tests of analytic theories of how the pattern of flow—specifically the creation and time evolution of vorticity near the labium—gives rise to the sound of the instrument. A new spectral analysis algorithm has been developed to extract the flow pattern at the fundamental frequency for a soprano recorder playing a steady tone. This analysis allows the flow pattern at the fundamental frequency to be separated from the flow patterns at other frequencies and from the uniform flow pattern, i.e., the time independent flow associated with the air jet emerging from the flue. This gives an especially clear elucidation of the time dependent process in which vortices are created and evolve during the course of a musical tone. This analysis technique can also be used to extract the flow patterns at the frequency of the second partial and at the frequency of the recently discovered half harmonic [1], which show a geometrical structure that is distinctly different from that found at the fundamental frequency. Our spectral analysis technique should allow more detailed tests of the theory of vortex produced sound for a flue instrument than have been possible to date. N. Giordano and K. L. Saenger, J. Acoust. Soc. Amer. 154, 2917 (2023). [Work supported by NSF under Grant No. PHY2306035.]