Low-frequency sound radiated by a nonlinearly modulated wavepacket of helical modes on a subsonic circular jet

Xuesong Wu (1, 2) , Patrick Huerre (3)

1 Department of Mathematics [Imperial College London]
2 Department of Mechanics, Tianjin University, Tianjin 300072, China
3 LadHyX - Laboratoire d'hydrodynamique

A possible fundamental physical mechanism by which instability modes generate sound waves in subsonic jets is presented in the present paper. It involves a wavepacket of a pair of helical instability modes with nearly the same frequencies but opposite azimuthal wavenumbers. As the wavepacket undergoes simultaneous spatialtemporal development in a circular jet, the mutual interaction between the helical modes generates a strong three-dimensional, slowly modulating mean-flow distortion. It is demonstrated that this mean field radiates sound waves to the far field. The emitted sound is of very low frequency, with characteristic time and length scales being comparable with those of the envelope of the wavepacket, which acts as a non-compact source. A matched-asymptotic-expansion approach is used to determine, in a self-consistent manner, the acoustic field in terms of the envelope of the wavepacket and a transfer factor characterizing the refraction effect of the background base flow. For realistic jet spreading rates, the nonlinear development of the wavepacket is found to be influenced simultaneously by non-parallelism and non-equilibrium effects, and so a composite modulation equation including both effects is constructed in order to describe the entire growthattenuationdecay cycle. Parametric studies pertaining to relevant experimental conditions indicate that the acoustic field is characterized by a single-lobed directivity pattern beamed at an angle about 4560 to the jet axis and a broadband spectrum centred at a Strouhal number St 0.070.2. As the nonlinear effect increases, the radiation becomes more efficient and the noise spectrum broadens, but the gross features of the acoustic field remain robust, and are broadly in agreement with experimental observations. © 2009 Copyright Cambridge University Press.

Domains: Fluid mechanics [physics.class-ph]; Fluids mechanics [physics.class-ph]

Xuesong Wu, Patrick Huerre. Low-frequency sound radiated by a nonlinearly modulated wavepacket of helical modes on a subsonic circular jet. Journal of Fluid Mechanics, 2009, 637, pp.173-211. ⟨10.1017/s0022112009990577⟩. ⟨hal-01002596⟩