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

Abstract

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 spatial-temporal 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 noncompact 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 characterising 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 growth-attenuation-decay cycle. Parametric studies pertaining to relevant experimental conditions indicate that the acoustic field is characterised by a single-lobed directivity pattern beamed at an angle about 45 o − 60 o to the jet axis, and a broadband spectrum centred at a Strouhal number St ≈ 0.07 − 0.2. 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.

Nonlinear dynamics of large-scale coherent structures in turbulent free shear layers

“…Latest efforts of modelling noise generation by CS have been reviewed by , but the precise mechanisms remain to be understood fully. They are probably similar to the mechanisms by which instability modes in a laminar jet radiate sound; those mechanisms have been described on the basis of first principles by Tam & Burton (1984) and Wu (2005) for supersonic and by Wu & Huerre (2009) for subsonic regimes.…”

Spectral broadening and flow randomization in free shear layers

“…Such a wavepacket radiates little sound directly, but the spatially and temporally modulated mean-flow distortion, generated by the self-interaction of the wavepacket, acts as a non-compact source to emit lowfrequency sound (Wu & Huerre 2009). In the simple case of two waves, the emission is from the nonlinearly generated beating component with the difference frequency.…”

Non-Normal Global Modes of High-Speed Jets

“…Nevertheless, recent studies [10,11] show that energy can be transferred into the radiative part of the spectrum through nonlinear interaction of two instability waves. Wu and Huerre [12] show that the nonlinear interaction of counterwinding helical modes of close frequency produces a slowly breathing mean-field distortion of azimuthal wavenumber m = 2 which efficiently radiates sound. In addition to nonlinear mode interactions, we propose the non-normality of the underlying linearized system as an alternate source of jet noise.…”