Triadic nonlinear interactions in harmonically forced jets*

Bispectral mode decomposition (BMD) is tailored to the extraction of flow structures associated with triadic interactions from spatio-temporal flow data. We use BMD to study the differences between the nonlinear dynamics of turbulent round jets with and without harmonic forcing. To this end, large-eddy simulations (LES) of unforced and axisymmetrically forced jets at $Re = 50,000$ and $M_j = 0.4$ are performed and validated with a companion experiments. Additional simulations are conducted for forcing azimuthal wavenumbers of $m=\pm 1$, and $m=\pm 6$ . The emphasis of the analysis is on the harmonics created by the fundamental forcing mode and its contribution to the mean flow deformation. Azimuthal wavenumber triads are investigated using the cross-spectral variant of BMD. Wu & Huerre (2009) have hypothesized that the interaction of a helical conjugate pair with $m=\pm 1$ is the most efficient radiator of low-frequencies sound to jet angles between $45^\circ - 60^\circ$, This hypothesis is the second objective of this contribution.

[1] Wu, X. & Huerre, P. 2009 Low-frequency sound radiated by a nonlinearly modulated wavepacket of helical modes on a subsonic circular jet. Journal of Fluid Mechanics 637, 173–211.