Flapping motion in screeching round jets

In this paper, an explanation for the existence of flapping modes in round jets is provided for the first time, through a consideration of both linear models and high-fidelity numerical data. Linear stability analysis demonstrates that pairs of helical and flapping modes are equally supported by an axisymmetric jet, with either forming a basis to represent StartAbsoluteValue m EndAbsoluteValue equals 1 | m | = 1 $|m|=1$ disturbances. However, once steady StartAbsoluteValue m EndAbsoluteValue equals 2 | m | = 2 $|m|=2$ streaks are introduced, only flapping modes are allowed as solutions of the linearised Navier–Stokes equations, with the characteristics of the resulting modes dependent on the amplitude of the streaks. Based on this result, it is hypothesised that the presence of sufficiently strong streaks in a screeching jet should dictate the existence and characteristics of flapping modes. This hypothesis is tested through decomposition of a high-fidelity large-eddy simulation of a hot overexpanded jet exhibiting a strong flapping instability. Despite the axisymmetry of the base flow, both the hydrodynamic and acoustic fields are shown to be highly modulated in azimuth, and streaks are identified at very low frequencies and azimuthal wavenumbers. It is shown that the phase difference between the m equals 1 m = 1 $m=1$ and negative 1 − 1 $-1$ screech modes evolves very slowly in time, characteristic of a precession of the flapping axis, consistent with the phase evolution of the m equals 2 m = 2 $m=2$ streak. Analysis of flow fluctuations along a cylindrical shell confirms the slow precession of the flapping mode’s axis in time, and this precession is shown to match the meandering of the streaks, providing a final connection between these two structures.