Precessing vortex core oscillations in a swirled jet - a weakly non-linear analysis

Swirled jets at high swirl number (S), show the formation of a central recirculation zone (CRZ) due to vortex breakdown. At high S values, CRZ precession about the streamwise axis generates a precessing vortex core (PVC) with a characteristic precession frequency, f_PVC. This occurs due to an internal feedback mechanism in the hydrodynamic field that results in coherent self-sustained flow oscillations.

We study the emergence of a PVC in a swirled jet (Re ~ 44000) where S is varied as a parameter for fixed net mass flow rate. Time resolved velocity field measurements are obtained using stereoscopic particle image velocimetry (sPIV) at 5 kHz. Wavelet and spatial cross spectral analysis of the data shows that a helical limit cycle flow oscillation emerges due to PVC formation at S=S_c=0.61. Global linear stability analysis using time averaged flow fields from sPIV accurately predicts f_PVC at S=Sc. Predictions of f_PVC for S > S_c from a weakly non-linear extension of linear theory agree well with experimental values. This confirms the fact that self-excited helical global modes can result in the emergence of PVCs through a supercritical Hopf bifurcation.