Absolute/convective instabilities in the Batchelor vortex: A numerical study of the linear impulse response

The absolute/convective instability properties of the Batchelor vortex are determined by direct numerical simulation of the linear impulse response. A novel decomposition procedure is applied to the computed wavepacket in order to retrieve the complex wavenumber and frequency prevailing along each spatio-temporal ray. In particular, the absolute wavenumber and frequency observed in the laboratory frame are determined as a function of swirl parameter and external flow. The introduction of a moderate amount of swirl is found to strongly promote absolute instability. In the case of wakes, the transitional helical mode that first undergoes a switch-over to absolute instability is found to be m = -1 without requiring any external counterflow. In the case of jets, the transitional helical mode is very sensitive to swirl and varies in the range -5 ≤ m ≤ -1. Only a slight amount of external counterflow (1.5% of centreline velocity) is then necessary to trigger absolute instability. The results of this numerical procedure are m good qualitative and quantitative agreement with those obtained by direct application of the Briggs-Bers criterion to the inviscid dispersion relation (Olendraru et al. 1996). Implications for the dynamics of swirling jets and wakes are discussed.