I. Delbende et al., ABSOLUTE CONVECTIVE INSTABILITIES IN THE BATCHELOR VORTEX - A NUMERICAL STUDY OF THE LINEAR IMPULSE-RESPONSE/, Journal of Fluid Mechanics, 355, 1998, pp. 229-254
The absolute/convective instability properties of the Batchelor vortex
are determined by direct numerical simulation of the linear impulse r
esponse. A novel decomposition procedure is applied to the computed wa
vepacket in order to retrieve the complex wavenumber and frequency pre
vailing along each spatio-temporal ray. In particular, the absolute wa
venumber 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 in
stability. In the case of wakes, the transitional helical mode that fi
rst undergoes a switch-over to absolute instability is found to be m =
-1 without requiring any external counterflow. In the case of jets, t
he transitional helical mode is very sensitive to swirl and varies in
the range -5 less than or equal to m less than or equal to -1. Only a
slight amount of external counterflow (1.5% of centreline velocity) is
then necessary to trigger absolute instability. The results of this n
umerical procedure are in 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). Implicat
ions for the dynamics of swirling jets and wakes are discussed.