IVAN DELBENDE, JEAN-MARC
CHOMAZ and PATRICK HUERRE
Laboratoire d'Hydrodynamique, CNRS-UMR 7646, École Polytechnique,
F-91128 Palaiseau Cedex, France
Absolute/convective instabilities in the Batchelor vortex: a numerical
study of the linear impulse response
J. Fluid Mech.355 (1998), 229-254.
Abstract:
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 m=-1, -2, ..., -5. Only a slight amount
of external counterflow (1.5% of centerline velocity) is then necessary
to trigger absolute instability. The results of this numerical 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). Implications for the dynamics
of swirling jets and wakes are discussed.