Absolute instability in axisymmetric wakes: compressible and density variation effects

Lesshafft & Huerre (Phys. Fluids, 2007; vol. 1, 024102) have recently studied the transition from convective to absolute instability in hot round jets, for which absolute instability is led by axisymmetric perturbations and enhanced when lowering the jet density. The present paper analyses similarly the counterpart problem of wake flows, and establishes that absolute instability is then led by a large-scale helical wake mode favoured when the wake is denser than the surrounding fluid. This generalizes to variable density and compressible wakes the results of Monkewitz (J. Fluid Mech. vol 192, 1988, p. 561). Furthermore, we show that in a particular range of density ratios, the large-scale helical wake mode can become absolutely unstable by increasing only the Mach number up to high subsonic values. This possibility of an absolute instability triggered by an increase of the Mach number is opposite to the behaviour previously described in shear flows such as plane mixing layers and axisymmetric jets. A physical interpretation based on the action of the baroclinic torque is proposed. An axisymmetric short-scale mode, similar to that observed in plane mixing layers, leads the transition in light wakes, but the corresponding configurations require large counterflow for the instability to be absolute. These results suggest that the low-frequency oscillation present in afterbody wakes may be due to a nonlinear global mode triggered by a local absolute instability, since the azimuthal wavenumber and absolute frequency of the helical wake mode agree qualitatively with observations.