Signalling problem in absolutely unstable systems

Benoît Pier (1)

1 LMFA - Laboratoire de Mecanique des Fluides et d'Acoustique

The dynamics of unstable systems crucially depends on the nature of the instability, either convective or absolute. The signalling problem, which is the study of the spatial response to a localized time-harmonic forcing, is generally believed to be relevant only for stable or convectively unstable systems and to be ill-posed for absolutely unstable systems, where the self-sustained perturbations grow faster than the forced harmonic response. The present investigation shows that the signalling problem may still be well-posed for media displaying absolutely unstable regions. Considering weakly spatially inhomogenous systems, conditions are derived for the validity of the signalling problem. The complete spatial response to harmonic forcing is first analytically derived in terms of asymptotic approximations and then confirmed by direct numerical simulations.

Mots clés: Absolute instabilities; Causality; Signalling problem; WKBJ

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Benoît Pier. Signalling problem in absolutely unstable systems. Theoretical and Computational Fluid Dynamics, 2011, 25, pp.7-17. ⟨10.1007/s00162-009-0166-x⟩. ⟨hal-00426387⟩