STABILITY OF ACOUSTIC PROPAGATION IN A 2D FLOW DUCT: A LOW FREQUENCY APPROACH

In this paper we derive a simplified “quasi-1D” limit model for the propagation of low frequency acoustic waves in a laminar flow filling a 2D duct. We analyze the well-posedness of this model in function of he Mach profile of the flow. This can be reduced to the study of the spectrum of a bounded non-normal operator. As a by-product of this analysis, we establish new resulta for hydrodynamic instabilities of Kelvin-Helnholtz type in compressible fluids.