Slow sound laser in lined flow ducts

Antonin Coutant (1) , Yves Aurégan (1) , Vincent Pagneux (1)

1 LAUM - Laboratoire d'Acoustique de l'Université du Mans

We consider the propagation of sound in a waveguide with an impedance wall. In the low frequency regime, the first effect of the impedance is to decrease the propagation speed of acoustic waves. Therefore, a flow in the duct can exceed the wave propagation speed at low Mach numbers, making it effectively supersonic. We analyze a setup where the impedance along the wall varies such that the duct is supersonic then subsonic in a finite region and supersonic again. In this specific configuration, the subsonic region act as a resonant cavity, and triggers a laser-like instability. We show that the instability is highly subwavelength. Besides, if the subsonic region is small enough, the instability is static. We also analyze the effect of a shear flow layer near the impedance wall. Although its presence significantly alter the instability, its main properties are maintained. We also point out the analogy between the present instability and a similar one in fluid analogues of black holes known as the black hole laser.

Mots clés: Acoustic waves; Quasi one dimensional flows; Partial differential equations; Black holes; Dynamical systems; Fluid flows; Laser instabilities; Dispersion function; Fluid mechanics; Transonic

Domaines: Acoustique [physics.class-ph]

Antonin Coutant, Yves Aurégan, Vincent Pagneux. Slow sound laser in lined flow ducts. Journal of the Acoustical Society of America, 2019, 146 (4), pp.2632-2644. ⟨10.1121/1.5128310⟩. ⟨hal-02336989⟩