# Slow sound laser in lined flow ducts

## TL;DR

This paper investigates how impedance variations in lined flow ducts can induce a laser-like acoustic instability, especially in subsonic regions acting as resonant cavities, with potential applications in controlling sound propagation.

## Contribution

It introduces a novel configuration where impedance-induced flow regimes create a resonant cavity leading to a laser-like instability, including effects of shear flow layers.

## Key findings

- Instability is highly subwavelength.
- Small subsonic regions lead to static instability.
- Shear flow layers significantly alter but do not eliminate the instability.

## Abstract

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.