Acoustic solitons in a periodic waveguide: theory and experiments

TL;DR

This paper investigates high-amplitude acoustic solitary waves in a periodically varying waveguide through simulations and experiments, highlighting the role of nonlinear losses and proposing a numerical scheme for studying dispersion, nonlinearity, and dissipation effects.

Contribution

It introduces a combined theoretical, numerical, and experimental analysis of acoustic solitons in a periodic waveguide, emphasizing the impact of nonlinear losses and presenting a new transmission-line based numerical method.

Findings

Nonlinear losses from vortex shedding are crucial in high-amplitude pulse dynamics.

Solitary waves retain their characteristics despite strong dissipation.

The proposed numerical scheme accurately captures experimental results.

Abstract

We study the propagation of high-amplitude sound waves, in the form of pulse-like solitary waves, in an air-filled acoustic waveguide of periodically varying cross section. Our numerical simulations, solving the compressible Navier-Stokes equations in two dimensions, as well as our experimental results, strongly suggest that nonlinear losses, originated from vortex shedding (at the segment changes) are crucial in the dynamics of high amplitude pulses. We find that, even in the presence of strong dissipation, the solitary wave roughly retains its characteristics (as described by the amplitude-velocity-width relations), obtained by the derivation and analysis of an effective Boussinesq equation. In addition, we propose a transmission-line based numerical scheme, able to capture well the experimental results. The proposed design offers a new playground for the study of the combined effects of dispersion, nonlinearity and dissipation in air-borne acoustics, while, due to its simplicity, it can be extended to higher dimensions.