Derivation of the spatio-temporal model equations for the thermoacoustic resonator

TL;DR

This paper derives a comprehensive spatio-temporal model for a thermoacoustic resonator with viscous medium, extending previous plane-wave models to include spatial effects, revealing pattern formation and localized structures.

Contribution

It introduces a new model that incorporates spatial effects in large aperture resonators, advancing understanding of pattern formation in thermoacoustic systems.

Findings

Model exhibits pattern formation

Localized structures are predicted

Spatial effects are significant in large aperture resonators

Abstract

We derive the model equations describing the thermoacoustic resonator, that is, an acoustical resonator containing a viscous medium inside. Previous studies on this system have addressed this sytem in the frame of the plane-wave approximation, we extend the previous model to by considering spatial effects in a large aperture resonator. This model exhibits pattern formation and localized structures scenario.