Abstract
This paper introduces thermoacoustic instability of a quiescent gas enclosed in a channel (or a tube) caused by thermoviscous diffusion under an axial temperature gradient. This instability may be regarded as that of heat flowing in background. Once the heat flow becomes unstable, it entails motions of the gas, which spread as acoustic waves. If the instability is promoted by an acoustic resonance of the gas column, then there emerge its oscillations. They are called thermoacoustic oscillations and exploited as a novel means of heat engines. To consider the instability, a thermoacoustic-wave equation is first introduced. This describes a spatial and temporal behavior of an excess pressure in the channel. While the equation is valid generally in linear theory, it may be approximated for short- and long-time behaviors. Linear stability analysis is briefly outlined and marginal conditions of instability are considered. As the amplitude of oscillations becomes higher, nonlinear effects tend to suppress the linear growth. The thermoacoustic oscillations observed in reality occur as outcome of a balance between linear instability and weak nonlinearity. Origins of nonlinearity may be classified into the one as wave and the other as vortex. The former concerns with emergence of an acoustic streaming and an acoustic shock wave, while the latter concerns with formation of jets, wakes and separated flows. Discussions are given on these problems.
