Asymptotic theories of nonlinear thermoacoustic waves in a gas-filled channel

Abstract eng:
This paper introduces two asymptotic theories for nonlinear thermoacoustic waves in a gas—filled channel subject to temperature gradient. On the basis of a narrow—tube approximation, the theories exploit, as an asymptotic parameter, the ratio of a typical thickness of thermoviscous diffusion layer to a channel width. If the ratio is large enough, thermoviscous effects are confined in a boundary layer so that they affect lossless propagation in a core outside of the boundary layer through a velocity component normal to the channel wall at the outer edge of the boundary layer. If the ratio is small enough, propagation is described by a nonlinear diffusion—wave (advection) equation. Even for an intermediate value of the ratio, it is expected that either asymptotic theory will be able to describe propagation of nonlinear thermoacoustic waves.

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