Linear and Nonlinear Theories for Thermoacoustic Waves in a Gas Filled Tube Subject to a Temperature Gradient

  • Nobumasa SugimotoEmail author
  • Dai Shimizu
Part of the Mathematics of Planet Earth book series (MPE, volume 6)


This article reviews briefly the linear and nonlinear theories of thermoacoustic waves in a gas filled tube subject to a temperature gradient. In the framework of fluid dynamics, asymptotic theories are developed by two parameters on the basis of a narrow tube approximation. One is a parameter measuring the order of nonlinearity, while the other is a parameter measuring diffusive effects by viscosity and heat conduction. Making use of these parameters as asymptotic ones, the full system of equations is reduced to compact and spatially one-dimensional (1D) equation(s). It is emphasised that the diffusive effects may be covered substantially by two cases where the layers are thin or thick enough in comparison with the tube radius.


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The authors wish to thank Grants-in-Aid for Scientific Research (KAKENHI No. 26289036, No. 18H01375, and No. 18K03938) by the Japan Society for the Promotion of Science.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Pure and Applied PhysicsKansai UniversityOsakaJapan
  2. 2.Department of Mechanical EngineeringFukui University of TechnologyFukuiJapan

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