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The flow of a compressible fluid with weak entropy changes

Published online by Cambridge University Press:  28 March 2006

Roy Gundersen
Roy Gundersen
Affiliation:
Department of Mathematics, Illinois Institute of Technology
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Abstract

Perturbations of a given flow are considered, and the equations which govern the one-dimensional, non-steady flow of an inviscid, ideal compressible gas are linearized in the neighbourhood of this known solution, assumed isentropic, by a formal perturbation expansion. The perturbed flow is not assumed isentropic. Explicit solutions are obtained for a basic flow which is uniform or a centred simple wave and for an arbitrary simple wave if the perturbed flow is isentropic.

The perturbation of a uniform shock and perturbations in a shock tube lead to functional equations of a particular type, and a discussion of their solution is given.

A similar analysis is used to discuss the flow in a tube of slowly varying cross-section.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 3 , Issue 6 , March 1958 , pp. 553 - 581
Copyright
© 1958 Cambridge University Press

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References

Chester, W. 1953 Quart. J. Mech. Appl. Math. 6, 440.
Chester, W. 1954 Phil. Mag. 45, 1293.
Germain, P. & Gundersen, R. 1955 C. R. Acad. Sci., Paris, 241, 925.
Gundersen, R. 1954 Brown University Report AF-1021/1.
Lighthill, M. J. 1948 Proc. Roy. Soc. A, 198, 454.