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A note on the unsteady motion of a compressible fluid

Published online by Cambridge University Press:  24 October 2008

D. C. Pack
D. C. Pack
Affiliation:
Department of MathematicsUniversity of Manchester
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Abstract

A solution is found in closed form for the one-dimensional motion of an ideal, inviscid and isentropic gas with ratio of specific heats (2m + 3)/(2m + 1), m being any positive integer, when the gas is supposed to start from rest with an inhomogeneous temperature distribution.

An example is given which is of interest in the study of interstellar gas clouds. A cloud is assumed to be initially at rest in contact with a vacuum; the Riemann invariant r is assumed to increase linearly for a finite distance into the cloud (from zero at the surface), beyond which it remains constant. The r-characteristics from the inhomogeneous strip meet simultaneously in the distance-time plane at a point of the gas surface; the surface does not move until this happens, when it acquires instantaneously a finite non-zero velocity. A numerical estimate is made of the time during which the surface remains at rest for an actual gas cloud, under the above conditions. In the subsequent development the gas motion takes the form of a growing simple wave.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 3 , July 1953 , pp. 493 - 497
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

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