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A note on the breakdown of continuity in the motion of a compressible fluid

Published online by Cambridge University Press:  28 March 2006

D. C. Pack
D. C. Pack
Affiliation:
Department of Mathematics, The Royal College of Science and Technology, Glasgow
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Abstract

By a consideration of the relationships holding along the characteristics in an unsteady motion involving plane, axially or spherically symmetrical flow of compressible inviscid fluid, it is shown that the existence of a region of compression anywhere in the flow must lead eventually to the breakdown of continuity. The paper generalizes and unites previous work on this topic, and discusses some recent numerical calculations in which the expected discontinuity was not found.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 8 , Issue 1 , May 1960 , pp. 103 - 108
Copyright
© 1960 Cambridge University Press

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References

Burton, C. V. 1893 Phil. Mag. (5), 35, 317.
Challis, J. 1848 Phil. Mag. (3), 32, 494.
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. New York: Interscience Publishers.
Durand, W. F. (ed.) 1935 Aerodynamic Theory, 3, 216. Berlin: Springer.
Fox, P. & Ralston, A. 1957 J. Maths. Phys. 36, 313.
Hantzsche, W. & Wendt, H. 1940 Jb. dtsch. Luftfahrtf.
Kuo, Y-H. 1947 Quart. Appl. Maths. 4, 349.
Lighthill, M. J. 1948 Quart. J. Maths. Appl. Mech. 1, 309.
Pack, D. C. 1948 Quart. J. Math. Appl. Mech. 1, 1.
Poisson, S. D. 1808 J. Éc. Polyt., Paris, 7, 319.
Roberts, L. 1957 J. Maths. Phys. 36, 329.
Stokes, E. E. 1848 Phil. Mag. (3), 33, 349.
Taylor, Sir Geoffrey 1946 Proc. Roy. Soc. A, 186, 273.
Unwin, J. J. 1941 Proc. Roy. Soc. A, 178, 153.