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The breakdown of the hodograph transformation for irrotational compressible fluid flow in two dimensions

Published online by Cambridge University Press:  24 October 2008

J. W. Craggs
J. W. Craggs
Affiliation:
The University Manchester13
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Extract

It has been noticed by various authors that the use of the hodograph transformation for problems of compressible fluid flow leads to flows having singularities where the acceleration becomes infinite, streamlines have cusps and the solution of the equations of motion in the hodograph plane ceases to represent any possible physical flow. In this paper we investigate the nature of the singularities which can occur in the representation of one plane upon another and apply our results to the hodograph transformation. Finally, we discuss the significance for practical purposes of such singularities and in particular their connexion with the occurrence of shock waves.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 3 , July 1948 , pp. 360 - 379
Copyright
Copyright © Cambridge Philosophical Society 1948

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References

REFERENCES

(1)Craggs, J. W. The application of the hodograph method to problems of subsonic compressible flow in two dimensions (Aeronautical Research Committee, no. 9801).Google Scholar
(2)Tollmien, W.Limit lines in adiabatic potential flows (R.T.P. transl. 1610, Z. angew. Math. Mech. 21 (1941), 140–52.CrossRefGoogle Scholar
(3)Lighthill, M. J. The hodograph transformation in trans-sonic flow. (1) Symmetrical channels (Aeronautical Research Committee, no. 9856).Google Scholar
(4)Bickley, W. G. Critical conditions for compressible flow (Aeronautical Research Committee, no. 9657).Google Scholar