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Some physical interpretations of potentials representing supersonic motion of compressible fluids

Published online by Cambridge University Press:  24 October 2008

R. K. Tempest
R. K. Tempest
Affiliation:
Department of Applied MathematicsThe UniversityLiverpool
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Extract

1. Compressible and incompressible flow. Small perturbations in an otherwise uniform stream of compressible fluid moving at supersonic speed are described by the approximate linearized equation for the velocity potential. When the stream flows in the z-direction, the equation assumes the form

where M is the Mach number of the flow and α2 is positive. In cylindrical polar coordinates (r, z), the equation may be written as

which is Laplace's equation in coordinates (iαr, z). We may therefore relate potentials of incompressible flow which are solutions of (1·2) to potentials of compressible flow which are solutions of (1·1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 2 , April 1949 , pp. 246 - 250
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

REFERENCES

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