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On axially symmetric waves

I. Linearized compressible flow with axial boundary conditions

Published online by Cambridge University Press:  24 October 2008

J. W. Craggs
J. W. Craggs
Affiliation:
The University, Leeds, 2
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Abstract

The wave equation with axial symmetry is reduced, by the assumption of dynamic similarity, to an equation in two variables, r/t and θ A basic solution, having some of the attributes of a source, is introduced, and it is shown that, by use of this solution and a suitable contour integral representation, the solution of any appropriate boundary-value problem may be reduced to the determination of an analytic function, with boundary conditions given by an integral equation.

The method of solution is illustrated by reference to some basic problems in the theory of linearized compressible flow.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 3 , July 1963 , pp. 637 - 654
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Craggs, J. W.Proc. Roy. Soc. London, Ser. A, 237 (1956), 372.Google Scholar
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(3)Craggs, J. W.Proc. Cambridge Philos. Soc. 56 (1960), 269.CrossRefGoogle Scholar
(4)Mackie, A. G.J. Bat. Mech. and Anal. 4 (1955), 733.Google Scholar
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