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A line source on an interface between two media

Published online by Cambridge University Press:  28 March 2006

V. M. Papadopoulos
V. M. Papadopoulos
Affiliation:
Division of Engineering, Brown University
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Abstract

The assumption of dynamic similarity is used to determine the velocity potential of an unsteady line source which lies on a plane separating two media of different density and sound velocity. The solution first derived is for a source whose strength varies with time as a step function; the pressure in this case may be identified with Hadamard's elementary solution which in a homogeneous fluid is (c/2π) (c2t2-r2)−½ if r < ct, and 0 if r > ct. We next derive the solution for a source whose strength has a delta-function time dependence; we then describe the results for a supersonic point source moving on the interface, and finally we transfer the results to solve the corresponding electromagnetic problem.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 8 , Issue 1 , May 1960 , pp. 41 - 48
Copyright
© 1960 Cambridge University Press

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References

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Hadamard, J. 1923 Lectures on Cauchy's Problem. Yale University Press.
Keller, J. B. & Gardner, C. S. 1959 U.R.S.I. Symposium on electromagnetic theory, Toronto (to be published).
Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press.
Papadopoulos, V. M. 1959a Proc. Roy. Soc. A, 252, 520.
Papadopoulos, V. M. 1959b U.R.S.I. Symposium on electromagnetic theory, Toronto (to be published).