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A variational method for determining eigenvalues of the wave equation applied to tropospheric refraction*

Published online by Cambridge University Press:  24 October 2008

G. G. MacFarlane
G. G. MacFarlane
Affiliation:
Telecommunications Research EstablishmentMalvern
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Extract

A simple and direct variational method is described for finding both complex and real eigenvalues of the wave equation of anomalous propagation in a horizontally stratified atmosphere. It may be looked upon as an extension of Rayleigh's method to complex eigenvalues. In this paper it is illustrated by an example, taken from the duct theory of super-refraction, in which the refractive index of the air varies with height according to a power law. Numerical agreement in the values for the lowest order eigenvalues with those obtained by the differential analyser is better than ½%.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 43 , Issue 2 , April 1947 , pp. 213 - 219
Copyright
Copyright © Cambridge Philosophical Society 1947

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References

REFERENCES

(1)Booker, H. G. and Walkinshaw, W. The mode-theory of tropospheric refraction and its relation to waveguides and diffraction. To be published in Proc. Phys. Soc. Reference to the unpublished work of T. Pearsey and M. H. L. Pryce is made in this paper.Google Scholar
(2)Courant, and Hilbert, . Methoden der Mathematischen Physik (2nd ed. 1931), 345.Google Scholar