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A note on group velocity

Published online by Cambridge University Press:  28 March 2006

G. B. Whitham
G. B. Whitham
Affiliation:
Mathematics Department, Massachusetts Institute of Technology
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Abstract

The kinematic approach to group velocity given in Lighthill & Whitham (1955) for one-dimensional waves is extended to cover the general three-dimensional case. The ideas have particular bearing on the theory developed by Ursell (1960) for treating steady wave patterns on non-uniform steady fluid flows.

Although this note was written in ignorance of the fact, all the main ideas presented here are implicit in §§66 and 67 of the book by Landau & Lifshitz (1959). However, these ideas do not seem to be well known to fluid dynamicists, and it was suggested to the author by the editor that a useful purpose would still be served by publishing this note as an expository article amplifying the paragraphs in Landau & Lifshitz. It also serves the original purpose of providing a supplement to Ursell's paper.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 9 , Issue 3 , November 1960 , pp. 347 - 352
Copyright
© 1960 Cambridge University Press

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References

Jeffreys, H. & Jeffreys, B. S. 1956 Methods of Mathematical Physics (3rd ed.). Cambridge University Press.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. London: Pergamon Press.
Lighthill, M. J. & Whitham, G. B. 1955 Proc. Roy. Soc. A, 229, 281–316.
Ursell, F. 1960 J. Fluid Mech. 9, 333–46.