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Surface waves on water of non-uniform depth

Published online by Cambridge University Press:  28 March 2006

Joseph B. Keller
Joseph B. Keller
Affiliation:
Institute of Mathematical Sciences, New York University
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Extract

Gravity waves occur on the surface of a liquid such as water, and the manner in which they propagate depends upon its depth. Although this dependence is described in principle by the equations of the ‘exact linear theory’ of surface waves, these equations have not been solved except in some special cases. Therefore, oceanographers have been unable to use the theory to describe surface wave propagation in water whose depth varies in a general way. Instead they have employed a simplified geometrical optics theory for this purpose (see, for example, Sverdrup & Munk (1944)). It has been used very successfully, and consequently various attempts, only partially successful, have been made to deduce it from the exact linear theory. It is the purpose of this article to present a derivation which appears to be satisfactory and which also yields corrections to the geometrical optics theory.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 4 , Issue 6 , November 1958 , pp. 607 - 614
Copyright
© Cambridge University Press

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References

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