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Bounds for surface solitary waves

Published online by Cambridge University Press:  24 October 2008

G. Keady  and
W. G. Pritchard
G. Keady
Affiliation:
Fluid Mechanics Research Institute, University of Essex
W. G. Pritchard
Affiliation:
Fluid Mechanics Research Institute, University of Essex
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Extract

In these notes we give proofs of some properties of surface solitary waves. Assuming the existence of solitary-wave solutions to the nonlinear boundary-value problem (P) defined below, it is shown (i) that the wave is a wave of elevation alone, and (ii) that at large distances it is asymptotic to a uniform supercritical stream (i.e. the Froude number , where c is the speed of the stream, h is its depth, and g is the gravity constant).

We also deduce a number of inequalities relating F2 to a/h, where a is the maximum displacement of the free surface from its value at infinity. In particular, it is shown for the wave of greatest height that 1·480 < F2 < 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 345 - 358
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

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