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On the existence theory for irrotational water waves

Published online by Cambridge University Press:  24 October 2008

G. Keady  and
J. Norbury
G. Keady
Affiliation:
University of Western Australia
J. Norbury
Affiliation:
University College London
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Abstract

This paper concerns steady plane periodic waves on the surface of an ideal liquid flowing above a horizontal bottom. The flow is irrotational. The volume flow rate is denoted by Q, the velocity potential by ø, the period in ø of the waves by 2L, and the maximum angle of inclination between the tangent to the surface and the horizontal by θm.

Krasovskii (12) established that, at each fixed Q and L, there exist wave solutions for each value of θm strictly between zero and ⅙π. We establish that, at each fixed Q and L, there exist wave solutions for each value of qc strictly between c and zero. Here qc is the flow speed at the crest, and

where g is the acceleration due to gravity. Krasovskii's set of solutions is included in the set that we obtain.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 1 , January 1978 , pp. 137 - 157
Copyright
Copyright © Cambridge Philosophical Society 1978

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