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Water waves and conjugate streams

Published online by Cambridge University Press:  29 March 2006

G. Keady
Affiliation:
Mathematics Department, University of Western Australia
J. Norbury
Affiliation:
Mathematics Department, University College London

Abstract

Steady plane periodic waves on the surface of an ideal liquid above a horizontal bottom are considered. The flow is irrotational. Let Q denote the volume flow rate, R the total head and S the flow force for the wave train. Bounds on wave properties are obtained in terms of the properties of (i) the conjugate streams with the same Q and R, and (ii) the conjugate streams with the same Q and S.

Type
Research Article
Copyright
© 1975 Cambridge University Press

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References

Benjamin, T. B. & Lighthill, M. J. 1954 On cnoidal waves and bores. Proc. Roy. Soc. A 224, 448.Google Scholar
Keady, G. & Pritchard, W. G. 1974 Bounds for surface solitary waves. Proc. Camb. Phil. Soc. 76, 345.Google Scholar
Krasovskii, Yu. P., 1960 The theory of steady-state waves of large amplitude. Doklady, 5, 62.Google Scholar
Krasovskii, Yu. P., 1961 On the theory of steady-state waves of large amplitude. U.S.S.R. Comp. Math. & Math. Phys. 1, 996.Google Scholar
Lavrentiev, M. A. 1964 Variational Methods. Noordhoff.
Long, R. R. 1946 Solitary waves in one and two-fluid systems. Tellus, 8, 460.Google Scholar
Serrin, J. B. 1952a Existence theorems for some hydrodynamical free boundary problems. J. Rat. Mech. Anal. 1, 1.Google Scholar
Serrin, J. B. 1952b Two hydrodynamic comparison theorems. J. Rat. Mech. Anal. 1, 563.Google Scholar
Starr, V. P. 1947 Momentum and energy integrals for gravity waves of finite height. J. Mar. Res. 6, 176.Google Scholar