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A note on numerical computations of large amplitude standing waves

Published online by Cambridge University Press:  19 April 2006

Philip G. Saffman
Affiliation:
California Institute of Technology, Pasadena, CA 91125
Henry C. Yuen
Affiliation:
TRW Defense and Space Systems Group, Redondo Beach, CA 90278

Abstract

Numerical solutions of the inviscid equations that describe standing waves of finite amplitude on deep water are reported. The calculations suggest that standing waves exist of steepness, height and energy greater than the limiting wave of Penney & Price (1952). The computed profiles are found to be consistent with Taylor's (1953) experimental observations.

Type
Research Article
Copyright
© 1979 Cambridge University Press

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References

Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves on water. I. A numerical method of computation. Proc. Roy. Soc. A 350, 136.Google Scholar
Michell, J. H. 1893 The highest waves in water. Phil. Mag. 36 (5), 430–437.Google Scholar
Penney, W. G. & Price, A. T. 1952 Finite periodic stationary gravity waves in a perfect liquid. Phil. Trans. Roy. Soc. A 244, 254284.Google Scholar
Stokes, G. G. 1880 Considerations relative to the greatest height of oscillatory waves which can be propagated without change of form. Mathematical and Physical Papers, vol. I, pp. 225–238. Cambridge University Press. Also: Supplement to a paper on the theory of oscillatory waves. Mathematical and Physical Papers, vol. I, pp. 314–326.
Taylor, G. I. 1953 An experimental study of standing waves. Proc. Roy. Soc. A 218, 4459.Google Scholar
Toland, J. F. 1978 On the existence of a wave of greatest height and Stokes's conjecture. Proc. Roy. Soc. A 363, 469485.Google Scholar