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Standing Stokes waves of maximum height

Published online by Cambridge University Press:  29 March 2006

Malcolm A. Grant
Malcolm A. Grant
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology Present address. Applied Mathematics Division, D.S.I.R., Wellington, New Zealand.
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Abstract

An analytic expression is found for an infinite subset of the coefficients of the perturbation expansion. They are the coefficients of the terms most rapidly varying at each order, which are also the first terms in the expansion of each Fourier coefficient. The sum of these terms gives a nonlinear approximation to the solution. At greatest height this approximation has a profile with a 90° corner.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 3 , 18 September 1973 , pp. 593 - 604
Copyright
© 1973 Cambridge University Press

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References

Edge, R. D. & Walters, G. 1964 The period of standing gravity waves of largest amplitude in water J. Geophys. Res. 69, 1674–1675.Google Scholar
Grant, M. A. 1972 Finite amplitude Stokes waves. Sc.D. thesis, Massachusetts Institute of Technology.
Penney, W. G. & Price, A. T. 1952 Finite periodic stationary gravity waves in a perfect fluid. Phil. Trans A 244, 254–284.Google Scholar
Tadjbakhsh, I. & Keller, J. B. 1960 Standing surface waves of finite amplitude J. Fluid Mech. 8, 442–451.Google Scholar
Taylor, G. I. 1953 An experimental study of standing waves. Proc. Roy. Soc A 218, 44–59. (See also Scientific Papers, vol. 4, pp. 208–224. Cambridge University Press.)Google Scholar
Wilton, J. R. 1914 On deep water waves. Phil. Mag. 27 (6), 6–385.Google Scholar