Summary
A long circular cylinder half immersed in the free surface of an ideal fluid undergoes small time periodic motions. The method of matched asymptotic expansions is used to give a solution in the high frequency limit. Of particular interest are the surface waves generated by this motion, and a three term asymptotic series for their amplitude is found. It is proved that there are no eigensolutions of the infinite vertical barrier problem containing waves which are purely outgoing, and it is shown how this can be used to predict the wave amplitude to a higher order than that of the matching solution.
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References
F. Ursell, Short surface waves due to an oscillating immersed body,Proc. Roy. Soc. Land., A220 (1953) 90–103.
A. J. Hermans, A perturbation method for the radiation of surface waves,J. Eng. Maths., 6 (1972) 323–330.
M. van Dyke,Perturbation Methods in Fluid Mechanics, Academic Press (1964).
F. G. Leppington, On the radiation and scattering of short surface waves, Part 1,J. Fluid. Mech., 56 (1972) 101–119.
F. G. Leppington, On the radiation and scattering of short surface waves, Part 2,J. Fluid. Mech., 59 (1973) 129–146.
F. G. Leppington, On the radiation and scattering of short surface waves, Part 3,J. Fluid. Mech., 59 (1973) 147–157.
A. M. Ayad, To be published.
G. Alker, High frequency waves trapped in a two-dimensional canal,Quart. J. Mech. Appl. Math., 27 (1974) 347–363.
D. G. Crighton and F. G. Leppington, Singular perturbation methods in acoustics: diffraction by a plate of finite thickness,Proc. Roy. Soc. Lond., A335 (1973) 313–339.
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Alker, G. On the radiation of short surface waves by a heaving circular cylinder. J Eng Math 9, 197–205 (1975). https://doi.org/10.1007/BF01535445
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DOI: https://doi.org/10.1007/BF01535445