Summary
An analysis is made of the generation of surface waves by the time-periodic oscillations of smooth submerged cylinders in the limit when the cylinder is at a large depth h below the free surface, and the frequency ω/(2π) of the oscillations is high. Specifically, the parameters of the problem are such that ω2 d 2/g ≫ 1 and h/d 1 ≫ 1 subject to the condition that ω2 d 1 d 2/(gh) ≪ 1 where g is the acceleration due to gravity and d 1 and d 2 denote the maximum and minimum diameters of the body wave maker. The amplitude of the radiated waves if found to be exponentially small and to relate to certain critical points inside the cylinder.
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Ayad, A.M. Radiation of short surface waves by oscillating submerged smooth cylinders. J Eng Math 17, 55–72 (1983). https://doi.org/10.1007/BF00042838
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DOI: https://doi.org/10.1007/BF00042838