Perturbed orbital model applied to surface gravity waves
A point mass rotating and vibrating on one end of an idealized spring, fixed at the other end, is studied when the plane of motion is vertical and gravity is acting downward. In magnitude, the gravity force is taken small compared with the spring force. Calculations involving the force balance method and an energy budget predict that the general shape of the orbit has a slight top/bottom asymmetry: more pointed on top and blunter on the bottom. This asymmetry in the particle orbits is consistent with the wave profiles of propagating surface gravity waves which have often been observed to have narrow crests and broad troughs. It has not been possible theoretically to find the exact shape of the orbits by known analytical methods because of the interference of the gravity torque acting on the mass.
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Document Type: Research Article
Publication date: 30 December 2013
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