Abstract
We study the high-harmonic surface wave associated with nonlinear diffraction and radiation of gravity waves by a near-surface circular cylinder. Based on nonlinear potential-flow theory, we show analytically, using a boundary-integral equation method, that: (a) for a circular motion of the cylinder, the leading-order outgoing radiated waves at any harmonic are generated only in one direction; (b) for a cylinder free to respond to regular incident waves, the total leading-order scattered waves at any harmonic are two orders smaller upstream of the body. These theoretical results are substantially confirmed by direct time-domain simulations of the problem.
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