Nonlinear radiated and diffracted waves due to the motions of a submerged circular cylinder

We study the high-harmonic surface wave associated with nonlinear diffracti on and radiation of gravity waves by a near-surface circular cylinder. Base d on nonlinear potential-flow theory, we show analytically, using a boundar y-integral equation method, that: (a) for a circular motion of the cylinder , the leading-order outgoing radiated waves at any harmonic are generated o nly in one direction; (b) for a cylinder free to respond to regular inciden t waves, the total leading-order scattered waves at any harmonic are two or ders smaller upstream of the body. These theoretical results are substantia lly confirmed by direct time-domain simulations of the problem.