Nonlinear wave reflection from a submerged circular cylinder

Abstract

The paper discusses analytically the nonlinear wave reflection caused by a circular cylinder, submerged under a free surface in water of infinite depth. For monochromatic incident waves it is shown that there is no reflection of order m and frequency mω (m integer). This means that the dominant part of the mode of frequency mω is not reflected. For bichromatic incident waves it is found that the second-order wave with ‘sum frequency’ has no reflection. It is shown that the x- and y-components of the oscillatory force of order m and frequency mω have identical amplitudes and a phase-difference ½π. A corresponding result is also true for bichromatic waves.