The drift force and moment on floating and submerged bodies in long waves

Asymptotic approximations are derived for the drift force and moment acting on bodies in incident plane surface waves. These approximations are based on the assumption that the wavelength is long compared with the length scale of the body or, equivalently, the frequency and wavenumber are small. Expansions in ascending powers of the wavenumber are developed for the Kochin function, which represents the far-field waves diffracted and radiated by the body. From these expansions the approximations of the drift force and moment are derived. If the body is unrestrained its motions in long waves are the same as the incident waves, to leading order, resulting in cancellation between the components of the Kochin function due to diffraction and radiation. It is necessary to expand these functions up to third order in the wavenumber to evaluate the leading-order terms of the drift force and moment. The approximations are compared with computations for small finite wavenumbers for several different floating and submerged bodies including spheres, spheroids and parallelepipeds. The characteristics of the drift moment are analysed to determine the angles of stable and unstable equilibrium relative to the waves.