The Diffraction Potential for a Slender Ship Moving Through Oblique Waves

Abstract

The diffraction problem of a fixed slender ship in incident waves is formulated. Both the conditions of zero and constant forward velocity are considered. The waves are assumed to be of the same order as the beam of the ship and are from an oblique heading. &&The boundary value problem is linearized with respect to wave amplitude and solved by the method of matched asymptotic expansions. The first order zero speed solution is described in terms of an integral representation and means for numerically evaluating it are given. The forward speed potential is solved to two orders of magnitude. The first order is just the zero speed case while the second order problem involves solving a boundary value problem with a non-homogeneous free surface condition. The solution to this second order problem is given in terms of three auxiliary potentials, each satisfying a separate part of the boundary conditions. &&For zero forward speed, the sectional exciting force is calculated and compared with the commonly used integrand of the Khaskind relations. The two give different values, but when integrated over the hull both show the same total exciting force. &&The pressure distribution on an ore carrier for both zero forward speed and an abbreviated form of the forward speed case are given and compared with experiments. The theory compares well with the measured pressures on the mid-ship section, and on a forward section with stern seas. However, the theory does not compare well for the case of a forward section and bow seas.