Scattered waves and motions of marine vessels advancing in a seaway

The steady forward motion of a marine vessel modifies the incident and scattered waves as well as its dynamic characteristics in a seaway. Small amplitude assumptions of the surface waves and vessel dynamic responses lead to linearization of the potential flow problem and its solution in the frequency domain. The mathematical formulation adopts a translating coordinate system at the vessel forward speed. The free surface boundary condition accounts for the modification of the uniform current around the vessel and a new radiation condition takes into account the Doppler shift of the scattered waves. A boundary element model, based on the Rankine source distribution, describes the steady and oscillatory flows around the vessel. Stokes' theorem allows evaluation of the surface integrals involving the so-called m-terms due to oscillation of the vessel in a current. Through a numerical experiment with a Wigley hull form, we establish the convergence of the numerical model, verify the radiation condition, and examine the scattered wave patterns for a full range of forward speeds. Previous laboratory data provides validation of the computed hydrodynamic coefficients and dynamic response as well as the potential flow model for general seakeeping applications. (C) 2011 Elsevier B.V. All rights reserved.