A finite-depth unified theory for the linear and second-order problems of slender ships

In this paper an extension of the unified slender-body theory is introduced to solve the finite-depth seakeeping problem of a slender ship. The far- a nd near-field behaviors of the velocity potential in finite depth are intro duced, and a new kernel of the integral equation is derived for the heave a nd pitch motions of a slender ship at zero speed. The kernel of the integr al equation is expressed in a series form which makes the integral equation easy to solve. Based on the present theoretical background, computations w ere carried out, and the hydrodynamic coefficients and motion RAOs were obt ained. The computational results are compared with WAMIT, and a nice agreem ent is shown. The present method is extended to the computation of the seco nd-order mean drift forces and moment in infinite and finite depth. Motion RAOs of sway. roll and yaw are obtained using strip theory. and the drift f orces using the far-field momentum equations. The results show favorable ag reement with WAMIT. Using the drift forces, the wave drift damping matrix i s obtained for infinite depth. Aranha's formula is applied, and the damping coefficients are compared with the existing data. The present study shows that unified theory is an efficient and accurate design tool for slender sh ips.