FIRST- AND SECOND-ORDER WAVE EFFECTS ON A SUBMERGED SPHEROID

Computations are presented for the linearised force and moment acting on a submerged slender spheroid in regular waves, the resulting pitch and heave motions, and the second-order mean force and moment. These numerical results, which are based on the use of a three-dimensional panel code, are compared with the approximations based on slender-body theory. The accuracy of the slender-body approximation is relatively good for the first-order forces and body motions, but substantial errors are revealed for the second-order mean drift force and pitch moment. Unlike the approximate result, the more correct numerical prediction of the mean pitch moment is non-zero, and generally acts in the bow-down direction in head seas. To explain this result it is shown that the wave elevation directly above the spheroid increases in amplitude from bow to stern, thus causing a greater upward force on the afterbody relative to the forebody.