The quest for a three-dimensional theory of ship-wave interactions

The radiation and diffraction of water waves by ships can be analysed in classical terms from potential theory. The linearized formulation is well studied, but robust numerical implementations have been achieved only in cases where the vessel is stationary or oscillating about a fixed mean position. Slender-body approximations have been used to rationalize and extend the strip theory of ship motions, providing analytic solutions and guidance in the development of more general numerical methods. The governing equations are reviewed, with emphasis on the interactions between the steady-state velocity field due to the ship’s forward translation and the perturbations due to its unsteady motions in waves. Recent computations based on the boundary-integral-equation method are described, and encouraging results are noted. There is growing evidence that the influence of the steady-state velocity field is important, and the degree of completeness required to account for the steady field depends on the fullness of the ship. Benchmark computations are needed to test theories and computer programs without the uncertainty inherent in experimental comparisons.