sulting from the interaction of a steep wave train with the ship hull; c) roll damping mechanisms arising from viscous separation, viscous lift forces from appendages and transom sterns; d) slamming and e) nonlinearities in the radiated and diffracted wave disturbance. The simultaneous treatment of all these nonlinear effects, even by a potential flow computational method, leads to a prohibitively expensive seakeeping simulation of little use in ship design. The strategy was therefore adopted to treat the nonlinearities outlined above progressively and to assess their importance before proceeding towards a more complete treatment.
This paper treats the seakeeping problem in head waves, therefore only the surge, heave and pitch motions and wave loads are considered. The ambient wave train is modeled independently of the seakeeping problem using the techniques of perturbation theory to first, second, and, if necessary, higher orders, along the lines of  and . This approach allows the efficient generation of long wave records designed to correspond to a given sea spectrum, indepedently of the computation of the wave ship interaction which represents the bulk of the seakeeping simulation.
The nonlinear hydrostatic and Froude Krylov effects are treated by introducing a time dependent panel mesh over the ship wetted surface defined by the intersection of the ambient wave profile with the ship hull. Upon integration of the hydrostatic and ambient wave hydrodynamic pressure over the ship hull, the nonlinear hydrostatic and Froude Krylov exciting forces are obtained. Efficient meshing algorithms have been developed which allow the discretization of realistic hull shapes with cruiser or transom sterns in ambient wave trains of high steepness.
The ship wave disturbance arising from its forward translation, the surge, heave, and pitch oscillatory motions, and the interaction with the ambient wave, are initially treated by linear theory. Heave and pitch motion simulations are carried out by combining the nonlinear treatment of the hydrostatic and Froude-Krylov effects and the linear solution of the surface wave disturbance. Comparisons with experimental measurements reveal that a significant portion of the nonlinearity is accounted for by these effects.
The nonlinear coupling of the ambient-and ship-wave disturbances is next treated according to the “weak scatterer” hypothesis. It is postulated that the ship wave disturbance is small compared to the ambient waves and therefore can be linearized about the ambient wave profile, an assumption justified by observations of seakeeping experiments in steep waves. Evidently the weak scatterer hypothesis is violated in the vicinity of the ship waterline where strong spray roots are often seen to form, caused by the ship forward motion or slamming. These effects and slamming in particular, are however not treated in the present study.
Boundary value problems have been derived for the ship wave disturbance and stated around the time-varying (but a priori known) ambient wave profile. The body boundary condition is stated exactly over the instantaneous position of ship hull, therefore the need to introduce the so-called m-terms of linear seakeeping theory is avoided. Assuming potential flow, integral equations are derived for the unknown velocity potential over the ship hull and the ambient wave profile, using the Rankine source as the Green function. The set-up and solution of the integral equation is carried out along lines similar to those in the linear time-domain problem discussed in . The radiation condition is satisfied as in the linear problem via an absorbing beach located at some distance from the ship, and designed to dissipate the energy carried by the ship wave disturbance. An outline of the solution algorithm and a brief review of the linear problem are given in Section 2.1. The weak scatterer hypothesis and corresponding boundary value problem is presented in Section 2.3.
An important component of a nonlinear seakeeping simulation is the enforcement of the exact body boundary condition. In Section 2.3