Variations in the wetted hull surface due to severe sea waves and/or large amplitude motions may contribute significantly to nonlinear hydrodynamic loads. In such cases, the perturbation approach with wave amplitude and motion as small parameters (that is, the second order wave force theory) may no longer be valid.

Analysis of motion response in severe sea states is performed with Aqwa-Naut, which involves meshing the total surface of a structure to create a hydrodynamic and hydrostatic model. Nonlinear hydrostatic and Froude-Krylov wave forces over the instantaneous wetted surface (i.e. beneath the incident wave surface) can then be calculated from this model. This calculation is performed at each time step of the simulation, along with instantaneous values of all other forces. These forces are then applied to structures, via a mathematical model (i.e. a set of nonlinear equations of motion), and the resulting accelerations are determined. The position and velocity at the subsequent time step are found by integrating these accelerations in the time domain, using a two stage predictor-corrector numerical integration scheme.

However, for large floating structures modeled by diffracting panel elements, the diffraction and radiation components are of comparable magnitude and are linear quantities.

The diffraction force in short crest waves contributed by all the diffracting panels is:

(13–36)

where is the Euler rotation matrix at time defined by Equation 1–7, is the relative heading angle of the wave direction with respect to the structure where is the yaw motion angle of the structure, and is the diffraction wave force induced by a unit amplitude incident wave with frequency and relative wave direction . The components of the diffraction wave excitation force are expressed in Equation 4–48 and are calculated by a hydrodynamic analysis prior to the current time domain analysis, is the number of wave directions and is the number of wave components in the m-th wave direction.

The radiation force consists of the impulse function convolution and the inertia force due to the added mass at infinite frequency, which are the same as those in Equation 13–30.