A CONDITIONAL MEAN SECOND-ORDER WAVE THEORY

In the design of bottom supported offshore structures for oil exploration and oil production the wave loading is often determined by subjecting the structure to a periodic wave with prescribed wave height and period. The advantage of this procedure is that a non-linear wave theory, for instance Stokes` fifth-order, can be applied to predict the instantaneous submerged parts of the structure and the wave kinematics up to the free water surface. In a stationary stochastic sea state the mean wave profile and associated wave kinematics conditioned on a given wave elevation at a specified point in space or time are derived. The results are based on the second-order, unidirectional, deep water Stoke`s wave theory, but can easily be extended to other moderate non-linear wave formulations. The application of the proposed wave theory as a design wave is discussed together with methods to overcome convergence problems associated with wideband wave spectra.