The displacement of the ocean surface has been derived for the region around a wave crest in a random sea. The solution has a random part and a deterministic part. The latter provides an excellent, deterministic model for the surface elevation and water particle velocities and accelerations induced by extreme ocean waves. It is essentially a linear, broad-banded wave theory in which the component wavelets have amplitudes and phases such that the most probable extreme wave is obtained immediately. The formulation is equivalent to the extensively validated random wave theories, but it involves the simulation of just one wave rather than many hours of a sea state. Application of this theory to fluid load assessment may offer the realism of time domain simulation of random wave fields with the speed and convenience of deterministic analysis. The agreement between the present theory and the time domain simulations is excellent.
Environmental loads induced by extreme storms largely determine the fitness for purpose of offshore structures for areas such as the North Sea and the Gull of Mexico. Accurate and consistent prediction of extreme loads is essential for effective new designs, efficient utilisation of existing platforms and, thereby, the economic development of marginal oil and gas fields. Efthymiou and Graham (1990) have outlined the elements required for an improved "package" for loading analysis: improved analysis of met-ocean conditions accounting for joint probability; realistic hydrodynamic force coefficients; use of a reduced current accounting for blockage; and a new, more realistic wave kinematics theory. The last requirement is addressed in this paper. The ocean surface is a random process. In spite of this, in conventional design and assessment practices wave loads on fixed offshore structures are calculated using a deterministic, periodic wave theory such as Stokes V.
