A generalized approach to the mechanics of three-dimensional nonlinear ocean waves

•A nonlinear stochastic family is given for 3D ocean waves at a finite depth.•A nonlinear deterministic family is given for short-crested wave groups conditional to the occurrence of extreme wave episodes.•Both the stochastic and the deterministic family up to 2nd order are given for undisturbed sea waves or for standing sea waves.•The nonlinear families include the free-surface displacement, the velocity potential, and thus the wave kinematics.•The theoretical results are validated with Monte Carlo simulations of wind-generated random ocean waves.

The paper suggests a generalized approach to the analysis of second-order three-dimensional random wave fields that can represent either ocean waves in an undisturbed field or standing ocean waves. A nonlinear stochastic family is introduced that has a linear stationary Gaussian random contribution and a second-order correction exact in a Stokes expansion. This family can describe the nonlinear mechanics of a random wave field. Subsequently, in the considered random ocean field, the nonlinear mechanics of wave groups can be investigated conditional to the occurrence of a very high wave. The free-surface displacement and velocity potential may be obtained, as well as the nonlinear wave velocity and acceleration, for both the stochastic family and the very high wave groups. The results are of interest for the analysis of nonlinear wave kinematics when extreme surface wave events occur and thus for Morison′s wave forces on slender structures.