Non-linear random wave groups with a superimposed current

In this paper a new solution for non-linear random wave groups in the presence of a uniform current is obtained, by extending to the second-order the Boccotti's 'Quasi-Determinism' (QD) theory. The second formulation of the QD theory gives the mechanics of linear random wave groups when a large crest-to-trough wave height occurs. Here the linear QD theory is firstly applied to the wave-current interaction. Therefore the non-linear expressions both of free surface displacement and velocity potential are obtained, to the second-order in a Stokes' expansion. Finally some numerical applications are presented in order to analyze both the wave profile and the wave kinematics.