On Non-Linear Very Large Sea Wave Groups

The paper deals with the non-linear effects for sea wave groups.
Boccotti’s quasi-determinism theory, which is exact to the first-order in a Stokes expansion, gives
the mechanics of sea wave groups when either a very high crest (first formulation of the theory — ‘New wave’), or a large crest-to-trough wave height (second formulation of the theory) occurs.
In this paper, the quasi-determinism theory, in both formulations, is extended to the second-order,
by obtaining the expressions of free surface displacement and velocity potential, as a function of
wave spectrum.
Finally it is shown that analytical predictions are in good agreement with both field data and data
of Monte Carlo simulations of non-linear random waves.