Spectral Analysis and non-linear high wave groups in wind generated sea states

One of the most important applications of information on random seas in the naval, ocean and civil engineering fields is the prediction of responses (motions and wave-induced forces and bending moments) of ships and offshore structures in a seaway and the evaluation of hydro-dynamic forces acting on near-shore marine structures.
In order to carry out stochastic prediction of linear and nonlinear responses for design of marine systems, wave spectra representing desired sea states are mandatory.
Wave spectra can be described by considering that sea waves, which at first sight appear very random, can be analyzed by assuming that they consist of an infinite number of wave with different frequencies and directions. The distribution of the energy of these wave when plotted against the frequency and direction represents the wave spectrum. More precisely, the wave energy distribution with respect to the frequency alone, irrespective of wave direction, is called the frequency spectrum, whereas the energy distribution expressed as a function of both frequency and direction is called the directional wave spectrum.
The way in which the component waves are distributed is expressed by plotting the component wave energy, or the square of the component amplitude, against the frequency of component waves.