Introduction

The principles of wave prediction were already well known at the beginning of the sixties (§ I.I). Yet, none of the wave models developed in the 1960s and 1970s computed the wave spectrum from the full energy balance equation. Additional ad hoc assumptions have always been introduced to ensure that the wave spectrum complies with some preconceived notions of wave development that were in some cases not consistent with the source functions. Reasons for introducing simplifications in the energy balance equation were twofold. On the one hand, the important role of the wave–wave interactions in wave evolution was not recognized. On the other hand, the limited computer power in those days precluded the use of the nonlinear transfer in the energy balance equation.

The first wave models, which were developed in the 1960s and 1970s, assumed that the wave components suddenly stopped growing as soon as they reached a universal saturation level (Phillips, 1958). The saturation spectrum, represented by Phillips' one-dimensional f-5 frequency spectrum and an empirical equilibrium directional distribution, was prescribed. Nowadays it is generally recognized that a universal high-frequency spectrum (in the region between 1.5 and 3 times the peak frequency) does not exist because the high-frequency region of the spectrum not only depends on whitecapping but also on wind input and on the low-frequency regions of the spectrum through nonlinear transfer. Furthermore, from the physics point of view it has now become clear that these so-called first generation wave models exhibit basic shortcomings by overestimating the wind input and disregarding nonlinear transfer.