A common model for short crested seas is considered in view of wave measurements from the Norwegian continental Shelf. The directional spectrum is given as a product of a frequency spectrum and a frequency dependent spreading function. The spreading function is assumed to attain a cosine law and emphasis is herein given to the choice of the corresponding exponent. The sensitivity of the predicted response to uncertainties in the modeling of short crested sea is indicated for two different structural systems. Both extremes and fatigue life are considered. Based on these structural calculations a simplified spreading function being convenient for structural response calculation is recommended.
To the first order the wavy sea surface is conveniently modeled as a Gaussian stochastic process. For short time periods and limited spatial areas, the process can furthermore be assumed to be stationary and homogeneous. The adequacy of the assumption of a cosine-law will not be explicitly considered herein. The difference is not expected to be crucial regarding structural response and we will adopt a cosine model for the spreading function. In order to easily compare the previous results with the available measurements, Eq. (3) will be adopted for the intermediate part of this work. However, in the structural response calculations, an equivalent spreading function in the form of Eq. (2) will be determined. This can be done by simply setting n = 0.46 s, Mitsuyasu et ale (1975).
The consideration is herein restricted to linear structural systems or systems which can be linearized with a reasonable degree of accuracy. By now introducing parameterized models for the frequency spectrum and the spreading function, long term response extremes and fatigue life can be estimated along the lines reviewed into some detail in Haver and Natvig (1990).