On the Shape of the Wind Wave Spectrum of the Norwegian Continental Shelf

Abstract

Abstract The ultimate aim of this work is to contribute to the understanding of the North Sea wave spectral shape, with special emphasis on design conditions. More than 6000 wave spectra from the North Sea have been analyzed. The JONSWAP 1 model is fitted to the spectra using a least squares technique with a varying number of free parameters. We observe a systematic tendency for the JONSWAPI model to fit empirical spectra better than that by Pierson and Moskowitz2. Methods are proposed for estimation of JONSWAP spectral parameters when the zeros order moment of the spectrum is known. Introduction Present knowledge of the shape of the wave spectrum can be summarized as follows: Under idealized conditions the spectrum has a standard shape that can be described by a set of shape parameters. The shape of the spectrum of a fully developed sea in deep water is given by the PiersonMoskowitz2 spectrum. It is therefore quite natural that this spectrum includes wind speed but not fetch as a scale parameter. For growing sea states the spectral shape is given by the JONSWAp1 spectrum. Dimensionless fetch is therefore one of the scale parameters of this spectrum. The JONSWAP model spectrum is recommended by the Norwegian Petroleum Directorate in computing the interactions between waves and marine structures. However, the values of the JONSWAP model parameters are subject to discussion and disagreements. The main purpose of the work described in this paper has been to estimate the JONSWAP model parameters on the basis of a large number of wind wave, samples. Efforts are concentrated on design spectra of high sea states. As extreme design sea states are likely to occur during growing or fully developed wave conditions, the analyses were concentrated partly on growing sea states. It is assumed that results on spectral shape from growing seas can be extrapolated to the extreme design sea states. Based on more than 6000 spectra the JONSWAP model has been parameterized in two slightly different ways that are both useful for engineering applications. Both methods are presented in this paper. The Design Sea State It is common practice to define the design sea state as an event having a return period of 50 or 100 years. In the North Sea this corresponds to Hs=15 m and individual waves of height from 30 to 33 m. The period corresponding to the spectral peak is estimated at 15 to 20 s. Such high and long waves will most likely appear during or close to the peak of a generation phase with strong winds of long duration and fetch. If swell is present it will most probably be mixed with the wind sea and therefore not appear as an independent spectral peak. The energy of swell present in a design sea state will be small compared to that of the wind sea. We therefore assume that the shape of a design wave spectrum is not influenced by swell, and we assume also that it is satisfactorily described by a model spectrum like the JONSWAP.