A spectral description for extreme sea states offshore Denmark Part II: Directional spreading function

Abstract

Power spectral density and frequency-dependent directional spreading functions are developed for describing extreme sea state spectra in the Danish sector of the North Sea. The input to the spectral models are the significant wave height, the spectral peak period, the spectral second-moment period, and the circular root-mean-square spreading at the spectral peak frequency. The new spectral functions have been developed from measurements of large sea states, made with a Directional Waverider buoy, at two sites in the Danish sector of the North Sea. This paper describes the new directional spreading function; a companion paper describes the new power spectral density function. The new directional spreading function is based on a simple parameterisation of measured frequency-dependent spreading derived from the Directional Waverider buoys. It is defined in terms of the peak period and significant wave height, with different expressions depending on whether the dominant component in the spectrum is a wind-sea or a swell. A form for a combined wind-sea and swell sea state is also defined. The new spreading function is compared against measurements for the location and found to provide an accurate representation of the spreading estimated from the measurements.