Second Order Wave Spectra and Heave/Slope Wave Measurements

Abstract

The paper discusses the impact of second order wave spectra on heave/pitch/roll wave measurements. It is found that the sharp increase of the directional spread and the check ratio below the spectral peak may be explained by the 2nd order spectrum. Sum-frequency contributions turn out to be of negligible importance. INTRODUCTION Ocean wave data for engineering applications are usually interpreted in terms of linear wave theory and directional wave spectra. When a model directional spectrum is needed, a popular choice is the JONSWAP frequency spectrum multiplied by a directional distribution of the cos-2s type with frequency dependent directional spread. The standard analysis of heave/pitch/roll (H/P/R) measurements provides the frequency spectrum and the first four directional Fourier coefficients from which the mean wave direction and the directional spread are derived. There is also an additional parameter, called the dispersion or check ratio, in essence the ratio between the estimated root mean square wavenumber at a certain frequency and the wavenumber given by the dispersion relation. Real H / P / R wave measurements all show two very characteristic features for simple open ocean wave fields: 9 the directional spread is smallest around the spectral peak and increases strongly towards both lower and higher frequencies; 9 the check ratio is close to 1 at and above the spectral peak, but increases sharply below the peak. Apart from various buoy and electronic filters, steady currents (Barstow and Krogstad, 1984), spectral leakage (Ezraty and Cavani@, 1980), and noise (2hcker, 1Dept. Mathematical Sciences, NTNU, N-7491 Trondheim, Norway. harald.krogstad 9