Estimation of wave directional spectra and applications to the study of surface gravity water waves

Abstract

<p>This thesis deals with the estimation of wave directional spectra and applications to the study of surface gravity water waves. Theoretical foundations and testing procedures are established to evaluate and compare different methods of extracting the wave directional spectrum from a wave record. An integrated software package for the analysis of directional seas is developed and used to test all methods, and to identify their properties, characteristics and biases. As a result, guidelines for the use of these methods are drawn. The findings indicate that all of the methods currently used for wave directional spectrum estimation have drawbacks. As a result, three new methods are proposed and tested against current methods. Test results indicate that a proposed closed-form of the Maximum Likelihood Method is the best choice, from both a theoretical and computational point of view. The new method was shown to outperform all other estimates for both heave-pitch-roll and wavestaff data. Field data from the Atlantic Ocean, Lake Ontario and Lake St. Clair (spanning two orders of magnitude in size) is investigated in an attempt to demonstrate the resolution potential of the newly developed method of estimating the wave directional spectra. As a result, completely decoupled spectra are observed for the first time in rapidly turning winds, and a clear relationship between the wave relaxation parameter and the wave age is established. Directional spreading parameter values are found to be higher than the established values in previous studies, for both Lake Ontario and Atlantic Ocean data. In addition, the Atlantic Ocean directional spectra are found to be narrower than their Lake Ontario counterpart. Finally, wave measurements in Lake St. Clair indicate that the structure of directional spectra can be very complicated, even in small lakes, and that a strong shear current can cause not only the refraction of an incoming wavefield, but can also inhibit the generation of waves propagating directly against it.</p>