A Statistical Analysis of Rogue Waves

Abstract

This master thesis studies the statistical properties of waves generated at the Hydrodynamics Laboratory of the Department of Mathematics at the University of Oslo. We look at two distinct experimental setups. First, we study the evolution of two different, fairly narrow banded spectra and verify the results found in K. B. Dysthe et al (2003). We show that the wave spectrum with the highest initial Benjamin-Feir index also has the sharpest increase in surface elevation kurtosis as the wave process propagates. Additionally, we discover that for the process with the highest initial Benjamin-Feir index, the surface elevation and velocity field kurtosis increase at different rates. Second, we study the effects of an asymmetric shoal on a wave process with a Pierson-Moskowitz wave spectrum. We show that the kurtosis and skewness of the surface elevation and velocity field display similar tendencies as the results in K. Trulsen et al (2020). The higher order comoments are studied and we show that the steeper the uphill slope of the shoal, the lower the cokurtosis. Then, by using Q-Q plots, estimated probability density functions and PDFs, we discover that the distribution of the surface elevation and velocity behave differently. Moreover, we show that the dependence structure of the surface elevation and velocity field is best described by a T-copula.