Ocean rogue wave analysis for the development of safer navigation systems. : A Thesis submitted to the University of Gävle for the degree of Bachelor of Mathematics

Abstract: Rogue waves are unexpectedly high waves of 2.5X the significant wave height and which occur in nearly all phases of nature, from  oceans, to fiber-optic cables and atmospheric air-masses. In the ocean, rogue waves pose a significant danger to shipping and fishing vessels and have been found to reach 27.8 meters in height, and attain velocities of up to 100 km/hr. Mechanisms on naval structures for the real-time prediction of rogue waves are currently non-existent, and their development requires a) a good equation for simulating rogue waves and b) a deep study of the wave-trains of rogue waves. In this work, we consider the time-series of four rogue wave trains collected from various sources, including the U.S. Coastal Data Information Program. The method of study encompasses the development piece-wise constant functions from the rogue wave readings by laser/buoys. We use these piece-wise constant functions to form regularized functions as Fourier series, which we consider as weak solutions to the stationary nonlinear Schrödinger equation. The resulting force functions are quantified and compared to physical data of the rogue wave trains. The results show that we obtain a good correlation between the norms of the obtained force functions and the rogue wave height $H_{max}$ and the wave-velocity. The methods developed in the study build a potentially useful foundation for the development of a prediction model in a future study.