Proposal Defense: Saulo Mendes

A proposal defense from UNC Marine Sciences graduate student, Saulo Mendes. Presented by the UNC at Chapel Hill Department of Marine Sciences. The location of this event will be in conference room 3204 on the 3rd floor of Murray Hall on UNC-CH campus in Chapel Hill, NC. This event will be held on Monday, May 6th at 10:00 am. This seminar will also be broadcast live to both UNC’s Institute of Marine Sciences room 222 and online via Zoom.

Seminar Title: Exceeding Probability Distribution of Rogue Waves – Physical Bounds and Extreme Value Theory

Abstract: The marine folklore has always contained wild stories of giant walls of waves much steeper and taller than the apparent average that seemed to appear out of nowhere. With the ever more complex set of regulatory measures for offshore operations, the past two decades witnessed the corroboration of such waves, detected by laser altimeters on the corners of oil rigs. Waves that are at least twice as tall as the significant wave height of a sea state are considered to be rogue, i.e. unexpected by the standard theory of water waves, thus being called rogue or freak waves. Remarkably, these waves have not been associated with a universal formation mechanism, being observed regardless of weather conditions, oceanic conditions and location. Therefore, they have been thought to be a general nonlinear feature of water waves, as there is also mounting evidence of their appearance in other nonlinear systems, such as optics and magneto-hydrodynamics. Moreover, several studies disagree amongst themselves on what should we expect for the likelihood of their occurrence, which ultimately leads to the impossibility of creating an accurate forecast system as well as a physical theory for the formation and evolution of rogue waves. The goal of my dissertation is to explain the uneven distribution of rogue waves, constrain the distribution by well-established bounds for the physical variables, give more accurate predictions for their expected maximum and extend it to higher dimensions. For the first issue, I propose to construct a geometrical composition of the standard Rayleigh distribution with one empirical model due to Haring and Tayfun’s model that holds the possibility for a master distribution to be converted into a Stoke’s wave. Even so, a combination of these models would fail if not modified in order to obey certain limits, such as the Miche-Stokes wave breaking limit. Using empirical bounds for the sea state variables, we are capable of finding an expression that fulfills this requirement, reconciles the wave statistics for the upper tail of the distribution, explains uneven behavior for different storms and singles out variables that are paramount for a forecast system. The physical bounds and probability distribution are indispensable to develop a theory for formation and evolution, as the latter can be rewritten in a Stokes-like perturbation model for water waves. Moreover, once a Tayfun-Stokes correspondence is found for the master distribution, we shall use Zakharov’s theory of Hamiltonian formalism for water waves to find its action and then obtain an amplitude probability according to Feynman’s path integration, thus combining all aspects of the problem: theory and forecast.