Extreme Wave Statistics of Surface Gravity Waves over Bathymetry

Abstract

Rogue waves are unexpected and unusually larger waves than their surrounding and can be dangerous to ship and offshore structures. In normally distributed wave fields also known as Gaussian sea, rogue waves actually exist, but their population can be greatly enhanced when the sea state deviates from Gaussian. Extreme deviation from Gaussian can be provoked by non-uniform bottom as a wave field propagates into shallower water. In this work, I studied how water waves propagate through varying bathymetry. Recent experiments of long-crested irregular waves propagating over a shoal showed that the deviation from Gaussian statistics occurs in the velocity field and is different from deviations in the surface elevation. In my thesis work, I developed a numerical code that is able to predict wave propagation in variable depth including the velocity field. The flexibility of numerical simulation allows me to investigate different types of bottom topography with different incoming waves. These simulations are useful to design new experiments. It turns out that the statistics of the surface elevation and the velocity field can be qualitatively different.