A simple model of the Draupner Wave Experiment

Abstract

Rogue Waves are large waves that appear “out of nowhere” in the open ocean and in near-shore waters. The Mathematics in Industry Study Group organized by Professor David Mason at the University of Witwatersrand in January, 2024, considered these waves due to their frequency at locations off the South African coast. There are a number of quite sophisticated models of these waves, but in this work we try to reproduce something like a rogue wave with a very simple free surface model, and in particular consider a wave generated in a circular tank by wave activity at the outer edge. Linear and nonlinear equations are derived and integrated to obtain the wave activity due to different generation mechanisms. The results indicate that a relatively simple model can produce something that approaches the form of a rogue wave.