Non-Linear Wave Dynamics: Modeling Rogue Waves in Open Ocean Environments
Authors
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Zoe Morgan
Crimson Education Trust
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Adam Bell
Northern Institute of Technology
https://orcid.org/0009-0000-0000-0000
Abstract
Rogue waves—extreme, unexpected, and highly localized surface waves—pose a significant threat to maritime navigation and offshore structures. For decades, their existence was debated, as traditional linear wave theory deemed them statistically impossible. This research applies principles of non-linear mathematical physics to model the genesis and dynamics of these extreme events. We focus on the non-linear Schrödinger (NLS) equation and its extensions, such as the Dysthe equation, which incorporate modulational instability as a primary mechanism for rogue wave formation. By simulating complex, multi-directional wave fields (sea states), our model demonstrates how energy from surrounding waves can become rapidly focused into a single, massive pulse. This work validates the NLS framework against real-world buoy data and satellite observations of rogue wave events. This study bridges the gap between theoretical mathematics and physical oceanography, providing a predictive mathematical tool to assess the probability of rogue wave occurrence in specific ocean basins.
Copyright (c) 2026 Zoe Morgan, Adam Bell (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.