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Carlson – An Exploration of Nonlinear Water Wave Generation

 

An Exploration of Nonlinear Water Wave Generation (2024)

Undergraduate: Joshua Carlson


Faculty Advisor: Roberto Camassa
Department: Mathematics

Nonlinear water wave generation occurs during flow-over-topography experiments, and many regimes of expected flow have been identified over the years. Subcritical and low-forced effects are well predicted by the current theoretical models, but shock formation and wave-breaking, which have been observed in the low-supercritical regime, are yet to be accurately predicted by a PDE model. The appearance of highly nonlinear features in experimental data motivates the extension of the Green-Naghdi model into a unidirectional, higher-order model that seeks to better predict these features. Numerical analysis is still needed to compare this model to experimental results, but it is clear that more nonlinear and forcing terms are generated as a result of higher-order expansions in the dispersive and nonlinear small parameters.