Discontinuous Galerkin methods for spectral wave/circulation modeling
Meixner, Jessica Delaney
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Waves and circulation processes interact in daily wind and tide driven flows as well as in more extreme events such as hurricanes. Currents and water levels affect wave propagation and the location of wave-breaking zones, while wave forces induce setup and currents. Despite this interaction, waves and circulation processes are modeled separately using different approaches. Circulation processes are represented by the shallow water equations, which conserve mass and momentum. This approach for wind-generated waves is impractical for large geographic scales due to the fine resolution that would be required. Therefore, wind-waves are instead represented in a spectral sense, governed by the action balance equation, which propagates action density through both geographic and spectral space. Even though wind-waves and circulation are modeled separately, it is important to account for their interactions by coupling their respective models. In this dissertation we use discontinuous-Galerkin (DG) methods to couple spectral wave and circulation models to model wave-current interactions. We first develop, implement, verify and validate a DG spectral wave model, which allows for the implementation of unstructured meshes in geographic space and the utility of adaptive, higher-order approximations in both geographic and spectral space. We then couple the DG spectral wave model to an existing DG circulation model, which is run on the same geographic mesh and allows for higher order information to be passed between the two models. We verify and validate coupled wave/circulation model as well as analyzing the error of the coupled wave/circulation model.