Full Euler equations for waves generated by vertical seabed displacements
DOI:
https://doi.org/10.5540/03.2025.011.01.0518Palavras-chave:
Seafloor displacement, Euler equations, Conformal mapping, Pseudo-spectral numerical methods.Resumo
This work consists on a concise summary of the author’s Master’s Dissertation. Further details can be found in the original thesis. We introduce a novel numerical method for simulating surface gravity waves generated by vertical seabed displacements. Our method utilizes a time-dependent conformal map to incorporate seabed geometry and wave profiles, allowing for handling various seabed and wave configurations. We validate our approach by replicating Hammack’s tsunami generation and propagation results, confirming accurate wave generation prediction according to Hammack’s linear theory. Then, we discuss the effect of nonlinearity on the generated wave. Additionally, we explore limitations of the passive generation approach in the context of the fully nonlinear Euler equations.
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