Numerical modelling of tsunamis generated by pyroclastic density currents

Abstract

This thesis utilises the open-source partial-differential equation solver ‘Basilisk’ and aims to advance understanding of tsunamis generated by pyroclastic density currents (PDCs). A two-dimensional numerical model is presented which simulates recentlypublished physical experiments exploring tsunami generation by high-mobility granularflows (representing PDCs). In the numerical model the granular-flow is approximated as a Newtonian fluid (a ‘granular-fluid’). This model is compared to the physical results and a strong agreement is demonstrated, confirming that the approximation is valid in the context of wave generation. The bottom boundary condition is shown to exert a first-order influence on the interaction dynamics between the granular-fluid and water, affecting the energy transfer process and influencing the far-field wave characteristics. The results suggest that capturing vertical velocity profiles and nonhydrostatic effects within numerical models of similar processes is important for future research. Following the initial comparison, the numerical model is updated to enable a pre-defined granular-fluid impact velocity and front height. The bottom boundary condition is shown to influence the interaction dynamics across a wider parameter space. The results also suggest that a two-dimensional approximation may be sufficient for capturing the initial wave-generation process, but when significant amounts of breaking and overturning are involved, a three-dimensional approximation is required for the accurate evolution of the wave front. Importantly, this approach also holds the novel advantage of providing the ability to vary the granularfluid impact Froude number and dimensionless thickness at impact independently of the slope angle, which is difficult to achieve in a laboratory setting. For large dimensionless thicknesses and large Froude numbers, the slope angle appears to play a more complex role in the resulting wave amplitude, while for low dimensionless thicknesses and Froude numbers, there is a clear decrease in wave amplitude with increasing slope angle. It is hypothesised that these relationships are a combined result of impact Froude number, dimensionless thickness and slope angle affecting the time and duration of momentum transfer between the granular-fluid and the generated wave. Overall, this thesis provides a robust numerical model and high-quality dataset which highlight the importance of capturing detailed mechanisms of tsunami generation by PDCs.