Advancing our understanding of the onshore propagation of tsunami bores over rough surfaces through numerical modeling

The propagation of tsunamis in the open ocean has been studied in detail with many excellent numerical approaches available to researchers. Our understanding of the processes that govern the onshore propagation of tsunamis is less advanced. Yet, the reach of tsunamis on land is an important predictor of the damage associated with a given event, highlighting the need to investigate the factors that govern tsunami propagation onshore. In this study, we specifically focus on understanding the effect of bottom roughness at a variety of scales. The term roughness is to be understood broadly, as it represents scales ranging from small features like rocks, to vegetation, up to the size of larger structures and topography. In this poster, we link applied mathematics, computational fluid dynamics, and tsunami physics to analyze the small scales features of coastal hydrodynamics and the effect of roughness on the motion of tsunamis as they run up a sloping beach and propagate inland. We solve the three-dimensional Navier-Stokes equations of incompressible flows with free surface, which is tracked by a level set function in combination with an accurate re-distancing scheme. We discretize the equations via linear finite elements for space approximation and fully implicit time integration. Stabilization is achieved via the variational multiscale method whereas the subgrid scales for our large eddy simulations are modeled using a dynamically adaptive Smagorinsky eddy viscosity. As the geometrical characteristics of roughness in this study vary greatly across different scales, we implement a scale-dependent representation of the roughness elements. We model the smallest sub-grid scale roughness features by the use of a properly defined law of the wall. Furthermore, we utilize a Manning formula to compute the shear stress at the boundary. As the geometrical scales become larger, we resolve the geometry explicitly and compute the effective volume drag introduced by large scale immersed bodies. This study is a necessary step to verify and validate our model before proceeding further into the simulation of sediment transport in turbulent free surface flows. The simulation of such problems requires a space and time-dependent viscosity to model the effect of solid bodies transported by the incoming flow on onshore tsunami propagation.