Quantifying the role of mitigation hills in reducing tsunami runup

Coastal communities around the world are being encouraged to plant or restore vegetation along their shores for the purpose of mitigating tsunami damage. A common setup for these projects is to develop 'mitigation hills' - an ensemble of vegetated hills along the coast - instead of one continuous stretch of vegetation. The rationale behind a staggered-hill setup is to give tree roots more space to grow and deepen. From a fluid-dynamical point of view, however, staggered mitigation hills may have significant drawbacks such as diverting the flow into the low-lying areas of the park, which could entail strong currents in the narrow channels between the hills and lead to erosion of the hills from the sides. The goal of this study is to quantify how mitigation hills affect tsunami runup and to provide constraints on the design of mitigation hills that mitigate tsunami damage using numerical simulations. Our computations of tsunami runup are based on the non-linear shallow water equation solved through a fully implicit, high-order, discontinuous Galerkin method. The adaptive computational grid is fitted to the hill topography to capture geometric effects accurately. A new dynamic subgrid-scale eddy viscosity originally designed for large eddy simulation of compressible flows is used for stabilization and to capture the obstacle-generated turbulence. We have carefully benchmarked our model in 1D and 2D against classical test cases. The included figure shows an example run of tsunami runup through coastal mitigation hills. In the interest of providing generalizable results, we perform a detailed scaling analysis of our model runs. We find that the protective value of mitigation hills depends sensitively on the non-linearity of the incoming wave and the relative height of the wave to the hills. Our simulations also suggest that the assumed initial condition is consequential and we hence consider a range of incoming waves ranging from a simple soliton to a more realistic N-wave and an actual measured wave train. Our results suggest that channelization of flow between the mitigation hills is likely to occur in most setting and that limiting the degree of energy focusing should be a consideration in the design of a tsunami mitigation park.