Abstract
Wave propagation and run-up in U-shaped channel bays are studied here in the framework of the quasi-1D Saint-Venant equations. Our approach is numerical, using the momentum conserving staggered-grid (MCS) scheme, as a consistent approximation of the Saint-Venant equations. We carried out simulations regarding wave focusing and run-ups in U-shaped bays. We obtained good agreement with the existing analytical results on several aspects: the moving shoreline, wave shoaling, and run-up heights. Our findings also confirm that the run-up height is significantly higher in the parabolic bay than on a plane beach. This assessment shows the merit of the MCS scheme in describing wave focusing and run-up in U-shaped bays. Moreover, the MCS scheme is also efficient because it is based on the quasi-1D Saint-Venant equations.
Highlights
Simulation of Propagation and Tsunamis are some of the devastating natural disasters that threaten the population in coastal areas
Since the bathymetry of Palu Bay has a form resembling a bay with a parabolic cross-section, the high tsunami run-up in Palu city can be attributed to the shoaling phenomenon in the
We discuss the implementation of the momentum conserving staggered-grid (MCS) scheme for simulating wave propagation and run-up in U-shaped bays
Summary
Simulation of Propagation and Tsunamis are some of the devastating natural disasters that threaten the population in coastal areas. If the bay has a U-shaped cross-section, the Saint-Venant conservative equation becomes explicit, allowing the formulation of a consistent conservative numerical scheme, as conducted here. These long, narrow bays and canyons are common in nature. With the same scheme, we get other results related to wave dynamics in U-shaped bays, including here shoaling and run-up, which are in good agreement with the analytical formula [16]. All these assessments show the merit of the proposed MCS-scheme.
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