Finite Volume Methods for the Multilayer Shallow Water Equations with Applications to Storm Surges
Coastal hazards related to strong storms such as hurricanes and typhoons are one of the most frequently recurring and wide spread hazards to coastal communities. Storm surges are among the most devastating effects of these storms, and their prediction and mitigation is of great interest to coastal communities that need to plan for the subsequent rise in sea level during these storms. Past efforts to model storm surge have usually focused on the single-layer shallow water equations, due to the ease of com- puting a simulation on the relevant scales and domains relative to three-dimensional modeling. The drawback to this approach is that the primary generating mechanism for storm surge is the wind-momentum transfer to the ocean. This boundary layer phenomenon is not well-represented by the shallow water equations, especially in the deep ocean. An alternative is to use the two-layer shallow water equations, with a shallow upper layer driven by the wind and an abyssal layer representing the rest of the water column. The focus of this thesis is on the development of a finite volume method for the multi-layer shallow water equations that is appropriate for application to storm surges. This has been done in the context of the GeoClaw framework, a code designed to handle the single-layer shallow water equations with adaptive mesh refinement al- gorithms, and uses many of the capabilities available to GeoClaw that are pertinent to storm surges. Approximations to the system are also discussed and tested along with methods for handling dry-states and inundation. Finally, idealized storm surge test cases comparing the single-layer and two-layer shallow water equations are explored.
- Applied mathematics