Kristina, W, Bokhove, O and van Groesen, E (2014) Effective coastal boundary conditions for tsunami wave run-up over sloping bathymetry. Nonlinear Processes in Geophysics, 21 (5). pp. 987-1005. ISSN 1023-5809
Abstract
An effective boundary condition (EBC) is introduced as a novel technique for predicting tsunami wave runup along the coast, and offshore wave reflections. Numerical modeling of tsunami propagation in the coastal zone has been a daunting task, since high accuracy is needed to capture aspects of wave propagation in the shallower areas. For example, there are complicated interactions between incoming and reflected waves due to the bathymetry and intrinsically nonlinear phenomena of wave propagation. If a fixed wall boundary condition is used at a certain shallow depth contour, the reflection properties can be unrealistic. To alleviate this, we explore a so-called effective boundary condition, developed here in one spatial dimension. From the deep ocean to a seaward boundary, i.e., in the simulation area, we model wave propagation numerically over real bathymetry using either the linear dispersive variational Boussinesq or the shallow water equations. We measure the incoming wave at this seaward boundary, and model the wave dynamics towards the shoreline analytically, based on nonlinear shallow water theory over bathymetry with a constant slope. We calculate the run-up heights at the shore and the reflection caused by the slope. The reflected wave is then influxed back into the simulation area using the EBC. The coupling between the numerical and analytic dynamics in the two areas is handled using variational principles, which leads to (approximate) conservation of the overall energy in both areas. We verify our approach in a series of numerical test cases of increasing complexity, including a case akin to tsunami propagation to the coastline at Aceh, Sumatra, Indonesia.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Authors 2014. This is an open access article under the terms of the Creative Commons Attribution 3.0 License |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 Jan 2017 10:51 |
Last Modified: | 25 Jan 2017 10:51 |
Published Version: | https://doi.org/10.5194/npg-21-987-2014 |
Status: | Published |
Publisher: | American Geophysical Union |
Identification Number: | 10.5194/npg-21-987-2014 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:109064 |