Numerical implementation of wave friction factor into the 1D tsunami shallow water equation model

ABSTRACT

In most of the current conventional tsunami numerical models, the steady flow friction law has been widely used to access the tsunami-induced bottom shear stress. However, according to our previous theoretical investigation showed that in almost the entire model domain from the tsunami source to the nearshore area, the tsunami-induced bottom boundary layer behaves like a wave boundary layer, rather than a quasi-steady flow boundary layer. The present study aims to develop a numerical method for tsunami simulation that elaborates a wave friction factor by implementing a correction method proposed by authors' previous work into the conventional 1D shallow water equation. As a result, the new method provides similar results to the original Manning method regarding the water level and the tsunami-induced velocity. However, the bottom shear stress estimated by the new method is higher than that from the Manning method over the entire computational domain. The transition locations from the wave friction zone to the steady friction zone are found at the water depth around 5 m under the present computational condition.

KEYWORDS:

• Tsunami
• shallow water equation model
• numerical simulation
• wave friction law
• steady friction law

Acknowledgments

The authors wish to express their grateful thanks for the matching fund by Tohoku-Tsinghua Joint Research Project (2020-2021).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Matching fund by Tohoku-Tsinghua Joint Research Project [2020-2021].