Study on boundary layer development and bottom shear stress beneath a tsunami

ABSTRACT

This paper presents a detailed investigation on unsteady effects in bottom boundary layer beneath a tsunami. In numerical simulation of tsunami, bottom shear stress has commonly been evaluated by using steady flow friction laws such as Manning equation, simply assuming that long-period wave motion satisfies quasi-steady flow conditions. However, the present study found that the behavior of tsunami-induced bottom boundary layer has an unsteady characteristics and acts similar to that induced by wind-generated waves even under long-period wave motion. As a result, bottom shear stress under tsunami is much larger than the estimation using steady friction coefficient due to a steep velocity gradient in the bottom boundary layer. Surprisingly, the steady flow friction law is not valid in almost the entire computational domain, from the source area to shallow region. This result highly coincides with the field measurement data obtained by Lacy group during the 2010 Chilean Tsunami at the Monterey Bay mouth in U.S. A correction coefficient is proposed to take into account unsteady effects in the conventional estimation method using a steady friction factor; this approach is validated by comparing with numerical simulation results using k-ω turbulence model.

KEYWORDS:

• Tsunami
• bottom shear stress
• bottom boundary layer
• steady friction factor
• wave friction factor
• k-ω turbulence model

Acknowledgments

The authors wish to express their grateful thanks for the financial support from the JSPS KAKENHI (16H04414) and the Taisei Foundation for carrying out this study. We would like to special thank anonymous reviewers for their constructive comments and suggestions which helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by JSPS KAKENHI Grant Number 16H04414.