Tsunami-induced bottom shear stress has commonly been evaluated using a friction coefficient for steady flow, such as Manning's roughness coefficient, Chézy formula and Darcy-Weisbach equation, assuming development of bottom boundary layer up to the water surface under tsunami. However, applicability of steady friction law to tsunami wave has never been scientifically investigated, and it has simply been assumed that long-period wave motion satisfies quasi-steady flow condition. In the present study, the k-ω model is used to calculate velocity profile and resultant sea bottom shear stress under shoaling hypothetical tsunami propagating from tsunami source area to nearshore region. It is found that steady friction is not valid in the entire computational region from the source area to shallow region due to extremely thin boundary layer thickness beneath tsunami.
In numerical modeling of tsunamis, bottom shear stress is usually evaluated by Manning roughness coefficient n or friction coefficient f which is valid under steady flow motion. Tsunami energy loss due to bottom friction is an important physical process causing attenuation of tsunami wave height during wave shoaling process. In addition, when we deal with sediment movement and subsequent sea bottom morphology change due to both bed load and suspended sediment movement, it is highly important to estimate accurate bottom friction exerting on the sea bottom, since both modes of the sediment transport rate have generally been formulated as a function of acting bottom shear stress (e.g., Takahashi et al., 2000).
It is well known that in a steady open channel flow, bottom boundary layer develops up to the water surface, whereas the thickness of bottom boundary layer under wind-generated waves is extremely thin as compared with water depth (Jonsson, 1966), resulting in a fact that the water depth is not dominating representative length in turbulent sea bottom boundary layer. In addition, it is noted under wave motion that due to steep velocity gradient near the sea bed, bottom shear stress acting on the sea bottom surface is much larger than that estimated from steady friction coefficient. Amid these two limitations of "steady flow friction law" and "wave friction law", a question arises which is valid under tsunami wave as depicted in Fig. 1. This is a research motivation for the present investigation.
