On the role of energy balance for numerical modeling of tsunami sediment transport

Abstract:

Large-scale tsunamis in the shallow sea and on land are characterized by greater flow depth and speed than other natural open-channel flows. In-situ instrumental observation of tsunami sediment transport is practically impossible. Our understandings on the dynamics of tsunami sedimentation is mainly founded on the analysis of pre- and post-tsunami geomorphological data, field observation and laboratory analysis of tsunami deposits and modeling of tsunami sediment transport by means of hydraulic, mathematical and numerical approaches.

Based on massive dataset of the 2011 Tohoku tsunami deposits, Goto et al. (in press) identified a possible upper threshold of tsunami sedimentation. They found that sediment concentration, which is defined as a ratio of deposit thickness to the local flow depth, can be approximated by a constant value of 2% over the coastal plain of the Sendai Bay, northeast Japan.

Energy balance is an important physics to explain the upper threshold of tsunami sediment transport. The concept of energy constraint was described by Parker et al. (1986) for turbidity current. It declares the turbulent kinetic energy should be consumed to pick-up sediments from the bed and keep them in suspension. The loss of the turbulent energy results in decreased capacity of suspended load. Naruse et al. (2014) introduced the energy concept to tsunami sediment transport, and predicted the limiting sediment concentration of ~2% for a flow depth of 10 m and a flow speed of 10 m/s, which are typical for Sendai Plain.

The role of energy constraint for tsunami sedimentation was also investigated using a numerical approach. The saturation concentration for wash load (Bagnold, 1962; van Rijn, 2007), which also accounts the energy balance, was implemented to a numerical model of tsunami sediment transport, and the model was applied to the case study of the 2011 Tohoku tsunami. The modeling result showed that the observed limiting concentration of 2% may be caused from flow hysteresis. In addition, the concept of energy balance is important to explain both characteristic patterns of erosion and deposition, as well as spatial variability of sandy deposits.