## 6 Concluding Remarks  
This study applies the Bingham rheology model to studying the slump-type landslide tsunamis. The Bingham model is integrated into the Navier-Stokes equations and the LES turbulent model to have a detailed description of the vertical acceleration of the landslides and the induced waves. The free-surface kinematic is tracked by the VOF method. The model results are validated by the laboratory data from [PERSON] [16] with a good agreement. The sensitivity analysis is conducted to study the effect of three rheology variables, un-yield viscosity \(\mu_{A}\), yield viscosity \(\mu_{B}\), and yield stress \(\tau_{y}\) on the wave generation and the profiles of the slumps. The results show that both the tsunami and slump profiles are affected by the rheology parameters while the yield viscosity \(\tau_{y}\) isthe key factor in tsunami generation and slump movement. Faster slump sliding speed will induce larger negative tsunami waves. The analysis of the scale effect is conducted based on the Froude number, Bingham number, and normalized yield stress. The dimensional analysis of four cases with different length scales is performed. When both constraints, Froude number similarity and Bingham number similarity are satisfied; the free-surface and slump profiles are nearly identical in different length scales. The results and conclusions obtained from the laboratory scale can be extended to the field scale by satisfying the Froude number and Bingham number similarity.  
The difficulties of simulating the slump-generated tsunamis come from the following aspects. The kinematics and the dynamics of the slumps are complicated and difficult to be described by a single model. The behaviors of various landslides, such as sand slide, granular slide, rockslide, avalanche slide, and iceberg slide, have different characteristics and have to be described by different models. The model adopted in this study is the Bingham rheology model. The suitable situation for using the Bingham rheology model is the cohesive material with the property of yield stress. Other than that, the difference between the model and the physics will be significant. The strength of adopting the Bingham model with the Navier-Stokes solver is this method can fully describe the vertical acceleration and breaking waves. The effects of vertical acceleration and breaking wave are especially important to the near-source area. If the characteristics of the slump material satisfy the Bingham assumptions, a good result can be expected. However, the simulation time is long due to the large number of iterations for the viscous linear solver. This problem defines the present model as a research model, not a prediction model.  
The initial potential energy of the slide material mainly controls the wave height of the landslide tsunami. In detail, the wave height, especially away from the source area, is mainly affected by the initial centroid elevation and the initial acceleration of the slump [47]. In this paper, we conclude that, other than the initial potential energy of the slump, the Bingham parameters such as the yield stress and the yield viscosity will have significant effect on the wave form in the near-source region. Another finding in this study is the scale effect. The analyzed results show that both the Bingham number and Froude number have to be kept the same to accurately scale up the laboratory experiment to the filed scale. This study also demonstrates that using the material directly from the field in the laboratory will lead to a different result in terms of the slump shape. However, the effect on the wave height is marginal.  
The authors declare no conflict of interest.