## 3 Model Validation and Comparison  
### Numerical Setup  
In this study, the developed slump model is validated by the benchmark case proposed by [PERSON] [16]. In this case, the water waves were generated by slumps in the laboratory. A series of experiments was conducted by allowing a mass of sand sliding down along an inclined plane. The submarine slumps were initially triangular in shape and spanned the width as the channel width, making it a 2D scenario. The dimensions of the slump were 0.65 m \(\times\) 0.65 m. In this paper, the numerical setup is as same as the experimental set up of [PERSON] [16] shown in Figure 1. The computational domain is 4 m long, 0.3 m wide, and 2.0 m high and discretized by 529,000 grids as the grid size dx = dz = 4.35 mm. The water depth is 1.6 m and the top of the slide is initially 10 cm below the water surface. The boundary conditions are free-slip boundary conditions on the domain boundaries, except for the ceiling boundary, which is a pressure Dirichlet (P = 0) boundary condition. The dynamic viscosities of water and air are 10\({}^{-3}\) Pa s and 10\({}^{-5}\) Pa s respectively, whilst the yield viscosity of the slump is \(\mu_{B}=50\) Pa s. The slump un-yield viscosity \(\mu_{A}\) is 10\({}^{10}\) Pa s as addressed in Part I [42]. The yield stress of the slump suggested by [PERSON] [16] is \(\tau_{y}=1000\) Pa. The densities of the slump, water, and air are 1950 kgm\({}^{-3}\), 1000 kgm\({}^{-3}\), and 1.2 kgm\({}^{-3}\), respectively. Simulation results are compared with the laboratory experiments and the numerical results proposed by [PERSON] [16], as well as the numerical results from [PERSON] [53] and [PERSON] [10]. Figure 2 shows the snapshots of the water wave generated by the slump. At the initial stage (t = 0 s\(\sim\)t = 0.4 s), the slump accelerates and deforms into the water and the free surface depresses. At t = 0.6-0.8 s, the first rebounding wave forms and moves to the right side. At t = 1.0 s, the wave breaks at x = 0 m, z = \(-\)0.1 m, causing complex turbulence with a trapped air bubble in this area. Figure 3 presents the snapshots of the velocity magnitude. The slump starts to liquefy in the toe area at t = 0.2 s at x = \(-\)0.6 m, and z = \(-\)0.7 m. At t = 0.4 s, a negative free-surface wave forms at x = \(-\)0.4 m, z = \(-\)0.1 m while a positive wave (at x = \(-\)0.95 m, z = 0.02 m) is pushed toward the offshore direction. At t = 0.6 s, the discontinuous velocity profile can be easily observed on the interface between the slump and the ambient water (at x = \(-\)0.75 m, z = \(-\)0.5 m). This discontinuous behavior becomes significant at t = 0.8 s and t = 1.0 s. One can observe that the velocity on the slump head (at x = \(-\)1.2 m, z = \(-\)1.2 m at t = 1.0 s) is slower than that at the slump tail (at x = \(-\)0.6 m, z = \(-\)0.6 m at t = 1.0 s). This is due to the water resistance and the drag force from the bottom friction along the slope. Figure 1: The numerical setup of slump-type tsunami simulations. Figure 2: The distributions of free-surface profiles and slump profiles at t = 0.0 s \(\sim\) t = 1.0 s. The solid lines are the numerical results and the dot lines are the experiment result. Figure 4 shows the snapshots of the strain rate magnitude. When the slump starts to move, a relatively large strain rate can be seen at x = \(-0.6\) m, z = \(-0.2\) m at t = \(0.2\) s. After that, a strong strain rate along the slope can be observed from t = \(0.4\) s to t = \(1.0\) s. This large strain rate indicates the  
Figure 3: The snapshots of the velocity magnitude of the slump and the ambient water. yield material that plays a role of lubrication. The strain rate is small in the head area of the slump (at x = \(-0.75\) m, z = \(-0.75\) m at t = \(0.6\) s; x = \(-0.8\) m, z = \(-0.7\) m at t = \(0.8\) s; and x = \(-1.0\) m, z = \(-1.0\) m at t = \(1.0\) s). This indicates the un-yield behavior of the slump. Figure 4: The snapshots of strain rate profiles of the slump. [PERSON] [16] provided two numerical wave results with the experiment data.