**2.5. Effect of the offshore still water depth on tsunami generation due to a falling body**

The numerical results for the tsunami‐height distribution are shown in **Figure 15(a)**, and **15(b)**, where the offshore still water depth *h*off is 0.1 m, and 0.2 m, respectively, when the falling body is a light fluid. As the offshore still water depth decreases, the tsunami height near the gate, i.e., the shoreline increases, as shown in **Figure 15(a)**, for the falling body does not move seabed seawater. With less volumetric flow rate wasted, the falling body contributes to tsunami‐height growth, while it progresses near the seabed. Note, however, that as the offshore still water depth decreases, there is decreased rate in the tsunami height in tsunami propaga‐ tion, which increases especially for 2.0 m ≤ *x* ≤ 2.5 m, as shown in **Figure 15(a)**.

**Figure 15.** The distributions of the tsunami height *η*max for the different initial positions of a falling light fluid with a specific gravity of 1.0.

#### **2.6. Tsunami generation due to a submarine landslide**

Two‐dimensional vertical motion in a water basin, as illustrated in **Figure 16**, is numerically simulated to examine tsunami generation due to a submarine landslide. The slope gradient *β* is 45°, the offshore still water depth *h*off is 0.305 m, and the offshore water density is 1000 kg/m3 . The particle grid is 0.005 m, the same as in the present computation. The initial level of a falling‐body bottom from the offshore still water level, is −0.205, −0.105, 0.0, 0.1, and 0.2 m in Cases U1, U2, O1, O2, and O3, respectively, such that the falling body is under sea level even at the initial falling time in both Case U1, and Case U2, creating a submarine landslide, whereas the falling body is above sea level at the initial falling time in Cases O1, O2, and O3, with a subaerial landslide. The falling body is a heavy fluid, with a density of 2600 kg/m3 , and the initial shape of the falling body is an isosceles right triangle, where the initial height of its vertical front face is 0.105 m, in all cases.

**2.5. Effect of the offshore still water depth on tsunami generation due to a falling body**

tion, which increases especially for 2.0 m ≤ *x* ≤ 2.5 m, as shown in **Figure 15(a)**.

The numerical results for the tsunami‐height distribution are shown in **Figure 15(a)**, and **15(b)**, where the offshore still water depth *h*off is 0.1 m, and 0.2 m, respectively, when the falling body is a light fluid. As the offshore still water depth decreases, the tsunami height near the gate, i.e., the shoreline increases, as shown in **Figure 15(a)**, for the falling body does not move seabed seawater. With less volumetric flow rate wasted, the falling body contributes to tsunami‐height growth, while it progresses near the seabed. Note, however, that as the offshore still water depth decreases, there is decreased rate in the tsunami height in tsunami propaga‐

**Figure 15.** The distributions of the tsunami height *η*max for the different initial positions of a falling light fluid with a

Two‐dimensional vertical motion in a water basin, as illustrated in **Figure 16**, is numerically simulated to examine tsunami generation due to a submarine landslide. The slope gradient *β* is 45°, the offshore still water depth *h*off is 0.305 m, and the offshore water density is 1000

subaerial landslide. The falling body is a heavy fluid, with a density of 2600 kg/m3

initial shape of the falling body is an isosceles right triangle, where the initial height of its

. The particle grid is 0.005 m, the same as in the present computation. The initial level of a falling‐body bottom from the offshore still water level, is −0.205, −0.105, 0.0, 0.1, and 0.2 m in Cases U1, U2, O1, O2, and O3, respectively, such that the falling body is under sea level even at the initial falling time in both Case U1, and Case U2, creating a submarine landslide, whereas the falling body is above sea level at the initial falling time in Cases O1, O2, and O3, with a

, and the

specific gravity of 1.0.

kg/m3

46 Tsunami

**2.6.

**Figure 16.** A sketch of the initial positions of a falling body, in Cases U1, and U2, with a submarine landslide, and Cas‐ es O1, O2, and O3, with a subaerial landslide. The offshore still water depth *h*off is 0.305 m, and the slope gradient *β* is 45°.

Shown in **Figure 17** are the numerical results for the water surface displacements at Point Q, where the distance between the location for Point Q, and that for the shoreline in still water, is 0.71 m, as shown in **Figure 16**. **Figure 17** indicates that the tsunami height is lower when a falling body is initially submerged, as in both Case U1, and Case U2, the reason for which is the third question.

**Figure 17.** A relative value for the water surface displacement *η* at Point Q, indicated in **Figure 16**, where the falling body is a heavy fluid, with a specific gravity of 2.6. The offshore still water depth is 0.305 m, and *g* denotes gravitation‐ al acceleration, i.e., 9.8 m/s2 .

In the cases with a submarine landslide, a falling body is surrounded by seawater, from the time falling starts. In both Case U1, and Case U2, the density ratio between the falling heavy fluid, and the offshore water, is 2600 kg/m3 /1000 kg/m3 = 2.6, which is much smaller than the density ratio between the falling heavy fluid, and the air, i.e., about 2600 kg/m3 /1.0 kg/m3 = 2600. Thus the initial relative potential energy of a submerged falling body is lower, resulting in a slower motion, with a smaller volumetric flow rate, in the falling body. This is the reason why the tsunami height is lower in the cases where the submarine landslide occurs than in the cases where the landslide occurs above the offshore water level.