# Non-Hydrostatic Modeling of Waves Generated by Landslides with Different Mobility

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Laboratory Experiments

## 3. Theoretical Momentum Balance

^{2}), and this is equivalent to force per unit area (N/m

^{2}). In this approach, idealized theoretical equations are developed for landslides with a significant horizontal velocity component on moderate slopes, and are not valid for vertical rockfalls. The vertical fall velocity of a landslide is also important, and this is accounted for in the development of a limiting relationship based on the fluid continuity equation [2].

## 4. Numerical Modelling

#### 4.1. Model Set-up

#### 4.2. Model Results

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Landslide flume experimental apparatus, indicating the locations of wave probes (P1–P9) and acoustic velocity sensor (Vec). The numerical modeling domain begins at x = 0, with boundary conditions from observations at P1.

**Figure 2.**Images of the waves generated by landslides with different mobility: (

**a**) low mobility; (

**b**) high mobility.

**Figure 3.**Example time series of water surface elevation near the impact site for landslides with low and high mobility, adjusted such that the maximum amplitude occurs at t = 1 s. These waves were observed at wave probe P1 and correspond to the experimental conditions listed in Table 1.

**Figure 4.**Balance of momentum terms for a set of experiments with waves generated by landslides with low and high mobility. The solid line represents perfect correlation, the dashed lines are ±15% deviation, and correlation coefficients for each type of slide are shown.

**Figure 5.**Water surface elevation time series for the low landside mobility case from experimental observations and numerical simulation. Time t = 0 s is referenced to the slide impact time. Wave probe sites shown in Figure 1 are: (

**a**) P1; (

**b**) P2; (

**c**) P3; (

**d**) P4; (

**e**) P5; and (

**f**) P6.

**Figure 6.**Water surface elevation time series for the high landside mobility case from experimental observations and numerical simulation. Time t = 0 s is referenced to the slide impact time. Wave probe sites shown in Figure 1 are: (

**a**) P1; (

**b**) P2; (

**c**) P3; (

**d**) P4; (

**e**) P5; and (

**f**) P6.

**Figure 7.**Along-flume fluid velocity time series at probe P2 during the wave passage for the high landside mobility case: (

**a**) observed and predicted near-bottom velocity; (

**b**) simulated water surface elevation and color contours of horizontal velocity, with black lines indicating the vertical grid.

Mobility | ${\mathit{\rho}}_{\mathit{s}}(\mathbf{kg}/{\mathbf{m}}^{3})$ | V (m^{3}) | ${\mathit{v}}_{\mathit{s}}(\mathbf{m}/\mathbf{s})$ | s (m) | h (m) | a_{m} (m) |
---|---|---|---|---|---|---|

low LM (granular) | 1400 | 0.34 | 4.00 | 0.040 | 0.30 | 0.09 |

high LM (water) | 1000 | 0.30 | 5.38 | 0.043 | 0.31 | 0.29 |

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## Share and Cite

**MDPI and ACS Style**

Mulligan, R.P.; Take, W.A.; Bullard, G.K.
Non-Hydrostatic Modeling of Waves Generated by Landslides with Different Mobility. *J. Mar. Sci. Eng.* **2019**, *7*, 266.
https://doi.org/10.3390/jmse7080266

**AMA Style**

Mulligan RP, Take WA, Bullard GK.
Non-Hydrostatic Modeling of Waves Generated by Landslides with Different Mobility. *Journal of Marine Science and Engineering*. 2019; 7(8):266.
https://doi.org/10.3390/jmse7080266

**Chicago/Turabian Style**

Mulligan, Ryan P., W. Andy Take, and Gemma K. Bullard.
2019. "Non-Hydrostatic Modeling of Waves Generated by Landslides with Different Mobility" *Journal of Marine Science and Engineering* 7, no. 8: 266.
https://doi.org/10.3390/jmse7080266