# Tsunami Intrusion and River Ice Movement

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## Abstract

**:**

## 1. Introduction

## 2. Model Formulation

#### 2.1. Hydrodynamics Equations

#### 2.2. Numerical Method

#### 2.3. Ice Dynamic Model

## 3. Model Validations

#### 3.1. Case I: Oscillation in a Parabolic Container

#### 3.2. Case II: Conservation of Solitary Wave Propagation

#### 3.3. Case III: Tsunami Wave in a Laboratory Flume

## 4. Model Applications

#### 4.1. Ice Effect on Tsunami Wave Propagations over a Beach

#### 4.2. Ice Deposition on the Beach

#### 4.3. Ice jamming in River Channel with Incoming Tsunami Wave

^{3}/s with surface ice thickness of 0.4 m and concentration of 0.6. The velocities at upstream cross-section nodes are calculated based on the inflow discharge and simulated water depth. The downstream boundary condition is a solitary wave with 4 m height and a 900 s period. No special treatment is used for the reflective boundary as the wave dies out before it reflects back. The initial flow condition and longitudinal ice profiles are shown in Figure 8. The total simulation time is 3600 s.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Simulated water surface elevations over a parabolic topography at time = 0 s, 2000 s, 4000 s, and 6000 s.

**Figure 4.**Comparison between measured and simulated waveforms with different Manning roughness at x = (

**a**) 10 m, (

**b**) 14 m, (

**c**) 18 m, and (

**d**) 22 m.

**Figure 5.**Effect of ice concentrations on the surge run-up in the beach at times: 0 s, 8640 s, and 17,280 s.

**Figure 6.**Simulated ice depositions on the beach under a tsunami wave with different ice-bed friction coefficients: (

**a**) Initial water surface, ice bottom and top elevations, and the tsunami wave boundary conditions; simulated water surface and ice depositions on the beach with the ice-bed friction coefficient of (

**b**) 1.04, (

**c**) 2.08, and (

**d**) 5.20. The red line in the subfigure is the upstream water level boundary.

**Figure 9.**Scenarios of ice jam profiles produced by intrusion of tsunami wave. The colored contour plots indicate ice thickness distribution with two-dimensional velocity vectors.

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**MDPI and ACS Style**

Pan, J.; Shen, H.T. Tsunami Intrusion and River Ice Movement. *Water* **2019**, *11*, 1290.
https://doi.org/10.3390/w11061290

**AMA Style**

Pan J, Shen HT. Tsunami Intrusion and River Ice Movement. *Water*. 2019; 11(6):1290.
https://doi.org/10.3390/w11061290

**Chicago/Turabian Style**

Pan, Jiajia, and Hung Tao Shen. 2019. "Tsunami Intrusion and River Ice Movement" *Water* 11, no. 6: 1290.
https://doi.org/10.3390/w11061290