# The Role of Large-Scale Bedforms in Driftwood Storage Mechanism in Rivers

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Concept of Numerical Model

#### 2.2. Flow, Sediment Transort, and Morphodynamics: Eulerian Approach

#### 2.3. Driftwood Model: Lagrangian Approach

_{p}and v

_{p}are the velocities of the wood piece in the x and y directions, respectively; and u and v are the flow velocities in the x and y directions, respectively, which are obtained from the two-dimensional model, ρ is the density of water, C

_{D}is the drag coefficient of the wood piece, and A

_{x}and A

_{y}are the projections of the area of the wood piece in the x and y directions, respectively.

_{m}is the coefficient of the added mass.

**Figure 2.**Definitions of driftwood properties, flow velocity, and forces acting on wood pieces modeled as a cylinder. (

**a**) Flow velocities acting on edge of cylinder, (

**b**) force distribution, and (

**c**) moment balance.

_{p}is the rotational speed of the wood piece, and I is its moment of inertia.

_{0}and f

_{1}in Figure 2b). By defining the flow velocities at the edges of the wood piece as u

_{x}

_{0}, u

_{y}

_{0}, u

_{x}

_{1}, u

_{y}

_{1}(Figure 2a), we can calculate the flow velocity perpendicular to the longer axis of the wood piece, u

_{N}

_{0}and u

_{N}

_{1}, contributing to the rotational motion, as follows:

_{p}) can be calculated by:

_{r}is the drag coefficient of rotational motion.

_{w}, is calculated by assuming a linear force distribution along the wood piece, as shown in Figure 2c.

_{g}is the distance between the point of action and the point of mass. By substituting M and I into Equation (6), we calculated the rotational motion of the wood pieces.

## 3. Results

#### 3.1. Model Performance

^{3}. Some parameters for the driftwood model were determined considering it to be a cylindrical piece; C

_{d}and C

_{r}are approximated as constant, 1 since effect of Reynolds number on drag coefficient is not high for the condition we tested (Table 1) [28], and as used by Kang et al. [17], added mass coefficient, C

_{m}is set to 0.5.

#### 3.2. Role of Large-Scale Bedforms in Wood Storage

## 4. Discussion

## 5. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Driftwood deposition observed after large flood event in Otofuke River, Japan. Red color indicates single pieces, and blue denotes formation of logjams following driftwood deposition. (Courtesy of Hokkaisuiko Consultant Corporation).

**Figure 3.**Numerical simulation of braided channel pattern and depositional pattern of wood pieces for Case C1 of Bertoldi et al. [16]. (

**a**) bar and channel patterns by first 20 h obtained through morphodynamic calculation; (

**b**–

**f**) temporal changes during the latter 18 h calculated for channel, and depositional patterns of wood piece. Solid-black lines denote wood pieces. The diameter of wood pieces is increased by factor of 5 for visualization.

**Figure 4.**Comparison between experiment and simulation of rate of deposition of supplied wood pieces onto modeled braided channel.

**Figure 5.**Dominant bar modes in the numerical simulation predicted by bar regime diagram as proposed by Kuroki and Kishi [33]. S denotes channel slope.

**Figure 6.**Calculation results for channel pattern and depositional distribution of wood pieces in Case 2. (

**a**–

**e**) temporal changes during the latter 18 h calculated for channel, and depositional patterns of wood piece. Solid black lines denote wood pieces. The length and diameter of wood pieces are increased by factor of 3 and 5 for visualization, respectively.

**Figure 7.**Calculation results for channel pattern and depositional distribution of wood pieces in Case 4 at the end of 18 h. Solid black lines denote wood pieces. The length and diameter of wood pieces are increased by factor of 15 and 20 for visualization, respectively.

**Figure 8.**Temporal change in depositional rate of wood in numerical simulations. Red, blue, and green lines represent the results of cases 1, 2, and 4, respectively. Solid, dash, and dot-dash lines denote depositional rate of wood by different wood length, namely, values shown in Table 1, 3 cm, and 5 cm, respectively.

**Figure 9.**Spatial distribution of deposited driftwood in (

**a**) braiding dominated, and (

**b**) alternate-bar dominated reaches of Otofuke River, Japan after the 2016 flood event. Red circles denote wood deposition/logjam formation.

Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | |
---|---|---|---|---|---|

Water discharge, Q (l/s) | 1.26 | 1 | 2 | 0.2 | 10 |

Channel width, B (m) | 1.7 | 0.7 | 0.39 | 0.14 | 0.39 |

Uniform water depth, h (cm) | 0.38 | 0.57 | 1.22 | 0.57 | 3.22 |

Shields number, θ | 0.041 | 0.061 | 0.132 | 0.061 | 0.348 |

Reynolds number, Re | 741 | 1428 | 5128 | 1428 | 25641 |

Length of wood piece (cm) | 8 | 3.3 | 1.8 | 0.66 | 1.8 |

Diameter of wood piece (cm) | 0.3 | 0.12 | 0.069 | 0.025 | 0.69 |

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**MDPI and ACS Style**

Okitsu, T.; Iwasaki, T.; Kyuka, T.; Shimizu, Y.
The Role of Large-Scale Bedforms in Driftwood Storage Mechanism in Rivers. *Water* **2021**, *13*, 811.
https://doi.org/10.3390/w13060811

**AMA Style**

Okitsu T, Iwasaki T, Kyuka T, Shimizu Y.
The Role of Large-Scale Bedforms in Driftwood Storage Mechanism in Rivers. *Water*. 2021; 13(6):811.
https://doi.org/10.3390/w13060811

**Chicago/Turabian Style**

Okitsu, Takara, Toshiki Iwasaki, Tomoko Kyuka, and Yasuyuki Shimizu.
2021. "The Role of Large-Scale Bedforms in Driftwood Storage Mechanism in Rivers" *Water* 13, no. 6: 811.
https://doi.org/10.3390/w13060811