# 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

- Gurnell, A. Wood and river landscapes. Nat. Geosci.
**2012**, 5, 93–94. [Google Scholar] [CrossRef] - Wohl, E.; Iroume, A. Introduction to the wood in world rivers special issue. Earth Surf. Process. Land.
**2021**. [Google Scholar] [CrossRef] - Bair, R.T.; Segura, C.; Lorion, C.M. Quantifying the restoration success of wood introductions to increase coho salmon winter habitat. Earth Surf. Dyn.
**2019**, 7, 841–857. [Google Scholar] [CrossRef][Green Version] - Bertoldi, W.; Welber, M.; Gurnell, A.M.; Mao, L.; Comiti, F.; Tal, M. Physical modeling of the combined effect of vegetation and wood on river morphology. Geomorphology
**2015**, 246, 178–187. [Google Scholar] [CrossRef] - Bialik, R.; Karpinski, M.; Rajwa, A.; Luks, B.; Rowinski, P.M. Bedform characteristics in natural and regulated channels: A comparative field study on the Wilga River, Poland. Acta Geophys.
**2014**, 62, 1413–1434. [Google Scholar] [CrossRef] - Ruiz-Villanueva, V.; Blade Castellet, E.; Diez-Herrero, A.; Bodoque, J.M.; Sanchez-Juny, M. Two-dimensional modelling of large wood transport during flash floods. Earth Surf. Process. Landf.
**2014**, 39, 438–449. [Google Scholar] [CrossRef] - Schalko, I.; Lageder, C.; Schmocker, L.; Weitbrecht, V.; Boes, R.M. Laboratory flume experiments on the formation of spanwise large wood accumulations: I. Effect on backwater rise. Water Resour. Res.
**2019**, 55, 4854–4870. [Google Scholar] [CrossRef] - Wohl, E.; Scamardo, J.E. The resilience of logjams to floods. Hydrol. Process.
**2020**, 35, e13970. [Google Scholar] [CrossRef] - Ruiz-Villanueva, V.; Piegay, H.; Gurnell, A.M.; Marston, R.A.; Stoffel, M. Recent advances quantifying the large wood dynamics in river basins: New methods and remaining challenges. Rev. Geophys.
**2016**, 54, 611–652. [Google Scholar] [CrossRef][Green Version] - Abbe, T.; Montgomery, D.R. Patterns and processes of wood debris accumulation in the Queets River Basin, Washington. Geomorphology
**2003**, 51, 81–107. [Google Scholar] [CrossRef] - Gurnel, A.M.; PieGay, H.; Swanson, F.J.; Gregory, S.V. Large wood and fluvial processes. Freshw. Biol.
**2002**, 47, 601–619. [Google Scholar] [CrossRef][Green Version] - Kyuka, T.; Okabe, K.; Shimizu, Y.; Yamaguchi, S.; Hasegawa, K.; Shinjo, K. Dominating factors influencing rapid meander shift and levee breaches caused by a record-breaking flood in the Otofuke River, Japan. J. Hydro Environ. Res.
**2020**, 31, 76–89. [Google Scholar] [CrossRef] - Wyzga, B.; Zawiejska, J. Large wood storage in channelized and unmanaged sections of the Czarny Dunajec River, Polish Carpathians: Implications for the restoration of mountain rivers. Folia Geogr.
**2010**, 41, 5–34. [Google Scholar] - Van Der Nat, D.; Tockner, K.; Edwards, P.J.; Ward, J.V. Large wood dynamics of complex Alpine river flood-plains. J. N. Am. Benthol. Soc.
**2003**, 22, 35–50. [Google Scholar] [CrossRef] - MacVicar, B.; Piegay, H. Implementation and validation of video monitoring for wood budgeting in a wandering piedmont river, the Ain River (France). Earth Surf. Process. Landf.
**2021**, 37, 1272–1289. [Google Scholar] [CrossRef] - Bertoldi, W.; Welber, M.; Mao, L.; Zanella, S.; Comiti, F. A flume experiment on wood storage and remobilization in braided river systems. Earth Surf. Process. Landf.
**2014**, 39, 804–813. [Google Scholar] [CrossRef] - Kang, T.; Kimura, I.; Shimizu, Y. Numerical simulation of large wood deposition patterns and responses of bed morphology in a braided river using large wood dynamics model. Earth Surf. Process. Landf.
**2020**, 45, 962–977. [Google Scholar] [CrossRef] - Persi, E.; Petaccia, G.; Sibillia, S. Large wood transport modelling by a coupled Eulerian-Lagrangian approach. Nat. Hazards
**2018**, 91, 59–74. [Google Scholar] [CrossRef] - Kimura, I.; Kitazono, K. Effects of the driftwood Richardson number and applicability of a 3D-2D model to heavy wood jamming around obstacles. Environ. Fluid Mech.
**2020**, 20, 525–603. [Google Scholar] [CrossRef] - Shimizu, Y.; Takebayashi, H.; Inoue, T.; Hamaki, M.; Iwasaki, T.; Nabi, M. iRIC-Software: Nays2DH Solver Manual. 2014. Available online: https://i-ric.org/en/ (accessed on 16 March 2021).
- Nelson, J.M.; Shimizu, Y.; Abe, T.; Asahi, K.; Gamou, M.; Inoue, T.; Iwasaki, T.; Kakinuma, T.; Kawamura, S.; Kimura, I.; et al. The international river interface cooperative: Public domain flow and morphodynamics software for education and applications. Adv. Water Resour.
**2016**, 93, 62–74. [Google Scholar] [CrossRef] - Shimizu, Y.; Nelson, J.; Arnez, K.F.; Asahi, K.; Giri, S.; Inoue, T.; Iwasaki, T.; Jang, C.L.; Kang, T.; Kimura, I.; et al. Advances in computational morphodynamics using the International River Interface Cooperative (iRIC) software. Earth Surf. Process. Landf.
**2019**, 45, 11–37. [Google Scholar] [CrossRef] - Iwasaki, T.; Shimizu, Y.; Kimura, I. Sensitivity of free bar morphology in rivers to secondary flow modeling: Linear stability analysis and numerical simulation. Adv. Water Res.
**2016**, 92, 57–72. [Google Scholar] [CrossRef] - Iwasaki, T.; Nelson, J.; Shimizu, Y.; Parker, G. Numerical simulation of large-scale bed load particle tracer advection-dispersion in rivers with free bars. J. Geophys. Res. Earth Surf.
**2017**, 122, 847–874. [Google Scholar] [CrossRef] - Asahi, K.; Shimizu, Y.; Nelson, J.; Parker, G. Numerical simulation of river meandering with self-evolving banks. J. Geophys. Res. Earth Surf.
**2013**, 118, 2208–2229. [Google Scholar] [CrossRef] - Inoue, T.; Mishra, J.; Kato, K.; Sumner, T.; Shimizu, Y. Supplied sediment tracking for bridge collapse with large-scale channel migration. Water
**2020**, 12, 1881. [Google Scholar] [CrossRef] - Harada, D.; Egashira, S. Flood flow characteristics with fine sediment supply and driftwoods—Analysis on the Akatani River flood hazards in July, 2017. J. Jpn. Soc. Civ. Eng. Ser. B1
**2018**, 74, I_937–I_942. (In Japanese) [Google Scholar] - Shibuya, H.; Katsuki, S.; Ohsumi, H.; Ishikawa, N.; Mizuyama, T. Trap performance analysis of woody debris capturing structure by distinct element method using cylindrical element. J. Jpn. Soc. Civ. Eng. Ser. A2
**2011**, 67, 113–132. (In Japanese) [Google Scholar] - Akahori, R.; Hatta, N.; Shimizu, Y.; Ito, A. Response of woody debris for flows around hydraulic structures. J. Jpn. Soc. Civ. Eng. B1
**2014**, 70, I_691–I_696. (In Japanese) [Google Scholar] - Callander, R.A. Instability and river channels. J. Fluid Mech.
**1969**, 36, 465–480. [Google Scholar] [CrossRef] - Parker, G. On the cause and characteristic scales of meandering and braiding in rivers. J. Fluid Mech.
**1976**, 76, 457–480. [Google Scholar] [CrossRef] - Muramoto, Y.; Fujita, Y. The classification of meso-scale river bed configuration and the criterion of its formation. Proc. JSCE
**1978**, 22, 275–282. (In Japanese) [Google Scholar] - Kuroki, M.; Kishi, T. Regime criteria on bars and braids in alluvial straight channels. Proc. JSCE
**1984**, 342, 87–96. (In Japanese) [Google Scholar] [CrossRef] - Crosato, A.; Mosselman, E. Simple physics-based predictor for the number of river bars and the transition between meandering and braiding. Water Resour. Res.
**2009**, 45, W03424. [Google Scholar] [CrossRef][Green Version] - Parsons, R.; Best, J.L.; Orfeo, O.; Hardy, R.J.; Kostaschuk, R.; Lane, S.N. Morphology and flow fields of three-dimensional dunes, Río Paraná, Argentina: Results from simultaneous multibeam echo sounding and acoustic Doppler current profiling. J. Geophys. Res.
**2005**, 110, F04S03. [Google Scholar] [CrossRef][Green Version] - Shugar, H.; Kostaschuk, R.; Best, J.L.; Parsons, D.R.; Lane, S.N.; Orfeo, O.; Hardy, R.J. On the relationship between flow and suspended sediment transport over the crest of a sand dune, Río Paraná, Argentina. Sedimentology
**2010**, 57, 252–272. [Google Scholar] [CrossRef] - Inoue, T.; Watanabe, Y.; Iwasaki, T.; Otsuka, J. Three-dimensional antidunes coexisting with alternate bars. Earth Surf. Process. Landf.
**2020**, 45, 2897–2911. [Google Scholar] [CrossRef] - Federici, B.; Seminara, G. On the convective nature of bar instability. J. Fluid Mech.
**2003**, 487, 125–145. [Google Scholar] [CrossRef] - Defina, A. Numerical experiments on bar growth. Water Resour. Res.
**2004**, 39, 1092. [Google Scholar] [CrossRef] - Martin, D.J.; Benda, L.E. Patterns of instream wood recruitment and transport at the watershed scale. Trans. Am. Fish. Soc.
**2001**, 130, 940–958. [Google Scholar] [CrossRef] - Wohl, E.; Bledsoe, B.P.; Fausch, K.D.; Kramer, N.; Bestgen, K.R.; Gooseff, M.N. Management of large wood in streams: An overview and proposed framework for hazard evaluation. J. Am. Water Resour. Assoc.
**2016**, 52, 315–335. [Google Scholar] [CrossRef] - Visconti, F.; Camporeale, C.; Ridolfi, L. Role of discharge variability on pseudomeandering channel morphodynamics: Results from laboratory experiments. J. Geophys. Res. Earth Surf.
**2010**, 115, F04042. [Google Scholar] [CrossRef][Green Version] - Iwasaki, T.; Shimizu, Y.; Kimura, I. Numerical simulation of bar and bank erosion in a vegetated floodplain: A case study in the Otofuke River. Adv. Water Res.
**2016**, 93, 118–134. [Google Scholar] [CrossRef] - Masumoto, T.; Watanabe, Y.; Sasaki, A. Experimental study on channel formation at low flow on bars created at high flow. Adv. River Eng.
**2009**, 15, 225–230. (In Japanese) [Google Scholar] - Tubino, M. Growth of alternate bars in unsteady flow. Water Resour. Res.
**1991**, 27, 37–52. [Google Scholar] [CrossRef] - Sasaki, A.; Watanabe, Y.; Masumoto, T. An experiment on the flow-down of driftwood on riverbeds with sandbars. Adv. River Eng.
**2009**, 15, 177–182. (In Japanese) [Google Scholar] - Van Dijk, W.M.; Teske, R.; Van de Lageweg, W.I.; Kleinhans, M.G. Effects of vegetation distribution on experimental river channel dynamics. Water Resour. Res.
**2013**, 49, 7558–7584. [Google Scholar] [CrossRef][Green Version] - Kramer, N.; Wohl, E. Estimating fluvial wood discharge using time-lapse photography with varying sampling intervals. Earth Surf. Process. Landf.
**2014**, 39, 844–852. [Google Scholar] [CrossRef] - Ghaffarian, H.; Piegay, H.; Lopez, D.; Riviere, N.; MacVicar, B.; Antonio, A.; Mignot, E. Video-monitoring of wood discharge: First inter-basin comparison and recommendations to install video cameras. Earth Surf. Process. Landf.
**2020**, 45, 2219–2234. [Google Scholar] [CrossRef] - Braudrick, C.A.; Grant, G.E. When do logs move in rivers? Water Resour. Res.
**2000**, 36, 571–583. [Google Scholar] [CrossRef][Green Version] - Braudrick, C.A.; Grant, G.E. Transport and deposition of large woody debris in streams: A flume experiment. Geomorphology
**2001**, 41, 263–283. [Google Scholar] [CrossRef] - Kato, K.; Sumner, T.; Miura, T.; Kanno, T.; Chiba, K.; Inoue, T.; Shimizu, Y. Numerical analysis on the behavior of driftwood in driftwood capturing facility. J. Jpn. Soc. Civ. Eng. B1
**2019**, 75, I_1441–I_1446. (In Japanese) [Google Scholar] [CrossRef] - Davidson, S.L.; MacKenzie, L.G.; Eaton, B.C. Large wood transport and jam formation in a series of flume experiments. Water Resour. Res.
**2015**, 51, 10065–10077. [Google Scholar] [CrossRef] - Ader, E.; Wohl, E.; McFadden, S.; Singha, K. Logjams as a driver of transient storage in a mountain stream. Earth Surf. Process. Landf.
**2021**. [Google Scholar] [CrossRef]

**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