Computational modeling for large wood dynamics with root wad and anisotropic bed friction in shallow flows

Accepted Manuscript

Computational Modeling for Large Wood Dynamics with Root Wad and Anisotropic Bed Friction in Shallow Flows T. Kang , I. Kimura PII: DOI: Reference:

S0309-1708(18)30560-8 https://doi.org/10.1016/j.advwatres.2018.09.006 ADWR 3197

To appear in:

Advances in Water Resources

Received date: Revised date: Accepted date:

28 June 2018 8 September 2018 11 September 2018

Please cite this article as: T. Kang , I. Kimura , Computational Modeling for Large Wood Dynamics with Root Wad and Anisotropic Bed Friction in Shallow Flows, Advances in Water Resources (2018), doi: https://doi.org/10.1016/j.advwatres.2018.09.006

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Highlights We developed a computational model for motion of large wood (LW) in shallow flows.

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Lagrange type LW motion model was coupled with Euler type shallow flow model.



The laboratory tests were performed with different flow discharge and channel slope.

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Rolling, sliding and depositing motions of LW were simulated accurately.

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The root wad of wood piece reduced the velocity of wood motion in shallow flows.

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Computational Modeling for Large Wood Dynamics with Root Wad and Anisotropic

T. Kang1 and I. Kimura2 1

Hydraulic Research Laboratory, Hokkaido University, Japan

2

Faculty of Sustainable Design, University of Toyama, Japan

Corresponding author: Taeun Kang ([email protected])

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Abstract

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Bed Friction in Shallow Flows

This study developed a computational model for large wood deposition patterns in shallow flows considering the effect of a root wad based on laboratory experiments. We used the Nays2DH depth-averaged two-dimensional model of iRIC to simulate shallow flows. A newly developed large wood simulation model was combined with the shallow flow model. The laboratory tests

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were performed by changing several hydraulic parameters. In shallow water with a depth similar to the diameter of large wood, the root wad decreased the draft for wood motion (the depth at which large wood contacts the river bed) by lifting the head of large wood. The experimental

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results showed that the large wood tends to move toward the side walls and deposit on the bed after passing an obstacle. Computational results reasonably showed that the proposed coupling

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model reproduced the fundamental and physical aspects of the phenomena.

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1. Introduction In rivers, large wood is transported along with water and sediment. Deposited large wood affects river morphology by causing local scour and deposition of bed materials. Such large

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wood may initiate the formation of an island as a midchannel bar [1]-[8]. Large wood and deposition patterns can change in response to input processes, channel morphology, and

hydrological parameters, including flood events [9]. Previous research showed that the relative influence of these factors changes along the river system [1],[10]-[13], resulting in distinct

downstream trends in large wood accumulation style [1],[14]-[16]. The ratio of wood length to

channel width is a key parameter that affects large wood deposition patterns [18]. In addition, the

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patterns are influenced by diverse parameters such as drag force, water level, bed friction, and obstacles.

Numerous researchers have studied large wood dynamics. Braudrick et al. (1999) [18], Braudrick and Grant (2000) [19] and Braudrick et al. (2001) [20] provided the basic framework to approach large wood mobility and entrainment in rivers. Based on these frameworks, several researchers investigated large wood transport dynamics (e.g., [10], [21]-[25]). These studies

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successfully predicted a wood motion relationship between hydrodynamic and resistance forces, and a few of them examined transport systems. In studying large wood transport, the large wood

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shape and density for motion are considered first [16],[17]. A piece of large wood may consist of a stem, branch, and/or root wad. Among these, the stem and root wad are the major components, and they actively affect the motion of large wood. Large wood deposition is particularly sensitive

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to the characteristics of the root wad because this part increases the friction with the bed. In addition to experiments and observations, computational models for large wood dynamics have been developed, such as the Iber-wood two-dimensional (2D) hydrodynamic

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model [26]-[28] and the NaysCUBE [29] three-dimensional (3D) Reynolds-averaged Navier– Stokes model [30],[31]. Both models address large wood dynamics following a Lagrangian

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method, coupling water flow with wood transport. The Iber-wood model considers the wood shape to be a simple cylinder. In contrast, the NaysCUBE large wood model applies a particle method to consider the impinging motion of large wood using a discrete element method. These studies showed the mechanism of large wood dynamics in deep water flows (where water depth is larger than wood diameter) to demonstrate floating motion only, and they accurately

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reproduced large wood motion. However, the analysis of large wood dynamics through the integration of river bed and large wood, such as the root wad effect and anisotropic bed friction, is neglected in these models even though large wood dynamics show floating motion, sliding

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motion, and deposition in a natural river system. Clarifying such phenomena by coupling

motions (floating, sliding, and settling motions) is crucial in understanding large wood behavior in rivers and the role of large wood floating advection. Thus, it is required to study sliding

motion and deposition with the root wad effect and anisotropic bed friction as the key parameters of large wood dynamics for improving computational methods.

The main aim of this work is to develop a numerical method for simulating the transport

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of large wood along with hydrodynamics in shallow flows, considering the root effect under

various hydrologic parameters (flow discharge and channel slope). This study presents a newly developed numerical model that can simulate various behaviors of large wood. We use a 2D depth-averaged flow model (Nays2DH [32] of iRIC: International River Interface Cooperative [33]), which is an Eulerian model, for calculating water flow and bed morphology. A Lagrangetype large wood model is newly developed and combined with Nays2DH. The applicability of

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the present model is discussed through a comparison with experimental results.

2.1 Scale of the experiment

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2. Experimental setup

Among several studies related to large wood and river morphology, Gurnell et al. (2002)

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[10] first presented the classification of river scales (small, medium, and large). Kramer and Wohl (2017) [34] recently systematically categorized four river scales in relation to large wood (Table 1). We conducted laboratory tests on a medium scale river, which was arbitrarily selected,

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for a simplified experiment to examine the reproducibility of the large wood model. As obstacle was used to clearly describe the process of wood deposition with change in channel width. In addition, we could observe the transition of large wood motions, such as floating, sliding,

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settling, and re-moving in shallow flows. The root scale (diameter: approximately 0.01 m) was taken from Bertoldi et al. (2014) [25].

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Table 1. Main classification of the river scales based on Kramer and Wohl (2017) [34] Scale River size Transport Wood not reorganized or transported except during Channel width/stem length of large uncommon floods or debris flows with N decadal Small wood >1–2 recurrence intervals; large pieces mostly immobile; river Water depth/diameter of large wood long residence times regulated by decay and >1–2 physical breakdown rather than fluvial transport Hydrologic regime is dominant control; drives Channel width/stem length of large periodic transport of stored and newly recruited Medium wood >2–4 pieces during high flows; key pieces and jams river Water depth/diameter of large wood remain in place during smaller floods, accumulating >2–4 smaller pieces; larger, more infrequent floods break up and rearrange jams Channel width/stem length of large Wood exported downstream, laterally onto wood >5 or channel width> all wood floodplains, or buried; wood exported regularly lengths during high flow; amount of wood transfer highly Depth of flooded channel > diameter variable and largely dependent on pattern of Large of large wood antecedent peak flows; high variability in water river (note that the transition between levels during flooding creates numerous medium and large rivers at channel opportunities for wood sequestration in long-term widths: ~20–50 m wide because storage on the floodplain, causing large variability longest wood pieces are in this range) in wood residence time During most flows, rapid transfer of wood to deposition zones such as deltas, estuaries, or the ocean; lesser rapid fluctuations in discharge stage ~106 km2 or larger than large rivers create fewer opportunities for Mean annual discharge > 103 m3/s trapping of wood within channel or overbank Great (note that the perennial flow, deposition; wood transfer largely controlled by the river commonly have vast, seasonally, spatial distribution and timing of wood recruitment inundated floodplains, large fine from large tributaries; floodplain wood likely sediment loads, and deep channels) transported and redeposited within the floodplain rather than retransported to main channel; wood buried within channel bed may be transported downstream annually as part of the bed load

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2.2 Experimental model for large wood and flume The flume channel measured 0.3 m

2 m (Figure 1(a)), and the flume bed was created

using extremely smooth wood panels (Figure 1(d)). Obstacle size was 10 cm

10 cm,

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and two obstacles were attached to the side wall (Figure 1(a)).

10 cm

The large wood models were created using wood cylinders with diameters of 1 cm and lengths of 10 cm. The density of the large wood models was 650 kg/m3 in wet conditions (i.e., when floating on water). The root model was developed by attaching two thin wood cylinders

(0.18 cm in diameter and 2 cm in length) as a cross shape “+” at 90° to the end of the large wood

model [24],[25]. The shape of the stem was cylindrical; hence, the resistance to the motion in the

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lateral direction was considerably smaller than that to the motion in the stem-wise direction because of rolling motion. Hence, small pieces of wood (0.1 cm

0.2 cm) were attached at the

middle of the stem to increase the resistance to rolling motion (Figure 1(b)).

Table 2 shows the experimental cases. This study considered large wood deposition in relation to channel slope, flow discharge, and the root effect. In the experiments, we used two

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different flume slopes, i.e., 0.0045 and 0.007 (m/m), to consider the change in flow velocity under the same flow discharge. The following two cases of discharge were selected based on the minimal discharge (smaller case) for the motion of the wood piece with a root wad and

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approximately twice the minimal discharge (larger discharge): a smaller case (0.00065 m3/s and 0.00060 m3/s) and a larger case (0.0010 m3/s and 0.0011 m3/s). In addition, the root effect was examined for two cases, i.e., with and without roots. Therefore, eight cases were investigated in

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the experiments and computations. Each case was repeated thrice to verify reproducibility. Then, a typical case was selected.

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Wood pieces were supplied one by one at intervals of 4 s after the flow reached an equilibrium state (no wave with the back water effect). Ten wood pieces were supplied in each case. The initial input direction of the wood pieces was random. The range of the initial positions

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of the wood pieces was also random but limited within a circle with a radius of 5 cm (starting zone, Figure 1(a)) because the initial angle and position were difficult to control. These settings were identically applied to the computational conditions.

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Table 2. Experimental and simulation cases (for simplification cases: no prototype exists) Flow discharge (m3/s)

Channel slope (m/m)

Root wad

1

0.00065

0.0045

No

2

0.0010

0.0045

No

3

0.00060

0.0070

No

4

0.0011

0.0070

No

5

0.00065

0.0045

Yes

6

0.0010

0.0045

Yes

7

0.00060

0.0070

Yes

8

0.0011

0.0070

Yes

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b)

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a)

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Cases

d)

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c)

Figure 1. Experimental flume and wood piece: a) flume design, b) large wood design, c) large wood samples, and d) experimental flume.

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3. Simulation method We used a 2D plane numerical solver developed based on Nays2DH [32] of iRIC [33] to simulate the flows. A third-order total variation diminishing-monotonic upstream centered

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scheme for conservation laws method was used for the advection term, and a zero-equation model was used for the turbulence model. The coupled model was a two-way model that

considered the drag force exerted by the large wood on the flow. We estimated the Manning

roughness coefficient as 0.006 because the bottom of the flume was flat and smooth. Grid size was set as 1 cm

1 cm (the number of grids was 200 and 30 in the x-direction and y-direction,

respectively) to resolve the flows around the large wood with a diameter of 1 cm. The initial time t) was 0.0035 s, and the total simulation time was 70 s. Large wood pieces were supplied

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step

one by one every 4 s after the flow reached a stable condition (no back water effect close to the obstacle) in the same manner in which 10 pieces were supplied in the experimental cases. We

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reduced the simulation time using the parallelization method (OpenMP).

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Figure 2. Bed friction depending on the stem-wise angle of large wood (where the root wad component is expressed as a sphere with twice the diameter at one end of the large wood piece in the simulation).

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3.1 Particle method for modeling large wood dynamics 3.1.1 Governing equation for the large wood motion

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The large wood dynamics equation ([29]-[31]) in Cartesian coordinates is described as follows: {

(1-1)

where | (

(1-2)

)

(1-3)

(

{

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|

)

|

(1-5)

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|

(1-4)

The bed friction coefficient ( ) in Equation (1-5), which is an anisotropic friction

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coefficient, is changed by the stemwise angle of the wood piece (Figure 2). This parameter is expressed by Equations (1-6) and (1-7).

(1-6)

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√ √

(1-7)

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where ρ is the water density; σ is the density of large wood; CM is an additional mass coefficient (CM = 0.5 was used in this work); CD is the drag coefficient; A2 is the 2D shape coefficient (π/4 in this work); A3 is the 3D shape coefficient (π/6 in this work); d is the diameter of the particle

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sphere; u is the fluid velocity around the sphere; up is the velocity of the sphere; ν is the kinematic viscosity coefficient; t is time; g is gravitational acceleration; components of the friction coefficient, respectively; angle matching the x axis direction);

and

are the x and y

is the stemwise angle ( = 0 indicates the

is the number of particles for one large wood piece;

is the sliding friction coefficient (s = static, k = kinematic); Fbed is the bed friction force;

s or k

A-sub

is

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the submerged area rate;

V-sub

is the submerged volume rate; FD is the drag force; Fwa is the

effect of the acceleration of surrounding water; Fam is the effect of the added mass of water; hc is the critical draft for wood motion. When calculating sliding friction (Equations (1-6) and (1-7)), s or k)

should be multiplied by the total number of spherical

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the sliding friction coefficient (

particles ( ) in the large wood because the sliding frictions of all particles are in the same

direction and move as one material. The following drag force terms caused by the large wood are added for the Eulerian momentum equation for water flows: 1 1 ρCD 2 hAcell

N cell

A

n



ui -uip ui -uip



n =1

(1-8)

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Fdr  

where An is the projected area of a particle toward the flow direction; Acell is the area of a grid cell; and i is the number of particles in the large wood piece.

The present study neglects the effect of collisions among large wood pieces to focus on the large wood advection and deposition patterns. Therefore, each large wood dynamic is

independent. However, this numerical analysis includes motion that is indirectly changed by the

causing drag force and changing water depth.

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3.1.2 Anisotropic friction coefficient

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water alterations due to adjacent large wood because such a large wood piece is modeled as

The static friction coefficient between the wood used to construct the flume bed and the large wood is generally approximately 0.4–0.6 [35]. The friction coefficient under submerged

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conditions is uncertain; however, it may be expected to decrease. Therefore, we conducted trials to compare the experiment and simulation and adjusted the friction coefficients accordingly (Table 3). The static ( s) and dynamic ( k) friction coefficients refer to the cases when large

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wood is deposited and sliding, respectively. These coefficients are valid in the stemwise direction of the wood piece. If large wood slides in the direction perpendicular to the stemwise

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direction, the large wood rolls, and rolling friction becomes dominant. Table 3 shows the static, kinematic, and rolling friction coefficients.

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Table 3. Bed friction coefficients Friction coefficient

Value

Static friction coefficient ( )

0.4 )

Rolling friction coefficient (

0.05

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Kinematic friction coefficient ( )

0.001

3.1.3 Buoyancy and critical draft for wood motion

One important factor that affects large wood deposition is its buoyancy. This study

considers the sphere-by-sphere transition of the submerged volume based on the change in flow

depth and the presence of a root wad. In addition, the inclination of the settled large wood based

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on the root wad shape is considered to evaluate buoyancy. The large wood is deposited if

buoyancy is less than the weight of the large wood. The large wood floats if buoyancy is larger than gravitational force. If the density of the large wood is less than the water density, the draft of the large wood is determined by the balance between buoyancy and weight. The water depth that is the same as the draft is referred to as the critical draft for wood motion (CDM). In other words, the CDM is the minimum depth at which the large wood does not touch the bed. The

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CDM (hc) is the same as the maximum draft in the floating condition, which can be obtained as follows. The maximum unsubmerged volume of the large wood is calculated using Equation (2-

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1). 𝑉

,𝑊

𝜋

,𝐵

𝜋

(2-1)

where r is the diameter of a large wood particle; Wd is the weight of a large wood particle under

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the totally submerged condition; Bw is the buoyancy under the totally submerged condition; Ve is the unsubmerged volume of a particle under the totally floating condition (Figure 3).

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We can obtain the maximum unsubmerged volume, Ve, from Equation (2-1) and the submerged volume, Vs, using Equation (2-2).

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𝑉

𝑓 𝑦

√𝑟

𝑦

∫ 𝑓 𝑦 𝜋 𝑦, 𝜋∫ 𝑟

𝑦

𝑦

𝜋 [𝑟 𝑦

𝑦 ] (2-2)

𝜋 [(𝑟 𝑎

3

𝑎 )

(𝑟

3

𝑟 )]

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The unsubmerged volume, Ve, can also be calculated by Equation (2-11) from Equations (2-1) and (2-2). 𝑉

𝑉, 𝑉

𝜋𝑟

(2-3)

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𝑉

where Vs is the submerged volume of the large wood particle; Vt is the volume of the large wood

particle; ac is the water level from the center of the particle (Figure 3). We can obtain the CDM by iteratively executing these equations.

We assume that the diameter of a root wad particle is twice the diameter of a stem particle to model the different drag force and buoyancy of the root. The drag force of a root

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particle is larger than that of a stem particle because of the larger projection area of the root,

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whereas the weight of the root is large because of its increased volume at the same density.

Figure 3. CDM concept for each large wood particle in cross-sectional view: (left) structure of

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submerged large wood particle and (right) geometry of critical draft for wood motion. 3.1.4 Change in water depth by root effect

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When a root wad of floating large wood (Figure 4(a)) becomes deposited on the bed at a lower water depth than the CDM, the root wad effect is activated, thereby decreasing the draft of the wood piece (Figure 4(b)). The root wad lifts one edge of the stem up from the river bed; thus, the submerged volume of the large wood decreases. Then, the influence of buoyancy is decreases, and the normal force to the bed increases compared to the case of a large wood piece

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with no root wad. In the computation, we first determine the CDM of each particle in the large wood piece. Then, the change in water depth caused by the root wad effect is applied as follows

4(c)): ,

,

√

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if the average CDM of the large wood particles is lower than the present water depth (Figure

(3-1)

where hs is the present water depth under the root particle; hp is half the difference between the

stem diameter and root diameter; Ld is the stem length; La is the projection length of the stem into i the river bed; hr is the increase in height caused by the root effect; hsn is the calculated water p

wood; ip is the index of each particle. a)

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b)

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depth caused by the root effect for each particle; ipn, is the total number of particles in the large

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c)

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Figure 4. Change in draft of large wood because of the root wad effect: a) floating large wood, b) deposition of large wood, and c) change in draft of large wood.

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3.2 Interaction between water flow and large wood in the computation In this solver, the calculation schemes for water flow and large wood are different. In the

present large wood dynamics model, one large wood piece is expressed as connected particles, which are driven following the Lagrangian method. Therefore, a method for modeling the

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interaction between grid-based water flow and particle-based large wood motion is required. Accordingly, we use linear interpolation (Figure 5) to obtain the flow velocity and water depth at target points on the particles that compose the large wood. If each particle is located at an

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arbitrary position, the relative length (la, lb) from a standard grid point (F1) to the center of the particle can be calculated to determine the inverse distance weight. Here, all grid lengths

between all grid points are 1 on the generalized curvilinear coordinate system. Then, the value at the particle center (Fip) is calculated with reference to the values at four surrounding grid points

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using Equations (4-1) and (4-2).

Figure 5. Linear interpolation in the particle characterization area to determine the flow velocity and water depth based on a generalized curvilinear coordinate system. 4

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A

Fip 

k 1 4



k

1 Ak

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k 1

Fk

A1  la  lb , A2  la  1  lb  , A3  1  la   1  lb  , A4  1  la   lb

(4-1)

(4-2)

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where Fip is the interpolated value at the particle center; F1–F4 are the grid nodes in the  and  directions ( and  are generalized curvilinear coordinates); A1–A4 are the weighting areas considering the inverse distance from the particle (Fip); la and lb are the relative lengths from the target point based on the standard grid point (F1). The values of la and lb are 0 if the positions of F1 and Fip are the same. k is the index for the grid point.

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Through this interpolation, we can obtain the interpolated flow velocity and water depth values at each particle location from a grid node point in the generalized curvilinear coordinate

wood motion. The specific calculation procedure is as follows: 1) Water flow is calculated using the 2D shallow flow model based on Nays2DH.

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system. Figure 6 shows the process of calculating the interaction between water flow and large

2) The submerged volume of the large wood is calculated considering buoyancy and the CDM. If the large wood contains a root component, the CDM and submerged volume are recalculated.

3) The bed friction acting on the large wood is determined considering the CDM. No bed friction

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is applied to the large wood motion if the large wood is located at a water depth higher than the

CDM. The bed friction coefficient models static friction with rolling friction if the large wood is stopped; otherwise, the bed friction coefficient models kinematic friction with rolling friction. 4) Large wood particle velocity is calculated based on drag force with reference to water flow velocity. Bed friction is considered if the draft of the large wood particle is less than the CDM. 5) From the particle velocity calculation, the advection of each particle is calculated separately

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without connection for one time step (t). Then, the new location of the gravitational center of the large wood is determined by averaging the new particle locations. In each particle, the

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rotation angle of the large wood is calculated by averaging the rotation angle of each particle in relation to the center of gravity of the large wood piece (Figure 6(b)). 6) The position of each particle is rearranged into the shape of the large wood considering the

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averaged rotation angle and center of gravity (Figure 6(b)). 7) From the rearranged large wood, drag force is calculated and applied to the water flow

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calculation in the next time step.

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Figure 6. Calculation process of the water flow model and large wood dynamics model: a)

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algorithm for calculating the coupled dynamics of water flow and large wood motion and b) concept of the large wood dynamics model (cross shape indicates the center of gravity).

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3.3 Validation of simulation results for flow depth Figure 7 illustrates the final pattern of the flow velocity vector and water depth in the computational domain. The constriction caused by obstacle forces can cause a transition to

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subcritical flow upstream of the obstacle because the energy of the flow is lower than the minimum energy required to pass through the narrow section. Water depth rapidly decreases

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close to downstream obstacles because supercritical flow is dominant owing to the smooth bed. The effect of localized narrowing depends on the Froude number of the unaffected flow (upstream of obstacle) and on the constriction ratio (width of narrow section/width of wide section). In other words, water flow is supercritical with higher velocity and lower depth with respect to the nonuniform flow conditions. In addition, it tends asymptotically to uniform flow.

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Similarly, in the experiment (Figure 8), a hydraulic jump was observed because of the transition of water flow from supercritical flow. Figure 8 compares the water depth along the centerline between the simulations (at the final computation step) and experiments. The red box in these

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figures marks an obstacle section. Even though the simulation result overestimates the flow

depth upstream of the obstacle, this inconsistency can be neglected because we focused on the area downstream of the obstacle. In the downstream section, the difference between the simulation and experimental results is small. Therefore, the present flow model can be considered to capture flow depth well.

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a) S = 0.0045, Q = 0.00065

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b) S = 0.0070, Q = 0.00060

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d) S = 0.0070, Q = 0.0011

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c) S = 0.0045, Q = 0.0010

Figure 7. Final pattern of flow depth and the velocity vector in the simulation result (S is the

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channel slope (m/m), and Q is the flow discharge (m3/s)).

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Figure 8. Comparison of water depth between the experiments and simulations (red box indicates an obstacle): a) low discharge case (Sim1 and Exp1: S = 0.0045, Q = 0.00065, Sim2

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and Exp2: S = 0.0070, Q = 0.00060); b) large discharge case (Sim3 and Exp3: S = 0.0045, Q = 0.0010, Sim4 and Exp4: S = 0.0070, Q = 0.0011); S: channel slope (m/m); Q: flow discharge

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(m3/s).

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4. Results of the experiments and simulations 4.1 Large wood pieces with no root wad (cases 1–4)

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As shown in Table 2, we conducted eight cases of experiments and simulations. This section

describes the results of cases 1–4, which considered the wood piece without a root wad. Note that no

figure for the simulation results is presented in this paper. Only experiment results are shown in Figure 9 because none of the wood pieces without a root wad were deposited in the simulation results. The

experimental results show that the wood piece without a root wad can become deposited close to the

side wall (Figure 9). This is in contrast to the simulation results, which indicated that no deposition of

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wood pieces occurred in the flume channel. Rolling friction was dominant in the experiments; hence,

when the wood piece was touched the bed, it was immediately flowed by floating and rolling motion. We considered that the applicability of the depth-averaged 2D model was relatively poor close to the side wall because the strong secondary current at the corner between the bed and sidewall was not considered in the present 2D flow model, and this secondary current increased flow resistance. In addition, the simulations only considered the motion of the wood piece in the horizontal direction and

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neglected the advection in the vertical direction; thus, the downward motion of the wood piece induced

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by secondary flow was neglected.

Figure 9. Results of the experiments using the wood piece without root wad: a) Case 1, b) Case 2, c) Case 3, and d) Case 4.

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4.2 Large wood pieces with root wad (cases 5–8) In the simulations, the wood pieces without a root wad showed no deposition. However,

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the wood pieces with a root wad clearly exhibited deposition. Figure 10 illustrates the change in the proportion of the deposited wood with time. The range of the final proportion of the

deposited wood pieces in the simulation results (30–100%) reproduced the experimental results (20–80%) well. In particular, the deepening on the discharge increased, and the decrease in the proportion of the deposited wood pieces with time was similar between the simulation and

experimental results. On the contrary, the responses of the changes in channel slope were unclear

affect the motion of the wood pieces.

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because channel slope changed only flow dispersion (Figure 7), which may be insufficient to

We measured the final averaged position considering the center of gravity of a wood piece in a normalized coordinate system using flume width and length to compare the final

deposition patterns obtained through the experiments and simulations (Figure 10). Figure 11(a)

b)

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a)

d)

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c)

Figure 10. Change in the number of stored wood pieces with time: a) Case 5, b) Case 6, c) Case 7, and d) Case 8. (Exp. D and Sim. D: the number of stored wood pieces).

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b)

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a)

Figure 11. Final average position in the deposition of the wood pieces: a) average position in the

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streamwise direction and b) average position in the lateral direction.

shows the final averaged deposition in the streamwise direction, while Figure 11(b) presents the distribution of the wood deposition in the lateral direction (mean deviation value). In Figure 11(a), values of 1 and 0 indicate that all wood pieces are deposited downstream and upstream, respectively. Figure 11(b) indicates the wood deposition in the lateral direction, where values of

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0 and 1 indicate that the wood pieces are deposited along the channel centerline and close to a wall, respectively.

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According to Figure 11(a), if flow discharge is larger (cases 6 and 8), the value of the average position increases in the streamwise direction because the larger flow discharge increases water depth and flow velocity. Thus, drag force increases, and the influence of

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buoyancy becomes strong. The average values in Figure 11(b) show an unclear relation between wood piece deposition and two parameters (i.e., discharge and channel slope) because the wood

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piece deposition in the lateral direction depends on several parameters such as the strength of secondary flow, the angle of stem direction, and the initial position in the lateral direction. The initial conditions must be controlled more strictly (e.g., the input stemwise angle of the wood

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piece and input position should be set uniformly) to analyze this relation. Figure 12 shows the experimental and simulation results for the wood pieces with a root

wad. In the simulation results, the yellow items represent the wood piece, where the large head is a root and the small head is the opposite side. Two types of contours are indicated, i.e., water

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Table 4. Averaged final stemwise angle of the wood pieces (°)

Case 6

Case 7

Case 8

Simulation

20.41

12.98

20.84

17.84

Experiment

24.40

15.25

32.75

8.50

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Case 5

depth (0–0.025 m) and flow velocity (0–1 m/s). In this work, we focus on distances up to 80 cm from the obstacles.

Once a wood piece is deposited on the center of the flume bed, other wood pieces can

easily become deposited around the first piece because the settled wood piece exerts drag force

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on flow, decelerating flow velocity and increasing water depth. Thus, when the large wood

settles on the bed, it acts like vegetation. This implies that future work should carefully consider the bed morphology around settled large wood in actual rivers. Vegetation is known to increase the flow resistance and water level around it such that the vegetation area captures sediment even though the immediately adjacent area is eroded by increased flow velocity (e.g., [36]-[38]). Similar bed shape changes can be expected around settled large wood.

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The wood pieces with a root wad face upstream because the root lifts the wood piece from the bed when the wood piece flows into a zone with lower water depth. This lifting

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decreases the draft for the root wad section. The deposited wood piece tends to maintain the deposited state by reducing the projection area of the wood piece (e.g., [39]); hence, the stem section is immediately rotated to be parallel to the flow direction. We found that the angle of the

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deposited wood piece tends to depend on the flow discharge (Figure 12). As shown in Table 4, when the flow discharge is larger (cases 6 and 8), the angle between the streamwise and stemwise directions of the wood piece decreases as compared to the angle in the cases with

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smaller discharge (cases 5 and 7). This result indicates that the change in the deposition angle is associated with the projection area affected by the flow discharge [40]. However, the strength of

Comment [21]: R-1

the relationship between the discharge and the deposition angle due to the projection area is

I added reference (Wilcox and Wohl, 2006).

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unclear and should be further analyzed

c)

d)

e)

f)

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b)

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a)

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h)

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g)

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Figure 12. Experimental and simulation results for the deposition of wood pieces with root wad: Experimental results are for a) Case 5, c) Case 6, e) Case 7, and g) Case 8 and Simulation results are for b) Case 5, d) Case 6, f) Case 7, and h) Case 8.

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5. Discussion The results of the simulations and experiments showed that two deposition patterns are dominant in the presence and absence of root wads i.e., at the center of the flume and close to the

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side walls (Figure 13).

The water depth upstream of the obstacle is larger (>1.2 cm) than that of the CDM (root:

1.2 cm, stem: 0.6 cm); hence, all the wood pieces flow downstream. After passing the obstacles, the water depth becomes smaller than that in the CDM, and the wood pieces touch the bed

around the center of the flume. In this region, if the drag force is sufficient to drive a wood piece, sliding motion of the wood piece occurs and the piece may gradually flow downstream. In

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addition, the wood piece rotates in its stemwise direction along with the flow direction because

the increased flow velocity in the narrowing section enhances the drag force around the obstacle (Figure 13(a) and (b)). The wood piece with a root wad can easily be deposited after passing the obstacle because of the decrease in draft for wood motion at the root wad part, even though the diameter of the root wad is larger than that of the stem. The wood piece with the root wad is easily subjected to a larger drag force because the root wad can lift the head of the wood piece

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from the flume bed. This is because when the root first touches the flume bed, the buoyancy of the wood piece decreases owing to the decrease in the draft caused by the root wad [41],[42].

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After the wood piece comes into contact with the flume bed, the water depth around the wood piece and the velocity head increase because the wood piece affects the flow of water. This increases the buoyancy and drag force, and thus, the wood piece shifts toward the flume walls by

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rolling, even though the friction force in the stemwise direction remains larger (Figure 13(c)). If the root wad of the wood piece sticks to the flume walls, the wood piece settles in a stable manner and decelerates the water flow around it. Then, the wood piece can be considered to be Comment [22]: R-1

pieces are frequently deposited on the lateral margins (wall or bank) of a channel through a

I added this sentence considering the reference (Wilcox and Wohl, 2006).

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completely deposited near the walls [40]. Braudrick et al. (1997) [18] demonstrated that wood

flume experiment, and Braudrick and Grant (2000) [19] presented three equations to analyze the

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flotation threshold for wood motion for diverse densities. However, these studies neglected the bed friction for wood motion in the presented equations. On the contrary, the present study shows that rolling motion is a factor for deposition on lateral margins. Moreover, the flow velocity downstream of the obstacle has a component directed toward the wall as steering flow caused by the channel geometry close to the obstacle (Figure 7). This rolling occurs because the

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sliding friction (static

= 0.4 and kinematic

= 0.05) along the stemwise direction is

considerably larger than that along the lateral direction, in which the friction for wood motion is governed by rolling friction ( = 0.001) to a higher extent compared to sliding friction. Therefore,

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the wood piece cannot move in the stemwise direction. However, it can move in the lateral

direction; thus, it moves toward a flume wall. The wood piece flows downstream if drag force

and the stemwise angle are larger (Figure 13(d)). The wood piece without a root wad flows more easily downstream because its draft is larger than that of the wood piece with a root wad.

Such a deposition pattern, which is parallel to the flow direction, was observed in the experiments ([24],[25]) and field observations (e.g., Piegay and Gurnell (1997) [43] in the

Comment [23]: Other

Tagliamento River (Italy). However, rolling motion can be limited to occur within the artificial

I corrected this reference.

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Drôme River (France) and by Gurnell et al. (2000) [12] and Bertoldi et al. (2013) [44] in the

hydraulic structure, which contains a rigid and flat channel bed. This is because in the natural system, most channel beds are not flat in shape owing to sediment (e.g., sand, gravel, and boulder).

The results of the experiments and simulations showed that the presence of a root wad

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and the CDM had the most important roles in controlling deposition. Braudrick et al. (1997)[18]

Figure 13. Schematics of large wood deposition patterns.

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experimentally showed that large wood was mainly deposited at the most shallow water depth. Davidson et al. (2015) [45] demonstrated that root wads significantly decreased travel distance. Braudrick and Grant (2000) [19], Merten et al. (2010) [40], and Schenk et al. (2014) [46] showed

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that the presence of root wads is the most important determinant of mobilization and travel distance.

In this study, the root wad particles were regarded as having a diameter larger than that of the trunk particles by a factor of 2. Thus, the root wad particles were more easily subjected to

larger drag forces because of the larger projection area compared to the trunk particles. However, the root wad particles weighed more than the trunk particles, which had the same density, and

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thus, they had a higher CDM compared to the trunk particles. Moreover, we considered the

change in water depth caused by the root wad effect (Figure 3). Therefore, the deposition of a larger number of wood pieces with a root wad was observed in the simulation and experimental results, and the proportion of the deposited wood pieces with a root wad was clearly in good agreement with the experimental results (Figures 10 and 12). Thus, we have shown that the root wad effect is reasonably reproduced by the proposed numerical method and that wood motions

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can be accurately simulated using more diverse root wads (size and density). However, the root wad effect should be carefully refined using more detailed measurements. The present simulation model employed an empirical bed friction coefficient, and the bed friction coefficients of the root

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wad particles and trunk particles were tuned using a trial and error approach through a comparison with the experimental results. In addition, the deposition close to the wall was not reproduced for the wood pieces without a root wad. Thus, the motion of such wood pieces should

of a wood piece.

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also be improved considering several parameters such as the secondary flow and projection area

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This simulation considered a random stemwise angle of the wood piece at the starting zone because the stemwise angle cannot be controlled prior to an obstacle. Therefore, the positions of the wood pieces and the number of wood pieces may show slightly different patterns

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between the simulations and experiments. In the experiments, we observed floating wood pieces close to the obstacle in the upstream direction; these pieces did not flow downstream. This may be because the variable stemwise input angle caused different projection areas for wood motion. If we make the stemwise angle of the wood pieces constant before they pass the obstacle in the

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experiment and simulation, both sets of results may show more regular patterns of wood piece deposition and advection. The responses of the wood motion to the change in the channel slope exhibited an unclear

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pattern. The debris flow on the steep channel exhibited the active motion of large wood because

the steep channel can cause gravity flow through higher potential energy (e.g., [46]-[52]). In this steep channel, the large wood can move downward more easily compared to in a mild channel such as an alluvial river, because of the gravity flow. Such gravity flow was neglected herein

because we used a mild channel slope in the simulations and experiments. Therefore, the change in channel slope should be large to consider the gravity flow due to a steep channel; this will be

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performed in subsequent studies.

In contrast, the present study showed that the motion of the wood pieces is considerably affected by flow discharge. Wilcox and Wohl (2006) [40] conducted an experiment with a laboratory flume for investigating the flow resistance dynamics in step-pool channels,

considering diverse wood profiles, such as the effect of root wad, length of wood piece, and density. Their experiment showed that the wood pieces on the step-pool channels increase the

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water depth because these wood pieces increase the flow resistance. Moreover, they indicated that the position of deposited wood pieces is an important parameter for the flow resistance. The

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wood pieces in the present study exhibited two deposition positions (near walls and at the center in the flume), indicating the occurrence of sliding and rolling motions due to flow discharge. In addition, the deposition angles of the wood pieces were clearly dependent on the flow discharge

large wood dynamics.

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(Table 4). Thus, our study also demonstrated that the flow discharge is an important factor for

Interestingly, the experiments in this study showed simple jam formation by the

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deposited wood pieces (Figure 12). This jam formation was clearly observed when flow discharge was smaller (cases 5 and 7). The jam formation could be accelerated by the first wood

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piece, which could interrupt the motion of subsequent wood pieces. Several researchers (e.g., [18],[24],[25]) showed the characteristics of jam formation based on wood supply, bed elevation, and flow discharge through experiments. However, these studies only conducted a flume experiment, and several researchers are attempting to investigate this using a computational model for jam formation. The computational model is challenging to apply as a large wood

Comment [24]: R-1 I added the part of discussion, considering Wilcox and Wohl (2006).

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dynamics model because multiple parameters should be considered, such as wood collision, large wood shape, profile of the channel bed, and water flow. A large CPU time with a highperformance workstation is required to reproduce a number of wood motions similar to the

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experiments for jam formation. Therefore, our study would provide informative data for the

development of the computational model considering anisotropic bed friction, change in draft for wood motion, and the root wad effect.

The present study focused on the flume scale experiment and the computational model

was validated under such flume scale conditions; however, this model is required to be expanded into large-scale cases for practical purposes. Thus, in a future study, the large wood dynamics

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model should be considered for the natural system associated with the large-scale problem. For

instance, the large wood dynamics model can simulate larger scale experiments [24-25] and river scale observations [12][44]. Through comparisons among the simulation results, the results of the large-scale experiments, and the observations, the applicability of the present computational

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model to large-scale cases should be examined in a future study.

Comment [25]: R-2 I added sentences.

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6. Conclusions This study developed a numerical model for simulating large wood dynamics with floating, sliding, and settling motions in shallow flows by coupling a depth-averaged 2D flow

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model and a Lagrange-type large wood dynamics model. In the present numerical model, we

considered the change in draft for wood motion, anisotropic bed friction, and the root wad effect. The reproducibility of the proposed computational method is generally good. In addition, the

method produces a reasonable simulation of the different deposition patterns in relation to the changes in flow discharge and the root wad effect based on the experiment. The detailed conclusions are as follows:

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1) Responses of the wood motion to flow discharge and channel slope

A wood piece tends to move toward the side walls after touching down on a lower water depth zone because of small rolling friction. Such motion becomes more dominant when flow discharge decreases. In addition, drag force and water depth increase with flow discharge.

Moreover, the wood piece easily flows in the streamwise direction. However, the responses of

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wood motion to the change in channel slope show an unclear pattern because the employed values of channel slope are insufficient to affect wood piece motion.

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2) Root wad effect

In the experiments, a wood piece can become deposited more easily if it contains a root wad because the root wad decreases the draft for the wood motion in the wood piece by lifting its

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head, even though the weight and volume in part of the root wad are larger than the stem of the wood piece. The simulation results clearly reproduce the root wad effect well. However, in cases of wood pieces without a root wad, the experimental results only show deposited wood pieces

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close to the wall. Through these results, we discovered a relationship between the deposition angle of the large wood and flow discharge. The stemwise angle of the deposited wood piece becomes smaller when flow discharge is larger. Consequently, this implies that the deposited

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wood angle is associated with the projection area between the flow discharge and wood piece. Thus, further study should consider additional parameters, such as the projection area of the wood piece, considering the angle between the stemwise and streamwise directions. 3) Limitations of the developed model

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In the experimental and simulation results, the wood piece with a root wad tends to move toward the side walls because of the smaller rolling friction coefficient. We considered the shape of the wood piece stem to be a cylinder in the experiment. In the simulation, we considered the

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wood piece as a spherical particle. Therefore, the rolling friction coefficient is relatively smaller

than that of natural large wood, which contains branches, rough surfaces, and irregularly shaped

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cross sections.

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ACKNOWLEDGMENT We are thankful to the Ministry of Science & Technology (MEXT) and The River Foundation

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for providing funding for this research.

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I corrected this reference.