Influence of Bioroughness Density on Turbulence Characteristics in Open-Channel Flows

Chen, Zonghong; He, Guojian; Fang, Hongwei; Liu, Yan; Dey, Subhasish

doi:10.1061/JHEND8.HYENG-13704

Open access

Technical Papers

May 6, 2024

Influence of Bioroughness Density on Turbulence Characteristics in Open-Channel Flows

Authors: Zonghong Chen [email protected], Guojian He, M.ASCE https://orcid.org/0000-0003-2504-2904 [email protected], Hongwei Fang, M.ASCE [email protected], Yan Liu [email protected], and Subhasish Dey, M.ASCE [email protected]Author Affiliations

Publication: Journal of Hydraulic Engineering

Volume 150, Issue 4

https://doi.org/10.1061/JHEND8.HYENG-13704

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Abstract

Bioroughness plays an important role in modifying the velocity and sediment flux near the riverbed. It is therefore pertinent to study the influence of benthic fauna on the bed forms. To this end, large-eddy simulations are performed to investigate the influence of the arrays of mounds and their density on the turbulence characteristics in an open-channel flow. The simulated distributions of the time-averaged streamwise velocity and the turbulence intensity are in good agreement with the experimental data. Four numerical simulations are performed with varying streamwise spacings of mounds. Details of the time-averaged and instantaneous flow velocities are analyzed by multiple visualization methods, and the effects of the bioroughness density on the equivalent roughness height and the Darcy–Weisbach friction factor are quantified. The time-averaged flow in the wake of the mounds is characterized by a symmetric pair of vortices. The mounds behave like bluff bodies, increasing the riverbed roughness and heterogeneity in the flow environment. An increase in mound density is to promote the development of secondary currents and to increase the dispersive stress near the bed. The peaks of the Reynolds shear stress distributions decrease in both the streamwise and vertical directions for the high-density case due to a blockage effect. The instantaneous flow features, in the form of various turbulence structures, are generated near the top edge and the wake zone of mounds. The spacing between low-speed streaks decreases with an increase in equivalent roughness height. Multifrequency behavior that is observed is a result of shear layer roll-up from the edges of mounds and the flapping of wake. Finally, two formulas for equivalent roughness height and Darcy–Weisbach friction factor are proposed involving the bioroughness density and height. The findings demonstrate the effects of the bioroughness on the near-bed turbulence characteristics and sediment stability.

Practical Applications

Bed forms produced by aquatic benthos are usually of small scale but with a large abundance. We performed a flume experiment as well as large-eddy simulations (a high-fidelity numerical simulation approach) to answer whether these microtopographies are important when studying flow and transport processes near the riverbeds. Four numerical simulations are performed with varying mound density. It was found that the microtopographies created by benthos indeed change the near-bed turbulence characteristics and sediment stability. Specifically at high abundances, benthos-induced bed forms could raise the bed roughness and the friction factor eightfold and threefold, respectively. This suggests the necessity of a modified roughness height formula and a friction coefficient formula based on the benthos abundance, which has been carried out in this study. Thus, engineers who are concerned with the flow and sediment transport in habitats of high-abundance benthos (e.g., wetlands and estuaries) may prefer to use these modified formulas and to develop a more accurate model of sediment transport.

Introduction

River topography is complex at different scales, ranging from individual sediment grains to sand ripples and dunes. Although intensive studies have focused on the impact of large-scale bed forms on flow and sediment transport (Best 2005; Nikora and Rowinski 2008; Dey and Das 2012; Dey et al. 2020), there are a few studies on the hydrodynamic impact of benthos generated small-scale topographies (henceforth called the bioroughness), although they are commonly observed in rivers, lakes, and coasts (Dinehart 1992; Huettel and Gust 1992). For example, Zimmermann and Lapointe (2005) and Hassan et al. (2008) found that spawning salmons construct redds, disturbing the coarse sediment surfaces of riverbeds. Albertson and Daniels (2016) observed that crayfish locomotion in gravel substrates results in pits and mounds affecting the near-bed hydrodynamics.

Field research has revealed that impacts of bioroughness on the flow field and sediment fluxes are not negligible, particularly the aggregate effect of high benthos density (Rice 2021). Jones et al. (2011) found that benthic clams produced bioroughness of 1-cm height, which caused to reduce the near-bed (2 cm above beds) flow velocity by 40%. Guillén et al. (2008) reported that the bioroughness of 0.27–0.81-cm height accounted for about 20% of the total bed roughness in the sea bottom on the Ebro Delta coast. Bioturbation of fine sediments by crayfish contributed a minimum of

569 kg / month

to suspended sediment flux in the River Nene (Rice et al. 2016). However, Zimmerman and de Szalay (2007) found that when mussels were more sessile, they were to increase the shear strength of bed sediment by 24% over controls, which helped to resist erosion. In order to systematically quantify the effects of bioroughness and density on the sediment transport and to explain the results of the observed opposites, the influence of bioroughness on turbulent flow field is required to be well understood.

Earlier flume studies threw light on the flow patterns around isolated bioroughness elements in open-channel flows (Roy et al. 2002; Muzzammil and Gangadhariah 2003; Papanicolaou et al. 2012). Through particle image velocimetry measurements, the formation, shape, and coherence of the main vortex developing close to a mussel were captured precisely (Constantinescu et al. 2013). Besides, a mussel-covered bed was quantified to alter bed roughness and near-bed turbulent flow (Sansom et al. 2018). Mounds formed by crayfish on sandy beds can increase the turbulence anisotropy in the near-bed flow, generate acceleration and deceleration zones, and create more turbulence structures (Carollo and Ferro 2021). Furthermore, pits, such as egg redds, could cause to decrease the near-bed flow velocity due to an increase in vertical depth (Cardenas et al. 2016). However, it is difficult to obtain the flow information near bioroughness at high densities in flume experiments.

Recently, sophisticated high-resolution numerical simulation approaches, such as large-eddy simulation (LES), have been successfully applied to investigate the flow and transport processes near bioroughness at the sediment–water interface (SWI) (Han et al. 2019; Liu et al. 2019; Wu et al. 2020; Wu and Constantinescu 2022). Han et al. (2019) developed a LES model to simulate the impact of pits and mounds on near-bed and subsurface flow. Liu et al. (2019) simulated turbulent flow over mounds and burrows created by ghost shrimp to study the oxygen transport near the SWI. They found that the mounds and burrows enhanced oxygen flux across the SWI, which can be well described by a formula considering bioroughness densities. Wu et al. (2020) investigated the influence of a cluster of mussels on the turbulent flow field. They found necklace vortices formed close to a cluster of mussels affecting the sediment entrainment near mussels. Furthermore, numerical simulations are still needed to explain the zoogeomorphic mechanisms, especially the nonlinear interactions at high bioroughness density.

Compared with other natural or artificial bed roughness, for example boulder arrays (Liu et al. 2017; Wang et al. 2022c) or submerged vegetation (Lou et al. 2022; Wang et al. 2022a, b), bioroughness exhibits a larger density variation. The density of bioroughness is related to the species of benthos that create it. Typical density of the U-shaped burrows generated by midge larva Chironomus plumosus is 1,000 individuals per

m^{2}

(

ind. / m^{2}

) (Brand et al. 2013), whereas that of the U-shaped burrows of mud shrimp Callianassa truncata is

120 in d . / m^{2}

(Ziebis et al. 1996).

Hydrodynamics influence the population of bioroughness as well. For example, the population of benthos is about

20 in d . / m^{2}

in the high-discharged Yangtze River near Yichang City, China (Zhang et al. 2022), whereas in the Dongting Lake, a lake connected to the Yangtze River near Yichang City, the population of benthos increases to

187 in d . / m^{2}

(Wang et al. 2016). Other parameters, like seasons (Zou et al. 2018) and nutrients (Pascal et al. 2022), also contribute to the large variation of bioroughness density. In flow over other bed roughness, it has been well recognized that roughness density is a key parameter influencing the in-canopy flow velocity (Nepf 2012), vortex structures (Wang et al. 2022), and bed-load transport rate (Fang et al. 2018). However, it is not well understood how the flow field and sediment transport are influenced by these small-scale but high-density-variation bioroughness.

In this study, to investigate the influence of the bioroughness density on the turbulence characteristics, the LES was used to simulate flow over arrays of mounds. Data from a flume experiment were compared in order to validate the accuracy of the numerical models. The objective of the study reported here is to explore the following research questions:

•

How does the bioroughness influence the near-bed flow field locally and globally?

•

What is the role of the density of bioroughness to modify the near-bed turbulence characteristics?

•

How can the influence of bioroughness density on equivalent roughness height and Darcy–Weisbach friction factor be quantified?

The remainder of this paper is organized as follows. The flume experiment, the numerical framework, and the numerical setup and boundary conditions are introduced in the “Methodology” section. First- and second-order turbulence statistics are presented in the first part of the “Results” section to validate the numerical simulation. The time-averaged and instantaneous flows around the bioroughness are analyzed by multiple visualization methods in the second and third parts of the “Results” section. Then, quantification of the influence of the bioroughness density on the equivalent roughness height and Darcy–Weisbach friction factor, the comparison of mounds to other types of roughness elements, and the implications and limitations of this study are discussed in the “Discussion” section. Finally, conclusions are drawn in the last section.

Methodology

Experimentation

Based on a literature review (Huettel and Gust 1992; Volkenborn et al. 2012; Liu et al. 2019; Wu et al. 2020), common bioroughness can be divided into three categories, as given in Table 1. In an earlier study (Han et al. 2019), it was recognized that recess has little influence on the flow field. Researchers (Constantinescu et al. 2013; Wu and Constantinescu 2022; Wu et al. 2020) intensively investigated the influence of mussels on the flow field (isolated mussels, mussel filtered flow rate, and mussel facing angles), little is known about the effects caused by protrusions bioroughness and the density for the three kinds of bioroughness.

Table 1. Common categories of bioroughness

Categories	Bioroughness
Recesses	Trails, burrows, funnels, tubes, and egg redds
Protrusions	Mounds and siphons
Bodies	Mussels, chironomus, and crayfish

Among protrusion bioroughnesses, mounds of circular truncated cone shape are the most common (Huettel and Gust 1992; Volkenborn et al. 2012; Liu et al. 2019; Han et al. 2019) because benthos digs burrows and extracts sediments from their burrows. The extracted sediments accumulate at burrow openings and slide due to gravity and then automatically form circular truncated cone shape (Kristensen et al. 2012). This was confirmed from the visualization through video by Volkenborn et al. (2012). Therefore, in this study, representative mounds of circular truncated cone shapes were selected for the experiments. Besides, the typical habitat conditions of Callianassa truncata (Decapoda: Thalassinidea), described by Ziebis et al. (1996), were considered in experiments and simulations, such as flow velocity, mound geometry, and density. They are described in detail as follows.

Laboratory experiments were conducted in a 16-m-long, 0.5-m-wide, and 0.5-m-deep rectangular tilting flume at the State Key Laboratory of Hydro-Science and Engineering, Tsinghua University, Beijing (Fig. 1). A flow circulation device was installed to provide a steady flow condition, and a flow stabilizer was applied to avoid large-scale motions at the entrance. The average flow velocity and flow depth were set as

0.2 m / s

and 0.10 m, respectively, corresponding to a Reynolds number (

R e

) of 20,000 and an aspect ratio (ratio of channel width to flow depth) of 5. Thus, the effect of the secondary currents was minimal (Nezu and Rodi 1986).

Fig. 1. Top view of the flume showing the zone of simulated bioroughness within the dashed box with solid dots representing the individual bioroughness.

The mounds were simulated as a circular truncated cone made of nylon with bottom and top radii of 2 and 1 cm, respectively, having a height of 1 cm. The mounds were placed 5 m away from the flume inlet, and 3 m away from the flume outlet, with a total length of 8 m. The bioroughness was arranged in a staggered manner with the same streamwise (

x

-direction) and spanwise (

y

-direction) spacings of 10 cm. This gave a mound density of

100 in d . / m^{2}

[Fig. 2(a)], which was similar to the field observation of Ziebis et al. (1996).

Fig. 2. (a) Top view of the monitored bioroughness zone in the flume (dashed box shown in Fig. 1) with the concentric circles representing the bioroughness; and (b) elevation view of the monitored bioroughness zone along the spanwise midsection of the flume. Solid trapezoids represent bioroughness, open trapezoid represents near bioroughness, and the squares with crosses at the center represent the ADV measuring points.

An acoustic Doppler velocimeter (ADV) with a side-looking probe was used to measure the streamwise flow velocity at four vertical distances

z = 2

, 4, 6, and 8 cm, as shown in Fig. 2(b). Velocities were recorded over a period of 2 min at each location at a sampling frequency of 100 Hz. The acoustic frequency was 10 MHz in the experiment. The measurement was taken at

y = 25 cm

and

x = 25 cm

, i.e., the spanwise midsection of the flume and 625 cm downstream of the front edge of the roughness elements. It was also sufficiently away from the downstream tailgate, which ensured the development of a rough-wall turbulent flow (Tachie et al. 2004). Besides, the other three test vertical lines were located at

x = 5

, 10, and 15 cm downstream of the center point of this mound.

Numerical Method

In this study, a LES code called Hydro3D version 6.0, which was extensively validated in several flow conditions of similar complexity, was applied to simulate turbulent flow in an open channel (Kim and Stoesser 2011; Bai et al. 2013; Liu et al. 2022; Zhao et al. 2022). Based on finite differences on a staggered Cartesian grid, Hydro3D solves the filtered Navier–Stokes equations for incompressible, unsteady, and viscous flow

\frac{\partial u_{i}}{\partial x_{i}} = 0

(1)

\frac{\partial u_{i}}{\partial t} + \frac{\partial u_{i} u_{j}}{\partial x_{j}} = - \frac{1}{ρ} \frac{\partial p}{\partial x_{j}} + \frac{\partial (2 υ S_{i j})}{\partial x_{j}} - \frac{\partial τ_{i j}}{\partial x_{j}}

(2)

where

u_{i}

and

u_{j}

are the spatially resolved velocity vectors (

i

or

j = 1

, 2, and 3 represent

x

-,

y

-, and

z

-directions, respectively);

x_{i}

is the spatial location vectors in the three directions;

t

= time;

ρ

= mass density of fluid;

p

= resolved pressure;

υ

= fluid kinematic viscosity;

S_{i j}

is the strain-rate tensor given by

(\partial u_{i} / \partial x_{j} + \partial u_{j} / \partial x_{i}) / 2

; and

τ_{i j}

= subgrid-scale (SGS) stress defined by

- 2 υ_{t} S_{i j}

. Here, the wall-adapting local eddy viscosity (WALE) is used to compute

u_{t}

(Nicoud and Ducros 1999).

The convection and diffusion terms in the Navier–Stokes equations are estimated by fourth-order accurate central differences. An explicit three-step Runge–Kutta scheme is employed to integrate the equations in time, providing second-order accuracy. Within the time step, convection and diffusion terms are solved first explicitly in a predictor step, which is followed by a corrector step during which the pressure and divergence-free-velocity fields are obtained through a Poisson equation. The latter is solved iteratively through a multigrid procedure. More details about Hydro3D has been given by Ouro et al. (2019).

Numerical Experiments

Numerical simulations of the flow over an array of staggered mounds with different densities were arranged to explore the turbulence characteristics in the riverbed covered with bioroughness. The dimensions of mounds were the same as those used in the flume experiments of this study, and the computational domain for all simulations was

80 \times 50 \times 10 cm

(

x \times y \times z

). Four cases (T1–T4) were performed in which bioroughness was placed on the bed with a different streamwise spacing of 40, 20, 10, and 5 cm (25, 50, 100, and 200

ind. / m^{2}

), respectively. The spanwise spacing was maintained at 10 cm. Figs. 3(a–d) show the geometrical configurations of the four cases.

Fig. 3. Computational domains for (a) Case T1; (b) Case T2; (c) Case T3; and (d) T4. Validation Case T0 is similar to Case T3 but without spanwise bioroughness near the wall for solid wall boundary condition.

All simulations were carried out with a bulk flow velocity

U_{b} = 0.20 m / s

, corresponding to a Reynolds number of 20,000 and a Froude number of 0.2 (Table 2). In addition, a validation case (Case T0) was conducted to confirm the accuracy of the numerical model, in which the mounds’ arrangement, flow condition, and boundary condition were consistent with the flume experiment.

Table 2. Fluid parameters for Cases T0–T4

Case	Flow depth, $h$ (m)	Mean flow velocity, $U_{b}$ (m $s^{- 1}$ )	Reynolds number, $R e$	Froude number, $F r$	Density ( $ind. / m^{2}$ )
T0	0.10	0.20	20,000	0.20	100
T1	0.10	0.20	20,000	0.20	25
T2	0.10	0.20	20,000	0.20	50
T3	0.10	0.20	20,000	0.20	100
T4	0.10	0.20	20,000	0.20	200

Periodic boundary conditions were applied in both the streamwise and spanwise directions for all cases, except for Case T0, where the no-slip condition was applied in the spanwise direction for simulating the solid sidewalls in the flume experiment. Ideally, the boundaries for all cases are kept to be periodic in the streamwise and spanwise directions, because this boundary satisfies large rivers and lakes where benthos live. However, to validate the simulations, the experimental data are required in which the no-slip boundary condition is preserved in the spanwise direction. Thus, T0 is a specific case only for validations. The free-slip boundary condition was applied at the free surface. The surfaces of the mounds and the bed were set as no-slip walls, and a refined version of the direct-forcing immersed-boundary method proposed by Uhlmann (2005) was used in the code (Kara et al. 2015).

All the LES were performed in the Taiyi supercomputer at Southern University of Science and Technology, Shenzhen, China. Case T0 was carried out on a coarse mesh of

400 \times 250 \times 50

, a medium mesh of

800 \times 500 \times 100

, and a fine mesh of

800 \times 500 \times 200

grid points, in the

x

-,

y

-, and

z

-directions, respectively. Then,

Δ x^{+}

,

Δ y^{+}

, and

Δ z^{+}

can be calculated as

(Δ x, Δ y, Δ z / 2) \times (u_{*} / υ)

, respectively, where

u_{*}

is the friction velocity. Table 3 indicates that

Δ x^{+}

and

Δ y^{+}

range from 10.0 to 10.3, and

Δ z^{+}

ranges from 2.5 to 5.1 in fine and medium grids, respectively, indicating a good size to resolve the large scales of turbulence for the LES (Rodi et al. 2013).

Table 3. Grid parameters of the three validation simulations, Case T0, on different grids

Grid	Domain size, $L_{x} \times L_{y} \times L_{z}$ (cm)	Number of points, $N_{x} \times N_{y} \times N_{z}$	Grid spacing, $Δ x$ , $Δ y$ , $Δ z$ (mm)	Dimensionless grid spacing, $Δ x^{+}$ , $Δ y^{+}$ , $Δ z^{+}$
Fine	$80 \times 50 \times 10$	$800 \times 500 \times 200$	1.0, 1.0, 0.5	10.0, 10.0, 2.5
Medium	$80 \times 50 \times 10$	$800 \times 500 \times 100$	1.0, 1.0,1.0	10.3, 10.3, 5.1
Coarse	$80 \times 50 \times 10$	$400 \times 250 \times 50$	2.0, 2.0, 2.0	16.2, 16.2, 8.1

Furthermore, because the mounds produced a fair amount of pressure drag (comprising a large portion of the total drag,

d p / d x

), the formula

ρ u_{*}^{2} = μ d u / d z

was used to calculate

u_{*}

where

d u / d z

was obtained from the spatially averaged near-bed velocity gradient in the location without mounds; and

μ

is the coefficient of dynamic viscosity of water. In Figs. 4(a and b), two-point correlations of streamwise, spanwise, and vertical velocity components are used to verify if the domain was large enough. The data were taken along the streamwise and spanwise directions at an elevation of 5 cm above the bed surface. It can be observed that the correlations decreased to zero within

0.2 L_{x}

or

0.2 L_{y}

; so, the computational area was large enough to include all scales of vortices. Considering both simulation accuracy and efficiency (the detailed validation is given in the succeeding section), the medium mesh was used in performing Cases T1 to T4. Each simulation was initially run for 10 flow-throughs (FTs) to establish fully developed turbulence and then continued for another 30 FTs to collect the turbulence statistics.

Fig. 4. Two-point correlations $R_{i i}$ of the velocity fluctuations in all three spatial directions along the (a) $x$ -axis; and (b) $y$ -axis and over half of the extent of the domain.

Results

Validation and Grid Sensitivity

The velocity spectral density function

S

versus frequency

f

is plotted in Fig. 5. The velocity spectrum represents the velocity series in the frequency domain at

z / h = 0.1

in the computational domain, and the

- 5 / 3

slope spans about 10 Hz, which was sufficient for a LES considering the relatively low Reynolds number of 20,000. Then, the slope gets steep because the SGS model introduced energy dissipation at a high rate. The overall trend of the spectrum is also consistent with Nikora (2005), confirming that the LES results are reasonable.

Fig. 5. Velocity spectra for validation case detected at the midflow depth in the computational domain.

To evaluate numerical model accuracy and mesh sensitivity, simulated distributions of the streamwise velocity,

\bar{u} / U_{b}

, in Case T0 at different locations along the centerline of the channel were compared with the ADV measurement and are plotted in Fig. 6. The

\bar{u}

is calculated by averaging the instantaneous

u

over the LES measurement record. In general, there was a good agreement between the LES results and the experimental data, especially for the fine and medium grids. However, an obvious difference was evident for the coarse grid (dashed gray lines), including an underestimation of the near-bed velocity. The medium and fine grid simulations showed that a near-wake zone could be observed at

L_{x} = 0 - 5 cm

initiated by the strongly recirculating flow for

z / h < 0.1

. Below

L_{x} = 5 cm

, the flow velocity gradually recovered.

Fig. 6. Vertical distributions of the dimensionless time-averaged streamwise velocity, $\bar{u} / U_{b}$ , with different mesh accuracy at various locations along the centerline of the channel for Case T0.

Similarly, Fig. 7 shows the distributions of the streamwise turbulence intensity,

\sqrt{\bar{{u^{'}}^{2}}}

, at selected locations along the centerline of the channel. The simulated turbulence intensity was in good agreement with the monitored data except for the coarse grid, whose turbulence intensity was larger than the experimental data in the near-bed flow region. Due to flow separation at the top of the mound with a rolling-up of shear layer and a large-scale vertical flapping of the wake zone, the peak value of

\sqrt{\bar{{u^{'}}^{2}}}

appeared at

L_{x} = 5 cm

. In addition, the high streamwise turbulence intensity continued along the flow direction for

L_{x} = 10 cm

before gradually disappearing. By comparing the first- and second-order statistics of the experiment and the LES, the convincing results allow a more detailed analysis of the time-averaged flow and instantaneous flow in medium grid.

Fig. 7. Vertical distributions of the streamwise turbulence intensity, $\sqrt{\bar{{u^{'}}^{2}}}$ , with different mesh accuracy at various locations along the centerline of the channel for Case T0.

Time-Averaged Flow

Figs. 8(a–c) show the contours of the time-averaged streamwise velocity with streamlines in the longitudinal symmetry plane and horizontal planes at elevations

z = 0.33

and 0.66 cm, near an isolated mound in Case T1, which has the lowest bioroughness density and is basically consistent with the flow fields of other cases. In Fig. 8(a), mean flow accelerated over the upstream face of the mound, and the flow separation occurred near the middle of it, with a 1-cm-long vortex formed at the foot of the mound. Flow separation and deceleration similarly transpired at the leeside of the mound. Besides, a recirculation zone behind the mound with a length of 5 cm was formed, i.e., five times the mound height, which is consistent with previous studies (Han et al. 2019).

Fig. 8. Time-averaged streamwise velocity contours together with streamlines in (a) the longitudinal symmetry plane; the horizontal planes at (b) $z = 0.33$ ; and (c) 0.66 cm in Case T1.

Figs. 8(b and c) demonstrate that two symmetrical horizontal vortices formed behind the mound, having a length of about 4.5 times the mound height. However, the center locations of the vortex were different: leftward near the bed at

z = 0.33 cm

located at two times the mound height downstream, and rightward at

z = 0.66 cm

located at three times the mound height downstream. It indicates that the symmetric vortex downstream of the mound flow features the axial center shifting downstream with an increase in elevation.

Figs. 9(a–d) present the contours of the dimensionless secondary currents together with their vectors in cross sections through the center of mounds. In Fig. 9(a), for Case T1, it is evident that the peak value of secondary currents as 0.134 appeared around the mound edges, indicating a strong velocity gradient and causing the vortex shedding from the mound edge. The circulation flow in the spanwise direction was weak, given that almost no secondary current vector is apparent.

Fig. 9. Contours of the dimensionless value of secondary currents together with vectors of the secondary currents in selected cross sections: (a) Case T1 in the cross section at $x / L_{x} = 0.25$ ; (b) Case T2 in the cross section at $x / L_{x} = 0.125$ ; (c) Case T3 in the cross section at $x / L_{x} = 0.0625$ ; and (d) Case T4 in the cross section at $x / L_{x} = 0.03125$ .

Furthermore, Figs. 9(b–d) illustrate that as the bioroughness density increased, the locations of the secondary current peaks appeared in the middle of the mounds, and the peak values of secondary currents were 0.152, 0.162, and 0.175, respectively. In these cases, the secondary current vectors are apparent, starting from the top of the mounds and pointing to the middle of two rows of the mounds. This phenomenon also promotes the occurrence of spanwise vortex structure. Furthermore, the equation of Jung et al. (2019) is also adopted here to compare the secondary current intensity in Cases T1–T4 as follows:

SCI = \frac{1}{m} \sum_{i = 1}^{m} \frac{\sqrt{\bar{{(u_{n}^{'})}^{2}}}}{U_{c}}

(3)

where SCI = secondary current intensity for each section;

m

= number of the transverse velocity measurement points;

u_{n}^{'}

= deviation of the transverse velocity; and

U_{c}

= cross-sectional averaged values of the streamwise velocity.

The SCI values for Cases T1–T4 are 0.078, 0.089, 0.106, and 0.129, respectively, which also confirm that an increase in the density of bioroughness promotes the development of secondary currents.

Dimensionless double-averaged streamwise velocity distribution of the turbulent boundary layer over the rough wall can be defined as follows:

U^{+} = \frac{1}{κ} \ln z^{+} + B - Δ U^{+}

(4)

where

U^{+}

= dimensionless time-averaged flow velocity (

= \bar{u} / u_{*}

);

κ

= von Kármán constant;

z^{+}

= dimensionless vertical distance (

= z u_{*} / υ

);

B

= constant (= 5.1); and

Δ U^{+}

= roughness function dependent on the characteristics of the roughness elements.

The distributions obtained from the LES results of four different densities in Cases T1–T4 are plotted in Fig. 10. All the cases exhibited a relatively obvious logarithmic behavior above the viscous sublayer and the buffer layer.

Fig. 10. Mean velocity distributions of Cases T1–T4.

In addition, the roughness functions

Δ U^{+}

can be estimated from the downward shifts in the logarithmic layer of the velocity distributions, whose values are 7.50, 9.71, 12.04, and 13.78 for Cases T1–T4, respectively. Then, the linear regression fittings were made to match with Eq. (4). The values of the von Karman constant, roughness parameters, and flow characteristics for Cases T1–T4 were calculated, as given in Table 4. In this study, the formula

Δ U^{+} = κ^{- 1}

ln

k_{s}^{+} - 3.2

suggested by Raupach et al. (1991) was employed to calculate

k_{s}^{+}

, where

k_{s}^{+}

represents the roughness Reynolds number, given by

k_{s} u_{*} / υ

, which determines the flow regime. Accordingly, Cases T1 and T2 represent the transitional flow, and Cases T3 and T4 represent the rough flow. It can be found that as the bioroughness density increased, the bed roughness increased gradually.

Table 4. Roughness parameters and flow characteristics for Cases T1–T4

Case	LES friction velocity, $u_{*}$ ( $m s^{- 1}$ )	von Kármán constant, $κ$	Translation distance, $Δ U^{+}$	Roughness Reynolds number, $k_{s}^{+} = u_{*} k_{s} / υ$	Equivalent roughness height, $k_{s}$ (cm)
T1	0.01267	0.338	7.501	37	0.30
T2	0.01465	0.346	9.706	87	0.59
T3	0.01741	0.353	12.038	216	1.24
T4	0.02100	0.369	13.784	525	2.50

Figs. 11(a–d) display the vertical distributions of the dimensionless double-averaged stresses for Cases T1–T4. Taking

u

as an example,

u = \bar{u} + u^{'}

, where

u^{'}

is the temporal fluctuation. Then, dispersive component is

\tilde{u} = \bar{u} - ⟨ \bar{u} ⟩

, where

⟨ \bar{u} ⟩

is the double-averaged velocity. In Fig. 11(a), the vertical distributions of the dimensionless double-averaged Reynolds stresses for Cases T1–T4 are plotted. The linear gravity line represents the theoretical vertical distribution of Reynolds shear stress in two-dimensional flow in an open channel. The distributions for Cases T1–T4 were similar, attaining their respective peaks near the bed and exhibiting a linear decrease along the gravity line, which similarly validates the accuracy of the LES results as well. However, with an increase in

k_{s}^{+}

, the difference in the magnitude and the location of the peaks is apparent. The peak locations elevated from 0.12 to 0.14, and their values changed from 0.90 to 0.71.

Fig. 11. Vertical distributions of the dimensionless double-averaged stresses for Cases T1–T4: (a) Reynolds shear stresses; (b) dispersive stresses; (c) total shear stresses; and (d) Reynolds normal stresses.

In Fig. 11(b), the influence of different bioroughness densities for Cases T1–T4 on dispersive stresses are evident, which in turn can be subdivided into two parts: due to bed roughness and due to secondary currents. They reached their peaks near the bed at approximately

z / h = 0.05

. The peak value of the dispersive stresses increased from 0.07 to 0.43 with an increase in the bioroughness density. It is therefore substantiated that the bioroughness plays an important role in producing dispersive stress in the river where benthos is present. The distributions of the sum of the dispersive stresses and Reynolds stress are plotted in Fig. 11(c), and the deviation of the total shear stress from the gravity line in Fig. 11(a) nearly disappeared above the mounds. The distributions of the Reynolds normal stresses are also shown in Fig. 11(d). It is evident that the streamwise Reynolds normal stress in all cases had two local peaks near the bed (at approximately

z / h = 0.03

and 0.14).

Fang et al. (2018) also observed the similar feature in the distribution of streamwise Reynolds normal stress. Reverting to the change in peak location, it is also caused by the dispersive stress because its peak location is inconsistent with the peak location of double-averaged Reynolds normal stress. However, no obvious double-peak phenomenon was observed in the distributions of spanwise and vertical Reynolds stresses because the form-induced stresses in these directions were insignificant. This was validated by some flume experiment results in rough bed flows (Nikora et al. 2001; Mignot et al. 2009). Meanwhile, the presence of mounds induces formation of lower Reynolds normal stress levels, and the streamwise stress is most affected by the bioroughness. Turbulence intensity distribution was also studied by Nezu and Rodi (1986), who demonstrated the turbulence intensity distribution in outer flow region (

z / h > 0.2

) in the case of a two-dimensional steady-uniform flow in open channels, referring to an exponential distribution.

The contours of the Reynolds shear stress relative to the square of the friction velocity in the longitudinal and horizontal planes (

z / h = 0.1

) are depicted in Figs. 12(a–h). In Figs. 12(a and e), for a low-density case (Case T1), a symmetrical shear layer can be clearly found to exist between the recirculation zone and the overlying flow. It extended downstream about eight times the mound height and spanwise about three times the mound height, with a peak value of 5.27 appearing at four times the mound height downstream of the mound center. Figs. 12(b–h) show that the distributions of the Reynolds shear stress, whose peak values are from 4.18 to 2.40, being lower than Case T1, had similar trends to that in Case T1 because the bioroughness spacing still exceeded the length of the main distribution region of the Reynolds shear stress.

Fig. 12. Contours of the dimensionless Reynolds shear stresses in the longitudinal symmetry plane and horizontal plane ( $z / h = 0.1$ ): (a) Case T1 in the longitudinal symmetry plane; (b) Case T2 in the longitudinal symmetry plane; (c) Case T3 in the longitudinal symmetry plane; (d) Case T4 in the longitudinal symmetry plane; (e) Case T1 in the horizontal plane ( $z / h = 0.1$ ); (f) Case T2 in the horizontal plane ( $z / h = 0.1$ ); (g) Case T3 in the horizontal plane ( $z / h = 0.1$ ); and (h) Case T4 in the horizontal plane ( $z / h = 0.1$ ).

The contours of the streamwise Reynolds normal stresses relative to the square of the friction velocity in the longitudinal and horizontal planes (

z / h = 0.1

) are also shown in Figs. 13(a–h). They exhibited a similar trend to the one downstream of a cylinder, preserving a typical signature of shear layer flapping. The Reynolds normal stresses in Cases T1–T4 gradually increased toward the top edge of the mound, reaching their peak values of 14.47, 10.95, 8.26, and 6.84, respectively, at the location downstream two times the mound height, being extended downstream approximately eight times the mound height.

Fig. 13. Contours of the dimensionless streamwise Reynolds stresses in the longitudinal symmetry plane and horizontal plane ( $z / h = 0.1$ ): (a) Case T1 in the longitudinal symmetry plane; (b) Case T2 in the longitudinal symmetry plane; (c) Case T3 in the longitudinal symmetry plane; (d) Case T4 in the longitudinal symmetry plane; (e) Case T1 in the horizontal plane ( $z / h = 0.1$ ); (f) Case T2 in the horizontal plane ( $z / h = 0.1$ ); (g) Case T3 in the horizontal plane ( $z / h = 0.1$ ); and (h) Case T4 in the horizontal plane ( $z / h = 0.1$ ).

Relatively large Reynolds stress zones in Cases T1–T4 can be also found upstream of the mound, with the peak values of 8.88, 5.93, 4.30, and 2.25, respectively. As the spacing between mounds decreased, the Reynolds normal stress distribution pattern was similar to the Reynolds shear stress distribution, except that its vertical influence range became smaller and more concentrated in the area downstream the top of the mounds.

Instantaneous Flow

The contours of the dimensionless streamwise velocity fluctuations

u^{'} / u_{*}

on horizontal planes at

z^{+} = 200

are displayed in Figs. 14(a–d). In Fig. 14(a), the coherent structures near the wall involving high- and low-speed streaks can be clearly evident with approximately regular spanwise intervals, which is consistent with the study of Lee et al. (2011). By visualization, the dimensions of high- and low-speed streaks decreased greatly at higher bioroughness density, with most of them breaking into more and smaller irregular fragments in Figs. 14(a–c). For Case T4 [Fig. 14(d)], the relatively low streamwise intensity area (open areas) occupied a larger proportion than the other three cases, due to stronger secondary currents. It is a periodic process whereby the near-bed low-speed fluid entrains from the bed into the upper layers of the flow and high-speed fluid rushes from the upper layers flow toward the bed because of the secondary currents (Dey 2014). The distance between two adjacent low-speed streaks can be estimated as twice the separation distance at which the spanwise two-point correlation of the streamwise velocity fluctuations attains the maximum negative value (Mazzuoli and Uhlmann 2017).

Fig. 14. Contours of the dimensionless streamwise velocity fluctuations $u^{'} / u_{*}$ on $x y$ -planes at $z^{+} = 200$ for (a) Case T1; (b) Case T2; (c) Case T3; and (d) Case T4.

The spanwise two-point correlation of the streamwise velocity fluctuations was calculated and is shown in Fig. 15. By increasing the bioroughness density from 25 to

100 in. / m^{2}

(Cases T1 to T3), the width of near-bed streaks had a 40% reduction from

y^{+} = 800

to 480, consistent with the contour results. With a further increase in the density to

200 in. / m^{2}

(Case T4), the distance increased to

y^{+} = 670

. Considering the larger open area observed in Fig. 14(d), it should not be concluded that the width of near-bed streaks increased for Case T4. For this particular case, the width of near-bed streaks cannot be quantified from the two-point correlation, due to strong secondary currents.

Fig. 15. Two-point correlations $R_{u^{'} u^{'}}$ of the streamwise velocity fluctuations for Cases T1–T4 along the $y$ -axis at $x / L_{x} = 0.5$ at $z^{+} = 200$ .

Figs. 16(a–h) present the global and local views of the instantaneous coherent structures, respectively, identified by the

Q

criterion proposed by Hunt (1987), which can be estimated from the following expression:

Q = - \frac{1}{2} [{(\frac{\partial u_{x}}{\partial x})}^{2} + {(\frac{\partial u_{y}}{\partial y})}^{2} + {(\frac{\partial u_{z}}{\partial z})}^{2}] - \frac{\partial u_{x}}{\partial y} \frac{\partial u_{y}}{\partial x} - \frac{\partial u_{x}}{\partial z} \frac{\partial u_{z}}{\partial x} - \frac{\partial u_{y}}{\partial z} \frac{\partial u_{z}}{\partial y}

(5)

Fig. 16. Global and local perspectives of instantaneous isosurfaces with the $Q$ -vortex structures with a value of 0.2 colored by the instantaneous streamwise velocity for all three Cases T1–T4: (a) global perspective for Case T1; (b) global perspective for Case T2; (c) global perspective for Case T3; (d) global perspective for Case T4; (e) local perspective for Case T1; (f) local perspective for Case T2; (g) local perspective for Case T3; and (h) local perspective for Case T4.

The value

Q = 0.2

is used in extracting the isosurfaces, which are colored by the instantaneous streamwise velocity for Cases T1–T4. In Case T1, Figs. 16(a and e) show that the vortex structures periodically shedding from the top of the mounds gradually developed into hairpin vortexes downstream. Upstream the bottom of the mounds, large horseshoe (or arch) vortex structures were formed. However, there was no obvious vortex structure in the spanwise gap of the mounds. These phenomena are similar to flows around a sphere or cylinder (Sarkar and Sarkar 2009; Rodriguez et al. 2013).

In Cases T2–T4, Figs. 16(b–h) illustrate that with an increase in bioroughness density, the horseshoe vortex structures gradually disappeared, and hairpin vortex structures were more difficult to develop and form. Meanwhile, a large number of coherent structures also appeared in the spanwise gap of the mounds because of the strong secondary currents, and the streamwise vortex structures in Cases T2–T4 were also observed at

z / h = 0.3

, 0.4, and 0.5, respectively, with a relatively high velocity and far away from the bed compared with Case T1. The reason for this phenomenon is the fact that with a decrease in bioroughness spacing, the vortex structures in wake zone are suffered from a blockage effect by the adjacent mounds, causing the hairpin vortex structures to develop inadequately and move away from the beds or into the spanwise gaps between mounds. Furthermore, the strong flow fluctuations in the wake zone also inhibited the formation of horseshoe vortex structures upstream of the mounds.

Figs. 17(a and b) present the contours of the instantaneous vorticity magnitudes on selected horizontal and longitudinal planes around the mounds in Case T1. The maximum value of 4.3 of vorticity existed over the stoss side of the bioroughness. Moreover, shear layer flapping occurred in both the horizontal and vertical planes at the leeside of the mound. Then, the vorticity dissipated quickly within a distance nearly eight times the mound height in the flow direction.

Fig. 17. Contours of the instantaneous vorticity vector magnitude in Case T1: (a) on the horizontal plane ( $z / h = 0.1$ ); and (b) on the longitudinal symmetry plane.

In order to quantify the size of the turbulence structures, instantaneous velocity time serials were collected in the wake zone of the mounds. Then, the premultiplied spectra were calculated by the fast Fourier transform method and Taylor’s frozen turbulence hypothesis (Taylor 1938) and are plotted in Figs. 18(a–d). The time signals were collected at

L_{x} = 2

, 4, and 8 cm downstream of the center of the mound in the

x

-direction, 25 cm in the

y

-direction, and 1 cm in the

z

-direction, shown by the dots in Fig. 17. In Figs. 18(a–d),

k_{x}

is the wave number derived from the frequency

f

as

k_{x} = 2 π f / \bar{u}

, and the vortex size

λ

was calculated as

λ = \bar{u} / f

.

Fig. 18. Premultiplied spectra of the velocity fluctuations at $L_{x} = 2$ , 4, and 8 cm downstream from the center of the mound in the $x$ -direction, 25 cm in $y$ -direction and 1 cm in $z$ -direction with three different bioroughness density cases: (a) Case T1; (b) Case T2; (c) Case T3; and (d) Case T4.

Fig. 18(a) shows that the peak energy of the vortex structure appeared at

L_{x} = 4 cm

among the three locations, followed by

L_{x} = 2

and 8 cm, which meet the distribution of shear stress shown in Fig. 12. Furthermore, there is a clear multifrequency behavior around

L_{x} = 2 cm

. The first lower characteristic wave number is 12 and the second higher one is 108. In Fig. 17, it can be found that the high-frequency peak means the detachment of individual vortices as a result of the shear layer roll-up, and the low-frequency peak can be connected with the low-frequency flapping of the wake zone behind the mounds. This low-frequency flapping was noticeable at

L_{x} = 4 cm

and became the dominant turbulent structure at

L_{x} = 8 cm

for Case T1. Figs. 18(b–d) additionally show that compared with Case T1, the size of the characteristic wave number essentially remained the same under different density conditions, but the difference is that its energy decreased gradually at

L_{x} = 4 cm

. Moreover, the low-wave-number wake flapping was inhibited due to smaller mound spacing at a higher bioroughness density.

The vortex size

λ

corresponding to the peak value of premultiplied spectra at different positions are compared and analyzed in Fig. 19. At

L_{x} = 2

and 8 cm, the feature length corresponding to the peak intensity had little difference and both were about 5 and 50 cm. However, at

L_{x} = 4 cm

, the feature length of high bioroughness density in Case T4 was about 27 cm, significantly larger than that of low density in Case T1, which was about 17 cm. It can be justified as that in the shear layer after the mounds, the vortex became finer and more broken due to the strong shear effect in the low-bioroughness-density case.

Fig. 19. Vortex size $λ$ corresponding to the peak value of premultiplied spectra at different locations ( $L_{x} = 2$ , 4, and 8 cm) of each case.

Discussion

Influence of the Bioroughness Density on the Equivalent Roughness Height and Darcy–Weisbach Friction Factor

In order to explore the relationship between equivalent roughness height and roughness density, several empirical equations were proposed (Wooding et al. 1973; Paola 1985). Among them, the formulas proposed by Grant and Madsen (1982) and Sigal and Danberg (1990) are widely adopted. The Grant and Madsen (1982) formula is

k_{s} = 27.7 η_{bio}^{2} / λ_{bio}

(6)

where

η_{bio}

= roughness height; and

λ_{bio}

= distance between roughness given by the square root of the inverse roughness density (

= D_{e}^{- 0.5}

).

The method of Sigal and Danberg (1990) is as follows:

Λ_{s} = \frac{S}{S_{f}} {(\frac{A_{f}}{A_{s}})}^{- 1.6}

(7)

where

S

= reference area or the area of the smooth surface before adding on the roughness;

S_{f}

= total frontal area over the rough surface;

A_{f}

= frontal area of a single roughness element; and

A_{s}

= windward wetted surface area of a single roughness element. The ratio

S / S_{f}

is then a roughness density parameter and the ratio

A_{f} / A_{s}

is a roughness shape parameter. The ratios of roughness height to equivalent sand grain roughness,

k_{s} / k

, for different ranges of

Λ_{s}

are given by

k_{s} / k = 0.00321 Λ_{s}^{4.925} for 1.4 \leq Λ_{s} \leq 4.89 k_{s} / k = 8 for 4.89 \leq Λ_{s} \leq 13.25 k_{s} / k = 151.71 Λ_{s}^{- 1.1379} for 13.25 \leq Λ_{s} \leq 100

(8)

Based on the present simulations, a new formula for the relationship between

k_{s}

and

D_{e}^{- 1}

is proposed and plotted in Fig. 20, together with the results obtained from the formulas of Grant and Madsen (1982) and Sigal and Danberg (1990). Thereafter, a multiple-linear regression was performed to obtain the following equation for equivalent roughness with a correlation coefficient of 0.999:

k_{s} = 124.4 \frac{η_{bio}^{3}}{D_{e}^{- 1}}

(9)

Fig. 20. The –1 power of bioroughness density $D_{e}$ as a function of equivalent roughness height $k_{s}$ obtained from LES, the empirical formula of Grant and Madsen (1982), and the method proposed by Sigal and Danberg (1990).

The value of

k_{s}

can be readily estimated with two simple parameters that are easily obtained in natural rivers. In Fig. 20, all three lines follow a similar trend that the equivalent roughness increased as the bioroughness density increased. The

k_{s}

value calculated from Eq. (9) falls between the other two formulas in coincidence: larger than the Sigal and Danberg (1990) prediction and lower than the Grant and Madsen (1982) calculation.

Guillén et al. (2008) also adopted the Grant and Madsen (1982) formula to calculate

k_{s}

of the sea bottom on the Ebro Delta coast caused by shells. However, their case was different from ours, and their case was that the water depth was big, nearly 100 m, the near-bed velocity was about

1 cm / s

classified as laminar flow, and the height of the shell was only 0.3 cm, which was quite different from our shallow water and turbulent case. In the Sigal and Danberg (1990) formula, they only considered the roughness geometry with a pitch-to-height ratio almost bigger than 4, but our bioroughness’ pitch-to-height ratio was 1 and steeper, which was the reason why our results were bigger than theirs.

The relationship between Darcy–Weisbach friction factor

f

and bioroughness density is also discussed here. The equation for Darcy–Weisbach friction factor proposed by Nikora et al. (2019) is as follows:

f = \underset{f_{vis}}{\underset{⏟}{\frac{48}{R e} \frac{1}{N}}} + \underset{f_{turb}}{\underset{⏟}{\frac{48}{q^{2} N} \int_{Z_{t}}^{Z_{w s}} (Z_{w s} - Z) ϕ ⟨ - \bar{u^{'} w^{'}} ⟩ d z}} + \underset{f_{dis}}{\underset{⏟}{\frac{48}{q^{2} N} \int_{Z_{t}}^{Z_{w s}} (Z_{w s} - Z) ϕ ⟨ - \tilde{\bar{u}} \tilde{\bar{w}} ⟩ d z}}

(10)

where

N

= parameter characterizing flow-rough-bed interactions;

q

= specific flow rate per unit width;

Z_{w s}

= height of the free surface;

Z_{t}

= height of the roughness troughs;

ϕ

= roughness geometry function or spatial porosity (Nikora et al. 2001); and

f_{vis}

,

f_{turb}

, and

f_{dis}

= viscous, turbulent, and dispersive friction factors, respectively.

Considering the principle of dimensional consistency, the simulated results for

D_{e}^{0.5}

versus

f

are plotted in Fig. 21. It can be found that the

f

,

f_{turb}

, and

f_{dis}

increased with an increase in bioroughness density. The dispersive contribution accounted for the total friction factor from 4.2% to 15.1%, which also revealed that the dispersive stresses played a more decisive role in generating bed friction. Then, a multiple linear regression was performed to obtain the following equation for turbulent friction factor (Darcy–Weisbach friction factor) with a correlation coefficient of 0.964:

f_{turb} = 0.54 D_{e}^{0.5} η_{bio} = 0.54 B u

(11)

where

B u = {(burrow density)}^{1 / 2}

(burrow height) introduced by Liu et al. (2019).

Fig. 21. The 0.5 power of bioroughness density $D_{e}$ as a function of Darcy–Weisbach friction factor $f$ and each additive component, obtained from the large-eddy simulation.

This decomposition can be helpful when sediment transport in bioroughness-covered riverbeds is considered. Bed-load transport formulas should only use the turbulent components instead of the total shear stress because the form-induced components may not contribute to sediment motion (as in the case of dunes).

Comparison of Mounds with Other Types of Roughness Elements

In this study, the representative mounds in protrusions were selected for analysis. The mounds of different densities indeed have a great impact on the near-bed flow regardless of their physical size to the surrounding area, especially in the recirculation zone, compared with other types of bioroughness in natural rivers. As protrusions, the mounds play an important role in flow resistance, and usually have a longer distributional range of the Reynolds stress peak value than recesses structures, such as pits, tubes, tracks, and galleries (Jimenez 2004). The peak Reynolds shear stress often occurs at the downstream edge of the mound, where the friction angle is also low, making it easy for the grains to entrain. At the same time, two symmetrically horizontal vortices appear behind the mound featuring the shifting of axial center toward downstream with an increase in elevation. They are different from the wake downstream of boulders, columns, and mussels (Liu et al. 2017; Wu et al. 2020), where the upside-down tornado-shaped symmetrical eddies and the recirculation eddy beneath the separated shear layers occur. Horseshoe vortex structures can be found at the bottom of a mound or column, whereas the fine gap vortex is found at the bottom of boulders. Compared with sharp cubes, mounds are easier to retain on riverbed, e.g., by means of siphons (Huettel and Gust 1992), because of their natural angle of repose and smoother contour, having less influence on the flow (Zhou et al. 2016).

Implications and Limitations

Although without simulating the movement of sediment particles directly, the LES provides useful information to understand the sediment transport mechanics near benthos. The reach-averaged friction velocity increased to 65% as the bioroughness density increased eightfold (Table 4). It indicates a strong destabilizing effect of bioroughness on riverbeds. However, when calculating bed-load transport rate, the dispersive shear stress must be excluded from the total bed shear stress. Otherwise, bed shear stress might be overestimated by 25% at a high bioroughness density (Fig. 21). As a result, the overestimation of bed-load transport rate might be higher because it is proportional to the bed shear stress with an exponent of

3 / 2

(Yager et al. 2007). The LES results also help to understand the role of bioroughness on the aquatic habitat of benthos.

Biogeomorphology can be used as shelter from predators (Statzner et al. 2000) and as redds (Taylor 1991). The recirculation zone of mounds makes it easy for invertebrates to collect suspended particles, which increases the possibility of obtaining food in the corresponding area. Meanwhile, due to the low flow velocity in the recirculation zone, benthic invertebrates, such as crayfish, are more willing to inhabit there, bear lower hydrodynamic pressure, and try to avoid washing out by the flow (Maude and Williams 1983).

Despite qualitative and quantitative findings on the impact of bioroughness on near-bed turbulence statistics in the current simulations, more investigations are still required to systematically reveal the impact of benthos on turbulent flow and sediment transport. The present simulations quantified the impact of bioroughness density on

k_{s}

and

f

and proposed an applicable formula. However, it is essential to perform more simulations with different flow depths, velocities, and roughness shapes of organisms to support the proposed relationship.

Another important difference between zoogeomorphology and common riverbed terrains is that bioroughness usually contains disturbance of benthos, such as bioirrigation (Liu et al. 2019; Wu et al. 2020). Although this study focused on the topography formed by benthic disturbance, the total system including benthic topography, bioirrigation, sediment transport, and scalar transport can be further explored as a future scope. Besides, simulating underground flow caused by the sediment with different particle sizes is also required. A better understanding of these processes and the relationship among benthic vital activities, bed forms, and near-bed flow helps to develop more complex models of sediment transport and biological metabolism.

Conclusions

The effects of bioroughness and its density on the turbulence characteristics have been investigated in open-channel flows over an array of mounds by using large-eddy simulation. Distributions of the time-averaged streamwise velocity and turbulence intensity were used to evaluate the LES accuracy and to validate comparing with the experimental data. The complex flow field, secondary currents, Reynolds stresses, dispersive stress, mean velocity, and flow resistance have been analyzed by using contour plots and the double-averaging methodology. In addition, the instantaneous flow has been also explored by using two-point correlation,

Q

-criterion, and premultiplied spectra. Comparison of mounds with other types of roughness elements, the influence of bioroughness density on equivalent roughness height and Darcy–Weisbach friction factor, and the significance of the bioroughness to benthic animals have been discussed. The key outcomes of this study can be summarized as follows:

•

Time-averaged flow revealed that the mounds are to increase the roughness of riverbed and heterogeneity in the flow environment, indicating that the bioroughness behaves like a bluff body, with flow accelerating over and around them and recirculating downstream. The increase in the density of mounds promoted the development of secondary currents and increased the dispersive stress near the bed surface. The peak values of Reynolds stress in both streamwise and vertical directions decreased for limiting the leeside of mounds.

•

With an increase in the bioroughness density, the distance between two adjacent low-speed streamwise velocity fluctuation streaks decreased. The vortex structures forming from the head and wake zones of the mounds gradually became the dominant source in the near bed. Multifrequency behavior was observed in premultiplied spectra. Two distinct vortex-shedding mechanisms were identified: one is a result of shear layer roll-up from the mounds edges and the other is a result of weak flapping. Furthermore, it was also found that higher density of mounds is helpful to reduce the turbulent energy of vortex structure, which is beneficial to the survival of benthic organisms.

•

The influence of the bioroughness density on equivalent roughness height and Darcy–Weisbach friction factor has been quantified in the form of empirical formulations.

In essence, the LES results are helpful to understand the relationship among benthic vital activities, bed forms, and near-bed flow, and to develop more complex sediment transport and biological metabolism models.

Notation

The following symbols are used in this paper:

$A_{f}$: frontal area of a single roughness element ( $L^{2}$ );
$A_{s}$: windward wetted surface area of a single roughness element ( $L^{2}$ );
$B$: constant in log law;
$B u$: burrow number;
$D_{e}$: bioroughness density ( $L^{- 2}$ )
$E_{u u}$: power ( ${ML}^{2} T^{- 3}$ );
$F_{r}$: flow Froude number;
$f$: frequency ( $T^{- 1}$ );
$g$: acceleration due to gravity ( ${LT}^{- 2}$ );
$h$: flow depth (L);
$I_{i, H}$: conditional function;
$i$ , $j$: 1, 2, and 3, representing $x$ -, $y$ -, and $z$ -direction, respectively;
$k$: roughness height (L);
$k_{s}$: equivalent roughness (L);
$k_{x}$: wave number ( $L^{- 1}$ );
$k_{s}^{+}$: roughness Reynolds number;
$L_{x}$: streamwise distance off the mound center (L);
$m$: number of the transverse velocity measurement points;
$N$: parameter characterizing flow-rough-bed interactions;
$P_{i, H}$: frequency of each turbulent event;
$p$: resolved pressure intensity divided by mass density of fluid ( $L^{2} T^{- 2}$ );
$Q$: $Q$ criterion;
$q$: specific flow rate ( $L^{2} T^{- 1}$ );
Re: flow Reynolds number;
$S$: area of the smooth surface before adding on the roughness ( $L^{2}$ );
$S_{f}$: total frontal area over the rough surface ( $L^{2}$ );
$S_{i, H}$: joint-distribution quadrant fraction;
$S_{i j}$: strain-rate tensor ( $T^{- 1}$ );
$T$: dimension of time (s);
$t$: calculation time in the simulation;
$U^{+}$: dimensionless mean flow velocity;
$U_{b}$: depth-averaged velocity ( ${LT}^{- 1}$ );
$U_{c}$: cross-sectional averaged values of the streamwise velocity ( ${LT}^{- 1}$ );
$\bar{u}$: time-averaged velocity at measuring point ( ${LT}^{- 1}$ );
$u^{'}$: streamwise velocity fluctuations ( ${LT}^{- 1}$ );
$u_{i}$ , $u_{j}$: resolved fluid velocity vectors in $i -$ and $j$ -direction, respectively ( ${LT}^{- 1}$ );
$u_{n}^{'}$: deviation of the transverse velocity ( ${LT}^{- 1}$ );
$\sqrt{\bar{{u^{'}}^{2}}}$: streamwise turbulence intensity ( ${LT}^{- 1}$ );
$u_{*}$: friction velocity ( ${LT}^{- 1}$ );
$⟨ \bar{u^{'} u^{'}} ⟩$: double-averaged streamwise Reynolds normal stress ( $L^{2} T^{- 2}$ );
$⟨ \bar{u^{'} w^{'}} ⟩$: double-averaged Reynolds shear stress ( $L^{2} T^{- 2}$ );
$⟨ \bar{v^{'} v^{'}} ⟩$: double-averaged spanwise Reynolds normal stress ( $L^{2} T^{- 2}$ );
$w^{'}$: vertical velocity fluctuations (L);
$⟨ \bar{w^{'} w^{'}} ⟩$: double-averaged vertical Reynolds normal stress ( $L^{2} T^{- 2}$ );
$x$ , $y$ , $z$: Cartesian coordinates (L);
$x_{i}$ , $x_{j}$: spatial vectors in $i$ - and $j$ -direction, respectively (L);
$Z_{w s}$: height of water surface (L);
$Z_{t}$: height of roughness troughs (L);
$z^{+}$: dimensionless distance of $z$ -direction;
$Δ U^{+}$: roughness function;
$Δ x$ , $Δ y$ , $Δ z$: grid spacing in $x$ -, $y$ -, and $z$ -direction, respectively (L);
$Δ x^{+}$ , $Δ y^{+}$ , $Δ z^{+}$: dimensionless grid spacing in $x$ -, $y$ -, and $z$ -direction, respectively;
$η_{bio}$: roughness height (L);
$κ$: von Kármán constant;
$Λ_{s}$: roughness parameter;
$λ$: vortex size (L);
$λ_{bio}$: distance between roughness calculated as the square root of the inverse density (L);
$μ$: coefficient of dynamic viscosity of water ( ${ML}^{- 1} T^{- 1}$ );
$τ_{i j}$: subgrid-scale (SGS) stress ( $L^{2} T^{- 2}$ );
$υ$: coefficient of kinematic viscosity of fluid ( $L^{2} T^{- 1}$ );
$υ_{t}$: subgrid-scale eddy viscosity ( $L^{2} T^{- 1}$ ); and
$ϕ$: roughness geometry function.

Data Availability Statement

All data that support the findings of this study are available from the corresponding author upon reasonable request. They include the tabular data in an Excel file corresponding to the data presented in Figs. 4–21.

Acknowledgments

This investigation was supported by the National Key Research and Development Project (2022YFC3201803) and National Natural Science Foundation of China (Nos. U2040214 and 12372383).

References

Albertson, L. K., and M. D. Daniels. 2016. “Effects of invasive crayfish on fine sediment accumulation, gravel movement, and macroinvertebrate communities.” Freshwater Sci. 35 (2): 644–653. https://doi.org/10.1086/685860.

Google Scholar

Bai, J., H. Fang, and T. Stoesser. 2013. “Transport and deposition of fine sediment in open channels with different aspect ratios.” Earth Surf. Processes Landforms 38 (6): 591–600. https://doi.org/10.1002/esp.3304.

Google Scholar

Best, J. 2005. “The fluid dynamics of river dunes: A review and some future research directions.” J. Geophys. Res. Earth Surf. 110 (F4): F04S02. https://doi.org/10.1029/2004JF000218.

Google Scholar

Brand, A., J. Lewandowski, E. Hamann, and G. Nützmann. 2013. “Advection around ventilated U-shaped burrows: A model study.” Water Resour. Res. 49 (5): 2907–2917. https://doi.org/10.1002/wrcr.20266.

Google Scholar

Cardenas, M. B., A. E. Ford, M. H. Kaufman, A. J. Kessler, and P. L. M. Cook. 2016. “Hyporheic flow and dissolved oxygen distribution in fish nests: The effects of open channel velocity, permeability patterns, and groundwater upwelling.” J. Geophys. Res. Biogeosci. 121 (12): 3113–3130. https://doi.org/10.1002/2016JG003381.

Google Scholar

Carollo, F. G., and V. Ferro. 2021. “Experimental study of boulder concentration effect on flow resistance in gravel bed channels.” Catena 205 (Oct): 105458. https://doi.org/10.1016/j.catena.2021.105458.

Google Scholar

Constantinescu, G., S. Miyawaki, and Q. Liao. 2013. “Flow and turbulence structure past a cluster of freshwater mussels.” J. Hydraul. Eng. 139 (4): 347–358. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000692.

Google Scholar

Dey, S. 2014. Fluvial hydrodynamics: Hydrodynamic and sediment transport phenomena. Berlin: Springer.

Crossref

Google Scholar

Dey, S., and R. Das. 2012. “Gravel-bed hydrodynamics: Double-averaging approach.” J. Hydraul. Eng. 138 (8): 707–725. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000554.

Google Scholar

Dey, S., P. Paul, H. Fang, and E. Padhi. 2020. “Hydrodynamics of flow over two-dimensional dunes.” Phys. Fluids 32 (2): 025106. https://doi.org/10.1063/1.5144552.

Google Scholar

Dinehart, R. L. 1992. “Evolution of coarse gravel bed forms: Field measurements at flood stage.” Water Resour. Res. 28 (10): 2667–2689. https://doi.org/10.1029/92WR01357.

Google Scholar

Fang, H., X. Han, G. He, and S. Dey. 2018. “Influence of permeable beds on hydraulically macro-rough flow.” J. Fluid Mech. 847 (Jul): 552–590. https://doi.org/10.1017/jfm.2018.314.

Google Scholar

Grant, W. D., and O. S. Madsen. 1982. “Movable bed roughness in unsteady oscillatory flow.” J. Geophys. Res. Oceans 87 (C1): 469–481. https://doi.org/10.1029/JC087iC01p00469.

Google Scholar

Guillén, J., S. Soriano, M. Demestre, A. Falqués, A. Palanques, and P. Puig. 2008. “Alteration of bottom roughness by benthic organisms in a sandy coastal environment.” Cont. Shelf Res. 28 (17): 2382–2392. https://doi.org/10.1016/j.csr.2008.05.003.

Google Scholar

Han, X., H. W. Fang, M. F. Johnson, and S. P. Rice. 2019. “The impact of biological bedforms on near-bed and subsurface flow: A laboratory-evaluated numerical study of flow in the vicinity of pits and mounds.” J. Geophys. Res. Earth Surf. 124 (7): 1939–1957. https://doi.org/10.1029/2019JF005000.

Google Scholar

Hassan, M. A., et al. 2008. “Salmon-driven bed load transport and bed morphology in mountain streams.” Geophys. Res. Lett. 35 (4): L04405. https://doi.org/10.1029/2007GL032997.

Google Scholar

Huettel, M., and G. Gust. 1992. “Impact of bioroughness on interfacial solute exchange in permeable sediments.” Mar. Ecol. Prog. Ser. 89 (2–3): 253–267. https://doi.org/10.3354/meps089253.

Google Scholar

Hunt, J. C. R. 1987. “Vorticity and vortex dynamics in complex turbulent flows.” Trans. Can. Soc. Mech. Eng. 11 (1): 21–35. https://doi.org/10.1139/tcsme-1987-0004.

Google Scholar

Jimenez, J. 2004. “Turbulent flows over rough walls.” Annu. Rev. Fluid Mech. 36 (Jan): 173–196. https://doi.org/10.1146/annurev.fluid.36.050802.122103.

Google Scholar

Jones, H. F. E., C. A. Pilditch, K. R. Bryan, and D. P. Hamilton. 2011. “Effects of infaunal bivalve density and flow speed on clearance rates and near-bed hydrodynamics.” J. Exp. Mar. Biol. Ecol. 401 (1–2): 20–28. https://doi.org/10.1016/j.jembe.2011.03.006.

Google Scholar

Jung, S. H., I. W. Seo, Y. D. Kim, and I. Park. 2019. “Feasibility of velocity-based method for transverse mixing coefficients in river mixing analysis.” J. Hydraul. Eng. 145 (11): 0401904. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001638.

Google Scholar

Kara, S., M. C. Kara, T. Stoesser, and T. W. Sturm. 2015. “Free-surface versus rigid-lid LES computations for bridge-abutment flow.” J. Hydraul. Eng. 141 (9): 04015019. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001028.

Google Scholar

Kim, S. J., and T. Stoesser. 2011. “Closure modeling and direct simulation of vegetation drag in flow through emergent vegetation.” Water Resour. Res. 47 (10): W10511. https://doi.org/10.1029/2011WR010561.

Google Scholar

Kristensen, E., G. Penha-Lopes, M. Delefosse, T. Valdemarsen, C. O. Quintana, and G. T. Banta. 2012. “What is bioturbation? The need for a precise definition for fauna in aquatic sciences.” Mar. Ecol. Prog. Ser. 446 (Feb): 285–302. https://doi.org/10.3354/meps09506.

Google Scholar

Lee, J. H., H. J. Sung, and P. Å. Krogstad. 2011. “Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall.” J. Fluid Mech. 669 (Feb): 397–431. https://doi.org/10.1017/S0022112010005082.

Google Scholar

Liu, Y., D. Reible, F. Hussain, and H. Fang. 2019. “Role of bioroughness, bioirrigation, and turbulence on oxygen dynamics at the sediment-water interface.” Water Resour. Res. 55 (10): 8061–8075. https://doi.org/10.1029/2019WR025098.

Google Scholar

Liu, Y., T. Stoesser, and H. Fang. 2022. “Effect of secondary currents on the flow and turbulence in partially filled pipes.” J. Fluid Mech. 938 (May): A16. https://doi.org/10.1017/jfm.2022.141.

Google Scholar

Liu, Y., T. Stoesser, H. Fang, A. Papanicolaou, and A. G. Tsakiris. 2017. “Turbulent flow over an array of boulders placed on a rough, permeable bed.” Comput. Fluids 158 (Nov): 120–132. https://doi.org/10.1016/j.compfluid.2017.05.023.

Google Scholar

Lou, S., M. Chen, G. F. Ma, S. G. Liu, and H. Wang. 2022. “Sediment suspension affected by submerged rigid vegetation under waves, currents and combined wave-current flows.” Coastal Eng. 173 (Apr): 104082. https://doi.org/10.1016/j.coastaleng.2022.104082.

Google Scholar

Maude, S. H., and D. D. Williams. 1983. “Behavior of crayfish in water currents: Hydrodynamics of 8 species with reference to their distribution patterns in southern Ontario.” Can. J. Fish. Aquat. Sci. 40 (1): 68–77. https://doi.org/10.1139/f83-010.

Google Scholar

Mazzuoli, M., and M. Uhlmann. 2017. “Direct numerical simulation of open-channel flow over a fully rough wall at moderate relative submergence.” J. Fluid Mech. 824 (Aug): 722–765. https://doi.org/10.1017/jfm.2017.371.

Google Scholar

Mignot, E., E. Barthelemy, and D. Hurther. 2009. “Double-averaging analysis and local flow characterization of near-bed turbulence in gravel-bed channel flows.” J. Fluid Mech. 618 (Jan): 279–303. https://doi.org/10.1017/S0022112008004643.

Google Scholar

Muzzammil, M., and T. Gangadhariah. 2003. “The mean characteristics of horseshoe vortex at a cylindrical pier.” J. Hydraul. Res. 41 (3): 285–297. https://doi.org/10.1080/00221680309499973.

Google Scholar

Nepf, H. M. 2012. “Flow and transport in regions with aquatic vegetation.” Annu. Rev. Fluid Mech. 44 (1): 123–142. https://doi.org/10.1146/annurev-fluid-120710-101048.

Google Scholar

Nezu, I., and W. Rodi. 1986. “Open-channel flow measurements with a laser Doppler anemometer.” J. Hydraul. Eng. 112 (5): 335–355. https://doi.org/10.1061/(ASCE)0733-9429(1986)112:5(335).

Google Scholar

Nicoud, F., and F. Ducros. 1999. “Subgrid-scale stress modelling based on the square of the velocity gradient tensor.” Flow Turbul. Combust. 62 (3): 183–200. https://doi.org/10.1023/A:1009995426001.

Google Scholar

Nikora, V. 2005. “Flow turbulence over mobile gravel-bed: Spectral scaling and coherent structures.” Acta Geophys. 53 (4): 539–552.

Google Scholar

Nikora, V., D. Goring, I. McEwan, and G. Griffiths. 2001. “Spatially averaged open-channel flow over rough bed.” J. Hydraul. Eng. 127 (2): 123–133. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:2(123).

Google Scholar

Nikora, V. I., and P. M. Rowinski. 2008. “Rough-bed flows in geophysical, environmental, and engineering systems: Double-averaging approach and its applications.” Acta Geophys. 56 (3): 529–533. https://doi.org/10.2478/s11600-008-0037-7.

Google Scholar

Nikora, V. I., T. Stoesser, S. M. Cameron, M. Stewart, K. Papadopoulos, P. Ouro, R. McSherry, A. Zampiron, I. Marusic, and R. A. Falconer. 2019. “Friction factor decomposition for rough-wall flows: Theoretical background and application to open-channel flows.” J. Fluid Mech. 872 (Aug): 626–664. https://doi.org/10.1017/jfm.2019.344.

Google Scholar

Ouro, P., B. Fraga, U. Lopez-Novoa, and T. Stoesser. 2019. “Scalability of an Eulerian-Lagrangian large-eddy simulation solver with hybrid MPI/OpenMP parallelization.” Comput. Fluids 179 (Jan): 123–136. https://doi.org/10.1016/j.compfluid.2018.10.013.

Google Scholar

Paola, C. 1985. “A method for spatially averaging small-scale bottom roughness.” Mar. Geol. 66 (1–4): 291–301. https://doi.org/10.1016/0025-3227(85)90035-0.

Google Scholar

Papanicolaou, A. N., C. M. Kramer, A. G. Tsakiris, T. Stoesser, S. Bomminayuni, and Z. Chen. 2012. “Effects of a fully submerged boulder within a boulder array on the mean and turbulent flow fields: Implications to bedload transport.” Acta Geophys. 60 (6): 1502–1546. https://doi.org/10.2478/s11600-012-0044-6.

Google Scholar

Pascal, L., G. Chaillou, C. Nozais, J. Cool, P. Bernatchez, K. Letourneux, and P. Archambault. 2022. “Benthos response to nutrient enrichment and functional consequences in coastal ecosystems.” Mar. Environ. Res. 175 (Mar): 05584. https://doi.org/10.1016/j.marenvres.2022.105584.

Google Scholar

Raupach, M. R., R. A. Antonia, and S. Rajagopalan. 1991. “Rough-wall turbulent boundary layers.” Appl. Mech. Rev. 44 (1): 1–25. https://doi.org/10.1115/1.3119492.

Google Scholar

Rice, S. P. 2021. “Why so skeptical? The role of animals in fluvial geomorphology.” Wiley Interdiscip. Rev.: Water 8 (6): e1549. https://doi.org/10.1002/wat2.1549.

Google Scholar

Rice, S. P., M. F. Johnson, K. Mathers, J. Reeds, and C. Extence. 2016. “The importance of biotic entrainment for base flow fluvial sediment transport.” J. Geophys. Res. Earth Surf. 121 (5): 890–906. https://doi.org/10.1002/2015JF003726.

Google Scholar

Rodi, W., G. Constantinescu, and T. Stoesser. 2013. Large-eddy simulation in hydraulics. London: CRC Press.

Crossref

Google Scholar

Rodriguez, I., O. Lehmkuhl, R. Borrell, and A. Oliva. 2013. “Flow dynamics in the turbulent wake of a sphere at sub-critical Reynolds numbers.” Comput. Fluids 80 (Jul): 233–243. https://doi.org/10.1016/j.compfluid.2012.03.009.

Google Scholar

Roy, H., M. Huttel, and B. B. Jorgensen. 2002. “The role of small-scale sediment topography for oxygen flux across the diffusive boundary layer.” Limnol. Oceanogr. 47 (3): 837–847. https://doi.org/10.4319/lo.2002.47.3.0837.

Google Scholar

Sansom, B. J., J. F. Atkinson, and S. J. Bennett. 2018. “Modulation of near-bed hydrodynamics by freshwater mussels in an experimental channel.” Hydrobiologia 810 (1): 449–463. https://doi.org/10.1007/s10750-017-3172-9.

Google Scholar

Sarkar, S., and S. Sarkar. 2009. “Large-eddy simulation of wake and boundary layer interactions behind a circular cylinder.” ASME J. Fluids Eng. 131 (9): 091201. https://doi.org/10.1115/1.3176982.

Google Scholar

Sigal, A., and J. E. Danberg. 1990. “New correlation of roughness density effect on the turbulent boundary-layer.” AIAA J. Air Transp. 28 (3): 554–556. https://doi.org/10.2514/3.10427.

Google Scholar

Statzner, B., E. Fievet, J. Y. Champagne, R. Morel, and E. Herouin. 2000. “Crayfish as geomorphic agents and ecosystem engineers: Biological behavior affects sand and gravel erosion in experimental streams.” Limnol. Oceanogr. 45 (5): 1030–1040. https://doi.org/10.4319/lo.2000.45.5.1030.

Google Scholar

Tachie, M. F., R. Balachandar, and D. J. Bergstrom. 2004. “Roughness effects on turbulent plane wall jets in an open channel.” Exp. Fluids 37 (2): 281–292. https://doi.org/10.1007/s00348-004-0816-0.

Google Scholar

Taylor, E. B. 1991. “A review of local adaptation in salmonidae, with particular reference to Pacific and Atlantic salmon.” Aquaculture 98 (1–3): 185–207. https://doi.org/10.1016/0044-8486(91)90383-I.

Google Scholar

Taylor, G. I. 1938. “The spectrum of turbulence.” Proc. Math. Phys. Eng. Sci. 164 (A919): 476–490. https://doi.org/10.1098/rspa.1938.0032.

Google Scholar

Uhlmann, M. 2005. “An immersed boundary method with direct forcing for the simulation of particulate flows.” J. Comput. Phys. 209 (2): 448–476. https://doi.org/10.1016/j.jcp.2005.03.017.

Google Scholar

Volkenborn, N., L. Polerecky, D. S. Wethey, T. H. DeWitt, and S. A. Woodin. 2012. “Hydraulic activities by ghost shrimp Neotrypaea californiensis induce oxic-anoxic oscillations in sediments.” Mar. Ecol. Prog. Ser. 455 (May): 141–156. https://doi.org/10.3354/meps09645.

Google Scholar

Wang, J. Y., G. He, S. Dey, and H. Fang. 2022a. “Influence of submerged flexible vegetation on turbulence in an open-channel flow.” J. Fluid Mech. 947 (Sep): A31. https://doi.org/10.1017/jfm.2022.598.

Google Scholar

Wang, J. Y., G. He, S. Dey, and H. Fang. 2022b. “Fluid structure interaction in a flexible vegetation canopy in an open channel.” J. Fluid Mech. 951: A41. https://doi.org/10.1017/jfm.2022.899.

Google Scholar

Wang, X. M., F. P. Ou, and C. M. Wang. 2016. “Long-term evolution and influence factors of macrozoobenthos in Dongting Lake.” J. Agro-Environ. Sci. 35 (2): 336–345. https://doi.org/10.11654/jaes.2016.02.018.

Google Scholar

Wang, Y. S., Z. H. Yang, M. H. Yu, H. Y. Zhou, and D. W. Zhang. 2022c. “Study on flow characteristics and diversity index of diamond-type boulder cluster with different spacing ratios.” Environ. Sci. Pollut. Res. 29 (23): 34248–34268. https://doi.org/10.1007/s11356-021-18047-4.

Google Scholar

Wooding, R. A., E. F. Bradley, and J. K. Marshall. 1973. “Drag due to regular arrays of roughness elements of varying geometry.” Boundary Layer Meteorol. 5 (3): 285–308. https://doi.org/10.1007/BF00155238.

Google Scholar

Wu, H., and G. Constantinescu. 2022. “Effect of angle of attack on flow past a partially-burrowed, isolated freshwater mussel.” Adv. Water Resour. 168 (Oct): 104302. https://doi.org/10.1016/j.advwatres.2022.104302.

Google Scholar

Wu, H., G. Constantinescu, and J. Zeng. 2020. “Flow and entrainment mechanisms around a freshwater mussel aligned with the incoming flow.” Water Resour. Res. 56 (9): e2020WR027983. https://doi.org/10.1029/2020WR027983.

Google Scholar

Yager, E. M., J. W. Kirchner, and W. E. Dietrich. 2007. “Calculating bed load transport in steep boulder bed channels.” Water Resour. Res. 43 (7): W07418. https://doi.org/10.1029/2006WR005432.

Google Scholar

Zhang, X. T., W. M. Li, K. Zhang, W. W. Xiong, S. S. Chen, and Z. J. Liu. 2022. “Spatiotemporal distribution of macroinvertebrate functional feeding groups in Qiaobian River, a tributary of Yangtze River in Yichang.” Acta Ecol. Sin. 42 (7): 2559–2570. https://doi.org/10.5846/stxb202107061806.

Google Scholar

Zhao, C., P. Ouro, T. Stoesser, S. Dey, and H. Fang. 2022. “Response of flow and saltating particle characteristics to bed roughness and particle spatial density.” Water Resour. Res. 58 (3): e2021WR030847. https://doi.org/10.1029/2021WR030847.

Google Scholar

Zhou, Y. L., Y. F. Zhao, D. Xu, Z. X. Chai, and W. Liu. 2016. “Numerical investigation of hypersonic flat-plate boundary layer transition mechanism induced by different roughness shapes.” Acta Astronaut. 127 (Oct–Nov): 209–218. https://doi.org/10.1016/j.actaastro.2016.05.027.

Google Scholar

Ziebis, W., S. Forster, M. Huettel, and B. B. Jorgensen. 1996. “Complex burrows of the mud shrimp Callianassa truncata and their geochemical impact in the sea bed.” Nature 382 (6592): 619–622. https://doi.org/10.1038/382619a0.

Google Scholar

Zimmerman, G. F., and F. A. de Szalay. 2007. “Influence of unionid mussels (Mollusca: Unionidae) on sediment stability: An artificial stream study.” Fundam. Appl. Limnol. 168 (4): 299–306. https://doi.org/10.1127/1863-9135/2007/0168-0299.

Google Scholar

Zimmermann, A. E., and M. Lapointe. 2005. “Intergranular flow velocity through salmonid redds: Sensitivity to fines infiltration from low intensity sediment transport events.” River Res. Appl. 21 (8): 865–881. https://doi.org/10.1002/rra.856.

Google Scholar

Zou, L., X. Yao, H. Yamaguchi, X. Guo, H. Gao, K. Wang, and M. Sun. 2018. “Seasonal and spatial variations of macro benthos in the intertidal mudflat of Southern Yellow River Delta China in 2007/2008.” J. Ocean Univ. China 17 (2): 437–444. https://doi.org/10.1007/s11802-018-3313-4.

Google Scholar

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Journal of Hydraulic Engineering

Volume 150 • Issue 4 • July 2024

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This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.

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Received: Mar 18, 2023

Accepted: Jan 31, 2024

Published online: May 6, 2024

Published in print: Jul 1, 2024

Discussion open until: Oct 6, 2024

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Zonghong Chen [email protected]

Doctoral Research Fellow, State Key Laboratory of Hydro-Science and Engineering, Dept. of Hydraulic Engineering, Tsinghua Univ., Beijing 100084, China. Email: [email protected]

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Guojian He, M.ASCE https://orcid.org/0000-0003-2504-2904 [email protected]

Associate Professor, State Key Laboratory of Hydro-Science and Engineering, Dept. of Hydraulic Engineering, Tsinghua Univ., Beijing 100084, China (corresponding author). ORCID: https://orcid.org/0000-0003-2504-2904. Email: [email protected]

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Hongwei Fang, M.ASCE [email protected]

Professor, State Key Laboratory of Hydro-Science and Engineering, Dept. of Hydraulic Engineering, Tsinghua Univ., Beijing 100084, China. Email: [email protected]

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Yan Liu [email protected]

Assistant Professor, School of Environment, Southern Univ. of Science and Technology, Shenzhen 518055, China. Email: [email protected]

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Subhasish Dey, M.ASCE [email protected]

Distinguished Professor and Head, Dept. of Civil and Infrastructure Engineering, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan 342030, India; Visiting Professor, State Key Laboratory of Hydro-Science and Engineering, Dept. of Hydraulic Engineering, Tsinghua Univ., Beijing 100084, China. Email: [email protected]

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Abstract

Practical Applications

Introduction

Methodology

Experimentation

Numerical Method

Numerical Experiments

Results

Validation and Grid Sensitivity

Time-Averaged Flow

Instantaneous Flow

Discussion

Influence of the Bioroughness Density on the Equivalent Roughness Height and Darcy–Weisbach Friction Factor

Comparison of Mounds with Other Types of Roughness Elements

Implications and Limitations

Conclusions

Notation

Data Availability Statement

Acknowledgments

References

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