Flow and deposition in and around a finite patch of
vegetation
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Citation
Zong, Lijun, and Heidi Nepf. “Flow and deposition in and around
a finite patch of vegetation.” Geomorphology 116.3-4 (2010):
363-372.
As Published
http://dx.doi.org/10.1016/j.geomorph.2009.11.020
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Elsevier
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Author's final manuscript
Accessed
Thu May 26 18:26:27 EDT 2016
Citable Link
http://hdl.handle.net/1721.1/61314
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Flow and deposition in and around a finite patch of vegetation
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Lijun Zong and Heidi Nepf*
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* Corresponding author:
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48-216D
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Department of Civil and Environmental Engineering
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Massachusetts Institute of Technology
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Cambridge, MA 02139
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[email protected]
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Abstract
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This laboratory study describes the flow and deposition observed in and around a
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finite patch of vegetation located at the wall of a channel. Two patch densities are
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considered with 2% and 10% solid volume fraction. The velocity field, measured in and
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around the patch by acoustic Doppler velocimetry, revealed three distinct zones.
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First, there is a diverging flow region at the leading edge of the patch, where the flow in
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line with the patch decelerates, and the bulk of the flow is diverted toward the open
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channel. Second, there is a fully developed region within the vegetation, where the
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velocity is uniform across the patch width and along the length of the patch. Third, a
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shear layer forms at the interface between the patch and adjacent open channel. The
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pattern of deposition in and around the vegetation was characterized by releasing
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12-micron spherical, glass particles and recording net deposition on a set of glass
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slides. In the diverging region, net deposition increases in the stream-wise direction,
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as the local velocity decreases. In the fully developed region of the patch, deposition
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decreases with longitudinal position, as the concentration in the water column is
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depleted. The deposition pattern is nearly uniform across the patch width, consistent
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with the velocity field and suggesting that turbulent diffusive flux across the lateral
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edge of the patch is not a significant source of particles to the patch under the
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conditions studies here.
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1 Introduction
By baffling the flow and reducing bed-stress, vegetation creates regions of
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sediment retention (e.g. Abt et al. 1994, Lopez and Garcia 1998, Palmer et al. 2004,
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Cotton et al. 2006). In some channels vegetation has been shown to retain up to 80%
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of the sediment in transit downstream (Sand-Jensen 1998). Fonseca et al. (1983)
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observed that finite patches of seagrass are associated with local bed maxima, and
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attributed this to enhanced particle retention within the meadow. Similarly, Tal and
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Paola (2007) experimentally showed that single-thread channels can be formed and
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stabilized by vegetation. In addition to altering the bed morphology, the capture of
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particles within vegetation also enhances the retention of organic matter, nutrients,
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and heavy metals within a channel reach (e.g. Brookshire and Dwire 2003, Schultz et
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al. 2002, Windham et al. 2003).
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Because of the enhanced flow resistance associated with the plants, the
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time-mean velocity is reduced within a patch of vegetation, relative to the free stream.
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The stems of the vegetation may contribute additional turbulence, but this is generally
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offset by the significant decrease in bed-generated turbulence associated with the
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decreased mean velocity, such that the turbulence levels are generally lower within
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the vegetation than the adjacent free-stream (Nepf 1999). A notable exception is
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discussed in the results of this paper. The tendency for reduced mean flow and
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reduced turbulence within the patch, relative to the free stream, suggests that particles
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that remain in suspension in the free stream may deposit after entering the vegetation.
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The rate of net deposition within a patch will depend on the particle characteristics, the
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flow conditions within the patch, and the delivery of particles to the patch. Particles
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may enter the vegetation through advection by mean stream-wise velocity across the
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leading edge of the patch, or by turbulent diffusion across the lateral edge of the patch.
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We use the term turbulent diffusion to describe the net transport associated with the
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turbulent component of the velocity field. Molecular diffusion plays a negligible role
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for the particle sizes and flow conditions considered here. Below we discuss how the
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relative contributions of turbulent diffusion and mean-flow advection depend on patch
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length, flow speed and particle characteristics.
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White and Nepf (2007a,b) described the flow structure and exchange at the
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interface between parallel regions of emergent vegetation and open channel. The
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drag discontinuity at this interface creates a shear-layer that in turn generates large
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coherent vortices via the Kelvin-Helmholtz instability, as also seen in free and shallow
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shear layers (e.g. Ho and Huerre 1984, Chu et. al. 1991). Similar structures form at
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the top of submerged vegetation (Ghisalberti and Nepf 2002, 2004). The energetic,
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shear-layer vortices dominate mass and momentum exchange between the
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vegetation and the open water. In a free shear-layer, the shear-layer vortices grow
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continually downstream, predominantly through vortex pairing (e.g. Winant and
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Browand, 1974). However, in a vegetated shear-layer, the vortices reach a fixed
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scale and a fixed penetration into the vegetation at a short distance from the leading
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edge (Ghisalberti and Nepf 2004). Scaling analyses supported by observations have
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shown that the length-scale of vortex penetration, v, is inversely proportional to the
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density of the vegetation, which is parameterized by the frontal area per volume, a .
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
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If there are n stems per bed area, and each stem has a characteristic width d, then
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a =nd. Based on laboratory experiments,
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
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v = 0.5 (CDa)-1,
(1)
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with CD the drag coefficient for the vegetation (White and Nepf 2007a). It is important
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to note that the penetration scale is not a function of flow speed, except through a
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weak dependence of CD on the local velocity. If the vegetation patch has width b, and
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v is less than b, then the vegetation is segregated into two regions, an outer region of
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width v that has rapid exchange with the adjacent open water and an inner region that
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has much slower water renewal. The rate of turbulent diffusion of scalars is typically
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ten to one hundred times faster across the outer region, than across the inner region
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(Nepf et al. 2007). Sharpe and James (2006) used this two-region description to
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model the transport of sediment from an open channel into an adjacent, parallel region
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of vegetation. To isolate the lateral flux across the flow-parallel interface, they
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released particles only into the open channel and specifically excluded particles from
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entering the upstream edge of the vegetation.
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In contrast to White and Nepf (2007 a,b) and Sharpe and James (2006), who
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focused on transport at the lateral edge of a patch with effectively infinite length, this
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study will focus on the flow and transport at the leading edge of a finite-length patch.
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We denote the stream-wise coordinate as x, with x = 0 at the leading edge. The
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lateral coordinate is y, with y = 0 at the side boundary (Figure 1). Because the
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vegetation creates high drag, much of the flow approaching the patch from upstream
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will be diverted away from the patch. Based on studies of submerged canopies, we
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expect that the region of diversion will extend some distance into the vegetation (Nepf
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and Vivoni 2000). In Figure 1 xD denotes the end of the diverging region.
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Downstream of xD, the flow field evolves into the shear-layer described by White and
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Nepf (2007 a, b), for which the velocity within the vegetation, U1, is less than the
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velocity in the open channel, U2. The initial growth and final scale of the shear-layer
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vortices and their penetration into the patch, v, are shown schematically in Figure 1.
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In Figure 1 v is less than the patch width, b, so that the patch is divided into an
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outer region, in which the turbulent transport is enhanced by the shear-layer vortices
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(b-v < y < b), and an inner region of diminished turbulent transport (y < b-v), in which
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only stem-scale turbulence is present. The turbulent diffusivity in the outer region,
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Dt,o, scales on the velocity difference ∆U = U2-U1, and on the shear layer width, tsl,
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Dt,o   U tsl ,
(2)
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
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with  = 0.02 (±15%) for rigid vegetation and solid volume fractions between 1% and
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4% (Ghisalberti and Nepf, 2005). Sharpe and James (2006) found that the diffusivity
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of particles in the outer region, which they call the transition zone, increases with
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increasing stem density and increasing flow depth, both of which are associated with
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increasing velocity difference, ∆U. This is consistent with (2).
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The turbulent diffusivity in the inner region, Dt,i, depends on the turbulence
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generated by the vegetation and scales on the characteristic stem diameter, d, and
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stem spacing. Theoretical relations have been developed and tested by Nepf (1999)
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and Tanino and Nepf (2008) for homogeneous emergent vegetation. The models
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and observations do not have a strong dependence on stem density, so that a simple
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approximation was suggested by Nepf et al. (2007) for solid volume fractions up to
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10%.
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Dt,i = 0.17 U1d
(3)
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Because Dt,o is generally at least one order of magnitude larger than Dt,i
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(Sharpe and James 2006, Ghisalberti and Nepf 2005), we may assume that the lateral
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turbulent flux of sediment into the patch is limited by the inner layer transport. We
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also assume that the lateral flux of sediment associated with turbulent diffusion begins
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downstream of the diverging region, where the diverging flow out of the patch has
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ceased. If the open channel is a constant concentration source of suspended
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sediment, the concentration boundary layer associated with the lateral turbulent flux of
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suspended sediment will grow downstream of xD as,
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c  4 Dt,i ( x  xD ) / U1  4 0.17( x  xD )d .
(4)
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
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The final term in (4) uses (3) to replace Dt,i. Because the transport across the outer
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layer is rapid, we assume a constant suspended sediment concentration across that
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region, and the boundary layer described by (4) grows from the boundary defined by v,
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as shown in Figure 1. The region between the patch edge and the boundary
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delineated by c represents the potential spatial footprint for deposition associated
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with sediment that enters the vegetation through lateral turbulent diffusion. The
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lateral extent of this region grows with distance along the patch, until it reaches a
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maximum value set by the particle settling time. The particle settling time, Ts, is set
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by the settling velocity, Vs, and the water depth h. Specifically, Ts = h/Vs. In the
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absence of re-suspension, this represents the maximum time sediment can be carried
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from the edge into the vegetation, and it can be used to estimate the maximum
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distance, max, from the edge over which deposition will occur.
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max  4 Dt,i h / Vs
(5)
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
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If the only source of suspended sediment into the patch is the adjacent open channel,
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and conditions within the patch favor deposition, then the deposition profiles will be
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maximum near the edge and decrease into the vegetation, following the
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complementary error function (erfc) shape predicted for diffusion from a constant
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concentration boundary (Figure 2). Sharpe and James (2006), observed profiles
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similar to Figure 2. Further, they observed more extensive deposits for deeper flows
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and for smaller particles with lower settling velocities. These tendencies are
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consistent with (5), as a larger max is predicted for larger h and smaller Vs. Equation
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(5) suggests that transverse deposits will be graded by particle size, because it
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predicts that larger particles (higher Vs) will have a smaller lateral footprint of
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deposition. Deposits will be coarser near the interface and become finer moving
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away from the interface, as max increases with decreasing Vs.
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In contrast to White and Nepf (2007 a,b) and Sharpe and James (2006), this
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study considers conditions for which sediment can enter the patch from the upstream
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edge (Figure 1). The concentration of suspended sediment at the leading edge is
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comparable to that in the open channel, Co. However, as the fluid travels downstream
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inside the patch, deposition occurs and the suspended sediment concentration within
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the patch, Cc, is diminished relative to Co. The settling time-scale predicts the
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length-scale over which a significant portion of suspended particles will be deposited
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within the patch,
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xe = U1h/Vs.
(6)
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For x > xe, we expect the suspended sediment concentration within the patch to be
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significantly less than that in the adjacent open channel.
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Lateral turbulent transport of particles occurs at the edge and within the patch
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(Figure 1). However, the lateral turbulent transport will only produce a significant net
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flux into the patch if Cc is significantly less than Co, i.e. beyond xe. For this reason, the
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signature shape that lateral turbulent diffusion leaves on the deposition pattern (Figure
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2) will only be observed for x >> xe. In this study, we consider the deposition pattern
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for x < xe. New velocity measurements verify the flow field proposed in Figure 1.
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The flow field is then used to explain and model the observed pattern of deposition.
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2 Experiment Methods
Experiments were conducted in a 16-m long re-circulating flume whose test
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section is 1.2 m wide and 13 m long. A subsection of 3-m length is shown in Figure 3.
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A weir at the downstream end controlled the water depth. The depth measured at the
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upstream end was h = 140±1 mm. A patch of model emergent vegetation was
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constructed on one side of the channel, using a staggered array of circular cylinders of
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diameter d = 6 mm. The patch width b was 0.4 m (1/3 of the flume width). The patch
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was 8 m long, and began 2 m from the start of the test section. The cylinders were
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held in place by perforated PVC baseboards that extended over the entire flume width.
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Two stem densities were considered, with a equal to 4 m-1 and 20 m-1, which
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corresponded to solid volume fraction, Φ, of 0.02 and 0.1, respectively. These values
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were chosen to represent a range of vegetation density present in the field. In marsh
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grasses Φ is typically around 0.01. In channel vegetation Φ is 0.05 to 0.1. In
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mangroves Φ is 0.1 to 0.5.
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To characterize the flow field, simultaneous measurements of the three velocity
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components were made using two Nortek Vectrino ADVs, with a sampling volume that
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was 6 mm across and 3 mm high. A longitudinal transect was made through the
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center of the vegetation patch (y = 0.20 m), and at the edge of the patch (y = 0.40 m),
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starting 2 m upstream of the patch and extending to the end of the patch. A support
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structure crossing the flume prevented the carriage supporting the ADVs from
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traveling further downstream. In addition, lateral transects were made at x = 3.1 m
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and 6.7 m for the dense and sparse canopy, respectively. These positions were
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chosen to fall downstream of the diverging region (x > xD). At each position the
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longitudinal (u) and lateral (v) components of velocity were recorded at mid-depth for
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240 seconds at a sampling rate of 25 Hz. The probe was positioned mid-way
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between adjacent cylinders within the array pattern shown in Figure 3. Each record
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was decomposed into its time-average, ( u ,v ), and fluctuating components
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( u(t ),v (t ) ). The overbar denotes the time-average. The Reynolds stress is uv .
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
The intensity of turbulent fluctuations was estimated as the root-mean-square of the

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
fluctuating component of longitudinal velocity, urms  u .
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The model sediment was scaled to provide a desired ratio of settling velocity, Vs,
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
to bed friction velocity, u*, such that deposition would be favored in the vegetation
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(Vs/u* > 0.1), but not in the open channel (Vs/u* < 0.1, as in Julien 1995). From
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preliminary measurements, the average velocity in the open channel and in the
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vegetation was roughly 0.20 m/s and 0.005 m/s, respectively. Using the bed friction
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coefficient (Cf = 0.006) measured in previous studies over the same baseboards
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(White and Nepf 2007a, b), we anticipated that u* would be 15 mm/s and 0.4 mm/s, in
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the open channel and vegetation, respectively. Based on these estimates and the
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criteria above, we sought a particle with a settling velocity on the order of 0.1 mm/s.
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We selected a glass bead with diameter dP of 12 μm and a density  of 2500 kg/m3
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from Potters Industry, Inc., Valley Forge, PA.
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To begin the deposition study, 550 grams of particles were vigorously mixed
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with water in small containers. The mixture was poured across the width of the
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upstream tank and stirred. From visual inspection, the particles mixed over the width
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and depth of the flume within a minute, which was much shorter than the duration of
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the experiment (8.5 hrs). The particles circulated with the water through the closed
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flume system. The initial and final concentration in the water was measured by
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filtering a 500 ml sample from upstream of the patch.
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The net deposition was measured using rectangular microscope slides (75 mm
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× 25 mm), which were placed on the bed of the flume. The dry slides were weighed
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before placement. At the end of the experiment, the slides were baked overnight to
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remove moisture, and then reweighed. From visual inspection, the deposition on the
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slides was uniform, with no obvious edge effects. We also compared the deposition
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per area measured by slides of different size. The deposition per area was the same
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within uncertainty, indicating that the slide size did not influence the measurement.
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The weight of the slide after the experiment minus the weight before was taken as the
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net mass deposition. Three replicate experiments were made for each condition, and
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the uncertainty in net deposition was estimated from the standard error among
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replicates for each position in the flume.
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3 Results
Approaching along the centerline of the dense patch (y = 0.2 m), the
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longitudinal velocity began to decrease one meter upstream of the leading edge
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(Figure 4a). This distance was comparable to the effective width of an equivalent
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unbounded patch (2b = 0.8 m), because the wall located at y = 0 is a line of symmetry.
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Thus, the flow approaching the dense patch was similar to that approaching a solid
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body of the same width. For the sparse patch, however, the flow adjustment began
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less than one meter upstream of the patch (Figure 4c), indicating that the upstream
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adjustment distance decreased with decreasing stem density. This makes physical
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sense, because as the patch diminishes toward a = 0, the upstream adjustment length
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must also tend to zero. This trend is supported by velocity measurements made
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around patches of model vegetation of different stem density (Figs 4, 5, 6c in Bennett
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et al. 2002). Based on several velocity metrics, the perturbation to flow was minimal
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for a ≤ 0.7 m-1, and increased with increasing stem density for a > 1.5 m-1.
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The deceleration in longitudinal velocity was accompanied by an increase in
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lateral velocity, v , associated with the diversion of flow away from the patch (Figure 4).
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Within the patch (x > 0) u continued to decrease until the divergence ended at

roughly xD = 2 m for the dense patch and xD = 3 m for the sparse patch. The

deceleration in u occurred continuously, with no distinct behavior at the leading edge
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(x = 0). Beyond the diverging region (x > xD), the velocity within the vegetation was

fairly uniform (∂u/∂x = 0) until the end of the patch (x = 8 m). This will be called the
270
fully developed region within the patch.
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The velocity development along the patch edge (y = 0.4 m) is shown in Figures
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4b (dense patch) and 4d (sparse patch). For each case, the longitudinal extent of the
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diverging region was similar to that observed at mid-patch (y = 0.2 m). Beyond the
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region of divergence, the velocity at the patch edge (y = 0.4 m, Figure 4b and 4d)
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began to increase, in contrast to the velocity in the patch interior, which remained
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constant (Figure 4a and 4c). This increase reflected the reattachment of flow to the
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patch edge and the development of the shear-layer, as described above. At x = 5 m
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(dense patch) and x = 6 m (sparse patch) the outer shear-layer was fully developed,
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and the velocity at the edge remained constant along the remainder of the patch.
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The urms measured at mid-patch is shown in Figure 4e. Note that the
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turbulence levels increased at the leading edge of the patch, even as the mean
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velocity decreased across this zone. The turbulence remained elevated for 0.5 m into
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the dense patch and for 1.5 m into the sparse patch. The local elevation in turbulence
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level was probably associated with the additional production of turbulence in stem
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wakes. This production is mostly associated with the shedding of vortices from
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individual stems, which occurs for stem Reynolds number, Re = u d /  , greater than
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approximately 100, although the exact threshold is dependent on the stem density

(Nepf 1999). For d = 6 mm, this corresponds to u = 20 mm/s. For the dense patch,
288
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the mean velocity crossed this threshold at x = 0.5 m, suggesting that stem-generated

turbulence was present between x = 0 and 0.5 m, consistent with the observed region
291
of elevated turbulence. For the sparse patch, the stem Reynolds number suggested
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a potential for stem-generated turbulence between x = 0 and 3 m, which also roughly
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corresponded to the observed region of elevated turbulence (x = 0 to 1.5 m). Since
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the Reynolds number threshold is not exact and is known to depend on stem density,
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this agreement is reasonable. Further downstream the turbulence level dropped to a
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lower value in the dense vegetation, consistent with the lower mean velocity within that
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patch (U1 in Table 1). For both patch densities, the turbulence level in the
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fully-developed region of the patch (x > xD) was lower than in the adjacent open
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channel, where urms was between 18 and 20 mm/s.
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A lateral velocity profile was measured within the fully developed flow region of
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the patch, x > xD (Figure 5). The solid line in Figure 5 denotes the edge of the patch.
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Integrating the velocity over the patch width showed that 5% and 12% of the flow
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approaching from upstream (x < -2 m) penetrated to the interior of the dense and
304
sparse patch, respectively. The velocity was laterally uniform over most of the patch
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width, increasing toward the free stream only within a few centimeters of the edge.
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Using (1) and making the reasonable approximation that CD ≈ 1, the penetration scale
307
of the shear-layer vortices, v, was estimated to be 0.03 m and 0.1 m, for the dense
308
and sparse patch, respectively. The dashed line in Figure 5 shows this distance,
309
measured from the patch edge. As described above, the shear-layer at the edge of
310
the patch contains coherent vortices that dominate the turbulent flux of momentum
311
across the patch edge (White and Nepf 2007a). The activity of the shear-layer
312
vortices was reflected in the elevated values of Reynolds stress across the shear layer,
313
which extended mostly into the open channel and only the distance V into the patch.
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The elevated turbulent stress did not penetrate to the inner region of the patch (y <
315
b-v).
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The spatial-average deposition within the dense patch was 27±5 (S.D.) gm -2,
317
and the deposition in the open channel adjacent to this patch was 7±3 (S.D.) gm-2.
318
The average deposition within the sparse patch, 30±3 (S.D.) gm -2, was comparable to
319
the dense patch. However, deposition in the open channel, 14 ± 5 gm -2, was higher
320
with the sparse patch than with the dense patch, consistent with the lower open
321
channel velocity (U2 in Table 1). Based on the t-test, the mean deposition in the patch
322
was statistically higher than the mean deposition in the open channel for both cases
323
(with 99.9% confidence). The open-channel deposition estimate excludes the points
324
at the patch edge (y = 0.4 m), as well as the points upstream of the patch, where
325
deposition was enhanced by the flow deceleration associated with the patch.
326
The longitudinal profiles of net deposition are shown in Figure 6. Standard
327
error among the replicate trials was typically 12% or less. To avoid cluttering the
328
graph, standard error is shown by vertical bars only at those positions for which the
329
standard error was larger than this value. For comparison, the average deposition in
330
the open channel is shown at the vertical axis. In both cases, deposition was
331
enhanced upstream of the patch, relative to the open channel (Figure 6). The
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deposition of material upstream of a patch could promote patch extension in the
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upstream direction. However, we caution against the general expectation for
334
upstream deposition. Whether or not enhanced deposition can occur upstream of a
335
patch will depend on the particle properties, the stem density, and the flow conditions
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upstream of the patch. As discussed above, Bennett et al. (2002) observed that the
337
magnitude and spatial extent of flow disturbance upstream of a patch decreased with
338
decreasing stem density. For sparser patches the flow speed may not drop below the
339
threshold for enhanced deposition until closer to or beyond the leading edge of the
340
patch. For example, Cotton et al. (2006) observed enhanced deposition to begin at
341
the leading edge or somewhere after the leading edge of Ranunculus patches in the
342
field, but they did not record enhanced deposition upstream of the patches.
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For both the dense and sparse patches, the deposition generally increased
344
streamwise through the diverging flow region, as the mean velocity decreased (Figure
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6). In addition, within the diverging flow region the deposition was the same at all four
346
positions, y = 0.04, 0.2, 0.36, and 0.4 m, within uncertainty. A notable exception to
347
the stream-wise increasing deposition pattern occurs just downstream of the leading
348
edge. Here, the deposition was locally diminished within the first 0.2 m of the dense
349
patch and within the first meter of the sparse patch. These regions correspond to the
350
positions of enhanced turbulence associated with stem-wake generation (Figure 4e).
351
The position of maximum deposition for each patch corresponded with the end
352
of the diverging region at x = xD (Figure 6). Beyond this point (x > xD), the deposition
353
declined along the patch and the deposition was no longer uniform across the patch
354
width (Figure 6).
355
0.20 m and 0.36 m were the same, within uncertainty, and distinct from the deposition
356
at the edge (y = 0.4 m). In contrast, in the sparse patch the deposition at y = 0.36 m
357
was similar to the deposition at the edge (y = 0.4 m), and distinct from the deposition at
Notably, for the dense patch (Figure 6a), the deposition along y =
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the other interior points (y = 0.04 m and 0.020 m). These patterns were consistent
359
with the wider outer region in the sparse patch (v = 0.1 m) compared to the dense
360
patch (v = 0.03 m). In the sparse patch, the position y = 0.36 m was within the
361
energetic outer layer of the patch (see Figure 5b) and experienced higher velocity and
362
higher turbulence activity than the interior points. For the dense patch, the position y
363
= 0.36 m was within the inner region of the patch and experienced conditions
364
comparable to the other interior points, with lower mean velocity and lower turbulence
365
(Figure 5a).
366
The lateral variation in deposition is shown in Figure 7 for longitudinal positions
367
in the fully developed flow region within the patch, x > xD. The lateral distribution of
368
deposition was similar in the dense and sparse patches, and also similar at the two
369
longitudinal positions. Deposition was approximately uniform across the patch
370
interior (y < b-v), but decreased moving across the outer region toward the open
371
channel. This was consistent with the lateral distribution of velocity (Figure 5). The
372
velocity was low and uniform across the width of the patch, but increased across the
373
edge, so that deposition was higher where the velocity was lower, as expected.
374
The edge of the lateral flux boundary layer, c, is shown for each transect
375
position (Figure 7). Recall that this boundary delineates the spatial footprint over
376
which sediment carried from the patch edge by lateral turbulent diffusion may be
377
deposited (eq. 4). The observed deposition was nearly the same on either side of this
378
boundary, varying by less than 30% across the interior portion of the patch. This
379
nearly uniform deposition pattern suggests that the impact of lateral fluxes of
18
19
380
suspended sediment on the deposition pattern was comparatively small. This is
381
consistent with the patch scaling described above. According to equation (6), xe has
382
the value 7 m and 20 m, for the dense and sparse patches, respectively (Table 1).
383
Our measurements were taken at distances less than xe. Further, the pattern of
384
deposition observed here was quite unlike the distribution observed when particles are
385
supplied only through lateral turbulent diffusion, which is shown schematically in
386
Figure 2 and was observed experimentally by Sharp and James (2006). Specifically,
387
Sharpe and James (2006) observed deposition that varied by a factor of five (i.e.,
388
500%) or more across the lateral dimension of the patch, with the peak deposition
389
closest to the open channel interface. The comparison to Sharpe and James (2006)
390
highlights the two limits of deposition behavior in finite patches of channel vegetation.
391
Particles may enter a patch of vegetation through turbulent diffusion or through
392
advection by mean flow, and the relative importance of these two fluxes depends on
393
the patch length relative to the deposition length-scale xe (eq. 6). If the patch length is
394
less than xe, then deposition within the patch will be fairly uniform across the patch
395
width. If the patch length is greater than xe, then the deposition will be higher near the
396
patch edge, and decreasing away from the edge. Since xe depends on the settling
397
velocity (eq. 6), the deposition pattern will differ with particle size.
398
399
400
401
4. Modeling the Sediment Deposition Pattern
19
20
402
The observations described above suggest that net deposition in the diverging
403
flow region was controlled by the deceleration associated with the leading edge of the
404
patch. The net deposition rate, the sum of deposition and erosion, may be modeled
405
using a retention probability (e.g. as in James 1985, Engelund and Fredsoe 1976).
406
The rate at which mass, m, accumulates at the bed, dm/dt, is described by
407
408
dm
 pVsC ,
dt
(7)
409

410
with C the concentration of particles in the water and p the probability that a particle
411
reaching the bed will remain deposited. For simplicity, we focus on the dense patch,
412
but the behavior with the sparse patch was similar, as described above. Consider the
413
region of diverging flow, which was approximately 3 m long. Based on the average
414
velocity within this zone (≈ 0.05 m/s, Figure 4), the residence time of fluid in this zone
415
was 60s. This residence time was significantly shorter than the estimated settling
416
time (h/Vs = 1400 s), so it is reasonable to assume that the suspended sediment
417
concentration, C, in this zone was equal to the concentration in the open channel, Co,
418
measured upstream of the patch. Note that Co decreased over the duration of the
419
experiment (Table 1), due to deposition in the channel, vegetation, and tanks. The
420
total mass deposited per bed area is found by integrating (7) over the duration of the
421
experiment, T,
422
T
423
m( x )  pVs  Codt .
(8)
0
20

21
424
425
The deposition pattern in the region of deceleration can be described relative to that
426
observed at a position upstream that is not affected by the vegetation, denoted by x ,
427
428

m( x )
p( x )

m( x ) p( x )
(9)
429

430
The deposition probability given by Engelund and Fredsoe (1976) is
431
432
1/ 4
 
4 
K

/
6
p  1 1 
  .
   c  


(10)
433

434
K is a friction coefficient, taken to be 1, and  is the dimensionless shear stress.
435
436
2
  u* ( sp 1)gd p .
(11)
437

438
g is gravitational acceleration, sp is the ratio of particle density to fluid density, and dp is
439
the particle diameter. The critical shear stress, C, is the shear stress at which
440
sediment motion is initiated. As the flow decelerates, the local value of u* decreases,
441
and the probability of deposition increases, until reaches c. For < c, p is set to 1.
442
Based on the magnitude of the particle Reynolds numbers (Re* = u*dp/ ≤ 0.2), the
443
critical dimensionless shear stress is c ≈ 0.2 (Julien, Figure 7.5, 1995). Because it is
444
not possible to measure the turbulent stress near the bed, the friction velocity is
21
22
445
estimated from the total velocity, U = u 2  v 2 , measured along the y = 20 cm transect.
446
Specifically, u* = UCf1/2. Using the observed m( x ) = 0.0015 gcm-2, and the values of
447

p( x ) and p(x) found from (10), the deposition pattern m(x) can be predicted for the
448

region of diverging flow. This prediction is shown in Figure 6 as the solid line in the

449
region x < 0. The model correctly captures the pattern of increasing net deposition
450
with decreasing flow speed, suggesting that the net deposition pattern in this zone was
451
controlled by the flow deceleration.
452
In the developed region of the dense patch (x > xD) U1 = 5 ± 2 mm/s, with the
453
variation predominantly reflecting stem-scale heterogeneity within the patch, and
454
some longitudinal development. In this region the dimensionless bed stress was
455
O(0.001), which is significantly less than the critical value, c ≈ 0.2, indicating that this
456
region was purely depositional, and p = 1. The residence time in this region was
457
1200s (= 6m / 0.005m/s), which was comparable to the anticipated settling time
458
(1400s), suggesting that the particle concentration in the water declined over the
459
length of this region, which in turn influenced the pattern of net deposition. However,
460
since x < xe, the particle concentration in the water does not decline so much that we
461
must consider lateral fluxes (see discussion above). Because the velocity was
462
uniform over the majority of the patch width (Figure 5), it is reasonable to use a
463
plug-flow model. As explained above, the sediment concentration in the water can be
464
assumed to be constant across the diverging flow region, so that the concentration
465
entering the fully developed region was C(x=xD) = C0(t). For steady, plug-flow
22
23
466
conditions, the particle concentration in the water evolves longitudinally due to the
467
deposition, with p = 1
468
469
U1
C
V
  s C.
x
h
(12)
470

471
This yields the following water concentration
472
473
 V

C( x,t )  C0(t ) exp s ( x  xD ).
 hU1

(13)
474

475
The rate of deposition, dm/dt, can then be described by (7) and (13), with p =1.
476
Integrating over the duration of the experiment,
477
478
 T
  V


m( x )  Vs  C0 (t )dtexp s ( x  xD ).



 0
  hU1
(14)
479

480
The term in the square bracket represents the maximum net deposition, mmax, which
481
was set to the observed maximum deposition at x = 2 m, mmax = 33 gm-2. Then, (14)
482
was fit to the observed m(x) within the patch at y = 0.04, 0.20, and 0.36 m. The three
483
fits are shown as dashed lines in Figure 6a. The settling velocity estimated from
484
these model fits was Vs= 0. 04±0. 02 mm/s, with the uncertainty reflecting the
485
uncertainty in individual fits, the variation between the three fits, and the uncertainty in
486
U1. This is only a bit smaller than the value anticipated based on the manufacturers
23
24
487
specification of particle diameter and density, Vs = 0.1 mm/s, estimated using the
488
formula from Soulsby (1997), with  the kinematic viscosity,
489
490
1/ 2


g s 1  

3
2
Vs 
10.36  1.049 2 dp  10.36,

 
 
dp 

 




 
 
(15)
491

492
such that the time-scale analyses described above are still valid. As a consistency
493
check, the fitted value of Vs was used to predict the maximum deposition, mmax.
494
Because we have direct measures of Co only at the beginning and the end of the
495
experimental run (Table 1), we cannot resolve the details of Co(t), but we can generate
496
bounds by assuming an exponential decay with time (upper bound), and by assuming
497
an initial step-change loss to the tail tank (lower bound). The prediction, mmax = [20 to
498
80 gm-2], also reflects the uncertainty in Vs. These bounds are consistent with the
499
observed maximum deposition, giving support to the model and suggesting that within
500
the patch interior the pattern of net deposition was controlled by loss from the water
501
column with negligible erosion.
502
The transition between the longitudinally increasing and longitudinally
503
decreasing net deposition was expected to occur at the position where = c. Using
504
c = 0.2, as discussed above, and assuming that u* = UCf1/2, this transition should
505
correspond to u = 80 mm/s, which occurred close to x = 0 (Figure 4a). However, the
506
observed transition did not occur until x = 2 m in the dense patch. The likely factor

contributing to this apparent spatial delay was the elevated levels of turbulence
507
24
25
508
observed at the leading edge of the patch (Figure 4e). The presence of
509
stem-generated turbulence makes the velocity profile more vertically uniform and
510
brings fluid of higher velocity closer to the bed than in an open channel with the same
511
depth-averaged velocity (Nepf and Koch 1999). This would increase Cf, the
512
bed-friction coefficient, relative to the value measured for open channel conditions.
513
So, by using the value of Cf measured in open channel conditions we likely
514
underestimate the boundary shear stress within the patch. Further, in a turbulent flow
515
the instantaneous bed stress can be much higher than the mean. Within the
516
vegetation, the turbulence intensity, urms / u , was up to four times higher than that in
517
an open channel (data not shown). With stronger turbulence present, the likelihood
518

of instantaneous bed stresses exceeding the threshold for motion is increased,
519
relative to what it would be in an open channel for the same velocity.
520
521
5 Conclusion
522
This paper describes the flow and deposition pattern associated with a finite patch of
523
vegetation at the sidewall of a channel. Three distinct zones were identified. First,
524
there was a diverging flow region at the leading edge, where the velocity in line with
525
the vegetation decelerated rapidly, and the bulk of the flow was diverted away from the
526
patch. Within this region the deposition increased in the streamwise direction, as the
527
velocity decreased, but was laterally uniform across the patch width. Second, there
528
was a fully developed region within the vegetation, where the velocity was nearly
529
uniform across the patch width and along the length of the patch. In this region the
25
26
530
deposition decreased in the streamwise direction, consistent with a progressive
531
depletion of suspended sediment along the flow path. Third, a shear layer formed
532
along the edge between the patch and the open channel and penetrated a distance v
533
into the patch. Higher turbulence activity within the shear layer diminished deposition
534
at the patch edge, relative to the patch interior. The deposition pattern upstream and
535
within the patch were explained by models that consider only the advection of particles
536
by mean flow entering at the upstream edge of the patch. These models are
537
appropriate over the length-scale xe, for which net fluxes across the lateral edge
538
should not significantly influence the deposition pattern.
539
540
Acknowledgements
541
This material is based upon work supported by a NSF Grant, EAR 0738352. Any
542
opinions, conclusions or recommendations expressed in this material are those of the
543
author(s) and do not necessarily reflect the views of the National Science Foundation
544
26
27
545
Figure Captions:
546
547
Figure 1. Conceptual picture of the flow field near a finite patch of vegetation. Flow
548
divergence begins upstream of the patch and extends some distance into the patch.
549
The position xD indicates the end of the diverging flow and the beginning of shear-layer
550
development at the open-channel edge of the patch. The shear-layer penetrates a
551
distance v into the patch from the patch edge.
552
553
Figure 2. Deposition pattern observed when suspended sediment is delivered to a
554
vegetation patch only through lateral turbulent diffusion from the patch edge (y = b).
555
The suspended sediment concentration within the outer region, delineated by v, is
556
assumed to be equal to the concentration in the adjacent open channel. The
557
deposition pattern is not shown in this region, as it is strongly affected by the elevated
558
turbulence associated with the shear-layer vortices. Within the interior of the patch (y
559
< b-v), we assume that there is no resuspension so that deposition occurs over
560
time-scale Ts = h/Vs. Over this time scale the lateral turbulent diffusion can distribute
561
the sediment over a width max = 4(Dt,iTs)1/2.
562
563
Figure 3. Top view of channel over the first three meters of the vegetated zone. The
564
full patch length is eight meters. The distribution of microscope slides is repeated
565
along the patch length.
27
28
566
Figure 4. Longitudinal (open circles) and transverse (closed circles) velocity at the
567
centerline (y = 20 cm) and at edge of the patch (y = 40 cm). (a,b) dense patch, (c,d)
568
sparse patch. (e) Turbulence level, urms, measured along the centerline of each
569
patch. The uncertainty in each velocity measurement is ±0.1cm/s.
570
571
Figure 5. Lateral profiles of longitudinal velocity (closed symbol) and Reynolds
572
stress (open symbol). (a) Dense patch at x = 3.1 m. (b) Sparse patch at x = 6.7 m.
573
The solid line denotes the edge of the patch. The dashed line denotes the boundary
574
of the outer region, v.
575
576
Figure 6. Longitudinal profiles of net deposition at y = 0.04, 0.20, 0.36, 0.40 m. (a)
577
dense patch. (b) sparse patch. Error bars are shown when the error exceeds 12%.
578
The dashed lines represent a fit to individual data sets for y = 0.04, 0.20, 0.36 cm, as
579
marked. The solid line in the region x < 0 represents equation (9).
580
581
Figure 7. Lateral profiles of deposition measured in the (a) dense and (b) sparse
582
patch. The solid line denotes the edge of the patch. The dashed lines denote the
583
edge of the shear layer penetration, v, and the edges of the boundary layer, c, as
584
marked. The observations are made at distances less than the expected transition
585
distance, xe, which was 7 m and 20 m for the dense and sparse patch, respectively.
586
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589
590
591
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595
596
597
598
599
600
601
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Flow and deposition in and around a finite patch of vegetation