Flow and deposition in and around a finite patch of vegetation The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. 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 Publisher Elsevier Version Author's final manuscript Accessed Thu May 26 18:26:27 EDT 2016 Citable Link http://hdl.handle.net/1721.1/61314 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike 3.0 Detailed Terms http://creativecommons.org/licenses/by-nc-sa/3.0/ 1 1 Flow and deposition in and around a finite patch of vegetation 2 3 Lijun Zong and Heidi Nepf* 4 5 * Corresponding author: 6 48-216D 7 Department of Civil and Environmental Engineering 8 Massachusetts Institute of Technology 9 Cambridge, MA 02139 10 hmnepf@mit.edu 11 1 2 12 Abstract 13 This laboratory study describes the flow and deposition observed in and around a 14 finite patch of vegetation located at the wall of a channel. Two patch densities are 15 considered with 2% and 10% solid volume fraction. The velocity field, measured in and 16 around the patch by acoustic Doppler velocimetry, revealed three distinct zones. 17 First, there is a diverging flow region at the leading edge of the patch, where the flow in 18 line with the patch decelerates, and the bulk of the flow is diverted toward the open 19 channel. Second, there is a fully developed region within the vegetation, where the 20 velocity is uniform across the patch width and along the length of the patch. Third, a 21 shear layer forms at the interface between the patch and adjacent open channel. The 22 pattern of deposition in and around the vegetation was characterized by releasing 23 12-micron spherical, glass particles and recording net deposition on a set of glass 24 slides. In the diverging region, net deposition increases in the stream-wise direction, 25 as the local velocity decreases. In the fully developed region of the patch, deposition 26 decreases with longitudinal position, as the concentration in the water column is 27 depleted. The deposition pattern is nearly uniform across the patch width, consistent 28 with the velocity field and suggesting that turbulent diffusive flux across the lateral 29 edge of the patch is not a significant source of particles to the patch under the 30 conditions studies here. 31 2 3 32 33 1 Introduction By baffling the flow and reducing bed-stress, vegetation creates regions of 34 sediment retention (e.g. Abt et al. 1994, Lopez and Garcia 1998, Palmer et al. 2004, 35 Cotton et al. 2006). In some channels vegetation has been shown to retain up to 80% 36 of the sediment in transit downstream (Sand-Jensen 1998). Fonseca et al. (1983) 37 observed that finite patches of seagrass are associated with local bed maxima, and 38 attributed this to enhanced particle retention within the meadow. Similarly, Tal and 39 Paola (2007) experimentally showed that single-thread channels can be formed and 40 stabilized by vegetation. In addition to altering the bed morphology, the capture of 41 particles within vegetation also enhances the retention of organic matter, nutrients, 42 and heavy metals within a channel reach (e.g. Brookshire and Dwire 2003, Schultz et 43 al. 2002, Windham et al. 2003). 44 Because of the enhanced flow resistance associated with the plants, the 45 time-mean velocity is reduced within a patch of vegetation, relative to the free stream. 46 The stems of the vegetation may contribute additional turbulence, but this is generally 47 offset by the significant decrease in bed-generated turbulence associated with the 48 decreased mean velocity, such that the turbulence levels are generally lower within 49 the vegetation than the adjacent free-stream (Nepf 1999). A notable exception is 50 discussed in the results of this paper. The tendency for reduced mean flow and 51 reduced turbulence within the patch, relative to the free stream, suggests that particles 52 that remain in suspension in the free stream may deposit after entering the vegetation. 53 The rate of net deposition within a patch will depend on the particle characteristics, the 3 4 54 flow conditions within the patch, and the delivery of particles to the patch. Particles 55 may enter the vegetation through advection by mean stream-wise velocity across the 56 leading edge of the patch, or by turbulent diffusion across the lateral edge of the patch. 57 We use the term turbulent diffusion to describe the net transport associated with the 58 turbulent component of the velocity field. Molecular diffusion plays a negligible role 59 for the particle sizes and flow conditions considered here. Below we discuss how the 60 relative contributions of turbulent diffusion and mean-flow advection depend on patch 61 length, flow speed and particle characteristics. 62 White and Nepf (2007a,b) described the flow structure and exchange at the 63 interface between parallel regions of emergent vegetation and open channel. The 64 drag discontinuity at this interface creates a shear-layer that in turn generates large 65 coherent vortices via the Kelvin-Helmholtz instability, as also seen in free and shallow 66 shear layers (e.g. Ho and Huerre 1984, Chu et. al. 1991). Similar structures form at 67 the top of submerged vegetation (Ghisalberti and Nepf 2002, 2004). The energetic, 68 shear-layer vortices dominate mass and momentum exchange between the 69 vegetation and the open water. In a free shear-layer, the shear-layer vortices grow 70 continually downstream, predominantly through vortex pairing (e.g. Winant and 71 Browand, 1974). However, in a vegetated shear-layer, the vortices reach a fixed 72 scale and a fixed penetration into the vegetation at a short distance from the leading 73 edge (Ghisalberti and Nepf 2004). Scaling analyses supported by observations have 74 shown that the length-scale of vortex penetration, v, is inversely proportional to the 75 density of the vegetation, which is parameterized by the frontal area per volume, a . 4 5 76 If there are n stems per bed area, and each stem has a characteristic width d, then 77 a =nd. Based on laboratory experiments, 78 79 v = 0.5 (CDa)-1, (1) 80 81 with CD the drag coefficient for the vegetation (White and Nepf 2007a). It is important 82 to note that the penetration scale is not a function of flow speed, except through a 83 weak dependence of CD on the local velocity. If the vegetation patch has width b, and 84 v is less than b, then the vegetation is segregated into two regions, an outer region of 85 width v that has rapid exchange with the adjacent open water and an inner region that 86 has much slower water renewal. The rate of turbulent diffusion of scalars is typically 87 ten to one hundred times faster across the outer region, than across the inner region 88 (Nepf et al. 2007). Sharpe and James (2006) used this two-region description to 89 model the transport of sediment from an open channel into an adjacent, parallel region 90 of vegetation. To isolate the lateral flux across the flow-parallel interface, they 91 released particles only into the open channel and specifically excluded particles from 92 entering the upstream edge of the vegetation. 93 In contrast to White and Nepf (2007 a,b) and Sharpe and James (2006), who 94 focused on transport at the lateral edge of a patch with effectively infinite length, this 95 study will focus on the flow and transport at the leading edge of a finite-length patch. 96 We denote the stream-wise coordinate as x, with x = 0 at the leading edge. The 97 lateral coordinate is y, with y = 0 at the side boundary (Figure 1). Because the 5 6 98 vegetation creates high drag, much of the flow approaching the patch from upstream 99 will be diverted away from the patch. Based on studies of submerged canopies, we 100 expect that the region of diversion will extend some distance into the vegetation (Nepf 101 and Vivoni 2000). In Figure 1 xD denotes the end of the diverging region. 102 Downstream of xD, the flow field evolves into the shear-layer described by White and 103 Nepf (2007 a, b), for which the velocity within the vegetation, U1, is less than the 104 velocity in the open channel, U2. The initial growth and final scale of the shear-layer 105 vortices and their penetration into the patch, v, are shown schematically in Figure 1. 106 In Figure 1 v is less than the patch width, b, so that the patch is divided into an 107 outer region, in which the turbulent transport is enhanced by the shear-layer vortices 108 (b-v < y < b), and an inner region of diminished turbulent transport (y < b-v), in which 109 only stem-scale turbulence is present. The turbulent diffusivity in the outer region, 110 Dt,o, scales on the velocity difference ∆U = U2-U1, and on the shear layer width, tsl, 111 112 Dt,o U tsl , (2) 113 114 with = 0.02 (±15%) for rigid vegetation and solid volume fractions between 1% and 115 4% (Ghisalberti and Nepf, 2005). Sharpe and James (2006) found that the diffusivity 116 of particles in the outer region, which they call the transition zone, increases with 117 increasing stem density and increasing flow depth, both of which are associated with 118 increasing velocity difference, ∆U. This is consistent with (2). 6 7 The turbulent diffusivity in the inner region, Dt,i, depends on the turbulence 119 120 generated by the vegetation and scales on the characteristic stem diameter, d, and 121 stem spacing. Theoretical relations have been developed and tested by Nepf (1999) 122 and Tanino and Nepf (2008) for homogeneous emergent vegetation. The models 123 and observations do not have a strong dependence on stem density, so that a simple 124 approximation was suggested by Nepf et al. (2007) for solid volume fractions up to 125 10%. 126 127 Dt,i = 0.17 U1d (3) 128 129 Because Dt,o is generally at least one order of magnitude larger than Dt,i 130 (Sharpe and James 2006, Ghisalberti and Nepf 2005), we may assume that the lateral 131 turbulent flux of sediment into the patch is limited by the inner layer transport. We 132 also assume that the lateral flux of sediment associated with turbulent diffusion begins 133 downstream of the diverging region, where the diverging flow out of the patch has 134 ceased. If the open channel is a constant concentration source of suspended 135 sediment, the concentration boundary layer associated with the lateral turbulent flux of 136 suspended sediment will grow downstream of xD as, 137 138 c 4 Dt,i ( x xD ) / U1 4 0.17( x xD )d . (4) 139 7 8 140 The final term in (4) uses (3) to replace Dt,i. Because the transport across the outer 141 layer is rapid, we assume a constant suspended sediment concentration across that 142 region, and the boundary layer described by (4) grows from the boundary defined by v, 143 as shown in Figure 1. The region between the patch edge and the boundary 144 delineated by c represents the potential spatial footprint for deposition associated 145 with sediment that enters the vegetation through lateral turbulent diffusion. The 146 lateral extent of this region grows with distance along the patch, until it reaches a 147 maximum value set by the particle settling time. The particle settling time, Ts, is set 148 by the settling velocity, Vs, and the water depth h. Specifically, Ts = h/Vs. In the 149 absence of re-suspension, this represents the maximum time sediment can be carried 150 from the edge into the vegetation, and it can be used to estimate the maximum 151 distance, max, from the edge over which deposition will occur. 152 153 max 4 Dt,i h / Vs (5) 154 155 If the only source of suspended sediment into the patch is the adjacent open channel, 156 and conditions within the patch favor deposition, then the deposition profiles will be 157 maximum near the edge and decrease into the vegetation, following the 158 complementary error function (erfc) shape predicted for diffusion from a constant 159 concentration boundary (Figure 2). Sharpe and James (2006), observed profiles 160 similar to Figure 2. Further, they observed more extensive deposits for deeper flows 161 and for smaller particles with lower settling velocities. These tendencies are 8 9 162 consistent with (5), as a larger max is predicted for larger h and smaller Vs. Equation 163 (5) suggests that transverse deposits will be graded by particle size, because it 164 predicts that larger particles (higher Vs) will have a smaller lateral footprint of 165 deposition. Deposits will be coarser near the interface and become finer moving 166 away from the interface, as max increases with decreasing Vs. 167 In contrast to White and Nepf (2007 a,b) and Sharpe and James (2006), this 168 study considers conditions for which sediment can enter the patch from the upstream 169 edge (Figure 1). The concentration of suspended sediment at the leading edge is 170 comparable to that in the open channel, Co. However, as the fluid travels downstream 171 inside the patch, deposition occurs and the suspended sediment concentration within 172 the patch, Cc, is diminished relative to Co. The settling time-scale predicts the 173 length-scale over which a significant portion of suspended particles will be deposited 174 within the patch, 175 176 xe = U1h/Vs. (6) 177 178 For x > xe, we expect the suspended sediment concentration within the patch to be 179 significantly less than that in the adjacent open channel. 180 Lateral turbulent transport of particles occurs at the edge and within the patch 181 (Figure 1). However, the lateral turbulent transport will only produce a significant net 182 flux into the patch if Cc is significantly less than Co, i.e. beyond xe. For this reason, the 183 signature shape that lateral turbulent diffusion leaves on the deposition pattern (Figure 9 10 184 2) will only be observed for x >> xe. In this study, we consider the deposition pattern 185 for x < xe. New velocity measurements verify the flow field proposed in Figure 1. 186 The flow field is then used to explain and model the observed pattern of deposition. 187 188 189 2 Experiment Methods Experiments were conducted in a 16-m long re-circulating flume whose test 190 section is 1.2 m wide and 13 m long. A subsection of 3-m length is shown in Figure 3. 191 A weir at the downstream end controlled the water depth. The depth measured at the 192 upstream end was h = 140±1 mm. A patch of model emergent vegetation was 193 constructed on one side of the channel, using a staggered array of circular cylinders of 194 diameter d = 6 mm. The patch width b was 0.4 m (1/3 of the flume width). The patch 195 was 8 m long, and began 2 m from the start of the test section. The cylinders were 196 held in place by perforated PVC baseboards that extended over the entire flume width. 197 Two stem densities were considered, with a equal to 4 m-1 and 20 m-1, which 198 corresponded to solid volume fraction, Φ, of 0.02 and 0.1, respectively. These values 199 were chosen to represent a range of vegetation density present in the field. In marsh 200 grasses Φ is typically around 0.01. In channel vegetation Φ is 0.05 to 0.1. In 201 mangroves Φ is 0.1 to 0.5. 202 To characterize the flow field, simultaneous measurements of the three velocity 203 components were made using two Nortek Vectrino ADVs, with a sampling volume that 204 was 6 mm across and 3 mm high. A longitudinal transect was made through the 205 center of the vegetation patch (y = 0.20 m), and at the edge of the patch (y = 0.40 m), 10 11 206 starting 2 m upstream of the patch and extending to the end of the patch. A support 207 structure crossing the flume prevented the carriage supporting the ADVs from 208 traveling further downstream. In addition, lateral transects were made at x = 3.1 m 209 and 6.7 m for the dense and sparse canopy, respectively. These positions were 210 chosen to fall downstream of the diverging region (x > xD). At each position the 211 longitudinal (u) and lateral (v) components of velocity were recorded at mid-depth for 212 240 seconds at a sampling rate of 25 Hz. The probe was positioned mid-way 213 between adjacent cylinders within the array pattern shown in Figure 3. Each record 214 was decomposed into its time-average, ( u ,v ), and fluctuating components 215 ( u(t ),v (t ) ). The overbar denotes the time-average. The Reynolds stress is uv . 216 The intensity of turbulent fluctuations was estimated as the root-mean-square of the 217 218 fluctuating component of longitudinal velocity, urms u . 2 The model sediment was scaled to provide a desired ratio of settling velocity, Vs, 219 to bed friction velocity, u*, such that deposition would be favored in the vegetation 220 (Vs/u* > 0.1), but not in the open channel (Vs/u* < 0.1, as in Julien 1995). From 221 preliminary measurements, the average velocity in the open channel and in the 222 vegetation was roughly 0.20 m/s and 0.005 m/s, respectively. Using the bed friction 223 coefficient (Cf = 0.006) measured in previous studies over the same baseboards 224 (White and Nepf 2007a, b), we anticipated that u* would be 15 mm/s and 0.4 mm/s, in 225 the open channel and vegetation, respectively. Based on these estimates and the 226 criteria above, we sought a particle with a settling velocity on the order of 0.1 mm/s. 11 12 227 We selected a glass bead with diameter dP of 12 μm and a density of 2500 kg/m3 228 from Potters Industry, Inc., Valley Forge, PA. 229 To begin the deposition study, 550 grams of particles were vigorously mixed 230 with water in small containers. The mixture was poured across the width of the 231 upstream tank and stirred. From visual inspection, the particles mixed over the width 232 and depth of the flume within a minute, which was much shorter than the duration of 233 the experiment (8.5 hrs). The particles circulated with the water through the closed 234 flume system. The initial and final concentration in the water was measured by 235 filtering a 500 ml sample from upstream of the patch. 236 The net deposition was measured using rectangular microscope slides (75 mm 237 × 25 mm), which were placed on the bed of the flume. The dry slides were weighed 238 before placement. At the end of the experiment, the slides were baked overnight to 239 remove moisture, and then reweighed. From visual inspection, the deposition on the 240 slides was uniform, with no obvious edge effects. We also compared the deposition 241 per area measured by slides of different size. The deposition per area was the same 242 within uncertainty, indicating that the slide size did not influence the measurement. 243 The weight of the slide after the experiment minus the weight before was taken as the 244 net mass deposition. Three replicate experiments were made for each condition, and 245 the uncertainty in net deposition was estimated from the standard error among 246 replicates for each position in the flume. 247 248 12 13 249 250 3 Results Approaching along the centerline of the dense patch (y = 0.2 m), the 251 longitudinal velocity began to decrease one meter upstream of the leading edge 252 (Figure 4a). This distance was comparable to the effective width of an equivalent 253 unbounded patch (2b = 0.8 m), because the wall located at y = 0 is a line of symmetry. 254 Thus, the flow approaching the dense patch was similar to that approaching a solid 255 body of the same width. For the sparse patch, however, the flow adjustment began 256 less than one meter upstream of the patch (Figure 4c), indicating that the upstream 257 adjustment distance decreased with decreasing stem density. This makes physical 258 sense, because as the patch diminishes toward a = 0, the upstream adjustment length 259 must also tend to zero. This trend is supported by velocity measurements made 260 around patches of model vegetation of different stem density (Figs 4, 5, 6c in Bennett 261 et al. 2002). Based on several velocity metrics, the perturbation to flow was minimal 262 for a ≤ 0.7 m-1, and increased with increasing stem density for a > 1.5 m-1. 263 The deceleration in longitudinal velocity was accompanied by an increase in 264 lateral velocity, v , associated with the diversion of flow away from the patch (Figure 4). 265 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 266 267 269 (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. 268 13 14 271 The velocity development along the patch edge (y = 0.4 m) is shown in Figures 272 4b (dense patch) and 4d (sparse patch). For each case, the longitudinal extent of the 273 diverging region was similar to that observed at mid-patch (y = 0.2 m). Beyond the 274 region of divergence, the velocity at the patch edge (y = 0.4 m, Figure 4b and 4d) 275 began to increase, in contrast to the velocity in the patch interior, which remained 276 constant (Figure 4a and 4c). This increase reflected the reattachment of flow to the 277 patch edge and the development of the shear-layer, as described above. At x = 5 m 278 (dense patch) and x = 6 m (sparse patch) the outer shear-layer was fully developed, 279 and the velocity at the edge remained constant along the remainder of the patch. 280 The urms measured at mid-patch is shown in Figure 4e. Note that the 281 turbulence levels increased at the leading edge of the patch, even as the mean 282 velocity decreased across this zone. The turbulence remained elevated for 0.5 m into 283 the dense patch and for 1.5 m into the sparse patch. The local elevation in turbulence 284 level was probably associated with the additional production of turbulence in stem 285 wakes. This production is mostly associated with the shedding of vortices from 286 individual stems, which occurs for stem Reynolds number, Re = u d / , greater than 287 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, 288 290 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 292 a potential for stem-generated turbulence between x = 0 and 3 m, which also roughly 289 14 15 293 corresponded to the observed region of elevated turbulence (x = 0 to 1.5 m). Since 294 the Reynolds number threshold is not exact and is known to depend on stem density, 295 this agreement is reasonable. Further downstream the turbulence level dropped to a 296 lower value in the dense vegetation, consistent with the lower mean velocity within that 297 patch (U1 in Table 1). For both patch densities, the turbulence level in the 298 fully-developed region of the patch (x > xD) was lower than in the adjacent open 299 channel, where urms was between 18 and 20 mm/s. 300 A lateral velocity profile was measured within the fully developed flow region of 301 the patch, x > xD (Figure 5). The solid line in Figure 5 denotes the edge of the patch. 302 Integrating the velocity over the patch width showed that 5% and 12% of the flow 303 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 305 width, increasing toward the free stream only within a few centimeters of the edge. 306 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. 15 16 314 The elevated turbulent stress did not penetrate to the inner region of the patch (y < 315 b-v). 316 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 332 deposition of material upstream of a patch could promote patch extension in the 333 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 16 17 336 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. 343 For both the dense and sparse patches, the deposition generally increased 344 streamwise through the diverging flow region, as the mean velocity decreased (Figure 345 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 = 17 18 358 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 )dtexp 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. 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