Effect on flow structure of sand deposition on a gravel bed: Results from a two-dimensional flume experiment

Transcription

1 WATER RESOURCES RESEARCH, VOL. 41, W10405, doi: /2004wr003817, 2005 Effect on flow structure of sand deposition on a gravel bed: Results from a two-dimensional flume experiment Gregory H. Sambrook Smith School of Geography, Earth and Environmental Sciences, University of Birmingham, Birmingham, UK Andrew P. Nicholas Department of Geography, University of Exeter, Exeter, UK Received 17 November 2004; revised 13 June 2005; accepted 21 June 2005; published 11 October [1] Particle imaging velocimetry (PIV) was used to quantify the entire two-dimensional flow field over a series of fixed test beds in a laboratory flume. The test beds used in the experiments provide a two-dimensional representation of gravel beds with contrasting roughness. The two-dimensional form of the beds, combined with the nonintrusive nature of PIV, allowed the velocity field to be quantified right down to the bed surface. The three beds used were designed to simulate the progressive effect of sand deposition on a gravel bed with median grain size (D 50 ) of 25 mm. Such a situation is common in bimodal beds, but, as compared with gravel and sand cases, little work has been done to investigate the interaction between the variable roughness of a bimodal bed and the flow structure above it. The results demonstrate that as the effective roughness decreases the reverse flow often found in the lee of gravel particles is eliminated. Furthermore, near-bed velocities increase, while shear stress and turbulent kinetic energy decrease. Turbulent properties are also diminished higher up in the profile, although this is not the case for the mean downstream velocity, which remains unaffected except at the bed. Quadrant analysis reveals that Q2 and Q4 events become less frequent around high points as effective roughness decreases. All these responses to the changing bed conditions are most pronounced in areas where the effective roughness height (h) approaches 10 mm or less (h/d 50 = 0.4). Such a situation is often found immediately upstream of gravel-sand transitions in natural rivers. It is hypothesized that the hydraulic response outlined here provides a detailed physically based explanation for the gravel-sand transition; the combination of reduced bed shear stress and Q2/Q4 events around gravel particles will result in greater mobility of the sand fraction relative to gravel. These experiments thus appear to demonstrate that there is a fundamental threshold between gravel bed and sand bed states that has not previously been quantified. Citation: Sambrook Smith, G. H., and A. P. Nicholas (2005), Effect on flow structure of sand deposition on a gravel bed: Results from a two-dimensional flume experiment, Water Resour. Res., 41, W10405, doi: /2004wr Introduction [2] During the last ten years a considerable amount of research has been conducted to elucidate the detail of flow structures above river beds. This has been driven by the need for a better understanding of the mean and turbulent characteristics of flow over heterogeneous bed sediments, and the associated implications for sediment entrainment, transport and deposition processes. Acquisition of highresolution hydraulic data sets has been facilitated by technological advances in flow monitoring equipment (e.g., electromagnetic current meter (ECM), acoustic Doppler velocimeter (ADV), laser Doppler velocimeter (LDV), laser Doppler anemometer (LDA), ultrasonic Doppler velocimeter (UDV), particle imaging velocimetry (PIV)) that has enabled quantification of flow in two and Copyright 2005 by the American Geophysical Union /05/2004WR W10405 three dimensions and at high temporal frequencies. To date, the majority of this research has concentrated either on sand bed or gravel bed rivers. In sand bed rivers great progress has been made in quantifying the spatial and temporal characteristics of turbulence over bed forms such as dunes [e.g., Bennett and Best, 1995, 1996; Best et al., 2001; Best and Kostaschuk, 2002; Best, 2005]. Similar progress has been made in gravel bed rivers where both large-scale structures operating throughout the flow depth have been investigated, as well as smaller-scale structures such as those relating to individual pebble clusters [e.g., Robert et al., 1996; Buffin-Belanger and Roy, 1998; Lawless and Robert, 2001a, 2001b; Roy et al., 2004]. Although there has been some consideration of transitions between sand and gravel beds [e.g., Ferguson et al., 1989], there have been no detailed investigations of the type cited above into the flow structures associated with beds composed of bimodal sediments. This represents a significant gap in understanding for two reasons: First, because it has been 1of12

2 W10405 SAMBROOK SMITH AND NICHOLAS: EFFECT ON FLOW STRUCTURE OF SAND DEPOSIT W10405 demonstrated that bimodal sediments are more prevalent within river systems than previously thought [Sambrook Smith and Ferguson, 1995; Sambrook Smith, 1996]; and secondly, because it has been postulated that the presence of sand within a gravel framework, a key characteristic of bimodal beds, may have a considerable effect on the flow structure [Sambrook Smith and Ferguson, 1996; Sambrook Smith et al., 1997]. Other researchers have also noted that the presence of sand in a gravel bed can have a significant impact on the processes of sediment entrainment and transport [e.g., Iseya and Ikeda, 1987; Dietrich et al., 1989; Ferguson et al., 1989; Wilcock, 1993; Sambrook Smith and Ferguson, 1996]. For example, Iseya and Ikeda [1987] conducted flume experiments where total sediment feed was constant but the proportion of sand in that feed was varied. They found that when the proportion of sand was 30% the load could be transported at a reduced slope similar to that required to transport a sand-only load. To explain this type of effect, Sambrook Smith et al. [1997] combined flume measurements with a simple theoretical model to demonstrate that once the sand content of the bed surface exceeds a threshold content of 20 40% the hydraulic characteristics of the bed change dramatically (roughness undergoes a rapid transition from gravel bed to sand bed conditions). More recently, Wilcock and Crowe [2003] demonstrated that once the surface sand content reached 15 25% there was a marked decrease in the reference dimensionless Shields stress for the mean size of bed sediment. It is likely that this threshold surface sand content relates to a smoothing of the bed surface that Wilcock and Crowe [2003] associate with a transition from a framework-supported to a matrixsupported gravel bed. However, hypotheses concerning the possible influence of bimodal sediments on near-bed hydraulics (and associated feedbacks to sediment entrainment and transport) remain theoretical and untested. [3] The aim of this paper is to provide the first highresolution data set quantifying the effect on flow structure of the changes in bed roughness that are associated with sand infilling of a gravel bed. These data will allow an assessment of the possible existence of a sharp transition in hydraulic conditions as bed topography evolves, thus enabling the threshold theory of Sambrook Smith et al. [1997] to be properly tested. If such a threshold does exist it will have widespread implications for the prediction of sediment transport, since it is conceivable that modest inputs of sand, hitherto regarded as negligible, may have a large impact on flow and hence sediment transport processes. To elucidate the relationships between flow characteristics and changing bed roughness this paper reports results from flume experiments that examined the whole two-dimensional flow field associated with a range of fixed beds designed to represent degrees of sand deposition on a gravel bed. The results thus do not take account of any possible feedback between bed load in transport and the flow. Although it has been shown that bed load transport can cause a reduction in turbulence and an increase in mean flow velocity [e.g., Carbonneau and Bergeron, 2000], the focus of this paper is in the comparison between the different beds. Thus the absolute values reported in the results may differ slightly to the case where bed material is in motion. To obtain the highresolution data needed to quantify small-scale variations in near-bed hydraulics the relatively new technique of Particle Imaging Velocimetry (PIV) was employed. PIV allows data to be collected at a millimeter-scale resolution and used to quantify the velocity field to within a few mm of the bed surface. PIV thus provides an unrivalled nonintrusive high-resolution tool for quantifying spatial and temporal characteristics of turbulent flow. 2. Methodology [4] Laboratory experiments were conducted in a hydraulic flume with dimensions 10 m 0.3 m 0.3 m. Three different bed profiles were used in these experiments (Figure 1). Profiles were constructed to be two dimensional, with no variation in elevation in the cross-stream direction. Crucially, this meant that PIV measurements (see below) could be obtained right down to the bed (i.e., there were no particles blocking the view of the camera to the central section of the bed where the laser beam was focused and measurements taken). Bed profiles were designed to be broadly comparable to that used in the theoretical analysis of Sambrook Smith et al. [1997], to facilitate testing of their theory. The initial bed profile, used in experiment one, was based on that from a distal reach of the gravel bed Allt Dubhaig, Scotland, with D 50 = 25 mm. A mould totaling 1 m in length and m in width was made from the Allt Dubhaig bed profile from which 15 replicate concrete casts were taken. Five casts (i.e., a total of 5 m length) were used in each experiment. Each cast was butted up to the next and joints were sealed on all sides. Velocity data were collected over the fourth 1 m bed section (i.e., there was 3 m of bed upstream of the test section and 1 m downstream of it). The second and third experiments were conducted to represent successive amounts of sand deposition on the initial gravel bed profile. This was achieved by pouring floor leveling compound into the troughs of the casts up to a predetermined level, this level being higher for the five casts used in the third experiment as compared to the second. For each of the three experiments data were collected at the same discharge, giving a mean depth of 0.16 m and a mean velocity (depth-averaged) of 0.51 m s 1. Flow was fully turbulent (Reynolds numbers of the order 38,000) and subcritical (Froude numbers of the order 0.4) in all experiments. Water surface elevation data were collected at a downstream interval of 0.2 m along the centerline of the flume using a point gauge, giving a water surface slope of the order It should be noted that all these values varied slightly between experiments as the flow adjusted to the reduced roughness of the different test beds. Bed topography data (shown in Figure 1) were collected in the same way as the water surface but with a sampling interval of 0.01 m. [5] Flow data were acquired in all experiments over a 1 m test section of the bed using PIV. General reviews of the operating principles of PIV are given by Adrian [1991], Tait et al. [1996] and Schmeeckle et al. [1999]. More specifically, Best [2005] reports on experiments undertaken using the PIV system employed here. The advantages of PIV are that many velocity vectors can be quantified simultaneously and data can be collected from very close to the bed (within 1 mm). Data can also be collected at a rate of 15 Hz so that instantaneous velocity and turbulence characteristics can be quantified. The basic methodology and principles of the 2of12

3 W10405 SAMBROOK SMITH AND NICHOLAS: EFFECT ON FLOW STRUCTURE OF SAND DEPOSIT W10405 Figure 1. Topography of the three experimental beds. Points labeled 1/2, 6/7, and 10/11 are the same for all 3 beds, points 3 5, 8, 9, 12, and 13 become covered from bed 1 through to bed 3. technique are as follows. The flow is first seeded with 10 mm diameter silver coated glass spheres. These spheres are then illuminated (via a laser positioned just beneath the water surface) with a sheet of double-pulsed infrared laser light. The illuminated spheres in the test section are visually recorded as image pairs using a digital camera orientated perpendicular to the laser sheet. The laser/camera setup is controlled by using a Dantec FlowMap 2100 PIV processor and the resultant image pairs are then stored and analyzed using Dantec FlowManager 3.62 software. To derive the velocity field a grid of small interrogation areas is specified (32 32 pixels). The distance and direction that each sphere within the interrogation area has moved between the first and second image is then calculated using the fast Fourier transformation based spatial cross-correlation technique, from which the velocity vector can then be determined [Westerweel, 1997]. In the setup employed here the downstream and vertical components of velocity are thus measured simultaneously. [6] To ensure good quality results when using PIV several factors need to be considered. The time between the first and second image for each pair needs to be sufficient to allow particles to move a detectable distance, but not too long so that confidence in the correlation between particle locations is reduced. In this study the laser pulses were set to ensure that particles did not move by more than 21% of the length of the interrogation region between the first and second image pair. The field of view was set at 0.2 m, thus the camera was located in six positions to quantify the entire 1 m test section (allowing a degree of overlap between the positions so that data obtained from each could be combined into a single map of the flow field). At this scale the spatial resolution of the interrogation region and thus the resolution of the resulting data set was 3 mm by 3 mm. Keane and Adrian [1992] have shown that data quality is maximized when at least five particles are present in each interrogation region and that each one of these particles occupies 3 6 pixels. This recommendation was adopted during this study. To ensure 3of12 that there were no reflections from the bed surface that could lead to poor image quality and loss of data resolution at the bed all surfaces were painted matt black. [7] Before beginning data processing areas on the raw images that lay outside of the main area illuminated by the laser were masked or excluded from the analysis because measurements obtained from poorly lit areas can lead to erroneous velocity estimates. The areas masked in this way were either beneath the bed surface or higher up in the flow toward the water surface (the laser was directed toward the important near-bed area thus illumination was reduced higher in the flow). Following Keane and Adrian [1992], a critical signal-to-noise ratio of 1.2 was used to validate and remove low-quality vectors. Furthermore, vectors with a magnitude greater than 1 m s 1 were removed as these were deemed to be outside the range physically possible under the experimental conditions [Westerweel, 1994; Nogueira et al., 1997]. This value was chosen on the basis of measurements taken using an UVP (Ultrasonic Velocity Profiler) that showed the maximum instantaneous velocity was 0.8 m s 1. With the experimental setup as described, the velocity map generated for the 1 m test section consisted of data points (for the bottom part of the flow only). Instantaneous downstream (u n ) and vertical (v n ) velocity data were collected for 60 s at a frequency of 15 Hz. Prior to analyzing the instantaneous velocity data a moving average validation (based on a comparison between neighboring vectors) was run to remove any potential outliers, i.e., incorrect vectors resulting from noise peaks in the correlation function. This was done so as to avoid any bias in the subsequent analysis of the measurements. These data were then used to calculate mean velocity and RMS (root mean square) fluctuation about the mean in the downstream (U and s U, respectively) and vertical (V and s V, respectively) directions, mean Reynolds shear stress (t) and two-dimensional turbulent kinetic energy (k) within each interrogation region, using equations (1) to (6). U ¼ 1 N V ¼ 1 N X N u n n¼1 X N v v n¼1 ð1þ ð2þ " # s U ¼ 1 X N 0:5 ðu n UÞ 2 ð3þ N n¼1 " # s V ¼ 1 X N 0:5 ðv n VÞ 2 ð4þ N t ¼ r 1 N X N n¼1 n¼1 ðu n UÞðv n VÞ ð5þ k ¼ 0:5 s 2 U þ s2 V ð6þ

4 W10405 SAMBROOK SMITH AND NICHOLAS: EFFECT ON FLOW STRUCTURE OF SAND DEPOSIT W10405 the low-lying areas of this bed the number of high points in beds 2 and 3 are reduced to only 10 (points 3, 5 and 12 are covered) and 9 (points 3, 4, 5 and 12 are covered) respectively. In broad terms, the bed profile is dominated by 3 areas of higher elevation represented by points 1 2, 6 7 and There is a general decrease in elevation across the test section from upstream (points 1 2) to downstream (points 10 11). To provide some measure of the degree of infilling around the high points between the different experiments the principle of effective roughness height (h) was applied, as outlined by Gomez [1993]. h was calculated for each high point in each of the 3 beds. h is defined as the elevation of the high point minus the average of the lowest elevations immediately upstream and downstream of the point. h decreases from 10.9 mm to 9.7 mm to 8.2 mm for beds 1, 2 and 3 respectively. In terms of the 3 main areas of higher elevation the infilling has more impact on the downstream part of the bed where, for example, the effective roughness height of point 10 decreases from 12.2 mm to 8.1 mm to 5.9 mm between beds 1, 2 and 3 respectively. This is compared with point 1, the point furthest upstream, which experiences a relatively small decrease in effective roughness height from Figure 2. Distribution of mean downstream (U) velocity over (a) bed 1, (b) bed 2, and (c) bed 3. Note the similarity in the distribution between the three beds, the main difference being the increase in near-bed velocity in the downstream section of the bed from bed 1 through to bed 3. See color version of this figure in the HTML. where N is the number of instantaneous velocity measurements at each location (i.e., 900) and r is the fluid density. In addition, quadrant analysis was performed to quantify the frequency of turbulent events in the UV plane and their contribution to the velocity time series at each location, both in terms of time occupied and fractional contribution to the Reynolds stress. These analyses involve standard calculations that have been outlined in numerous previous studies [e.g., Nelson et al., 1995; Bennett and Best, 1996; Buffin- Belanger and Roy, 1998]. 3. Results 3.1. Topographic Variability of the Three Beds [8] To place the subsequent analysis of the monitored velocity fields in the context of the differences in topography between the 3 beds the latter will first be outlined briefly. As labeled in Figure 1, the first bed consists of 13 high points of varying magnitude. Following infilling of 4of12 Figure 3. Distribution of mean vertical (V) velocity over (a) bed 1, (b) bed 2, and (c) bed 3. See color version of this figure in the HTML.

5 W10405 SAMBROOK SMITH AND NICHOLAS: EFFECT ON FLOW STRUCTURE OF SAND DEPOSIT W10405 Figure 4. Diagram illustrating the variability in the velocity profile over the three experimental beds. The velocity profiles were grouped into 12 categories within which the velocity profiles were broadly similar. Note that the line styles used for the bed topography are the same as those used for the corresponding velocity profiles. The position along the bed where each profile type is present is shown by the bars beneath the bed topography. See color version of this figure in the HTML mm to 22.4 mm to 21.4 mm for beds 1, 2 and 3 respectively Mean Velocity [9] The general pattern of flow can be summarized with reference to the mean downstream and vertical velocity shown in Figures 2 and 3, respectively. Around the upstream (points 1 2) and central (points 6 7) topographic high points the velocity distribution appears to be very similar for all three bed conditions. These topographic highs are characterized by high velocities at their crests (and strong upward moving flow) with greatly reduced flow strengths and reverse flow in their lee. The direction and magnitude of the velocity is the same for all three beds, thus the infilling of topography around these high points as represented by beds 2 and 3 has little impact on the distribution of downstream velocity. In contrast, the velocity distribution around the high points at the downstream end of the test section (points 10 11) shows a distinct change from bed 1 through 3. For bed 1 the velocity distribution has the same pattern as for the upstream high points with a maximum over the crest with slower flow and a recirculation zone in the lee of the high point. The progressive infilling of the topographic low downstream of points in beds 2 and 3 results in downstream velocity vectors that are all positive (i.e., no reverse flow). Furthermore, the increase in the near bed velocity is such that the difference between the peak and the minimum velocities is greatly 5of12

6 W10405 SAMBROOK SMITH AND NICHOLAS: EFFECT ON FLOW STRUCTURE OF SAND DEPOSIT W10405 Figure 5. Downstream velocity (U) for each point along the test section taken at the lowermost sampling location in the vertical (i.e., the velocity within 3 mm of the bed surface). To illustrate the trends more clearly the lines shown are a 5 point moving average of the raw data. Also shown on the graphs is the bed topography for bed 1. diminished. It is also worth noting that as topographic relief diminishes, for beds 1 through 3, the strength of vertical fluid motion declines, particularly in the near-bed region (e.g., the stoss side of points 2 and 13) where areas of descending flow (for bed 1) are replaced by areas of weakly ascending fluid (for bed 3). [10] To quantify these general patterns in more detail all 280 mean velocity profiles for each bed were plotted and divided into groups displaying similar characteristics (Figure 4). A comparison of the velocity profiles for all 3 beds at each location shows that approximately half (53%) show no significant difference between the 3 beds (i.e., the change in bed topography has no discernible impact on the flow in terms of the shape of the profile). Velocity profiles for all three beds tend to be similar above high points, with high near-bed velocities and a relatively modest increase in velocity with height (e.g., profile type 12). Velocity profiles are also similar in the lee of the major high points (e.g., profile type 9), where again the reduction in bed roughness has little impact on the velocity distribution. This pattern is particularly clear between high points 1 and 2 where all 3 profiles are characterized by negative near bed flow and steep velocity gradients in the region below the crest of the roughness elements (Figure 4). [11] In contrast to the above, approximately half of the profiles do show some significant variability, with either all three profiles being different (e.g., profiles 6 and 11) or profiles from two of the beds being similar, but different to one other (e.g., profiles 4, 5 and 7). Velocity profiles measured in the lee of points 10, 11 and 13 (Figure 4) are influenced significantly by infilling of the bed as represented by beds 1 through 3. This is consistent with the substantial reduction in the effective roughness height of these points. For example, the effective roughness height of point 13 is 11.2 mm, 6.2 mm and 1.8 mm for beds 1, 2 and 3 respectively. In addition, some areas of bed 1 downstream of minor high points (e.g., points 5 and 12) are characterized by recirculating flow which is, not surprisingly, absent in the case of beds 2 and 3 for which these points have been covered. There are thus significant differences between the roughness characteristics of the 3 beds, most notably between bed 1 and bed(s) 2/3. Typically, near-bed velocity gradients are lower for beds 2 and 3 compared with bed 1, and marginally less for bed 3 compared with 2. Overall, the majority of the profiles do not display a simple logarithmic shape, but have either two or even three distinct sections (Figure 4). These two-stage profiles have also been reported in previous flume studies of flow over artificial roughness elements [e.g., Nowell and Church, 1979; Robert et al., 1992] and are characteristic of flow in coarse grained gravel bed rivers [e.g., Buffin-Belanger and Roy, 1998]. [12] The contrast in the response of the velocity profiles in different areas of the bed to infilling of low-lying areas demonstrates how the spacing of the roughness elements also influences the potential effect of changes in bed topography. For the upstream roughness elements (points 1 and 2), despite the reduction in effective roughness height there is no discernable difference in the near-bed velocity for the 3 beds (Figure 5). Importantly, the distance between points 1 and 2 is only 0.12 m (5 times the bed obstacle height). The impact of closely spaced obstacles such as this gives rise to what has been referred to as skimming flow [e.g., Nowell and Church, 1979]. This apparent lack of relationship between changing roughness and near-bed 6of12

7 W10405 SAMBROOK SMITH AND NICHOLAS: EFFECT ON FLOW STRUCTURE OF SAND DEPOSIT W10405 of the key high points also diminishes in the downstream direction Turbulence [13] Figures 6 and 7 show the patterns of 2D turbulent kinetic energy and Reynolds shear stress respectively. Maximum values of k and t occur at the level of the crest of the major roughness elements and in their lee. These patterns reflect the distribution of turbulent events (see below) and are associated with turbulence production along shear layers between the main flow and recirculation zones in the lee of topographic highs. The most striking aspect of these diagrams is the more obvious reduction in the magnitude of these turbulence parameters for beds 1 through 3 as compared with the more subtle changes in the mean velocity, which are largely restricted to the near-bed region. For example, downstream of points 1 2 and 6 7 where changes in velocity magnitude and direction are relatively minor there are significant reductions in k for beds 1 through 3. Maximum k values downstream of points 1 2 decrease from , to to m 2 s 2 for beds 1 through 3. This represents a decrease of 20% from bed 1 to bed 3. Likewise, downstream of points 6 7 k decreases Figure 6. Distribution of turbulent kinetic energy (k) over (a) bed 1, (b) bed 2, and (c) bed 3. Note the reduction in intensity and spatial extent of peak k values from bed 1 through to bed 3. See color version of this figure in the HTML. velocity is in contrast to that shown between points 6 7, and downstream of (Figure 5). All these sections show an increase in near-bed velocity from beds 1 through 3, being most pronounced downstream of points This behavior is similar to the wake interaction flow described by others [e.g., Nowell and Church, 1979] where particle spacing is greater. The pattern is slightly different downstream of point 7 where the near-bed velocity for beds 2 and 3 are both higher than that of 1, but very similar (i.e., velocities for bed 3 are not significantly greater than for bed 2). Another common pattern to the near-bed velocity is that immediately downstream of a high point the velocities for the 3 beds are very similar. Significant differences between the three beds only begin to appear >0.2 m (8 times the bed D 50 ) downstream of the high point. The distance between high point 1 and 2 is 0.12 m, whereas distances between points 1 2 and 6 7, 6 7 and 10 11, and and the next point downstream are 0.25 m, 0.31 m and 0.22 m, respectively. The distance between roughness elements in areas where infilling has a significant effect on the near-bed velocity is thus approximately twice that of where no effect is seen. The effective roughness height 7of12 Figure 7. Distribution of Reynolds shear stress over (a) bed 1, (b) bed 2, and (c) bed 3. Note the reduction in intensity and spatial extent of peak shear stress values from bed 1 through to bed 3. See color version of this figure in the HTML.

8 W10405 SAMBROOK SMITH AND NICHOLAS: EFFECT ON FLOW STRUCTURE OF SAND DEPOSIT W10405 Table 1. Summary Data for the Near-Bed Turbulent Kinetic Energy and Reynolds Shear Stress Mean SD Minimum Maximum k, m 2 s Bed ± Bed ± Bed ± Reynolds Shear Stress, N m 2 Bed ± Bed ± Bed ± from to to m 2 s 2 as bed relief becomes less pronounced. This represents a decrease of 26% from bed 1 to bed 3. Clearly, the simulated infilling of the gravel bed has a significant effect on the overall flow structure even downstream of the largest and most closely spaced roughness elements. As noted above, this was not always apparent in the case of the mean velocity field. The magnitude of the difference in the response of the mean and turbulent flow characteristics can be summarized by considering the average values of the flow variables over the measurement section as a whole (Table 1). For example, the average 2D turbulent kinetic energy at the bed decreases from m 2 s 2 for bed 1 to an average of m 2 s 2 for bed 3 (a decrease of 12.5%). Likewise the average value of t at the bed is 0.5 N m 2 (bed 1) declining to 0.29 N m 2 (bed 3), a drop of 42%. As with the mean near-bed velocity, the greatest differences between the near-bed turbulence response of the 3 beds is in the downstream section around points Overall, consideration of Figures 6 and 7 illustrates that while the reduction in topographic relief is reflected in the turbulence characteristics along the entire experimental bed higher up in the profile, this effect is largely restricted to regions downstream of the smallest and most isolated roughness elements when only the near-bed turbulence signature is considered. [14] To examine the turbulent characteristics of the flow in greater detail quadrant analysis was conducted to identify turbulent events above various threshold magnitudes defined by hole size (H) where jð H ¼ U u nþðv v n Þj s U s V In order to characterize low- and high-magnitude events H values of 0 and 2 were used in accordance with previous studies [Bennett and Best, 1995; Buffin-Belanger and Roy, 1998]. As expected, the vast majority of time series are dominated by periods spent in quadrant 2 (referred to here as burst or Q2 events) and quadrant 4 (sweep or Q4 events). For low-magnitude events (H = 0), and in the case of bed 1 (Figures 8a and 8b), Q2 events occupy the greatest proportion of the time series for locations below the crests of the roughness elements, whereas Q4 events dominate time series in the outer region of the flow above the roughness elements. However, the difference in the time spent in these two quadrants is relatively small for H = 0. For example, the ratio of time spent in quadrant 2 to that in quadrant 4 is typically in the near bed region and in the outer region. In the case of high-magnitude events (H =2) these patterns are reversed (Figures 8c and 8d), so that Q2 events dominate the outer flow while Q4 events dominate the near-bed region. These trends are consistent with previous studies of flow in gravel bed rivers [Robert et al., 1996; Buffin-Belanger and Roy, 1998]. Furthermore, in ð7þ Figure 8. Duration of turbulent events (as a percentage of the time series as a whole) above a threshold hole size (H) for bed 1. (a) Q2, H = 0; (b) Q4, H = 0; (c) Q2, H = 2; and (d) Q4, H = 2. See color version of this figure in the HTML. 8of12

9 W10405 SAMBROOK SMITH AND NICHOLAS: EFFECT ON FLOW STRUCTURE OF SAND DEPOSIT W10405 Figure 9. Duration of Q2 and Q4 turbulent events (as a percentage of the time series as a whole) in near-bed sampling locations for (a) bed 1 and (b) bed 3. Analysis is based on a constant threshold stress determined for H = 2 using the mean values of s U and s V at all near-bed sampling locations. the outer region the total duration of Q2 events is now 5 10 times that of Q4 events while near the bed the total duration of Q4 events is 2 5 times that of Q2 events. These patterns in the relative duration of low- and high-magnitude Q2 and Q4 events in near-bed and outer regions of the flow are repeated for beds 2 and 3. However, as topographic relief becomes less pronounced the tendency for events in one quadrant to dominate over another becomes weaker. [15] Interpretation of spatial patterns in the relative importance of turbulent events in each quadrant can be problematic where analysis is conducted using a constant value of H, since this implies a different instantaneous stress threshold (as defined by equation 7) for each velocity time series, because of spatial variations in s U and s V. To overcome this problem we also conducted quadrant analysis on velocity time series in near-bed sampling locations using a constant stress threshold for all time series. We set this threshold equal to the average threshold determined using equation 7 (with H = 2) at all near-bed sampling locations for beds 1 through 3. Figures 9a and 9b show the duration of Q2 and Q4 events in near-bed locations for beds 1 and 3 on the basis of analysis conducted using this constant threshold. The correlation between the duration of Q2 and Q4 events at each location is evident for both beds although it is stronger in the case of bed 3 (r 2 = 0.81) compared to bed 1 (r 2 = 0.67). Where topographic relief is greatest (bed 1) clear relationships between the duration of turbulent events and the location of major roughness elements are not evident. For example, obstacle clasts are associated with both maxima and minima in the duration of Q2 and Q4 events (see Figure 9a). In contrast, reduced topographic relief due to infilling of the bed leads to the emergence of clear spatial patterns in event duration. Time series for bed 3 are characterized by relatively short periods of Q2 and Q4 events at the locations of all major roughness elements. Conversely, most flat areas of the bed between these obstacle clasts are characterized by Q2 and Q4 events of much longer total duration. These differences are highlighted by comparing changes in the mean duration of Q2 events on the stoss side and peak of the major roughness elements (3.15% for bed 1 declining to 0.85% for bed 3), with equivalent changes in Q2 event duration for the remainder of the bed (3.27% for bed 1 declining to 2.54% for bed 3). Similarly, the mean duration of Q4 events immediately above the major roughness elements declines from 2.63% for bed 1 to 0.46% for bed 3, whereas in other areas of the bed the reduction in Q4 event duration is relatively modest (3.73% for bed 1 declining to 3.29% for bed 3). These data suggest that the decline in mean bed shear stress that occurs for beds 1 through 3 is associated with a reduction in the total duration of high-magnitude turbulent events at the bed, as might be expected. However, the reduced duration of turbulent events is most marked on the stoss side and peak of the major roughness elements, and is less substantial in the gaps between these obstacle clasts. 4. Discussion [16] The results presented above demonstrate that a reduction in bed relief, as associated with infilling of a gravel bed by sand deposition, has a significant impact upon the flow structure above the bed. It is pertinent to consider the degree to which flow structures associated with a twodimensional bed are likely to differ from those associated with the three-dimensional topography of a natural gravel bed river. The topography used in these experiments will clearly not generate the same lateral velocity vectors as would be found around a pebble cluster, for example. The important issue is thus to what extent this difference in lateral flow may affect the mean downstream and vertical 9of12

10 W10405 SAMBROOK SMITH AND NICHOLAS: EFFECT ON FLOW STRUCTURE OF SAND DEPOSIT W10405 flow velocities and turbulence characteristics. The theoretical three-dimensional flow structure around a particle is summarized by Best [1996, Figure 3.9] on the basis of the work of Best and Brayshaw [1985] and Acarlar and Smith [1987]. This shows that the vortex system around a particle will be generated by a combination of a standing and horseshoe vortex. The former is generated at the stoss side of the particle and then wraps round the sides to merge with the latter which is generated because of the flow separation in the obstacle lee. On this basis the horseshoe vortex will be largely unaffected by the two-dimensional nature of the bed. However, the standing vortex system while still likely to form on the stoss side of the obstacle will not be able to wrap around the two-dimensional topography of the test bed to merge with the horseshoe vortex. It is thus likely that the frequency and intensity of eddy shedding from the two-dimensional topography may be less than that from a three-dimensional obstacle. Comparison of our data with that collected from three-dimensional gravel bed topographies also provides an additional means of determining the robustness of our results. On the basis of detailed measurements above a pebble cluster Lawless and Robert [2001b] describe the main characteristics of the flow as; flow acceleration on the stoss, vortex shedding and a shear layer at the crest, recirculation in the lee, reattachment further downstream, upwelling of flow downstream from the point of reattachment and then a recovery of the flow to something similar to that before the cluster. These same general patterns can be seen over the obstacles of our two-dimensional bed as previously described in the results section. Likewise, when the turbulence characteristics are considered the results from the two-dimensional bed are similar to those that have been described from fully three-dimensional gravel bed topographies. For example, it was shown in the quadrant analysis described above that the frequency and distribution of burst and sweep events over bed 1 (designed to simulate a gravel bed with no sand deposition) was similar to that reported by Robert et al. [1996] and Buffin-Belanger and Roy [1998] from natural gravel bed rivers. We thus conclude that the results from our twodimensional experiment are applicable to natural gravel bed rivers. However, the specific magnitudes of the velocity vectors and calculated turbulence variables reported here will differ to those of a natural bed where lateral flow will be more variable. [17] Our results show that the effect of sand deposition on a gravel bed becomes most pronounced as the main roughness elements become more widely spaced and their effective roughness height diminishes. Buffin-Belanger and Roy [1998] concluded that the effects of a pebble on the flow structure would be significant over a distance of 9 15 times the effective height of the pebble. Thus for an obstacle height of 20 mm one might expect the effects of that particle to dominate the flow structure for 0.20 m downstream. These estimates would appear to be consistent with the findings of this work, further validating the use of the twodimensional bed. Where the effective roughness height of obstacles remains high (e.g., 20 mm or 0.8D 50 ), very substantial infilling of the bed (i.e., deposition of sand) will be required to have a significant impact upon the near-bed flow. Conversely, when the effective roughness is small (e.g., <10 mm or 0.4D 50 ) the influence of the particle will be felt over a shorter downstream distance and flow characteristics are more sensitive to infilling of the bed. Consequently, it is perhaps not surprising that the near-bed flow is affected most in the downstream sections of the test bed since effective roughness heights are lower and obstacle spacing greater in this area. Thus where the spacing of high points becomes large relative to their height only modest volumes of sand will need to be deposited around the primary roughness elements to have a significant impact upon the near-bed flow. Such a scenario becomes more likely as the effective roughness height diminishes and it is suggested on the basis of these results that once this value falls below 10 mm (approximately 0.4D 50 ) these effects will become apparent. The main effect of the infilling will be to reduce vertical velocity gradients and promote a reduction in near-bed shear stress over the sandy patches on the bed. This smoothing of the bed will also reduce the critical shear stress needed to entrain both gravel and sand. However, as Wilcock [1998] demonstrates, the decrease in critical shear stress is proportionately larger for sand than it is for gravel. Likewise, Ferguson [2003] has demonstrated that as shear stress declines the critical shear stress required to move different particle sizes becomes more pronounced, leading to a greater mobility of the finer sizes. The reduction in shear stress over the sand sections of the bed will thus have little impact on the sand transport rate, which will remain higher than that of the gravel fractions even though the critical shear stress for gravel entrainment has decreased. Thus in simple terms, for the gravel fraction the reduction in critical shear stress for entrainment does not offset the reduction in shear stress produced by the sand patches on the bed surface. The feedbacks associated with the sizeselective transport mechanisms described by Wilcock [1998] and Ferguson [2003] are essentially similar to the enhanced fining mechanism of Paola and Seal [1995] and Seal and Paola [1995] who state that when patches occur a larger but finer total load is transported. The sand fraction is thus preferentially moved downstream becoming ever more concentrated on the bed surface as the effects described above become more pronounced. A positive feedback thus prevails and the transition from a gravel to a sand bed occurs over a remarkably short distance. [18] On the basis of the results presented here we also hypothesize that changes in the duration of Q2 and Q4 turbulent events as bed topography is smoothed also act as an additional mechanism to that of sorting processes to enhance the relative mobility of sand over gravel. Once again this mechanism appears to be influenced by roughness element height and spacing as demonstrated by the data in Figure 9. These illustrate that obstacle clasts (e.g., gravel particles) and the gaps between them (e.g., areas of the bed covered by sand) experience markedly different changes in the duration of high-magnitude turbulent events as bed topography is smoothed. Critically, while the duration of both bursts and sweeps is reduced in the majority of areas as bed relief declines, this reduction is most marked on the stoss side and peak of roughness elements and weakest in many intervening areas of the bed. Indeed, some substantial areas of the bed between obstacles experience an increase in the duration of Q2 and Q4 events as relief declines. We argue that this is likely to further reduce the mobility and associated transport rate of gravel particles relative to sand 10 of 12

11 W10405 SAMBROOK SMITH AND NICHOLAS: EFFECT ON FLOW STRUCTURE OF SAND DEPOSIT W10405 particles. Whether these hydraulic changes are of primary or secondary importance to the sorting processes described by Wilcock [1998] and Ferguson [2003] as promoting the creation of a gravel-sand transition cannot be determined from our experiments. Further research will be required to quantify the relative roles of the two mechanisms. [19] Finally, it is relevant to consider these results in the context of field examples of gravel-sand transitions such as those examined by Sambrook Smith and Ferguson [1995]. All of these transitions share many features in common, occurring over very short distances when compared with the rate of fining evident in upstream gravels. The average gravel size immediately upstream of the 18 transitions examined by Sambrook Smith and Ferguson [1995] was 18.5 mm. A short bimodal section of bed typically occurred downstream of these gravel beds, followed by the gravelsand transition, and downstream from this a bed composed overwhelmingly of sand. A comparison of the suggested figure for the critical effective roughness height of 10 mm suggested above with the average grain size found immediately upstream of these transitions can be made with reference to Gomez s [1993] data. Using his data for angular gravel (it should be noted that his work was based on stable, armored gravel beds so may not be directly comparable), which is most representative of the bed sediment for the Allt Dubhaig from which the bed profiles in these experiments were constructed, an effective roughness height of 10 mm equates to a grain size with a diameter of 18 mm. This is very similar to the average gravel diameter of 18.5 mm reported by Sambrook Smith and Ferguson [1995] as noted above. The flume experiments reported in this paper thus seem to provide a clear physical basis with which to explain the phenomenon of the gravel-sand transition. 5. Conclusion [20] The experiments reported here, simulating sand infilling a gravel bed, have shown the following: [21] 1. As the level of infill around the primary roughness elements increases there is a corresponding increase in the mean downstream near-bed velocity. This effect becomes more pronounced as the effective roughness decreases, but may be absent entirely where effective roughness values are significantly greater than 10 mm (0.4D 50 ). [22] 2. Concurrent with the increase in near-bed velocity is a decrease in near-bed shear stress and turbulent kinetic energy. [23] 3. In contrast to the mean velocity, the modest levels of infill examined here are sufficient to reduce the shear stress and turbulent kinetic energy away from the bed at elevations higher in the profile. [24] 4. On the basis of the hydraulic responses quantified here it is argued that bimodal beds are inherently unstable. Once the gravel size approaches 20 mm (0.8D 50 ), even modest inputs of sand will smooth the bed sufficiently to reduce shear stress and alter the turbulence structure such that Q2 and Q4 event frequency declines around gravel particles. The combined effect of these two factors is likely to be to reduce the mobility of gravel relative to sand so that sand dominates the bed downstream after a relatively short distance. The change from a gravel bed to a sand bed thus perhaps represents less of a gradual transition and more a fundamental threshold. [25] Acknowledgments. Thanks to Jim Best for providing access to the facilities in the Sedimentological Fluid Dynamics Laboratory within the School of Earth Sciences at the University of Leeds. The assistance of Mark Franklin with the data collection was much appreciated. The editors, two anonymous referees, and especially Rob Ferguson are thanked for their detailed comments that improved the original version of this manuscript. References Acarlar, M. S., and C. R. Smith (1987), A study of hairpin vortices in a laminar boundary layer. part 1. Hairpin vortices generated by a hemispherical protuberance, J. Fluid Mech., 175, Adrian, R. J. (1991), Particle-imaging techniques for experimental fluidmechanics, Annu. Rev. Fluid Mech., 23, Bennett, S. J., and J. L. Best (1995), Mean flow and turbulence structure over fixed, two-dimensional dunes: Implications for sediment transport and dune stability, Sedimentology, 42, Bennett, S. J., and J. L. Best (1996), Mean flow and turbulence structure over fixed ripples and the ripple-dune transition, in Coherent Flow Structures in Open Channels, edited by P. J. Ashworth et al., pp , John Wiley, Hoboken, N. J. Best, J. L. (1996), The fluid dynamics of small-scale alluvial bedforms, in Advances in Fluvial Dynamics and Stratigraphy, edited by P. A. Carling and M. R. Dawson, pp , John Wiley, Hoboken, N. J. Best, J. L. (2005), The kinematics, topology and significance of dunerelated macroturbulence: Some observations from the laboratory and field, in Fluvial Sedimentology VII, edited by M. D. Blum, S. B. Marriott, and S. F. Leclair, Spec. Publ. Int. Assoc. Sedimentol., 35, Best, J. L., and A. C. Brayshaw (1985), Flow separation: A physical process for the concentration of heavy minerals within channels, J. Geol. Soc. London, 142, Best, J. L., and R. A. Kostaschuk (2002), An experimental study of turbulent flow over a low-angle dune, J. Geophys. Res., 107(C9), 3135, doi: /2000jc Best, J. L., R. A. Kostaschuk, and P. V. Villard (2001), Quantitative visualization of flow fields associated with alluvial sand dunes: Results from the laboratory and field using ultrasonic and acoustic Doppler anemometry, J. 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