Journal of Geophysical Research: Earth Surface

Coherent flow structures in a depth-limited flow over a gravel surface: The influence of surface roughness

Authors


Abstract

[1] Turbulent flows moving over a gravel bed develop large-scale, macroturbulent flow structures that are initiated at anchor clasts in the bed and grow and dissipate as they move upward through the flow depth. This paper extends previous research in which we investigated the influence of the Reynolds number on coherent flow structures generated over a gravel bed by assessing the importance of effective bed roughness. Here, we report on flume experiments in which flows over beds of decreasing surface roughness have been quantified through the application of digital particle imaging velocimetry, which allows study of the downstream and vertical components of velocity over the entire flow field. These results indicate that as the effective roughness increases (1) the visual distinctiveness of the coherent flow structures becomes more defined throughout the flow depth, (2) the upstream angle of slope of the coherent flow structure increases, and (3) the reduction in streamwise flow velocity and turbulence intensity toward the upstream side of the structure becomes greater. Applying standard scaling laws, these structures appear shear-generated and form through a combination of both wake flapping and the reattachment of localized shear layers associated with flow separation around individual topographic protrusions. As the effective protrusion decreases, the scale of these coherent flow structures also decreases.

1. Introduction

[2] Turbulence in rivers is not a simple random field: visualization and multipoint measurements show it is possible to decompose complex, multiscaled, quasi-random flow fields into elementary organized structures that possess both spatial and temporal coherence [Adrian, 2007] that have been termed either eddies [Townsend, 1976] or coherent flow structures [Cantwell, 1981]. Flow in rivers where the bed is composed of gravel is typically shallow, with the ratio of mean depth to effective roughness height often being less than 10–20 in flood conditions and less than 5 during low-flow conditions [Charlton et al., 1978; Bathurst, 1978, 1985; Hicks and Mason, 1999; Lee and Ferguson, 2002]. In such flows with high effective roughness heights, field and laboratory measurements, in addition to numerical model predictions, indicate that the detailed microtopography of the bed exerts a significant influence on the generation, evolution, and dissipation of turbulent coherent flow structures [Wiberg and Smith, 1991; Dinehart, 1992; Kirkbride, 1993; Best et al., 2001; Roy et al., 2004; Hardy et al., 2007, 2009]. Furthermore, it is clear that the initiation and transport of sediment over such gravel surfaces will be intimately linked to the structure of turbulence [Drake et al., 1988; Hardy, 2005; Garcia et al., 2007]. Several studies have combined flow visualization and quantitative measurement [Fidman, 1953, 1991; Klaven, 1966; Klaven and Kopaliani, 1973; Imamoto and Ishigaki, 1986, 1986b; Shvidchenko and Pender, 2001; Marquis and Roy, 2006; Hardy et al., 2009] to gain an understanding of the generation, evolution, and dissipation of coherent flow structures over both smooth and rough surfaces.

[3] The development of the size and morphology of these coherent flow structure has been found to be proportional to flow depth [Roy et al., 2004], Reynolds number [Shvidchenko and Pender, 2001; Hardy et al., 2009], and bed roughness [Klaven, 1966; Klaven and Kopaliani, 1973; Shvidchenko and Pender, 2001; Buffin-Bélanger and Roy, 1998]. They appear somewhat similar in structure to those formed through classical bursting in which low-momentum fluid is ejected from the bed [Grass, 1971; Talmon et al., 1986; Shen and Lemmin, 1999; Christensen and Adrian, 2001; Adrian, 2007]. The fundamental mechanism in the formation of coherent flow structures near gravel beds has commonly thought to be the horseshoe vortex formed upstream of topographic protrusions and shedding of vortices from the flow separation zone in the lee of the particle cluster [Robert et al., 1992, 1993; Kirkbride, 1993]. Indeed, the horseshoe vortex has been cast as analogous to a simple juncture vortex [Brayshaw et al., 1983; Best, 1996; Buffin-Bélanger and Roy, 1998; Lawless and Robert, 2001]. Thus, the origin of these larger-scale motions are Kelvin-Helmholtz instabilities generated along the separation zone shear layer [e.g., Müller and Gyr, 1982, 1986; Rood and Hicken, 1989; Bennett and Best, 1995; Best, 2005], forming a region where oscillatory structure growth and breakups predominate [Kim et al., 1971] and which has previously been classified as the wake layer (wake flapping) [Nowell and Church, 1979]. This implies the creation of larger-scale flow structures by either potential superimposition or coalescence of numerous smaller-scale structures [Head and Bandyopadhyay, 1981; Smith et al., 1991; Christensen and Adrian, 2001] or where smaller-scale structures exist upon larger-scale structures. Therefore, coherent flow structures over gravels owe their origin to bed-generated turbulence, and the large-scale outer layer structures appear to be the result of flow topography interactions in the near-bed region associated with wake flapping [Hardy et al., 2009].

[4] We currently have a poor understanding concerning how the sorting of the bed material affects the generation of coherent flow structures, especially with bimodal sediment distributions that are prevalent in many rivers [Sambrook Smith and Ferguson, 1995; Smith, 1996]. In river beds that are gravel clast supported, the sand fraction (fs) is less than 10% [Wilcock and Kenworthy, 2002] and the sand particles tend to become hidden within the gravel matrix [Parker et al., 1982; Wilcock et al., 2001] and will not significantly change the effective roughness. However, as fs increases, the pore spaces fill and gravel transport rates can be enhanced with fs as low as 10%–30% [Wilcock et al., 2001; Wilcock and Kenworthy, 2002]. This reduces the effective roughness and the relative protrusion of anchor clasts. If fs further increases, gravel particles become partially or temporarily buried, which suppresses the gravel transport rates and further reduces the effective roughness. But if a gravel particle is entrained, it will move faster over the relatively smooth bed [Wilcock and Kenworthy, 2002] in a phenomenon termed “gravel overpassing” [Allen, 1983; Carling and Glaister, 1987; Carling, 1990]. A reduced effective roughness will thus both decrease the local grain friction [Dietrich et al., 1989] and reduce the loss of fluid momentum from particle wakes around particles [Dietrich et al., 1989], which at higher flows will cause locally convergent near-bed flow [McLean, 1981]. The second potential effect of filling the pore space is the reduction in bed permeability and therefore the interaction between turbulent flow in an open channel and the turbulent flow within the bed. It has previously been shown that as the bed permeability increased the bulk flow resistance increased and modified the spatial structure of the flow most notably in the time-averaged bed-normal velocities [Pokrajac and Manes, 2009]. The question addressed in the present paper is how reduction in the degree of topographic protrusion affects the generation of large-scale coherent flow structures. Previous experimental work by Sambrook Smith and Nicholas [2005] has shown that as effective bed roughness decreases (1) there is an increase in the mean downstream near-bed velocity due to a decrease in local grain friction; (2) there is a decrease in near-bed shear stress and turbulent kinetic energy; and (3) both quadrant 2 (ejections of low downstream momentum fluid away from the near-bed region) and quadrant 4 (inrushes of high downstream momentum fluid toward from the near-bed region) events decline. These observations provided valuable first insight into the processes controlling coherent flow structures. Herein, we further investigate the importance of effective roughness (i.e., topographic protrusion) upon the generation, evolution, and dissipation of coherent flow structures over water-worked gravel surfaces.

[5] The present experiments concern the study of a depth-limited flow at two different flow Reynolds numbers over three water-worked surfaces that possess an increasingly bimodal sediment distribution. The present paper extends previous research, in which we investigated solely the influence of Reynolds number on the generation of coherent flow structures, and the experimental methodology and analysis sequence used herein is largely similar to that reported by Hardy et al. [2009]. For instance, flow velocities were quantified using two-dimensional digital particle imaging velocimetry (2-D PIV) that enables continuous measurement of the whole flow field. These PIV measurements were linked to high-resolution quantification of the bed surface topography obtained using digital photogrammetry. This experimental setup thus enabled study of the generation and evolution of coherent flow structures over known bed topographies that allowed identification of (1) the topographic characteristics required for generation of macroscale turbulent flow structures; (2) the geometric shape of the flow structures; (3) the temporal length scales of the flow structures; and (4) how these characteristics change with effective roughness height.

2. Experimental Methodology

[6] All experiments were conducted in a hydraulic flume 10 m in length (lc) and 0.3 m in width (w). A series of 4 “honeycomb” baffle plates (8 mm diameter, 90% porosity) were fastened to the channel inlet in order to dampen incoming turbulence and help establish a uniform, subcritical, depth-limited boundary layer upstream of the experimental sections. The slope of the flume was adjusted to achieve constant flow depth along the test section, which was located 5.5 m downstream from the channel inlet (see Figure 1).

Figure 1.

The digital elevation models measured by digital photogrammetry on a 1 mm × 1 mm spatial resolution with a vertical precision of ±1 mm. The box represents the field of view of the PIV, an area of 0.25 × 0.25 m. In Figure 1a, the circle labeled “A” represents a large upstream clast, which appears to affect the generation of flow structures. Figure 1d shows the topography along the centerline where the PIV measurements were taken. Surface1 is represented by a solid line; surface2 represented by the dashed line; and surface3 represented by the dotted line. The section discussed in this paper is identified in Figure 1a located between the two vertical lines (0.50–0.73m).

2.1. DEM Generation Using Digital Photogrammetry

[7] A bulk sample of gravel was placed in the flume and water-worked until a stable bed (no sediment transport) was obtained, and this bed formed the experimental surface1 over which photogrammetric and PIV measurements were taken. This produced a starting surface with a D50 of 8 mm and a D84 of 19 mm, which is smaller than the grain size used in the experiments of Wilcock et al. [2001] (D50 13.4 mm and D90 39 mm). In order to reduce the roughness, sand (D50 = 0.7 mm) was added to the flume upstream of the PIV interrogation sections (see Figure 1), water-worked, and allowed to form a uniform deposit within the gravel matrix, thereby forming surface2. The roughness characteristics were calculated (see section 2.2) from the measured DEM. After flow measurements were undertaken, this process was then repeated to form surface3.

[8] For all three bed surfaces, the morphology was measured using digital photogrammetry. The methodology used is identical to that employed in the work of Hardy et al. [2009], where images were collected in standard red, green, and blue bands at a resolution of 3060 × 2036 pixels. A feature-based stereo-matching algorithm was applied to match local pixel characteristics and thus automatically identified conjugate points in overlapping images. The study surface was covered by nine consecutive images with 60% overlap between images, and 84 control points were surveyed to obtain the x, y, and z coordinates of the targets. The resulting DEMs were not smoothed, although they were cropped to eliminate edge errors, and provided measurement of a 0.923 m × 0.26 m area on a 0.001 m resolution of the surface (Figure 1) with a vertical precision of ±0.001 m.

[9] These three DEMs were used to quantify the bed roughness. Typically, roughness characterization employs the 84th percentile of the grain size distribution (D84) with the assumption that roughness correlates with particle size. However, with topographic information on the spatial resolution of the DEMs collected, effective roughness can be calculated. Fractal analysis has previously been used to study the scale dependence and self-affinity of rough surfaces [e.g., Butler et al., 2002], although a limitation of this approach is that a single value with a physical dimension is not calculated. Herein, an alternative approach was employed that calculates a roughness value that is a scale-dependent measure of the 84th percentile (R84) of the elevation differences between pixels as a function of horizontal scale. In order to maximize the sample size, a maximum horizontal distance of w/2 (0.15 m) was used, which yielded a constant R84 over a search distance of 0.04 m (Figure 2). The calculated R84 values are 0.024 m for surface1, 0.021 m for surface2, and 0.015 m for surface3, representing a 12.5% and 37.5% reduction in R84 between surface1, surface2, and surface3, respectively.

Figure 2.

The R84 for the three DEMS as a function of horizontal search distance. Solid line, surface1; dotted line, surface2; dash-dotted line, surface3.

2.2. Hydraulic Conditions

[10] In these experiments, the water depth was maintained at a constant value of 0.2 m for each of the three different surfaces, at two different mean downstream velocities of 0.155 and 0.30 m s−1 (measured at 0.4 z/Y, where z and Y are height above the mean bed elevation and flow depth respectively). This allowed investigation of these three surfaces at two flow Reynolds numbers of about 13,000 and 25,000. These hydraulic conditions were chosen for specific theoretical and practical reasons. Theoretically, the present study aimed to understand the generation and nature of coherent flow structures forming over surfaces of decreasing roughness. However, it was also necessary to assess whether the trends in the flow structure identified with changing effective roughness were consistent for a range of flow Reynolds numbers as flow is rarely steady in natural rivers. Consequently, depth was held constant and mean flow velocity used to increase the flow Reynolds number. Additionally, two practical issues had to be considered. Primarily, it was not possible to illuminate the whole flow depth with the laser configuration used herein, and thus, if greater depths were used, it would not have been possible to track the flow structures to the water surface. Second, a maximum velocity of 0.3 m s−1 (Re 25,000) had to be used, as this was close to the entrainment threshold of the sand fraction, and sediment transport causes increasing opacity within the flow that impairs accurate PIV results being collected. However, it must be noted that working at these width-to-depth ratios there is the potential for secondary circulation although secondary flow is typically only a few percent of the average flow velocity [Colombini, 1993]. Table 1 summarizes the hydraulic conditions used in this study, and the experiments are subsequently referred to according to their surface roughness and Reynolds numbers (Re).

Table 1. The Hydraulic Conditions Used in These Experiments
 Experiment 1Experiment 2
Flow Velocity (m s−1)0.1550.300
Flow Depth (m)0.2000.200
Qs (m3 s−1)9.3 × 10−31.8 × 10−2
Froude Number≈0.11≈0.21
Flow Reynolds Number≈13,000≈25,000

2.2.1. Digital Particle Imaging Velocimetry (PIV)

[11] Velocity measurements were obtained using a two-dimensional DANTEC digital particle imaging velocimetry system (2-D PIV), which is a nonintrusive, whole flow field technique for velocity measurement. A major advantage of PIV is that it is multipoint and can be used to study the entire flow field instantaneously. The PIV methodology and postprocessing applied herein is identical to that previously used by Hardy et al. [2005, 2009]. Measurement is based upon seeding the flow with hollow glass spheres with a mean diameter of 10 μm and illuminating the flow field with a double-pulsed laser light sheet (NewWave Solo Laser; pulse energy, 0.120 J; time gap between flashes, 0.067 s). When the laser sheet illuminated the flow, light was scattered by the seeding material and detected by a charged-couple device (CCD) camera (1008 × 1016 pixel, Kodak Mega Plus ES1.0) positioned perpendicular to the light sheet. In order to derive a velocity vector map, a digital mesh of small interrogation regions (16 × 16 pixels, where 1 pixel ≈ 2.5 × 10−4 m) was draped over the images. For each interrogation region, in each pair of images, the displacement of groups of particles between the first and second image was measured using the fast Fourier transform (FFT)-based spatial cross-correlation technique and a velocity vector was determined [see Westerweel, 1997]. The entire process was repeated at 15 Hz until the flow was sampled for 1 min. This sample length provided a sufficient time period to obtain a stationary time series, which was tested by systematic convergence of the cumulative variance for both velocity components to a constant value.

[12] The camera was located perpendicular to the bed, so that slices of flow could be interrogated for the downstream (u) and vertical (w) components of velocity. The setup described above enabled data collection at a spatial resolution of 0.002 m. In order to maximize the signal-to-noise ratio of the particle cross correlations, a sequence of six quality checks as previously used by Hardy et al. [2005, 2009] were undertaken. With this methodology, the estimated precision of the derived velocities was greater than 1/10th of a pixel [Wilbert and Gharib, 1991; Huang et al., 1997; DANTEC, 2000], which equates to an uncertainty in the velocity measurement of better than ±0.08 mm s−1.

[13] The area illuminated by the light sheet over the surfaces was aligned along the centerline of the flume. For this transect, three sections, each ≅0.25 m in downstream length, were collected to enable a time-averaged map of 0.75 m length to be quantified (see location of PIV area in Figure 1). Although the camera had a 0.25 × 0.25 m field of view, the illumination by the laser only allowed for collecting useful data in 0.25 m long and 0.12 m high areas, and therefore data need to be collected in two distinct illumination areas in the vertical dimension (1) covering the bed region and (2) extending to the free surface. Thus, six interrogation regions were collected for each of the three surfaces (see Figure 1) for both flow conditions and are located upstream of the sections reported by Hardy et al. [2009].

2.3. Analysis Methodology

[14] The PIV data are collected on a regular grid (125 × 126) with each point providing a time series for 1 min at a temporal resolution of 15 Hz. The whole flow field can then be analyzed by either time-averaged or time-dependent techniques. In this study, we employ a similar analysis sequence to that used by Hardy et al. [2009], which explored the flow characteristics through (1) time-averaged flow fields; (2) instantaneous flow visualization, which is achieved through the analysis of consecutive images of both the calculated u and w component velocity maps; (3) the root mean square (rms) values of velocity; (4) the Reynolds stresses (τxz) and turbulence production (Pxz); (5) the analysis of turbulent structures through quadrant analysis; and (6) the identification of temporal length scales through wavelet analysis. In all the PIV images (Figures 38), flow can only be measured where adequate illumination is detected by the cameras. Therefore, it is not always possible to measure directly over the bed due to reflection where the laser reflects off the bed (especially for sand in surface3) or if a large particle blocks the field of view from the side. In this case, the large particles (>D90) were removed from between the interrogation region and the camera. All images were masked near the bed according to the quality of the PIV data. Accordingly, masking varied between runs and between measured quantities for a given run. The actual bed surface corresponding to each image is displayed in Figure 1d.

Figure 3.

Time-averaged velocity for (a–c) the downstream (u) component and (d–f) the vertical (w) component of the velocity for Reynolds number 25,000 for (a, d) surface1, (b, e) surface2, and (c, f) surface3. 0.6 z/Y is equal to 0.12 m, and x/l is equal 0.25 m. In all images, flow is from right to left.

Figure 4.

(a) A time series of the instantaneous u component of velocity normalized by 0.35 mean u component for Re 25,000 for surface1, surface2, and surface3. Each image is separated by 0.13 s. 0.6 z/Y is equal to 0.12 m, and x/l is equal 0.25 m. In all images, flow is from right to left. (b) A time series of the instantaneous w component of velocity normalized by 0.35 mean w component for Re 25,000 for surface1, surface2, and surface3. Each image is separated by 0.13 s. 0.6 z/Y is equal to 0.12 m, and x/l is equal 0.25 m. In all images, flow is from right to left. The time step used is identical to the u component in Figure 4a. (c) A time series of the instantaneous u component of velocity normalized by 0.35 mean u component for Re 13,000 for surface1, surface2, and surface3. Each image is separated by 0.13 s. 0.6 z/Y is equal to 0.12 m, and x/l is equal 0.25 m. In all images, flow is from right to left. (d) A time series of the instantaneous w component of velocity normalized by 0.35 mean w component for Re 13,000 for surface1, surface2, and surface3. Each image is separated by 0.13 s. 0.6 z/Y is equal to 0.12 m, and x/l is equal 0.25 m. In all images, flow is from right to left. The time step used is identical to the u component in Figure 4b.

Figure 4.

(continued)

Figure 5.

The turbulence intensity calculated as the root mean square of the velocity fluctuations for (a–f) u component and (g–l) w component of velocity for Reynolds number of (a–c, g–i) 25,000 and (d–f, j–l) 13,000 and for (a, d, g, j) surface1, (b, e, h, k) surface2, and (c, f, i, l) surface3. 0.6 z/Y is equal to 0.12 m, and x/l is equal 0.25 m. In all images, flow is from right to left.

Figure 6.

(a–f) The Reynolds stresses (τxz) and (g–l) turbulence production (Pxz) for (a, d, g, j) surface1, (b, e, h, k) surface2, and (c, f, i, l) surface3 for (a–c, g–i) Re 25,000 and (d–f, j–l) Re 13,000.

Figure 7.

The flow structures examined through quadrant analysis, (a–f) quadrant 1 (Q1), (g–l) quadrant 2 (Q2), (m–r) quadrant3 (Q3), and (s–x) quadrant4 (Q4), and two Reynolds numbers, (a–c, g–i, m–o, s–u) 13,000 and (d–f, j–l, p–r, v–x) 25,000, for (a, d, g, j, m, p, s, v) surface1, (b, e, h, k, n, q, t, w) surface2, and (c, f, i, l, o, r, u, x) surface3. 0.6 z/Y is equal to 0.12 m, and x/l is equal 0.25 m. In all images, flow is from right to left.

Figure 7.

(continued)

Figure 8.

The time frequency of the (a–f) primary and (g–l) secondary peak calculated in the time-averaged wavelet power spectra for the two Reynolds numbers, (a–c, g–i) 13,000 and (d–f, j–l) 25,000, and for (a, d, g, j) surface1, (b, e, h, k) surface2, and (c, f, i, l) surface3. In all images, flow is from right to left.

3. Results

3.1. Time-Averaged Flow Fields

[15] The time-averaged flow fields for the downstream (u) and vertical (w) components of velocity (Figure 3) show the influence of different bed topographies on near-bed flow. Although the mean components of velocity do not identify individual coherent flow structures, they do reveal the effect of topographic protrusion (effective roughness) on the localized flow field. Here the results from the Re = 25,000 experiment are shown. Analysis of the time-averaged downstream (u) component for the three surfaces (Figures 3a3c) shows areas of flow recirculation in the wakes of protruding clasts, above which there is an increase in average flow velocity with depth. The magnitude of these negative (i.e., upstream) u velocities decreases as the bed is infilled, although the regions of low u velocity become more continuous along the entire bed. For surface1, localized areas of recirculation are observed in the lee of topographic protrusions (maximum ≈ 0.2 m in length; Figure 3a, region A). These regions of lower u velocity become more elongated for surface2 (Figure 3b) as the bed becomes smoother, until an undisturbed velocity profile appears for surface3 across the field of view (≈ 0.25 m), except between the two large protruding clasts (Figure 3c, region B). Thus, as the bed becomes smoother, although there are fewer topographic protrusions to initiate flow separation, there is a greater spatial area between the topographic protrusions in which recirculation zones can persist. For all bed roughnesses, the effect of the bed surface on the mean u component is not detected above 0.18 z/Y at which height the horizontal velocities become comparable. The vertical (w) component more clearly identifies regions of both flow separation and reattachment over individual particles (Figures 3d3f). The most apparent features within the mean w component flow field are (Figure 3d, region C): (1) localized regions of flow separation behind individual clasts, which appear to influence flow further from the bed over rougher surfaces and (2) at the upstream part of the test section, the area of flow recirculation that appears associated with the prominent topographic protrusion located upstream of the interrogation window (see Figure 1a, region marked as A; Figure 1d in region <0.4 m on the abscissa axis) increases in length as the bed roughness decreases.

3.2. Instantaneous Flow Visualization

[16] Analysis of both the instantaneous downstream (u) and vertical (w) components of velocity in a series of consecutive images provides a visualization of flow (Figure 4). The simplest approach to analyze a turbulent flow is to decompose the field into a constant velocity plus the deviatoric component [Adrian et al., 2000]; however, there is no dynamical basis for preferring one frame of reference. In the present study, both components of velocity at each point are multiplied by 0.35 of the mean component of velocity, thus enabling better detection and visualization of vortical structures within the flow.

[17] All of the images demonstrate the high spatio-temporal variability in the flow over the surfaces and that the turbulent structures close to the bed can be detected visibly in the u component: these are clearly seen as “bulges” of lower-velocity fluid originating at the bed and intruding into the outer flow. These “bulges” of fluid are most visibly detectable in the u component at Re = 25,000 for surface1 (Figure 4a, column 1), where it can be seen that they extend to 0.65 z/Y. The backs (upstream side) of these large-scale turbulent structures adopt a defined boundary, sloping upstream at an angle visually estimated to be ∼60° (marked as dotted line A, Figure 4i, column 1). It is more difficult to define the front of the structure visually, although the downstream lead angle may be steeper at ∼80° (marked as dotted line B, Figure 4i, column 1) than the upstream back of the structure. There is also an apparent decrease in the streamwise velocity toward the back of the flow structure, with a clearly defined region of higher-velocity flow between each of these low-velocity structures (Figures 4i and 4ii). As the surface becomes smoother to surface2 (Figure 4i, column 2, line labeled C), several features are apparent: (1) the defined boundary at the back of the structure slopes upstream at a shallower angle (45°); (2) the front of the structure becomes more difficult to define; (3) there is a smaller decrease in relative streamwise velocity toward the back of the structure; and (4) the flow structure does not extend as far above the bed (≈0.4 z/Y). When surface3 (R84 = 0.015m) is examined (Figure 4i, column 3), the back of the flow structure slopes upstream at an angle of 45° but does not protrude high into flow (∼0.2 z/Y) and appears to be entrained by the surrounding flow (Figure 4i, labeled line D), forming a region close to the bed that has low flow velocities.

[18] The large-scale coherent flow structures are not as visibly apparent in the vertical (w) component of velocity (Figure 4ii), which is characterized by much smaller packages of high-positive (upward) and low-negative (downward) fluid moving through the flow field. The direct influence of the bed is also hard to identify, with no consistent flow pattern originating from a particular topographic protrusion. However, packets of high-magnitude, upward-directed flow can be clearly seen defining the top of the structures identified in the u component (Figure 4ii, regions A, B, and C), with possible smaller-scale structures with higher w values being superimposed on the large coherent flow structures (Figure 4ii). Finally, the numbers of events, later implied through quadrant analysis, of high w component flow appear to decrease as the effective roughness decreases.

[19] The visual distinctiveness of these coherent flow structures decreases at lower Reynolds numbers, although they do show similar geometric characteristics (Figure 4iii, column 1, region A). Furthermore, for surface2, a trace of an older flow structure that has been generated further upstream is observed higher in the flow (Figure 4iii, column 2, region B). At Re = 13,000, the geometry of the flow structures over surface3 appears different to that over either surface1 or surface2. Although a steep, clearly defined, boundary is present at the back of the structure, this penetrates no more than 0.25 z/Y and then a long, low-angle structure forms (Figure 4iii, column 3, labeled line C). As this flow structure evolves into the flow, it does so at a low angle (∼5°), that is a little higher in angle than that visualized at Re = 25,000 (Figure 4i, column 3). A similar pattern can also be observed in the w component to that observed at Re = 25,000, in that packets of high-magnitude upward velocity fluid (+w′) are present along the top of the coherent flow structures (Figure 4iv). However, in general, as with the u component, the intensity of the w component decreases at lower Reynolds numbers.

3.3. Turbulence Intensity

[20] Turbulence intensity was evaluated using the root mean square value (rms) of each velocity component at each point and reveals regions of highly turbulent flow in the near-bed region (Figure 5). Similar to the results of the time-averaged u component of flow, the greatest turbulence intensities occur within the near-bed region (<0.3 z/Y), and by 0.5 z/Y the turbulence intensity becomes comparable for both components of velocity for all surfaces and both Reynolds numbers.

[21] For surface1 (Figure 5d), an intense continuous band of high turbulence intensity is observed forming over the bed, across the whole field of view, originating in shear layers that develop over protruding clasts. As the surface becomes smoother, the continuous band diminishes into more localized zones of high turbulence intensity (Figure 5e, region A) associated with topographic forcing around more isolated and increasingly smaller roughness elements. In addition, some isolated regions of very low turbulence intensity occur in the lee side of some particles. For surface3, the turbulence intensity is the lowest of the three roughnesses investigated (Figure 5, column 3), with only a few very localized regions of higher turbulence intensity being apparent. Furthermore, the presence of lower turbulence intensities at the bed as the surface becomes smoother results in a lower gradient of turbulence intensity throughout the flow depth, since by 0.5 z/Y the turbulence intensity is comparable for all three surfaces. These spatial trends in turbulence intensity with changing bed roughness are also similar at Re = 13,000, with regions of higher turbulence intensity becoming lower in magnitude, smaller in spatial extent, and increasingly isolated as the effective roughness decreases. The turbulence intensity values of the vertical (w) component show less spatial coherence than the u component, especially higher in the flow. The values of vertical turbulence intensity at first become higher as the roughness decreases (Figure 5, surface1-surface2), possibly due to the decreasing interaction between shear layers as the roughness elements become more isolated and there is less wake interference between particles. However, as roughness decreases further (Figure 5, surface2- surface3), the w component turbulence intensities decline as the roughness elements become smaller and local topographic forcing becomes less influential.

3.4. Reynolds Stresses and Turbulence Production

[22] The degree of momentum exchange from structures generated at the bed to the mean flow was assessed through both the time-averaged Reynolds stresses (the turbulent stresses) (τzx = τxzρequation image) and turbulence production through vertical shear (equation image) as described by Nelson et al. [1995] (Figure 6). The results are similar to the time-averaged u component of flow and turbulence intensities in that the greatest Reynolds stresses and turbulence production occur within the near-bed region and demonstrate the influence of the bed topography on near-bed flow. For the Reynolds stresses, a continuous band of high turbulent stresses exists across the whole field of view in a region of <0.3 z/Y. However, as the bed becomes smoother, the band of high-intensity Reynolds stresses becomes thinner and located lower in the flow, and also appears to comprise more localized regions of high-intensity. When the turbulence production is analyzed for all three surfaces, the high turbulence production is located in a region <0.2 z/Y, and by 0.5 z/Y the turbulence production becomes comparable for all surfaces and both Reynolds numbers. Furthermore, the highest turbulence production appears to be associated from shear (wake flapping) from topographic protrusions in the bed. As the bed becomes smoother, a series of consistent trends are identifiable and include a decrease in (1) the number of high turbulence production regions; (2) the intensity of turbulence production; (3) the downstream length of the high intensity regions; and (4) regions of high turbulence production do not merge into a single band.

3.5. Quadrant Analysis

[23] Quadrant analysis has previously been used to discriminate turbulent boundary layer events [e.g., Lu and Willmarth, 1973; Bogard and Tiederman, 1986; Bennett and Best, 1995]. By applying the standard definition of Lu and Willmarth [1973], four quadrants can be defined around a zero mean: (1) quadrant 1 events or outward interactions (positive u component, positive w component); (2) quadrant 2 events or bursts (negative u component, positive w component); (3) quadrant 3 events or inward interactions (negative u component, negative w component); and (4) quadrant 4 events or sweeps (positive u component, negative w component). In the present analysis, all four quadrants and each velocity pair were studied using a “hole” size [Lu and Willmarth, 1973; Bogard and Tiederman, 1986; Bennett and Best, 1995] of one standard deviation.

[24] In agreement with the earlier work of Hardy et al. [2009], the spatial pattern of quadrant events over individual surfaces is independent of the flow Reynolds numbers used in this experiment (see similarity between Figures 7a and 7d, 7g and 7j, 7h and 7k, and 7i and 7l). However, the distribution of quadrant events is seen to change with varying surface roughness and suggests that the surface topography (effective roughness) dominates the nature of the flow field. Localized flow structures can be identified in the near-bed region (<0.1 z/Y) and consist of alternating patterns of quadrant 2 (stoss side) and quadrant 4 (lee side) events, demonstrating topographic forcing of flow around individual clasts. This observation is evident for surface1 and surface2, but this pattern is less apparent over surface3 (Figure 7). Furthermore, a dominant band of intense quadrant 2 events (>8%) is identified above all three surfaces. This is located closer to the bed with decreasing surface roughness; for surface1 the region is located between 0.2 and 0.55 z/Y, although it is connected to the bed at 0.3 x/l; for surface2 the band decreases in spatial area and is lower within the flow (<0.35 z/Y); while for surface3 the band is located in a region <0.3 z/Y. Quadrant 2 events identify large-scale flow structures, potentially generated by Kelvin-Helmholtz instabilities that are formed along the lee side shear layers [Bennett and Best, 1995; Buffin-Bélanger and Roy, 1998; Best et al., 2001; Best, 2005]. When quadrant 1 and quadrant 3 events are studied, a similar alternating pattern is apparent in the near-bed region to the relationship between quadrants 2 and 4. Quadrant 1 events are located on the stoss side of particles with quadrant 3 events occurring in the lee side. Furthermore, for quadrant 3 events over both surface2 and surface3, a higher percentage of Q3 events (>4%) is present higher in the flow (0.3 z/Y). This pattern is interpreted to represent these structures being generated by a larger upstream particle (Figure 1d), which causes the flow, as it approaches the clast, to decelerate or reverse close to the bed, but otherwise accelerate as it is forced over or around the particle. Localized flow deceleration occurs in the separation zones that form downstream of the large anchor clasts: flow within these separation zones recirculates and a shear layer that extends downstream is associated with the lee side of each clast.

3.6. Wavelet Analysis

[25] Wavelet analysis was identified as the most beneficial method to quantify the temporal length scales of the flow structures because visual inspection of the extracted time series suggested that (1) the scales of variability were only intermittently present and (2) the scales of variability evolved temporally and spatially as a function of time (or space). Wavelet analysis is now a standard methodology to decompose turbulence signals [e.g., Roussel et al., 2005; Schneider et al., 2006; Fischer et al., 2007; Keylock, 2007; Joshi and Rempfer, 2007; Ma and Hussaini, 2007; Hardy et al., 2009]. The approach employed in the present analysis is identical to that used by Hardy et al. [2009] and includes use of the Morlet wavelet since it is morphologically similar to the schematic diagram of the elementary decomposition of turbulent energy from a characteristic eddy (as proposed by Tennekes and Lumley [1972]) and has been suggested as the most appropriate wavelet for studying the dynamics of turbulence [Liandrat and Moret-Bailly, 1990]. The statistical significance of the wavelet was tested following the approach of Torrence and Compo [1997], who show that the most apt method is based upon the choice of an appropriate background spectrum that is associated with noise: if a point in the wavelet power spectrum is statistically distinguishable from the associated point in the background spectrum, then it can be assumed to be a significant fit at the confidence level chosen. As is commonly observed in turbulent time series, we assumed that white noise would be present [Biron et al., 1998].

[26] Following Hardy et al. [2009], the approach was applied to every point within the flow field by calculation of the time-averaged wavelet power spectrum. This permitted identification of the two main peaks in the wavelet power spectrum and their temporal frequency (Figure 8), thus enabling a spatial plot of the dominant frequencies throughout the flow field. The principal difference between the primary and secondary peaks (Figure 8) is that much larger, spatially coherent, regions of similar frequencies are observed in the primary peak, a feature that is more apparent for Re = 13,000. For Re = 13,000 over surface1 (Figure 8a), a well-defined band exists from the bed to 0.4 z/Y that contains flow structures with a temporal length scale of between 3 and 5 s. Within this band, the temporal length scale appears to increase with height in the flow above the bed. The only region of shorter temporal length scale (Figure 8a, region A) is located behind a protruding clast (<0.05 z/Y), but this region is not continuous downstream across the entire flow field. As the surface becomes smoother, the region containing longer temporal length scale structures decreases in its height in the flow and shortens in its spatial extent (for surface2, <0.3 z/Y and ≈0.6 x/l; for surface3, <0.2 z/Y and ≈0.4 x/l). This trend in periodicities also mirrors the similar patterns identified in quadrant 2 events (Figure 8) and the mean components of flow (Figure 3) and appears to be generated by flow structures originating from a large protruding clast outside of the field of view (see Figure 1a, marked A). Above this intense band of longer-period structures, flow structures with a temporal length scale of ≈2 s are present. Furthermore, localized regions of long temporal length scale (>4–5 s) are evident (Figures 8a8c, regions B, C, and D) toward the top of the flow (≈0. 5 z/Y) for surface1 but decrease in the height at which they occur (≈ 0.25 z/Y) for both surface2 and surface3. Finally, for surface2 and surface3, especially at Re = 13,000, little consistent spatial pattern is apparent besides the longer temporal length scales that occur near the stoss and top of the clasts.

[27] For the secondary peak in periodicities, a far less coherent pattern exists than for the primary peak, with the temporal length scale generally being smaller than that of the primary peak. The one identifiable trend that can be observed is narrow bands of flow structures >3 s in temporal length scale that originate from the bed and extend into the main body of flow (Figures 8g and 8h, lines E1 and E2). Similar features can be observed in all of the secondary peaks and suggest that these structures are forming at the bed and being entrained into the flow.

[28] In order to collapse the data in Figure 8, the time frequencies have been grouped into wavelet frequency time bins (Figure 9), enabling examination of the primary frequencies and formative mechanisms generating these coherent flow structures. The results are presented as a percentage of the whole of the sample length, for each time bin, of the total number of structures detected and are also displayed as cumulative percentage plots (Figures 9d, 9h, 9l, and 9p) to illustrate the distribution of flow structure periodicities.

Figure 9.

The distribution of the primary time peak (a–c and e–g) calculated in the time-averaged wavelet power spectrums for the two Reynolds numbers: (a–d) 13,000 and (e–h) 25,000 and for (a, e) surface1, (b, f) surface2, and (c, g) surface3. (d, h) For the cumulative plots, surface1 is line with dot marker, surface2 is line with the circle marker, and surface3 is line with plus marker).

[29] For the primary peak, which is identified as the dominant flow structure, a consistent pattern is detectable as the surface becomes smoother. Initially, all the primary peaks possess some degree of bimodality (Figures 9a9c and 9e9g). For example, at Re = 13,000, surface1 (Figure 9a) has 24% of its flow structures with a temporal length scale of 2.2 s (0.45 Hz) and possesses a second set with temporal length scales between 3 and 3.8 s (0.33–0.25 Hz), which account for 55% of the total. These two frequencies account for 80% of the total number of detected structures. As the bed surface becomes smoother (surface2), a dominant time peak is still identified but the range of frequencies increases (i.e., 2.2–2.4 s (0.42–0.45 Hz)) and accounts for 45% of flow structures detected. Some degree of bimodality is still detected in these temporal length scales over surface2, with the second peak detected between 3.2 and 3.4 s (0.29–0.1 Hz) and decreasing in its magnitude to represent 14% of the flow structures detected in the primary peak. These two temporal length scales account for ≈60% of the structures detected over surface2. For the smoothest bed (surface3), the dominant temporal length scale is between 1.8 and 2.4 s (0.42–0.56 Hz) and accounts for 54% of structures. Again, bimodality exists in this distribution (Figure 9c), with longer temporal length scales identified between 3.2 and 3.4 s (0.29–0.1 Hz) and accounting for 18% of the total structures identified. These two temporal length scales account for ≈73% of the total flow structures over surface3. For all three surfaces, two main temporal length scales thus dominate the whole flow field (surface1 ≈ 80%, surface2 ≈ 60%, and surface3 ≈ 73%). However, the temporal length scale of these flow structures changes with increasing effective bed roughness; the range of temporal length scales increases within the main peak, with the percentage contribution of these period structures to the whole flow field increasing. Furthermore, for the roughest surface, there is a greater contribution from the secondary peak showing the influence of processes with longer temporal length scales. For surface2 and surface3, the contribution of events with longer temporal length scales is equal and contributes less than 20% of the total number of flow structures. Thus, the overall effect of the bed smoothing is that the temporal length scale of the structures shortens (Figure 9d).

[30] For Re = 25,000, the degree of bimodality in these distributions is not as obvious (Figures 9e9h), although it is still detectable over surface2 and surface3. For surface1, a single peak is detected between 2.2 and 2.8 s (0.36–0.45 Hz) that accounts for 68% of the flow structures detected. Over surface2 the main peak is identified between 2 and 2.2 s (0.45–0.5 Hz) and accounts for 30% of the flow structures, in addition to a peak at 1.4 s (0.71 Hz) that accounts for 10% of the structures and a minor tail to the distribution between 3.2 and 3.8 s (0.26–0.31 Hz). For surface3, periods of between 1.4 and 2.2 s (0.48–0.71 Hz) account for 50% of the structures with a secondary peak between 3.8 and 4.4 s (0.23–0.26 Hz) accounting for 16% of the structures. Therefore, as the bed becomes smoother (Figures 9e9g), the number of structures detected within a single time bin decreases, thus causing a concurrent significant grouping of flow structures within a narrower range of frequencies. Again, as at Re = 13,000, there appears to be a change in the scale and periodicity of the flow field between surface1 and the smoother surfaces, as shown in the plots of cumulative distributions of the primary peak frequencies (Figures 9d and 9h).

[31] Several different generalized relationships have been proposed to calculate dimensionless numbers for bluff bodies that define the period of large-scale turbulent structures and aid understanding of the overall turbulence signature. These relationships include (1) the Strouhal number (fstr = Us/2πδ, where fstr is the Strouhal frequency, Us is free stream velocity, and δ is the flow depth (d = h)) that describes the frequency of shear layer generated turbulent structures [Levi, 1983, 1991]; (2) the vortex shedding frequency (fv = 0.6–0.8U/xr, where fv is the vortex shedding frequency, U is mean velocity, and xr is reattachment length) [Simpson, 1989; Driver et al., 1987]; and (3) the wake flapping frequency of the reattaching shear layer (fw < 0.1U/xr, where fw is the period of wake flapping) [Simpson, 1989]. The underlying problem with all of these relationships is that the flow reattachment point can be variable and extremely difficult to determine [Nelson and Smith, 1989; Kostaschuk, 2000; Best and Kostaschuk, 2002], except in a time-averaged sense [Schmeeckle et al., 1999]. Additionally, the reattached flow may not fully recover its “upstream” hydraulic and sediment transport characteristics within the expected length of reattachment [Carling et al., 2000]. However, these relationships do provide a first step toward deducing the processes generating the temporal length scales detected (Figure 9) and can also allow estimations of reattachment lengths.

[32] The main topographic protrusions were identified from the PIV data (Figure 10). This approach was used rather than extracting the locations from the DEM (Figure 1d) as near-bed curvature, especially for surface2 and surface3 where fs concentrations are high, can cause laser reflection preventing the measurement of velocity. From these points on the bed, the following hydraulic variables were extracted; flow depth, mean flow velocity, and one standard deviation of flow velocity at the cell nearest to the bed and at 0.4 z/Y. Use of the standard deviation of velocity provided a window of frequencies by following the modified U-level technique [Luchik and Tiederman, 1987] for the detection of large-scale structures. The hydraulic variables were used to calculate the Strouhal frequencies [Levi, 1983, 1991] (fstr, Table 2) and compared to the primary and secondary frequencies from the calculated wavelet power spectrum (WPS, Table 2). In general, when using the velocities derived from the near-bed region (UBED), an order-of-magnitude difference exists between the two frequencies, with the experimentally estimated Strouhal frequencies being smaller. However, when using flow velocities derived at 0.4 z/Y, a slightly greater level of agreement exists, especially when Re = 25,000. This suggests that a bulk flow velocity may be more appropriate in Strouhal number calculations rather than the local near-bed velocity near the point of flow separation.

Figure 10.

The locations of the topographic protrusions where the depth, mean velocity (Figure 2), and the time frequency of the primary and secondary peak in the time-averaged power spectrum (Figure 8) are extracted to calculate the Strouhal numbers (Table 2) and estimate reattachment lengths using the dimensionless relationships of Simpson [1989] (Table 3). The identified protrusions (triangles) are labeled in Tables 2 and 3 in numeric values with protrusion 1 located in the far left of the image increasing in numeric value across the image. The solid line represents the bed identified from the PIV data, while the actual topography measured from the DEM is represented by the dotted line.

Table 2. The Flow Depth, Mean, and Standard Deviation of the Free Stream Velocitya
ProtrusionFlow Depth, YUBEDUBEDσfstr (mean)fstr (range)WPSprWPS2ndU0.4U0.4σFs (mean)Fs (range)WPSprWPS2nd
  • a

    The flow depth (Y), the mean (UBED), and the standard deviation (UBEDσ, where range = ±1σ) of the free stream velocity at the bed and at 0.4 z/h and calculated Strouhal numbers (fstr) above the protruding clasts identified in Figure 10. WPS is the wavelet power spectrum calculated in Figure 9.

Surface1Re 13,000
10.1740.0300.0100.0270.02–0.040.3200.5390.1670.0100.1530.14–0.160.4530.736
20.172−0.0160.017−0.015NA0.5980.6410.1680.0100.1560.15–0.160.4380.736
30.1700.0880.0280.0820.06–0.110.3320.5200.1690.0110.1580.15–0.170.4530.289
40.1620.1050.0310.1030.07–0.130.3200.6410.1630.0110.1600.15–0.170.4530.260
50.1700.0910.0340.0850.05–0.120.2990.2790.1590.0120.1590.14–0.160.4380.687
 
Surface1Re 25,000
10.1740.0440.0150.0400.03–0.050.3090.2430.3160.0250.2890.26–0.310.3940.663
20.1720.0450.0460.0420.00–0.080.2510.4380.3190.0250.2950.27–0.320.3311.005
30.1700.1660.0640.1550.10–0.220.7113.5000.3230.0210.3020.28–0.320.4080.663
40.1620.1880.0600.1850.13–0.240.4530.3200.3160.0260.3110.28–0.340.8160.875
50.1700.1690.0850.1580.08–0.240.2890.3090.3070.0260.2870.26–0.310.4231.195
 
Surface2Re 13,000
10.1700.0200.0230.0190.00–0.040.2340.5390.1570.0100.1470.14–0.160.3810.243
20.1680.0200.0140.0190.01–0.030.3090.7110.1600.0100.1520.14–0.160.4231.326
30.1680.0140.0070.0130.01–0.020.3320.9060.1560.0100.1480.14–0.160.4230.320
40.1660.0320.0120.0310.02–0.040.3090.3320.1540.0100.1480.14–0.160.3320.251
50.1600.0510.0180.0510.03–0.070.3090.5200.1570.0090.1560.15–0.170.3680.598
 
Surface2Re 25,000
10.1700.0170.0210.0160.00–0.040.2790.2510.3200.0250.3000.28–0.320.5200.938
20.1680.1690.0540.1600.11–0.210.2890.5030.3210.0260.3040.28–0.330.4380.260
30.1680.0960.0360.0910.06–0.130.2510.5580.3210.0260.3040.28–0.330.2511.237
40.1660.0390.0160.0370.02–0.050.2790.4270.3210.0260.3080.28–0.330.4081.005
50.1600.1060.0490.1050.06–0.150.2430.4850.3250.0210.3230.30–0.341.0410.711
 
Surface3Re 13,000
10.170–0.0090.0080.00NA1.0050.7110.1530.0120.1430.13–0.150.2690.438
20.1680.0070.0090.0070.00–0.020.6630.6190.1500.0120.1420.13–0.150.2990.687
30.1660.0840.0290.0800.05–0.110.2890.4850.1500.0120.1440.13–0.160.2790.736
40.1680.0340.180.0330.00–0.200.5390.5770.1520.0110.1440.13–0.150.2890.663
 
Surface3Re 25,000
10.1700.0320.0240.0300.01–0.050.9061.2810.3090.0240.2890.27–0.310.6630.381
20.1680.1400.0660.1330.07–0.200.2430.7360.3070.0260.2910.27–0.320.5201.421
30.1660.0760.0280.0720.05–0.100.4690.2690.3080.0270.2950.27–0.320.7890.423
40.1680.1170.0480.1120.07–0.160.6630.3090.3100.0230.2940.27–0.320.5390.577

[33] The frequencies obtained from the wavelet power spectrum (WPS) from the near-bed locations were used to calculate the reattachment length for both vortex shedding [Simpson, 1989; Driver et al., 1987] and wake flapping [Simpson, 1989] (Table 3). The reattachment lengths for wake flapping range between 1 and 30 mm for Re = 13,000 and 3–60 mm for Re = 25,000, and these agree with the visual identification of localized bed structures observed in Figures 36 that have been discussed previously. Furthermore, as the effective roughness height is reduced, the reattachment lengths shorten. This again agrees with previous observations that a reduced effective roughness height will thus both decrease the local grain friction and reduce the loss of fluid momentum from wakes around particles [Dietrich et al., 1989], which at higher flow velocities will cause locally convergent near-bed flow [McLean, 1981]. The calculated reattachment lengths from vortex shedding appear too long (20–260 mm for Re 13,000 and 60–470 mm for Re 25,000) for vortex shedding to be a possible mechanism for generating this frequency of coherent flow structures over these roughness elements.

Table 3. The Calculated Reattachment Lengths Using the Empirical Formulae of Simpson [1989] Calculated for the Two Reynolds Numbersa
ProtrusionRe 13,000Re 25,000
Xr WakePrXr Wake2ndryXr VortPrXr Vort2ndXr WakePrXr Wake2ndryXr VortPrXr Vort2nd
  • a

    The frequencies used are the time frequency calculated from the time-averaged wavelet power spectrums. Xr wake is the reattachment length for wake shedding (Fw < 0.1U/Xr) and Xr vort is the reattachment length for vortex shedding (Fv = 0.8U/Xr) for the primary (Pr) and secondary peaks (2nd) identified in Figure 8.

Surface1
10.0090.0060.0750.0450.0140.0080.1100.066
20.0030.0030.0210.0200.0080.0070.0600.056
30.0270.0170.2120.1350.0500.0320.4010.255
40.0330.0160.2620.1310.0590.0290.4690.235
50.03100.0330.2440.2610.0570.0610.4530.485
 
Surface2
10.0090.0040.0680.0300.0060.0070.0490.054
20.0070.0030.0520.0230.0590.0340.4680.270
30.0040.0020.0340.0120.0380.0170.3080.138
40.0100.0100.0830.0770.0140.0090.1120.074
50.0170.0100.1320.0780.0440.0220.3490.175
 
Surface3
10.0010.0010.0070.0100.0040.0030.0280.020
20.0010.0010.0090.0090.0580.0190.4610.152
30.0290.0170.2330.1380.0160.0280.1300.226
40.0060.0060.0510.0470.0180.0380.1410.302

4. Discussion and Conclusions

[34] This study has examined the characteristics of turbulent flow generated over three known bed topographies of decreasing roughness at two different flow Reynolds numbers. The analyses have detected coherent flow structures with defined spatial and temporal characteristics. The present experiments investigated the importance of effective roughness for the generation of coherent flow structures and observed that as the effective roughness increased (Figure 11) (1) the visual distinctiveness of the coherent flow structures became more defined throughout the flow depth; (2) the upstream slope angle of the coherent flow structure increased; and (3) the reduction in streamwise flow velocity and turbulence intensity, which occurs toward the upstream side of the coherent flow structure, became more pronounced. Thus, as the effective roughness and Reynolds number decrease, the effective protrusion of the clast becomes less and leads to the geometric structure of these coherent flow structures becoming modified (Figure 11).

Figure 11.

A schematic summary model of the principal characteristics of flow over a gravel bed for high and low relative roughnesses (see text for explanation).

[35] The source of these coherent flow structures has been identified through examination of the mean flow, turbulence intensity, Reynolds stresses, turbulence production, and quadrant analysis. Analysis of the mean u and w components identifies flow recirculation over distances that are scaled and limited by the spacing of the topographic protrusions available to generate flow separation and shear layers associated with individual clasts. This localized flow separation and reattachment is further identified in the turbulence intensity plots that show the greatest turbulence intensities are present in the near-bed region and linked to shear layers associated with individual clasts. Furthermore, turbulence intensity decreases with a reduction in the effective roughness. At a higher effective roughness, a continuous band of high turbulence intensity is formed that appears linked to the amalgamation of shear layers associated with flow separation around the larger clasts, thus forming a more unified region of higher turbulence intensity at ∼0.12 z/Y (Figure 11). As the bed becomes smoother, three factors contribute to the observed changes in flow structure (Figure 11): (1) the effective height of the clasts becomes less, which can be expected to lead to smaller separation zones and thus less intense and spatially smaller shear layers associated with this roughness; (2) as the spacing between the topographic protrusions increases, there is a greater space for the shear layers and their associated turbulence to dissipate, rather than being forced up and over the next roughness element; and (3) related to item (2), there is less interaction between the shear layers of adjacent obstacles, and this lessening of the interaction between shear layers may lead to lower turbulence intensities as has been illustrated by recent work on amalgamating bed forms [Fernandez et al., 2006]. All of these factors lead to a decrease in the spatial extent and intensity of the band of higher turbulence intensity as the effective roughness decreases. Finally, in the near-bed region, quadrant analysis identifies alternating patterns of quadrant 2 (stoss side) and quadrant 4 (lee side) events, again demonstrating localized bed/topographic forcing of the flow associated with individual roughness elements. Furthermore, a band of quadrant 2 events (>8% occurrence) is detected higher in the flow, although this region decreases in area and does not extend as far into the outer flow as surface roughness decreases, matching the observations of turbulence intensity. This trend also mirrors that found over the transition from ripples to dunes, where the extent of turbulence generated as large-scale Kelvin-Helmholtz instabilities along a shear layer increases with larger form roughness [e.g., Bennett and Best, 1995, 1996; Schindler and Robert, 2005; Best, 2005]. Significantly, the spatial pattern (but not absolute magnitude) of quadrant events over individual surfaces is independent of Reynolds number, implying that the surface topography (i.e., effective roughness) defines the entire field of view at this range of Reynolds numbers. The present results thus demonstrate the importance of topographic protrusions around which flow separation and its associated shear layers can form and agrees with stability calculations, which theoretically show that topographic forcing generates absolute and convective instabilities [Socolofsky and Jirka, 2004] through the pressure drag [Robert et al., 1992] that forms these structures.

[36] Wavelet analysis also enables the signal to be decomposed and analyzed for the whole flow field, allowing identification of the dominant temporal length scales of the turbulent structures. The most obvious difference between the primary and secondary peaks of frequencies identified herein is that much larger, spatially coherent, regions of similarity are observed for the primary peak. A clearly defined frequency band exists in the primary peaks, generated from structures with a temporal length scale of between 3 and 5 s, with this temporal length scale increasing with height above the bed. As the surface becomes smoother, this region of primary peaks decreases in its vertical and lateral extent, once again mirroring the trends found in turbulence intensity and quadrant structure. Once the signal is decomposed into wavelet time bins, a consistent pattern is detectable as the surface becomes smoother. Initially, all the distributions of the primary peaks possess some degree of bimodality but, as the surface becomes smoother, the shorter temporal length scale structures increase in both their temporal length scale and their percentage of the structures identified. Applying standard scaling laws, these flow structures appear shear generated and form through a combination of both wake flapping [Nowell and Church, 1979] and reattachment of localized shear layers from particles (shear layer instability) generated by individual topographic protrusions.

[37] The results obtained in the present experiments agree with previous work in which the development of the flow structure has been found to scale with effective roughness height [Buffin Bélanger and Roy, 1998] and also identifies structures similar in their velocity structure to the classical bursting phenomenon in which low-momentum fluid is ejected from the bed [Grass, 1971; Talmon et al., 1986; Shen and Lemmin, 1999]. However, previous work [Smith, 1996; Best et al., 2001; Hardy et al., 2009] has shown that these flow structures develop over the large clasts in the bed, potentially by flapping of the separation zone shear layer and the consequent variations in the size of the wake region. Studies of turbulent boundary layers over flat surfaces have also suggested a change in the form and angle of hairpin vortices dependent on the flow Reynolds number [Head and Bandyopadhyay, 1981], with the hairpin vortices becoming stretched and narrower at higher Reynolds numbers. However, it is worthy of note that over rough beds the effective clast width may only vary a little as roughness height declines, and thus if the flow structures are linked to these clasts, then the lateral scale of the structures may not change appreciably with either changing Reynolds number or roughness height. The 2-D PIV in the u-w plane employed herein cannot address this issue and awaits full 3-D measurements.

[38] Additionally, in smooth bed canonical boundary layers, the number of hairpins traversing the boundary layer has been found to decrease at higher Reynolds numbers, although the vortices still penetrated through the entire boundary layer but can merge to form “packets” of hairpin vortices [e.g., Christensen and Adrian, 2001]. Such trends are also apparent in the present study over rough gravel surfaces where the flow structures appear to merge into a single layer, perhaps forming a skimming flow [Grass, 1971; Grass et al., 1991; Nowell and Church, 1979; Krogstad et al., 1992] generated over the largest roughness elements. This layer tends to become dominant as the Reynolds number increases and may form the larger-scale flow structures. However, the size and packing density of the roughness elements must also be considered. As the effective roughness decreases, the number of potential locations for generating flow separation and its associated shear layers also decreases. This reduction in roughness and the number of potential sites of flow separation reduces the turbulence intensity near the bed and changes the geometrical characteristics of the flow. As the effective roughness decreases, the flow structures are able to elongate as they undergo less downstream topographic forcing, and their intensity declines since they are generated off smaller height obstacles within the flow. The coherent flow structures generated over this smoother bed thus do not evolve into such steeply-angled bulges that are formed over rougher beds (Figure 11). At the flow Reynolds numbers used herein over the smoothest surface, these structures do not penetrate high into the flow. The origin of these larger-scale motions is thus as Kelvin-Helmholtz instabilities generated along the separation zone shear layers of the roughness elements, as has been demonstrated for flows over bed forms in past studies [e.g., Müller and Gyr, 1982, 1986; Rood and Hicken, 1989; Bennett and Best, 1995, Best, 2005], forming a region similar to that where oscillatory structure growth and breakups predominate [Kim et al., 1971] and which has previously been classified as the wake layer (wake flapping) [Nowell and Church, 1979]. This implies that the creation of larger-scale flow structures over gravel surfaces is either by potential superimposition or coalescence/grouping of numerous smaller-scale structures [Head and Bandyopadhyay, 1981; Smith et al., 1991]. Such larger structures may explain the entrainment patches revealed in the work of Drake et al. [1988], which show entrainment of gravel by turbulent flow structures that have an appreciable width across the flow (several grain diameters wide). Significantly, the present analysis suggests that large-scale coherent flow structures over gravel beds owe their origin to bed-generated turbulence and that large-scale outer layer structures are the result of flow topography interactions in the near-bed region.

Acknowledgments

[39] We thank Mark Franklin for assistance with the flume experiments and PIV and J. H. Chandler, University of Loughborough, for loan of the Kodak DCS 460 digital camera and discussion regarding errors in camera geometry. R.J.H. was funded on NERC fellowship NER/J/S/2002/00663 and the DANTEC PIV system was funded by NERC JREI grant GR3/JE140 to J.L.B. We are grateful to the Associate Editor and three anonymous referees for providing helpful comments that have led to significant improvements in this manuscript.

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