1. Introduction
Bedload transport is one of the major components of sediment dynamics and includes the granular solids that roll, slide, or saltate over the underlying stationary bed (Bagnold 1973). Bedload affects the geomorphology of coastlines, rivers, and beaches (Bailard and Inman 1981; Liebault and Piegay 2001; Hoekstra et al. 2004), as well as scour around offshore or riverine foundations (Sumer and Fredsøe 2002; Yang et al. 2010). However, the challenges to investigate bedload transport in the field, resulting from strong hydrodynamic conditions and the often thin vertical extent of the bedload layer in the order of millimeters to a few centimeters, lead to a lack of in situ data (Gomez 1991). Invasive methods, such as sediment traps, potentially influence the ongoing bedload transport and require an elaborate installation (Masselink and Hughes 1998). Methods of particle tracking are limited by the number and recoverability of marked tracers (Ergenzinger and Conrady 1982).
Recently, commercially available acoustic Doppler profilers (ADPs) were introduced to bedload investigations for the assessment of bedload transport rate (Rennie et al. 2002; Kostaschuk et al. 2005; Gaeuman and Jacobson 2006). However, issues have been noted regarding the differentiation between suspended load and bedload due to the rather large along beamwidth of the ADP range bins, and regarding measurement noise caused by spatially hetereogeneous bedload processes associated with the relatively large horizontal separation between the points where the different monostatic acoustic beams of standard ADPs intersect the bed (Rennie et al. 2002). In contrast, frame-based ADPs implementing bistatic beam geometries provide information about three-component velocity measurements within an essentially columnar sample volume at high vertical resolution (≤1 mm) (Lemmin et al. 1999; Hurther et al. 2011; Hay et al. 2012a,b,c). These features promise a significant improvement of acoustic techniques for bedload transport investigations. Additional motivation for this approach is provided by the work of Traykovski (1998), who used coherent Doppler to estimate bedload and suspended load flux in laboratory experiments with sand-sized material, obtaining promising results.
This study presents laboratory results of applying the MFDop (Hay et al. 2012a,b,c), a prototype wideband coherent ADP, on coarse sediment bedload transport. Sediments were chosen with regard to future field experiments on mixed sand and gravel beaches, which are commonly found in areas characterized by strong hydrodynamics in northern Europe (especially Russia, the United Kingdom, and Ireland), Canada, the United States, New Zealand, and Latin America (Buscombe and Masselink 2006). A first series of experiments was carried out observing the transport behavior of pea-sized, rounded to well-rounded gravel depending on the tilt angle of the tray α, which represents the variation in initial forcing. Different sediments were investigated with regard to the variations in grain size (d = 1–32 mm) and grain shape (rounded, angular, elliptic to angular) in a second series of experiments. The results were compared to videos, allowing the determination of single or group particle speeds.
The primary objectives of the study were to (i) test instrument configurations and data processing techniques needed to measure coarse sediment bedload transport, (ii) provide data quality control regarding three-component motion of bedload transport, and (iii) improve the understanding of bedload transport mechanisms of coarse sand and gravel. The study demonstrates the suitability of the MFDop for the acoustic investigation of coarse sediment bedload transport with high resolution, and served as a preparatory experiment for a field study at a highly active mixed sand gravel beach in Advocate Harbour, Nova Scotia, Canada.
2. Methods
The MFDop was introduced by Hay et al. (2008) and is a prototype wideband (operating in the ~1.2- to ~2.3-MHz frequency band), pulse-coherent acoustic Doppler profiler implementing an isosceles bistatic transducer geometry. It offers operation in multifrequency modes (here: dual frequency) and allows three-component velocity measurements within the sample volume with a vertical resolution better than 1 mm over a profile of 20–30 cm in length (Hay et al. 2012a,b,c). In pulse-to-pulse coherent Doppler profiling, the velocity is estimated from the rate of change in phase of the scattered sound, and the phase differences were determined from the ensemble average of 10 pulse-pair transmissions. The ensemble profiling rate was ca. 50 Hz.
This study consists of two experiment sequences. The first (conducted in February and March 2012) focused on testing a variety of different MFDop configurations, in particular with regard to monostatic versus bistatic sampling, the angle β of the MFDop transmit beam relative to the vertical, and the transmit pulse length. Motivation for testing the different configurations were to determine (i) if the bistatic configuration leads to an improvement of the data quality compared to the more common monostatic configuration, (ii) the impact of changes in the transmit beam angle with regard to seafloor inclination and instrument arrangement in future experiments, and (iii) potential impacts of longer pulse lengths motivated by studies utilizing long pulses to estimate sediment transport flux (Traykovski 1998; Traykovski et al. 1998). The detailed MFDop operating parameters for the first part of this study (trials I–IV) are listed in Table 1. In the second series of experiments in July 2012 (trials V–VIII), different sediments were tested, applying the same MFDop configuration as in trial I (Table 1).
MFDop operating parameters and the tilt angle of the tray of the different trials.
During trials I–IV, well-sorted and well-rounded gravel with a median grain size of d50 = 6 mm was used. This gravel was commercially available and is mainly used as an imitation of the seabed in aquaria. Gravel of a similar size class (d50 = 4 mm) but with angular shapes was tested for the investigation of the sensitivity to particle shape. This gravel was also commercially available. Similar gravel but in significantly larger size ranges was used in trial VI (d = 8–32 mm, angular). Beach sediments sampled at a macrotidal mixed sand gravel beach in Advocate Harbour were investigated in trials V and VIII. In trial V, larger fractions (d = 8–16 mm) were used. The particle shapes can be described as angular to elliptic. Coarse sands from Advocate Harbour in a size range of mainly d = 1–2 mm were tested in trial VIII. The sand also had an angular to elliptic and platelike shape, which has been found to be characteristic for sediments from Advocate Harbour (Stark et al. 2012). The dataset allowed comparison between different particle size ranges and particle shapes. The sediment characteristics are summarized in Table 2.
Description of the different sediment types used.
The MFDop was positioned in a 0.53-m3 glass-walled tank with the profiling axis aimed down at a smooth-surface tray of high-density polyethylene, which served as a slippery plane for the sediment (Fig. 1). Prior to each run, the MFDop was arranged at a chosen angle relative to the vertical β (Table 1), and sediment was spread out over the tray as a layer of one particle in thickness and filled into a hopper at one end of the tray. Additionally, a submerged GoPro HERO2 video camera (120 frames s−1) was installed for independent measurement of the moving sediment. Each experiment run started with tipping of the tray to a chosen angle from the horizontal α (Table 1; Fig. 1) to initiate sediment motion. Both angles, α and β, were determined using a digital level (±0.1°). For trials I and II and IV–VIII, the MFDop was kept at β = 24°. In the case of the angle of the tray α, a lifting bar attached to the tray allowed easy tilting of the tray and application of the level. However, small variations of α ± 0.5° were noticed while the bar and tray were held (manually) in position. MFDop data acquisition and the video camera were switched on 1–5 s prior to tilting the tray and recorded for about 42 s, ensuring that all sediment motion was captured. Each experimental run was carried out 3 times.
Conceptual sketch of experiment setup (black), and velocity directions with regard to the setup (gray). The bistatic MFDop transducer arrangement is shown with regard to the tray in (a) lateral view and (b) top view. (c) The monostatic configuration utilizing the center transducer XDR3.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Conceptual sketch of experiment setup (black), and velocity directions with regard to the setup (gray). The bistatic MFDop transducer arrangement is shown with regard to the tray in (a) lateral view and (b) top view. (c) The monostatic configuration utilizing the center transducer XDR3.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Conceptual sketch of experiment setup (black), and velocity directions with regard to the setup (gray). The bistatic MFDop transducer arrangement is shown with regard to the tray in (a) lateral view and (b) top view. (c) The monostatic configuration utilizing the center transducer XDR3.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Data processing of the MFDop recordings was carried out according to the following sequence:
Identification of the sediment bed in the vertical range using the backscatter amplitude. Because of the low amount of fine and/or suspended material in the tank, the bed provided a clearly distinguishable signal as a function of range.
Review of correlation values. High correlation values (→1) indicate a good correlation between consecutive pulses and provide a measure of velocity accuracy (Dillon et al. 2012). Lower correlation values can be related to a lack of scatterers in the monitored range in this study. Data points with a correlation averaged over the four slant beams of less than 0.9 were discarded (Fig. 2).
Calculation of downslope velocity (u), cross-slope velocity (τ), and vertical velocity (w) with respect to the tray normal and the downslope direction (Figs. 1 and 2).
Vertical averaging over three bins (i.e., bin size 1.5 mm) chosen with respect to the identified bed position from backscatter amplitude (Fig. 2).
Determination of a mean velocity over the period of major particle motion, as a function of the tilt angle of the tray α (Fig. 3).
Preliminary display of results (trial I, α = 27°) after calculation of u, υ, and w including start position (0–3 s), lifting up of the tray (3–6 s), movement of gravel (6–25 s), and final stop (>25 s). If the correlation values were smaller than 0.9, then the data point was discarded (dark blue). The range with the best correlations was identified (here at 40.2 cm), and an average of this bin and the vertically adjacent bins was determined for each time step, representing u for the respective time step in the following analysis.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Preliminary display of results (trial I, α = 27°) after calculation of u, υ, and w including start position (0–3 s), lifting up of the tray (3–6 s), movement of gravel (6–25 s), and final stop (>25 s). If the correlation values were smaller than 0.9, then the data point was discarded (dark blue). The range with the best correlations was identified (here at 40.2 cm), and an average of this bin and the vertically adjacent bins was determined for each time step, representing u for the respective time step in the following analysis.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Preliminary display of results (trial I, α = 27°) after calculation of u, υ, and w including start position (0–3 s), lifting up of the tray (3–6 s), movement of gravel (6–25 s), and final stop (>25 s). If the correlation values were smaller than 0.9, then the data point was discarded (dark blue). The range with the best correlations was identified (here at 40.2 cm), and an average of this bin and the vertically adjacent bins was determined for each time step, representing u for the respective time step in the following analysis.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Terms (top) u, (middle) υ, and (bottom) w of sheetlike particle motion along the tray with α = 27° during trial I (Table 1) determined using the MFDop (Fig. 2). The tray was lifted up ~5 s after the start of recording. Sheetlike motion was during a time frame of 5.5–15 s (dashed box), and umean (dark gray line) was determined. In this case, umean = 27 ± 8 cm s−1 (standard deviation, light gray shade). After 15 s, the motion decreased, before a second wave of particles slipped down the tray (18–24 s). Such secondary motion was related to the release of particles that were previously stuck in the hopper. The υ values exhibit a wide range of scatter and trends of movement to both directions of the tray, while w is being characterized by a minor oscillation. The negative trend of w can be explained with the fact that β was kept constant at 24° during the trial, leading to a possible misalignment of ±4° from the vertical.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Terms (top) u, (middle) υ, and (bottom) w of sheetlike particle motion along the tray with α = 27° during trial I (Table 1) determined using the MFDop (Fig. 2). The tray was lifted up ~5 s after the start of recording. Sheetlike motion was during a time frame of 5.5–15 s (dashed box), and umean (dark gray line) was determined. In this case, umean = 27 ± 8 cm s−1 (standard deviation, light gray shade). After 15 s, the motion decreased, before a second wave of particles slipped down the tray (18–24 s). Such secondary motion was related to the release of particles that were previously stuck in the hopper. The υ values exhibit a wide range of scatter and trends of movement to both directions of the tray, while w is being characterized by a minor oscillation. The negative trend of w can be explained with the fact that β was kept constant at 24° during the trial, leading to a possible misalignment of ±4° from the vertical.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Terms (top) u, (middle) υ, and (bottom) w of sheetlike particle motion along the tray with α = 27° during trial I (Table 1) determined using the MFDop (Fig. 2). The tray was lifted up ~5 s after the start of recording. Sheetlike motion was during a time frame of 5.5–15 s (dashed box), and umean (dark gray line) was determined. In this case, umean = 27 ± 8 cm s−1 (standard deviation, light gray shade). After 15 s, the motion decreased, before a second wave of particles slipped down the tray (18–24 s). Such secondary motion was related to the release of particles that were previously stuck in the hopper. The υ values exhibit a wide range of scatter and trends of movement to both directions of the tray, while w is being characterized by a minor oscillation. The negative trend of w can be explained with the fact that β was kept constant at 24° during the trial, leading to a possible misalignment of ±4° from the vertical.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Regarding the video observations, the frame size equaled 480 × 848 pixels and covered the full tray including hopper. Frame sequences were extracted and lens distortion was removed (using the software package available at http://www.vision.caltech.edu/bouguetj). To improve the visibility of single particles in the videos, ca. 10% of the particles was painted in signal colors. In the case of the white aquarium gravel (trials I–IV), ca. 10% of the gravel was replaced by black particles of the same physical characteristics. The images were equalized by adjusting gray scales to compensate for the spatially variable illumination, and then image contrast was enhanced. Single particles were resolved in the range of 25–150 pixels per particle for particles with a size of ~6 mm (trials I–IV). In the case of sand (trial VIII), suspended sediment lowered the visibility. If the visibility prohibited the resolution of single sand particles, then the moving front of the sand avalanche and painted larger particles embedded in the sand were used as representatives. The average velocity of the painted/black particles (up) was analyzed from the progress of at least five different particles versus time in the resulting images and compared to the MFDop results. The chosen particles were part of the major motion detected; if secondary phases of motion were observed, then the velocity was determined for motion in the center of the tray in accordance to the location of the MFDop.
3. Results
Trial I served as a base study. The major objective was to find out if gravel bedload transport characteristics can be determined using the MFDop. In the subsequent three trials (II–IV), different variations in the configuration parameters of the MFDop were tested, and in the final experiment series (trials V–VIII), potential differences in bedload transport behavior related to changes in particle size and shape were investigated. In the following sections, we address each of these objectives and corresponding experiments separately.
a. First observations (fine gravel, trial I)
The backscatter amplitude as well as the correlation values allowed a clear identification of the gravel layer (Fig. 2). The measured velocities (u, υ, w) over time revealed three distinct periods of motion as indicated in Fig. 3: a period of major particle motion; followed by decreasing motion; and in some cases, ending with a period of secondary particle motion, which was induced by slight movement of the tray. Decreasing motion was mainly related to a decrease in the number of concurrently sliding particles. Secondary particle motion occurred as a result of released particles that had been previously stuck in the hopper. This progression was confirmed by comparison with the videos. The magnitude of different velocity components identified u to be the prevailing direction of motion by being consistently greater than υ and w (Fig. 3). Furthermore, υ was characterized by alternating trends to positive and negative values, expressing small changing trends to the left and the right of the downslope direction, whereas w showed small, high-frequency (e.g., for α = 27° ~ 10 Hz) oscillations around 0 cm s−1, potentially representing the up- and downward motion during rolling.
The mean velocity and the standard deviation for the phase of major particle motion was determined for each run (e.g., for run 23 with α = 27°: umean = 27 cm s−1 ± 8 m s−1; Fig. 3). Figure 4 shows an example of the u-component probability distribution, indicating the approximately symmetric distribution of deviations from umean.
Probability density of deviations from umean (bars) for run 23 of trial I (α = 27°; see also Fig. 2 and 3), and Gaussian fit (gray line).
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Probability density of deviations from umean (bars) for run 23 of trial I (α = 27°; see also Fig. 2 and 3), and Gaussian fit (gray line).
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Probability density of deviations from umean (bars) for run 23 of trial I (α = 27°; see also Fig. 2 and 3), and Gaussian fit (gray line).
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Figure 5 summarizes such results for a range of tray tilt angles (trial I): three different stages of motion behavior were identified. For 20° ≤ α ≤ 22°, single grains just started moving, umean remained smaller than 3 cm s−1 ± 1 m s−1, and increased approximately linearly (R2 = 0.79) with increasing tray angle α. In the range of 22 ≤ α ≤ 25°, variations of motion patterns were observed, from single to group grain movements, showing more unsteady motion up to avalanches. During this stage, umean ranged from 4 ± 1 cm s−1 to 14 ± 4 cm s−1. The best fit to describe the increase of umean with tilt angles was achieved with ln(umean) = 18.7 lnα − 57.26 (R2 = 0.94) (Fig. 5). Approaching α ≥ 25°, sheetlike movement of the particles down the tray in one major motion was observed, with speeds reaching 29 ± 8 cm s−1. The gradient of umean versus α decreased compared to the second stage of motion and let R2 = 0.78 when applying a linear fit (Fig. 5).
The term u during trial I (Table 1) determined using the MFDop (black) and the video analysis (red). Three different zones of motion behavior with regard to the tilt angle (α) can be distinguished (dashed lines): 20°–22°, 22°–25°, and 25°–27°. A linear fit (dashed lines) was applied on each respective zone (R2 = 0.79 for 20°–22°; R2 = 0.90 for 22°–25°; R2 = 0.78 for 25°–27°); however, for the center zone, a power law (solid line; R2 = 0.94) is a better fit to the rapid changes within this zone.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
The term u during trial I (Table 1) determined using the MFDop (black) and the video analysis (red). Three different zones of motion behavior with regard to the tilt angle (α) can be distinguished (dashed lines): 20°–22°, 22°–25°, and 25°–27°. A linear fit (dashed lines) was applied on each respective zone (R2 = 0.79 for 20°–22°; R2 = 0.90 for 22°–25°; R2 = 0.78 for 25°–27°); however, for the center zone, a power law (solid line; R2 = 0.94) is a better fit to the rapid changes within this zone.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
The term u during trial I (Table 1) determined using the MFDop (black) and the video analysis (red). Three different zones of motion behavior with regard to the tilt angle (α) can be distinguished (dashed lines): 20°–22°, 22°–25°, and 25°–27°. A linear fit (dashed lines) was applied on each respective zone (R2 = 0.79 for 20°–22°; R2 = 0.90 for 22°–25°; R2 = 0.78 for 25°–27°); however, for the center zone, a power law (solid line; R2 = 0.94) is a better fit to the rapid changes within this zone.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
The average particle velocity (up) determined using the video analysis compared favorably to umean (Fig. 5). For some of the tilt angles, up was slightly higher than umean but remained mainly within the range of uncertainty. The standard deviations of umean ranged between 22% and 35%, excluding periods of single particle motion only, while the standard deviations of up were less than 25%.
b. Different MFDop configurations (fine gravel, trials II–IV)
A range of MFDop configurations was explored in four different trials (Table 1), all yielding similar results (Figs. 6 and 7). The monostatic mode (trial II) seemed to suffer more from low correlations caused by an irregular coverage of the tray with gravel. With increasing gaps between the particles, the correlation values decreased significantly (Fig. 8), resulting in an increase of standard deviations (Fig. 6). Different angles between the MFDop transmit beam and the plane normal γ (Fig. 1) of up to 30° (turning toward the downslope direction) were tested by varying the MFDop angle β while keeping the tilt angle of the tray α stable (trial III, Table 1). The correlations for the transducer in the downslope direction (XDR5 in Fig. 1a) decreased (by ~33%), whereas those for the other transducers were acceptable, leading to reasonable average correlation values ≥ 0.9 (Fig. 8). The lowest standard deviations were achieved at γ ≈ 10° (Fig. 6, bottom-left panel). Using long pulses (trial IV in Table 1), and an associated larger bin size exceeding the thickness of the bedload layer, resulted in lower correlations and a decrease in the accuracy of the velocity estimates compared to trial I (Fig. 6). Also, a larger difference between umean and up than in trials I–III was noticeable (Figs. 6 and 7), likely being a consequence of larger bin sizes and the resulting water bias.
The term umean measured using the MFDop (black), and up (gray) for all four trials of the first experiment series (I–IV). Manual nudges to initiate motion of some grains stuck in the hopper and differences in the manual lifting of the tray explained an often slightly higher umean for trial IV. During trial III, the tray was kept constant at 25° and the angle of the MFDop was changed, while during trials I–II and IV the tray angle was varied and the MFDop position was kept constant (see Table 1; Fig. 1).
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
The term umean measured using the MFDop (black), and up (gray) for all four trials of the first experiment series (I–IV). Manual nudges to initiate motion of some grains stuck in the hopper and differences in the manual lifting of the tray explained an often slightly higher umean for trial IV. During trial III, the tray was kept constant at 25° and the angle of the MFDop was changed, while during trials I–II and IV the tray angle was varied and the MFDop position was kept constant (see Table 1; Fig. 1).
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
The term umean measured using the MFDop (black), and up (gray) for all four trials of the first experiment series (I–IV). Manual nudges to initiate motion of some grains stuck in the hopper and differences in the manual lifting of the tray explained an often slightly higher umean for trial IV. During trial III, the tray was kept constant at 25° and the angle of the MFDop was changed, while during trials I–II and IV the tray angle was varied and the MFDop position was kept constant (see Table 1; Fig. 1).
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
The averaged particle velocity determined from the videos (up) vs the mean down-slope velocity determined using the MFDop (umean) for trials I–IV. Different tray angles α are indicated by different symbols. A linear fit was applied in the case of the trials that included different tray angles α, and consequently a larger range of particle velocities. The gradient ranged from 0.71–0.74 with R2 = 0.88–0.95 for the bistatic and the monostatic configuration (trials I and II) and to only 0.65 with R2 = 0.90 when using longer pulses.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
The averaged particle velocity determined from the videos (up) vs the mean down-slope velocity determined using the MFDop (umean) for trials I–IV. Different tray angles α are indicated by different symbols. A linear fit was applied in the case of the trials that included different tray angles α, and consequently a larger range of particle velocities. The gradient ranged from 0.71–0.74 with R2 = 0.88–0.95 for the bistatic and the monostatic configuration (trials I and II) and to only 0.65 with R2 = 0.90 when using longer pulses.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
The averaged particle velocity determined from the videos (up) vs the mean down-slope velocity determined using the MFDop (umean) for trials I–IV. Different tray angles α are indicated by different symbols. A linear fit was applied in the case of the trials that included different tray angles α, and consequently a larger range of particle velocities. The gradient ranged from 0.71–0.74 with R2 = 0.88–0.95 for the bistatic and the monostatic configuration (trials I and II) and to only 0.65 with R2 = 0.90 when using longer pulses.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Correlation vs time for a bistatic run with gaps between the (a) grains, (b) a monostatic run with gaps between the grains, (c) a monostatic run without observed gaps between the grains, and (d) a bistatic run with γ ≈ 30°. In the case of the bistatic runs, the correlations presented are an average of the correlations of the different transducers.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Correlation vs time for a bistatic run with gaps between the (a) grains, (b) a monostatic run with gaps between the grains, (c) a monostatic run without observed gaps between the grains, and (d) a bistatic run with γ ≈ 30°. In the case of the bistatic runs, the correlations presented are an average of the correlations of the different transducers.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Correlation vs time for a bistatic run with gaps between the (a) grains, (b) a monostatic run with gaps between the grains, (c) a monostatic run without observed gaps between the grains, and (d) a bistatic run with γ ≈ 30°. In the case of the bistatic runs, the correlations presented are an average of the correlations of the different transducers.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
As indicated in Fig. 7, umean was observed to be generally slightly smaller than up . In trial I, umean = 0.71up with R2 = 0.95. In the monostatic mode (trail II), we found a similar trend (umean = 0.74up) with more scatter (R2 = 0.88), corresponding to lower correlation values and higher standard deviations than in trial I. The above-mentioned larger difference between umean and up when using longer pulses was also confirmed by the correlation of umean = 0.65up (R2 = 0.90; Fig. 7).
c. Particle size effects (coarse gravel to coarse sand: trials V–VIII)
A significant difference between the transport behavior of the sand (trial VIII) and of the gravel (trials I–VII) was observed (Fig. 9). In the case of gravel, sediment started moving at 20° ≤ α ≤ 24° (Fig. 9). The sand from Advocate Harbour, on the other hand, was not mobilized before α ≥ 31° and reached only umean < 30 cm s−1. Thus, the initiation of bedload transport of the sand required higher tray tilt angles α, and transport velocities were smaller than those observed for gravel.
Summary of mean u determined using the MFDop umean (filled symbols) and from the videos up (open symbols) vs α for the different sediment types tested. In (top) different particle sizes are compared. In (bottom) sand (diamonds) is compared to all gravelly sizes (circles), whereas in (top right) medium gravel (squares) and fine gravel (triangles) are shown. In (bottom), the impact of particles shapes is illustrated. In (bottom left), rounded gravel (circles) is compared to angular gravel (squares). In (bottom right), results from angular gravel (squares) and elliptic to fractured particles (circles) are shown.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Summary of mean u determined using the MFDop umean (filled symbols) and from the videos up (open symbols) vs α for the different sediment types tested. In (top) different particle sizes are compared. In (bottom) sand (diamonds) is compared to all gravelly sizes (circles), whereas in (top right) medium gravel (squares) and fine gravel (triangles) are shown. In (bottom), the impact of particles shapes is illustrated. In (bottom left), rounded gravel (circles) is compared to angular gravel (squares). In (bottom right), results from angular gravel (squares) and elliptic to fractured particles (circles) are shown.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Summary of mean u determined using the MFDop umean (filled symbols) and from the videos up (open symbols) vs α for the different sediment types tested. In (top) different particle sizes are compared. In (bottom) sand (diamonds) is compared to all gravelly sizes (circles), whereas in (top right) medium gravel (squares) and fine gravel (triangles) are shown. In (bottom), the impact of particles shapes is illustrated. In (bottom left), rounded gravel (circles) is compared to angular gravel (squares). In (bottom right), results from angular gravel (squares) and elliptic to fractured particles (circles) are shown.
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Trials VI and VII can be compared to study the influence of particle size on transport behavior within the group of gravel size fractions (Fig. 9). Both gravel types were angular, but the gravel used in trial VI was significantly larger (Table 2). It was found that the larger gravel (trial VI) was lacking the stage of single particle and single particle group motion. No particles were mobilized until α ≥ 24° (Fig. 9). This was also confirmed by trial V using larger gravel from Advocate Beach. However, as soon as such large gravel was mobilized, it moved with noticeably higher downslope velocities (Fig. 9). At 24° ≤ α ≤ 30°, the larger gravel reached velocities approximately 10–15 cm s−1 faster than the smaller size fractions.
d. Particle shape effects (gravel, trials I and V–VII)
The impact of particle shape was compared using mainly trials I and VII, and trials V and VI. The angular particles (trial VII) remained at the stage of single and single group movements with low transport speeds (u ≤ 10 cm s−1) up to tilt angles of α ≤ 26°, whereas the rounded particles (trial I) made the transition to faster major motion at lower tilt angles of α ≥ 24°. Also for the stages of motion that followed, rounded particles moved significantly faster, reaching sheetlike motion with α ~ 26°, at which angle the angular particles just started to pick up speed and to show overall movement. Comparing angular (trial VI) to elliptic particles (trial V), no significant difference was noticed. The angular particles appeared slightly faster, but this likely resulted from including bigger size fractions than in the gravel used for trial V. Furthermore, some of the gravel from Advocate Harbour (trial V) broke into very angular particles, leading to a similarity of particle shapes compared to the angular gravel (trial VI).
4. Discussion
We simulated bedload transport in a laboratory using fine gravel on a smooth inclined plane and measured three-component velocities using the MFDop (trial I). Independent experiments (trials I–IV in Table 1) with different beam geometry and pulse lengths were carried out, and complementary video analysis supported the determined values and trends.
During most of the runs, video-based velocities (up) were on average slightly greater than the velocities determined using the MFDop (umean) (Fig. 7). Nevertheless, up matched umean well, considering the range of uncertainty (Figs. 5 and 6), excluding cases of single particle motion only (α ≤ 22°). The discrepancy can be explained by the fact that umean resulted from averaging over time, whereas up was determined by averaging over a number of single moving particles. Thus, a decrease in umean can correspond to a generally slower bed velocity or to a patchy and sporadic motion of the particles. The MFDop velocity distributions (Fig. 10) showed a variability of velocity measurements u, exceeding the range of velocity distributions obtained from the video analysis. This suggested that the difference in umean resulted rather from patchy motion and velocity inhomogeneity due to particle–particle interaction that was observed in the videos but underrepresented in the video analysis. The limited number of observed particles and the choice of particles, which were characterized by a rather regular and undisturbed transport (up), likely led to a narrower velocity distribution, with a higher mean.
Velocity distributions determined using the MFDop and video particle velocity analysis from a trial I run 23 (see also Figs. 2–4).
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Velocity distributions determined using the MFDop and video particle velocity analysis from a trial I run 23 (see also Figs. 2–4).
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
Velocity distributions determined using the MFDop and video particle velocity analysis from a trial I run 23 (see also Figs. 2–4).
Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00095.1
This study focused on downslope velocity (u), but we also presented some insight into the results regarding cross-slope velocities (υ) and vertical velocities (w). The MFDop results indicated that lateral motion was a consequence of impacts with other particles, and that sliding was the dominant type of motion, consistent with the video observations. Understanding the initiation and maintenance of different motion is important (Bagnold 1973; Van Rijn 1984). The results of the present study suggest that the MFDop would be well suited to future experiments designed to investigate specific types of bed material motion.
With regard to umean, three stages of motion were observed depending on the tilt angle, and consequently initial forcing: single grain movement, a highly varying sequence of single and group grain motion up to small avalanches, and sheetlike motion. Similar behavior can be anticipated in nature and is of interest in a wide range of field studies. Depending on the mobilizing forcing (in marine environments represented by hydrodynamics and geomorphology), the intensity and behavior of bedload particle motion likely varies (Bagnold 1973; Van Rijn 1984). However, such investigations have not yet been realized in the field. Instruments such as the MFDop will make such studies possible in the future.
Using the monostatic configuration (trial II), low correlation values and an increase in standard deviation were associated with the occurrence of gaps between particles and particle groups. Such disturbances were mainly related to the acoustic properties of the high-density polyethylene tray and the resulting absence of scattering. This issue would not occur in field experiments. The reason why this issue impacted the monostatic more than on the bistatic configuration is likely related to geometry, and the resulting limited beam angle and smaller sample area in the monostatic configuration. In the field, this effect might impact the velocity estimates in terms of an acoustically reflecting nonmoving bottom, potentially leading to a reduced estimate of velocity.
Regarding inclination between MFDop and the bed slope (trial III), reasonable results were obtained for angles of up to γ ≈ 30°. However, standard deviations increased significantly when γ < 5° and γ > 15° downslope (Fig. 6). It has to be noted that the transducer pointed in the downslope direction (XDR5 in Fig. 1a) showed decreased correlation values for larger tilt angles. The impact on the other transducers was negligible. This is a promising result for the investigation along large bedforms in the field, where inclination of the bed easily reaches similar angles (Yalin and Karahan 1979).
Long pulses resulted in a significant decrease in vertical resolution and a potential increase in water bias (Rennie et al. 2002). Although the overall results were still in the same range as those from the short pulse experiments, standard deviations increased (Fig. 6), and a larger difference between the velocity estimates by the MFDop and the video analysis were observed. High vertical resolution is one of the major issues for the investigation of bedload and particle transport behavior, and the present results indicated that a vertical resolution smaller than the grain size yielded a better assessment of three-component bed velocity and particle motion. Approaching such high vertical resolution of velocity measurements of the bed promises new possibilities of in situ bedload investigations in areas characterized by coarse sediment transport. On the other hand, Traykovski (1998) and Traykovski et al. (1998) showed that the application of longer pulses can be used to determine the sandy sediment transport flux. This is important in the case of sandy and finer sediments, which are known to develop bedload layer thicknesses many grain diameters thick (Nielsen 1992). For coarse sediments and gravel, a bedload layer thickness in the range of the largest particle sizes (DeVries 2002) is more common, allowing an experimental setup with only one layer of moving sediments. Future investigations including finer sediments will include the testing of longer pulse analysis, as suggested by Traykovski (1998), for estimating sediment transport flux. Also, the lack of flow in the current experiment is an important factor when considering velocity deviations associated with larger bin sizes. The deviations seen here when bin sizes increased are related to water bias, and they might decrease under active flow conditions in the field or in a flume. This will be a major objective in a planned flume experiment.
Differences between these laboratory experiments and natural processes of sediment remobilization in the field have to be considered for the discussion of the transport behavior of different sediments ranging in size from coarse sand to coarse gravel (Fig. 9). For mobilization of the sand (trial VIII), higher tray tilt angles were required than for gravel. In classical approaches to estimate the threshold of particle motion, particle diameter and packing act predominantly as stabilizing parameters (Shields 1936). The particle arrangements used here were very loose compared to possible flume or field settings, where dense packing arrangements can hamper the entrainment and mobilization of particles. Thus, the particle diameter should be the major controlling factor. It would be expected that sands should be more easily brought into motion than the gravel. One reason for the aberration can be found by the fact that gravitational force was used to mobilize sediments, instead of a fluid flow, which likely helped heavier particles to overcome drag forces and friction, and also explains why heavier gravel particles reached higher speeds for the respective tilt angles α. Considering all trials and excluding the stage of single particle motion, a clear trend of higher transport velocities with larger particle sizes can only be found for similar particle shapes. Hence, our experiments showed an impact of particle shape despite the smooth surface of the tray, and it can be inferred that the reluctant behavior of the Advocate Beach sand was a consequence of the specific particle shape too.
The impact of particle shape on sediment transport behavior has been noted before and corresponds to a change in bed roughness, possible grain protrusion, and friction angle (Kirchner et al. 1990). The impact of intergranular stress on the Shields parameter was shown by Bagnold (1956), who included a dynamic equivalent of a soil mechanical friction angle Φ′ to the stabilizing forces. Later, Fredsøe and Deigaard (1992) introduced an “effective” Shields parameter, acknowledging the impact of a sloping bed and friction angle. In this study, grain protrusion and bed roughness can be neglected because of the absence of fluid flow as the motion initiating force. The friction angle of the Advocate Harbour sand was tested by directional and ring shear tests, which confirmed exceptionally high friction angles (~40°) for the coarse sands from Advocate Beach (Stark et al. 2012). An increase in friction angle, due to an angular particle shape during trial VII compared to rounded grains in trial I (Das 1990), is likely the reason for the different behavior of the angular gravel compared to the rounded gravel of the same particle size range.
5. Conclusions
Bedload transport was simulated in the laboratory using gravel and coarse sand sliding down an inclined, smooth plane. Three-component velocities were monitored using a prototype wideband pulse-to-pulse coherent Doppler profiler (MFDop) and compared to video analysis. Only data points with a correlation value of ≥0.9 contributed to the acoustic estimates of particle velocity, expressing a high data quality. A series of experiments with different configurations and subsequent experiments testing different sediments led to the following conclusions:
Determination of the downslope velocity using the MFDop and video analysis led to a favorable comparison. On average, umean equalled 71%–74% of up with standard deviations of 21%–35%, including observed irregular motion. Thus, the downslope bedload velocity of gravel and coarse sand can be considered successfully measured using the MFDop in the laboratory.
Three different phases of motion were observed depending on the tray tilt angle and the resulting force on the particles: single grain movements, a varying sequence of single and group grain motion, and fast sheetlike motion.
The investigation of three-component velocities indicated grain sliding as the dominant type of particle motion.
Changes in the relative inclination of the MFDop transmit beam to the bed of up to 30° did not lead to significant deviations in the estimated velocities, promising the suitability of the device for surveys along subaqueous bedforms.
In the monostatic configuration, the velocity estimates suffered more from gaps between the particles and the resulting low correlations. In consequence, the data quality improved when using the bistatic configuration.
Short pulses and bin sizes smaller than the bedload layer thickness are preferable for the investigation of coarse sediment bedload transport to reach a maximum vertical resolution and minimize water bias. However, possible bias from a stationary, acoustically reflecting bottom was not investigated in this study.
Testing of different sediments highlighted the strong impact of particle size and shape on the transport behavior and initiation of motion. These variations were well reflected in the MFDop results and confirmed by the video results.
The presented experiments were carried out as a preliminary study for in situ surveys at mixed sand gravel beaches and for flume experiments targeting the influence of particle size and shape, and resulting friction angle on coarse sediment transport. They proved that coarse particle velocities and coarse particle motion behavior was well reflected in the MFDop results. For the inclusion of finer sediments in future experiments, or in areas where a major sediment mobilization is anticipated that exceeds the expected bedload layer thickness in the range of one to two particle sizes (DeVries 2002), the MFDop measurements should be complemented by other survey methods that allow an estimate of the thickness of the mobile layer (e.g., repeated high-resolution bathymetric surveys, or dynamic penetrometer measurements; Stark et al. 2011) to aim for determining bedload sediment flux. Another option would be the application of a method by Traykovski (1998) utilizing a similar system in a long pulse configuration. This approach is another aim in the methodological testing of the MFDop and will be targeted in future flume experiments. Such flume experiments, exchanging gravitation as a mobilizing force by flow-induced bed shear stresses, will also enable tests of Fredsøe and Deigaard’s (1992) estimate of effective Shields parameter. The results are promising for the future field investigations of apparent bedload velocity, but they also indicate the potential for the investigation of particle motion behavior, which would allow new insights into the understanding of bedload transport in the strongly varying natural environments.
Acknowledgments
The authors acknowledge funding from the Natural Sciences and Engineering Research Council of Canada, the Atlantic Innovation Fund, and Nortek. Furthermore, we thank Walter Judge for his technical support, and Craig Lake for his support with geotechnical testing of the sand from Advocate Harbour. We acknowledge the suggestions and comments of Peter Traykovski and an anonymous reviewer, which contributed to the improvement of this article.
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