Understanding the physical processes that govern sediment resuspension has significant implications for aquatic ecosystems and fish habitats as well as sustainable engineering applications such as beach nourishment, maintenance of hydraulic structures, dam breaching flows, sedimentation in reservoirs, defence schemes against erosion due to floods, and aggregate dredging (Buffington, 1999; Paphitis, 2001; van Rijn et al., 2007; Thompson et al., 2011; Aagaard and Jensen, 2013; van Rijn, 2013), all of which require improved predictive models of sediment transport. However, resuspension of sediment is a complex mechanism due to the difficulty in defining the fluctuating nature of turbulent flow. Shields (1936), the pioneer to investigate the entrainment of granular particles, concluded that a mean critical or threshold shear stress existed below which particles did not move. At velocities lower than the threshold, shear stress represented the viscous drag imparted by the moving fluid to the bed particles, whereas at velocities higher than the critical, it was related to the pressure differential between the upstream and downstream sides of the particle. Shields also defined the non-dimensional critical shear stress, θcr, as a function of the boundary Reynolds number, Rep, defined as θcr=τ0/ρs-ρgds,Rep=u∗ds/υ, where τ0 is the critical bottom shear velocity, ρs and ρ are the sediment and fluid densities, g is the acceleration due to gravity, ds is the particle diameter, u∗=τ0/ρ is the critical shear velocity, and υ is the kinematic viscosity of the fluid.

Such a criterion (commonly implemented via a Shields diagram, e.g. Kennedy, 1995; Buffington, 1999; Paphitis, 2001) states that sediment is entrained once bed shear stress exceeds the Shields mean critical value. The Shields diagram has been extensively applied and investigated by numerous researchers (Brownlie, 1981; van Rijn, 1984; Pattiaratchi and Collins, 1985; Soulsby and Whitehouse, 1997; Wu and Wang, 1999; Paphitis, 2001). The impact of turbulence, however, was traditionally represented only by a mean quantity such as Reynolds shear stress (e.g. widely used bedload and suspended load formulations presented in van Rijn, 2013). Further attempts to characterize sediment entrainment advocated that it solely depended on fluid lifting force, with near-bed sediment being entrained due to instantaneous near-bed vertical velocity (Einstein, 1950; Velikanov, 1955; Yalin, 1963; Ling, 1995). In contrast, Bagnold (1956) hypothesized that particles remain in suspension as long as the turbulent eddies have dominant vertical velocity components, which would scale with the flow shear velocity, that exceed the particle settling velocity. This implies that to establish a dynamic equilibrium of sediment exchange, the flow must continuously pick up the sediment at the same rate with an upward velocity equalling terminal fall velocity.

The critical bed shear stress concept asserts that bedload grain does not move below the mean critical value of bed shear stress. However, Lavelle and Mofjeld (1987) studied historical data for incipient sediment motion and found that no true threshold value existed, and bedload transport could occur at any predicted threshold. This suggested that a single critical shear stress should not be included as an essential parameter when calculating bedload transport rates, agreeing with previous work from Paintal (1971) who observed that there was no distinct shear stress below which no single grain entrained. Laursen et al. (1999) found that many values of the critical shear stress could be found for an equal-sized sediment particle, matching a similar number of sediment transport formulas available at the time. Since earlier developed diagrams showed a gap within the smooth and rough-flow regimes (Yalin and Karahan, 1979), further attempts conducting additional experiments and analysing the problem theoretically based on deterministic and probabilistic approaches, have been made to amend the Shields diagram to account for turbulent effects. Greater details on this approaches can be found in the comprehensive surveys made by Miller et al. (1977), Buffington and Montgomery (1997), Paphitis (2001), and Dey and Papanicolaou (2008). Conclusions reached by these authors agree that a single mean value of shear stress is not an accurate estimate for sediment transport, and further consideration must be given to instantaneous turbulent parameters for a better characterization of flow–sediment interactions.

The scatterplots of the Reynolds and TKE bottom shear stresses for the AMCV and BMCV runs (Fig. 3a and b) showed that higher bed shear stress (i.e. values >5Nm-2 of TKE and Re shear stress estimations of both AMCV and BMCV runs) was produced to generate sediment resuspension (as evidenced with backscatter intensity in Figs. 4c and 5c). Such comparison of the TKE and Re shear stress methods also suggested the presence of coherent flow structures in the turbulent flow which created highly localized and persistent variability near the bed, hence affecting the bed shear stress.

The velocity fluctuations (u′,w′), Reynolds shear stress (u′,w′), and backscatter over a 2 min period (for better visualization of bursting events) from the AMCV and BMCV runs were compared identifying ejection and sweep events (Figs. 4 and 5, respectively). This comparison offered considerable insight into the contribution of turbulence in terms of the events associated with sediment resuspension. Overall, in the time series significant variability and intermittency both in Reynolds stress (u′,w′) and sediment resuspension (backscatter) was also revealed. Such intermittent nature of u′w′ was expected and observed previously in the laboratory (Grass, 1974; Sumer and Oguz, 1978; Sumer and Deigaard, 1981; Niño et al., 2003; Schmeeckle, 2015) and in the field (Heathershaw and Thorne, 1985; Drake et al., 1988; Soulsby et al., 1994; Kularatne and Pattiaratchi, 2008 and Yuan et al., 2009). In more detail, the time series of the AMCV run showed 28 major resuspension events (Fig. 4), of which 18 demonstrated ejections (at 5, 9, 17, 24, 30, 38, 49, 54, 66, 77, 83, 86, 98, 99, 101, 107, 109, and 116 s) and 10 of these events revealed sweeps (at 21, 25, 32, 42, 46, 53, 58, 61, 75, and 90 s), which confirmed that high resuspension events were mostly associated with ejection and sweep type motions rather than up-acceleration and down-deceleration events during the analysed record. The same pattern was observed for the 2 min period of BMCV run where 25 major resuspension events were observed (Fig. 5), of which 15 were identified as ejections (at 2, 7, 19, 26, 38, 47, 52, 72, 77, 87, 90, 93, 100, 113, and 116 s) and 10 of these events confirmed sweeps (at 1, 32, 41, 46, 54, 60, 67, 79, 107, and 112 s). Such resuspension events identified below the measured critical velocity support the theory of the non-existence of a unique time-averaged critical shear stress as suggested by Paintal (1971) and Lavelle and Mofjeld (1987). The plot of the BMCV run further indicated that though flow conditions were below the critical velocity conditions, sediment resuspension was observed due to ejection and sweep events.

Contributions to u′w′ were also observed in four quadrants of the u′–w′ plane with a threshold value (backscatter above 10 dB) both for AMCV and BMCV runs (Fig. 6). The plots clearly showed that the large contribution of u′ and w′ were associated with ejections and sweeps rather than up-acceleration and down-deceleration events. AMCV results were similar with previous studies (Cellino and Lemmin, 2004; Yuan et al., 2009). The distribution of turbulent components for BMCV in the u′–w′ plane reflected a similar pattern which established that resuspension events can occur even below a critical threshold value. BMCV conditions, where mean velocity was 59 % of the critical velocity, showed a similar behaviour to AMCV conditions. Similarities were also found in the other data sets within the range of u‾/u‾cr, measured ratio; for AMCV between 1.04 and 1.57, and for BMCV between 0.53 and 0.94.

We performed a quadrant analysis to determine the frequency of different bursting events and their contributions to the Reynolds stress (i.e. u′w′). The occurrence percentages of four types of bursting motions, as well as their contributions to the momentum flux (u′ w′) and sediment flux (c′,w′) for the AMCV and BMCV experiments, are shown in Figs. 7 and 8, respectively. The results for the u′w′ signals for the AMCV and BMCV experiments agreed with the results from earlier studies (Wallace et al., 1972; Willmarth and Lu, 1972). For both AMCV and BMCV experiments, ejection and sweep events were the dominant source of the Reynolds stress; however, although the time occupied by ejection was comparable with, or even less than, that of sweep, ejection contributed more to the net Reynolds stress (AMCV =49 %; BMCV =43 %) as shown in Figs. 7a and b and 8a and b. Ejection (AMCV =38 %; BMCV =38 %) and sweep (AMCV =37 %, BMCV =30 %) mainly generated the upward sediment flux (Figs. 7c and 8c), which suggested the intense upwelling of low-speed fluid parcels with high-sediment-entrainment events was the main source of the overall sediment flux. In contrast, up-acceleration (AMCV =12 %; BMCV =14 %) and down-deceleration (AMCV =13 %; BMCV =18 %) events transported less sediment (Figs. 7c and 8c). Thus ejection and sweep contributed more to the total turbulent sediment flux (AMCV =75 %; BMCV =68 %) than up-acceleration and down-deceleration events (AMCV =25 %; BMCV =32 %). Such consistent results in both AMCV and BMCV confirm the need to develop transport rate formulas that consider instantaneous Reynolds stress concepts along time-averaged critical velocities.

CWT and WTC analysis (Grinsted et al., 2004) for AMCV and BMCV runs offered a more intuitive way to visualize the turbulence data in both time and space (Figs. 9 and 10, respectively). In the presented scalograms, at higher periods (i.e. low-frequency events), the power felt within the range of COI (i.e. the shaded region in the scalograms) which limited the capability to investigate the temporal evolution of the specific peak frequencies as stated in Sect. 2.2. Hence, investigation was restricted to examine high-frequency events occurring at timescales up to 32 s for both runs. Overall, the scalograms (Figs. 9 and 10) traced the dynamics of coherent structures and its measured contribution to the sediment flux. It also revealed that within the large-scale motions (considering period bands >0.5 s as large-scale motions), there existed multi-scale [e.g. in AMCV time series of ∼47–52 s, period band ∼2–8 s (large scale) and ∼0.0625–1 s (small scale); in BMCV time series of ∼82–85 s, period band ∼2–8 s (large scale) and ∼0.0625–2 s (small scale)] and some embedding small fine-scale (e.g. in AMCV at ∼22–25 s, period band ∼0.0625–0.5 s; in BMCV at ∼22–23 s, period band ∼0.0625–1 s) features. This suggested that both for AMCV and BMCV runs, near the bed, most of the energy was concentrated within the high period (warmer colour >0.5 s) associated with the mean flow properties for both momentum flux and sediment flux. Results also showed that highly energetic turbulent events (i.e. warmer colour >0.5 s) occurred: i.

Sporadically throughout the time series (e.g. in AMCV at 5, 9, 17, 21, 24, etc; in BMCV at 1, 2, 7, 19, etc.), especially in gradually developing clusters (considering clusters developed taking >2 s time) that sustained short periods (i.e. lasted <1 s) in the dominant streamwise-vertical plane of the flow near the bed.

This was evident in the colour coded contours (Fig. 9a) which were associated with ejection and sweep events for AMCV runs (Table 2a). Similarly, for BMCV runs; it was evident with ejection and sweep events (Table 2b). In addition to that, in AMCV runs; momentum flux corresponded to the contour in sediment flux within similar period bands both in ejection and sweep events as shown in Fig. 9a and b in relation to Table 2a. A similar pattern was also observed in BMCV runs in the ejection events, as well as in the sweep events where momentum and sediment flux coincide with each other showing similar period bands (Fig. 10a and b, in relation to Table 2b). The WTC was applied to the momentum and sediment flux for both runs where common features were noticed as shown in Figs. 9c and 10c in relation to Table 2a and b. Both for AMCV and BMCV runs, during the identified ejection and sweep events (as mentioned in Table 2a and b) the coherence was found to be higher (i.e. warmer colour >0.5 s), suggesting that the transport mechanism greatly relies on the production of momentum flux by coherent structures in order to contribute to the sediment flux. For instance, the ejection event identified at 9 s in the AMCV run (Table 2a, Fig. 9c) shows higher correlation between momentum and sediment flux (i.e. warmer colour >0.5 s) with period band ranging between ∼0.5 s and 3 s. A similar trend was observed throughout the time series of AMCV and BMCV runs.

In this study, the well-known Shields criterion, estimated using mean velocities, along with some of the most commonly used empirical curves (i.e. van Rijn, 1984; Soulsby, 1997; Soulsby and Whitehouse, 1997, which are also derivatives of Shields diagram) were investigated in order to re-examine the prediction of sediment threshold performance (Fig. 11). In the figure, the grey shaded areas defined the range of the AMCV and BMCV mean velocities presented in this study. The calculated critical values using different approaches were shown in red dotted lines. Our measured critical velocity is clearly below the calculated Shields (1936), van Rijn (1984), Soulsby (1997), and Soulsby and Whitehouse (1997) critical velocity conditions [i.e. measured mean critical velocity, u‾cr, measured=0.163<0.210 ms-1 (Fig. 11d), 0.259 ms-1 (Fig. 11e), 0.297 (Fig. 11f), and 0.312 (Fig. 11g) respectively]. This suggested that the widely used above-mentioned empirical methods which are believed to be significant for the design of movable-bed channels as well as for future experimental investigations, potentially underestimated the transport of sediment by 1.29, 1.82, 1.59, and 1.91 times considering Shields (1936), van Rijn (1984), Soulsby (1997), and Soulsby and Whitehouse (1997) (Fig. 11) approaches respectively. Both reported cases, with mean velocities of AMCV (u‾=0.200 ms-1) and BMCV (u‾=0.096 ms-1), above and below our measured threshold (u‾cr, measured=0.163 ms-1), showed evidence of sediment in suspension, further showing that the mean critical stress approach also underpredicts the transport of sediment. Although it is still common to conceptualize the mechanics of sediment transport as a time-averaged approach, this approach sustained due to the lack of enough experimental and/or field data to perform stochastic analyses. Availability of such data, as those we present, advance understanding of the turbulence structure and their role in transport processes.

Comparison of test results where mean velocity was 1.23 times higher as well as 0.59 times lower than the measured mean critical velocity showed strong similarities without major exceptions (Figs. 4 and 5). Although near-bed velocity and average transport rate were greater in AMCV runs, the peak instantaneous Reynolds stress were close (i.e. u′w′>0.05 m2s-2 in the identified peak ejection and sweep events shown in the Figs. 4b., 5b) in both AMCV and BMCV runs. Both ejection and sweep events contributed to the forward momentum flux as well as sediment flux, showing that the concept of time-averaged critical velocity by itself cannot provide a full representation of the physical processes in action in the resuspension of sediment.

In both tests (AMCV and BMCV), ejection and sweep events were the largest contributors to momentum transfer. Up-acceleration and down-deceleration events led to marginal effect on transport of momentum and sediment flux compared to the other two events (Fig. 6). Previously, performance of quadrant analysis by Heathershaw and Thorne (1985) and Nelson et al. (1995) and performance of octant analysis by Keylock et al. (2014) advised that up-acceleration and down-deceleration events were the individually effective means of resuspending sediments. However, less net sediment flux was accomplished by these events in our AMCV and BMCV runs. This could be related to the strength of the up-acceleration and down-deceleration events which were much weaker and could not carry sediment particles to a higher level where the sampling volume was placed (i.e., 5 cm above the bed). It is also noteworthy to mention that up-acceleration and down-deceleration events contributed less significantly with a positive stress.

Buffington and Montgomery (1997) put forward a survey suggesting that many attempts have so far been made to modify the Shields diagram, conducting additional experiments and analysing the problem theoretically based on deterministic and probabilistic approaches. Several researchers have presented laboratory or field evidence supporting the close correlation between the instantaneous sediment flux and instantaneous streamwise velocity (u), suggesting that only sweeps and up-accelerations play a significant role in the entrainment and transport of sediment, since these motions were associated with positive u′ and thus greater streamwise velocities (Thorne et al., 1989; Nelson et al., 1995; Weaver and Wiggs, 2008). However, our investigation in the AMCV and BMCV conditions showed similarities with other research groups which documented that sweeps and ejections were the primary contributors to sediment entrainment (Grass, 1970, 1974; Sumer and Deigaard, 1981; Best, 1992; Niño and Garcia, 1996; Hurther and Lemmin, 2003). In contrast, direct numerical simulation (DNS) provides a new tool for examining turbulent structure of the flow (e.g. Mathis et al., 2013). However, further development is required to apply the DNS approach to intermittent turbulent bursting events both in fluvial and geophysical flows (Venditti et al., 2013). For example, Mathis et al. (2014) estimated bed shear-stress using conventional methods and the DNS modelling approach and reported a large disparity between the two methods where an order of magnitude difference between the levels of energy spectra was observed. While DNS has the potential to develop methodologies for the prediction of bursting events and associated sediment resuspension mechanisms, its application on large-scale, complex flows still remains limited (e.g. Schmeeckle and Nelson, 2003). Experimental investigations such as the one developed herein, will allow the use of new and existing data from acoustic velocimetry sensors to further identify and characterize such turbulent events. Direct observations of bursting events will in turn better inform DNS methods to better account for flow interactions.

Quadrant analysis showed that, in BMCV runs, ejection (in which low-speed fluid moves away from the boundary towards the outer layer) entrained particles away from the bed in order to maintain them in suspension as it was in AMCV runs (Figs. 7 and 8). Sweeps (in which high-speed fluid moves near the wall), with a negative contribution, impacted on the particles in resuspension by pushing them towards the bed. Moreover, the time occupied in both AMCV and BMCV runs was almost identical and contributed in similar percentage to instantaneous momentum and sediment flux as well. Diplas et al. (2008) demonstrated that in addition to the magnitude of the instantaneous turbulent forces applied on a sediment grain, the duration of these turbulent forces is also important in determining the sediment grain's threshold of motion, and that their product, or impulse, is better suited for specifying such conditions. This was evident in our results both in AMCV and BMCV conditions where the time occupied by the ejection and sweep events (which were also evidenced to play the dominant role in the momentum flux and sediment flux) were significantly higher in comparison to the up-acceleration and down-deceleration events. The understanding of accounting temporal contribution of bursting events presented in this study as well as discussed in Diplas et al. (2008) and Diplas and Dancey (2013) calls for consideration of the hydrodynamic impulse (i.e. value of force multiplied by required time for the accomplishment of the event) as a comprehensive criterion in the development of future models to predict particle entrainment.

Wavelet analysis was useful to diagnose characteristics of turbulence in order to explain information about the spatial structure of the flow. Particularly, we were interested in its frequency content and energy variation (Figs. 9 and 10). Previously, experimental investigation by Shugar et al. (2010) showed that stacked series of wavelet plots indicated that clusters of low-frequency coherent flow structures initiated close to the bed, grew with height above the bed, and then broke up as they were advected downstream, with their decay possibly being linked to topographically induced flow acceleration. The frequency at which these structures were generated was suitably predicted by the models of Driver et al. (1987) and Simpson (1989) for variation in separation zone size and wake flapping, respectively. Our measured data in BMCV runs were consistent with AMCV runs as well as with previous investigations. Therefore, it can be stated that the cross-wavelet transform method was effective at visualizing and detecting the coherent structures from the raw turbulent data, which enabled us to study the correlation between wall turbulence structures and sediment resuspension.

This paper reports on an investigation on the validity of using the mean critical shear velocity of sediment to define thresholds of sediment resuspension. Although Lavelle and Mofjeld (1987) previously reviewed the concept of critical stress for the initial motion of non-cohesive sediment beds under turbulent flow conditions suggesting the non-existence of true threshold in the movement of sediment, their conclusions were based on photographic observations employed in conjunction with current measurements to infer sediment thresholds in the field. Likewise, the work from Niño and Garcia (1996) and Niño et al. (2003) identified such instantaneous events from high-speed videos, which limit the number of captured and analysed events. We examined the influence of turbulent coherent structures on sediment resuspension for flows both above and below the measured mean critical resuspension velocity over a flat sandy bed using widely used acoustic instruments. The presented methodology can be used on existing data sets from researchers using ADVs or ADCPs in either laboratory or field settings to identify turbulent structures and their effect on suspended sediment concentration if synchronous records of acoustic backscatter exist. Such observations presented in this paper are also necessary to clarify our view of turbulent coherent structures in resuspending sediments both in low and high Reynolds-number flows while leading to widespread application of DNS.

Our results show that the measured mean critical velocity alone is not sufficient to predict episodic initiation of motion, as turbulent events can move sediment even at mean flow conditions below the thresholds defined by time-averaged stresses. Measured fluctuations of turbulent Reynolds stress evidenced to move sediments at lower turbulent stresses than expected. Instantaneous particle entrainment occurred earlier than the suggested measured time-averaged critical velocity due to the stochastic nature of turbulence. Although near-bed shear stress can be used to estimate bedload transport, significant special variations in the magnitudes and durations of the ejection, sweep, up-acceleration, and down-deceleration play a significant role in sediment resuspension. The implications of sediment motion at Reynolds shear stress below the expected critical conditions further suggested that instantaneous shear stress has an important contribution to entrain particles, which cannot be predicted with a time-averaged critical velocity.

To the best of our knowledge, there is no universal agreement on identifying a unique threshold for initiation of motion or resuspension of sediment (e.g. how many grains rolling, for how long, over what area coverage) in the literature. Our study shows that turbulent bursting events produce sediment resuspension even at mean velocities well below such typical critical values. Our statistical assessment suggests that the existing definition of threshold can be improved by incorporating turbulent effects for a more accurate description of the processes involved which will result in better predictions of sediment transport. The results of this study are instrumental in resolving an important research question: how can the turbulent bursting events best be incorporated into a theoretical model describing the sediment entrainment process? The analysis detailed herein on identification of bursting events and their contribution toward the near-bed Reynolds shear stress production governing sediment motion provide new avenues to answer such question, incorporating the use of wavelet analysis on time series of acoustic backscatter or signal intensity readily available from commonly used acoustic velocimetry instruments (ADVs and ADCPs) as a powerful tool for investigating such processes. The fact that a similar methodology can be applied to existing field and laboratory data sets that focused on velocity but collected an indicator of signal backscatter as part of the data record, further highlights its potential in future research to elucidate a more complete understanding of the interactions between flow and sediment transport over complex topography.