# Water-Worked Gravel Bed: State-of-the-Art Review

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analysis of Bed Roughness Structures in WGBs

_{s}approximately to be 3–3.5 d

_{84}, where d

_{84}is the 84th percentile of a particle-size distribution belonging to the range of 240–500 mm. However, the roughness height k

_{s}cannot be estimated considering only a single gravel size, e.g., d

_{84}, because other factors, such as gravel shape, orientation, alignment and structural arrangements, are of equal importance, providing significant impact on the estimation of the roughness height k

_{s}[2,3,4,5,6,7]. Considering this fact, Kirchner et al. [5] were the first to measure the friction angle of the sediment mixtures having median size d

_{50}ranging 1.2–12 mm in both WGBs and SGBs. They observed that the difference in friction angles increases with a decrease in gravel size. Tp To quantify the impact of water-work on the bed roughness structures, they compared the difference between the bed roughness structures in WGBs that were created by the water action and SGBs that were manmade. The results reveal that, for an identical particle-size distribution, the distributions of friction angles in a WGB and an SGB are different, because the friction angles in the former are smaller than those in the latter. They argued that the difference in the friction angles occurs owing to the difference in gravel packing geometries in these beds. Hence, they concluded that the friction angle measured in an SGB cannot be directly applicable to a WGB.

#### 2.1. Use of Probability Density Function

^{−1}, 0.0922 kg m

^{−1}and 0.152 kg m

^{−1}, respectively. The PDFs of these four beds revealed that the SGB has a slightly negatively skewed distribution of the roughness structure, while the WGBs have a very slightly positively skewed distribution (Figure 3). Moreover, they found that, with an increase in feeding rate, the skewness value decreases. Interestingly, in both the WGBs and the SGB, the kurtosis coefficients were found to be positive, indicating a leptokurtic curve.

#### 2.2. Use of the Second-Order Structure Function

_{x}, l

_{y}) is the second-order structure function of the bed elevation, z′ is the bed surface fluctuation with respect to the mean bed elevation $\overline{z}$, l

_{x}is the sampling interval in streamwise direction (= nδx), l

_{y}is the sampling interval in spanwise direction (= mδy), j = 1, 2, 3, …, n, n is the number of points in streamwise direction, k = 1, 2, 3, …, m, m is the number of points in spanwise direction, and δx and δy are the sampling intervals in x and y directions, respectively. However, following the concept of Monin et al. [13], Nikora et al. [8] obtained the D(l

_{x}, l

_{y}) as follows:

_{z}is the standard deviation and R(l

_{x}, l

_{y}) is the correlation function of the bed elevations. Interestingly, Nikora et al. [8], instead of computing D(l

_{x}, l

_{y}) for all the measured points, computed the D(l

_{x}, l

_{y}= 0) and D(l

_{x}= 0, l

_{y}) assuming that the main anisotropy axes of the roughness coincide with their chosen x and y axes in a WGB and an SGB. From the analysis, they found that the data form both beds collapsed onto two curves, indicating the existence of two different universal classes of gravel-bed roughness.

_{x}, l

_{y}) is composed of three regions: scaling, transition and saturation regions. However, the first and last regions play the main role. For a small spatial lag, the D(l

_{x}, l

_{y}) acts as a power function (that is, the scaling region), while, for a large spatial lag, the D(l

_{x}, l

_{y}) becomes constant (that is, the saturation region). Goring et al. [14] extended the work of Nikora et al. [8] by computing the second-order structure function for a two-dimensional roughness structure and obtained similar results. Later, Butler et al. [15] analyzed the roughness structure in a WGB using the fractal analysis in both streamwise and spanwise directions. To do so, they applied a two-dimensional fractal method to high-resolution digital elevation models. They identified a mixed fractal behavior with two characteristic fractal bands; one associated with the subgrain scale and the other associated with the grain scale. The subgrain and grain scales features are isotropic and anisotropic, respectively. They also observed that, owing to the streamwise orientation of the longest axis of particles, the fractal dimensions are higher in the streamwise direction than in the other directions. It implies that the effects of water-work are to modify the organization of roughness structure by increasing the surface irregularities and hence the roughness height. Then, similar to Goring et al. [14], Marion et al. [9] used Equation (2) to analyze the variation of roughness structure with time in a WGB under a mobile bed condition. They showed that the roughness structures captured at different time intervals are directly associated with the bed mobility conditions. Moreover, their second-order structure function for roughness structure depicted the development of two different grain scale classes. One grain class was developed under a static armoring condition, where the gravels formed a bed surface with strong streamwise and spanwise coherences. The other one was developed under the dynamic armoring condition, where the gravels formed a bed surface very quickly, but only with very strong streamwise coherence. However, they were unable to establish a relation between the grain scale features with the bed mobility condition. Following the method proposed by Nikora et al. [8], Cooper and Tait [12] used the second-order structure functions for roughness structures of three fed WGBs and an SGB. They calculated the correlation lengths in the WGBs and an SGB. They indicated that the correlation lengths in both streamwise and spanwise directions in the WGBs are larger than those in the SGB, confirming that the WGBs have larger scale bed features than the SGB. Later, Qin and Ng [16] performed the second-order structure function analysis in a WGB and an SGB. They found similar results as obtained by the aforementioned researchers.

#### 2.3. Use of Higher-Order Structure Function

_{p}(l

_{x}, l

_{y}) is the higher-order structure function and p is the order of the moment of the structure function.

_{p}(l

_{x}, l

_{y}) can be divided into three regions: scaling, transition and saturation regions (Figure 4) [17]. Interestingly, they revealed that, in WGBs, the boundary between the scaling and transition regions is of the order of the median gravel size d

_{50}, while the boundary between the transition and saturation regions is of order of d

_{90}, where d

_{90}is the 90th percentile of a particle-size distribution. Akin to Nikora et al. [8], in Nikora and Walsh [17], the analysis of D

_{p}(l

_{x}, l

_{y}) suggested that the grain scales are isotropic, indicating that the D

_{p}(l

_{x}, l

_{y}) is independent of the axis rotation. However, within the transition region, the D

_{p}(l

_{x}, l

_{y}) becomes anisotropic. Further, within the scaling region, the scaling exponent ξ plays an important role. For small values of l

_{x}and l

_{y}, the ξ varies linearly with p. Nevertheless, as p increases, the ξ varies nonlinearly with p, suggesting a multiscaling behavior of roughness structures in WGBs, being sensitive to the flow direction (Figure 5). The reason is attributed to the shape and the spatial arrangements of gravels [17].

^{3}s

^{−1}), Aberle and Nikora [10] found that the WGB roughness structures possess multiscaling behavioral features, which is in conformity with the findings of Nikora et al. [17].

_{j}+ nδx) − z′(x

_{j}) > 0],

_{j}+ nδx) − z′(x

_{j}) < 0],

_{p}and E

_{n}are the positive and negative bed slopes, respectively, and n

_{p}and n

_{n}are the number of positive and negative slopes, respectively.

_{p}and E

_{n}in the WGBs and found that, at small lags, the frequency of negative slope is less than that of positive slope, owing to the gravel imbrication. Further, they revealed that the ξ of the gravels is directly associated with the armoring discharge and the individual large gravels create less complex roughness structure than a large number of small gravels.

## 3. Turbulence Characteristics in WGBs

#### 3.1. Effects of Water-Work on Streamwise Velocity

^{5}, 2.2 × 10

^{5}and 2.9 × 10

^{5}) in a WGB. They observed that the spatial heterogeneity of the time-averaged velocity decreases with a decrease in the vertical distance, but it increases with an increase in Reynolds number. At a high Reynolds number, the spatial heterogeneity was found to be maximum in the near-bed flow zone. Further, they analyzed the mean and skewness maps of the time-averaged streamwise velocity on the horizontal plane at two different vertical distances: one near the bed and the other in the main flow layer. They observed that the mean and skewness maps for the near-bed case were more complex than those for the main flow layer case. The skewness values suggested that the shapes of the velocity distributions are different for these cases. In the near-bed flow zone, the skewness is mostly positive, while in the main flow layer, the skewness is almost negative. Buffin-Bélanger et al. [11] argued that the positive skewness values in the near-bed flow zone possibly reflect incursions of high-speed fluid streaks, while the negative values in the main flow layer indicate the incursions of low-speed fluid streaks. To be explicit, the low-speed and high-speed fluid streaks refer to the ejections and sweeps.

^{5}, 2.5 × 10

^{5}and 2.7 × 10

^{5}). They observed that, for all Reynolds numbers, the flows are highly inconsistent in the near-bed flow zone. Further, the turbulent structures that originate from the near-bed zone are to intrude into the main flow layer. These structures change their form and magnitude at higher Reynolds numbers, becoming more distinct, having a clearer velocity signature and a steeper upstream-dipping slope.

_{*}is the frictional velocity, z is the vertical distance, ν is the kinematic viscosity, B

_{r}is the constant of integration, κ is the von Kármán coefficient, Π is the Coles’ wake parameter, Δz is the virtual bed level (≈0.25 k

_{s}, according to Dey et al. [31]), z

_{0}is the zero velocity level, k

_{s}is the average roughness height, and h is the flow depth.

_{r}are lower in both the smooth and the rough (WGB and SGB) beds than the traditional values: B

_{r}= 5.5 and 8.5 for the smooth and rough beds, respectively. Further, even though the flow conditions of both the WGB and SGB were identical, they observed that the B

_{r}in the WGB was smaller than that in the SGB. It implies that, in the near-bed flow zone, a WGB roughness structure affects B

_{r}and, in turn, the velocity profile. In addition, the comparison of Π values in the WGB and SGB revealed that the values of Π remain the same in the velocity profiles of both the beds, suggesting that the water-work has an insignificant impact on the Π, which mainly governs the velocity profile in the outer layer.

#### 3.2. Effects of Water-Work on Reynolds Shear Stresses and Form-Induced Shear Stresses

_{f}〉 is the SA form-induced shear stress (= −ρ〈$\tilde{u}\tilde{w}$〉), ρ is the mass density of fluid, ũ and $\tilde{w}$ are the spatial velocity fluctuations in the streamwise and vertical directions, respectively, 〈${\overline{\tau}}_{uw}$〉 is the SA Reynolds shear stress (= −ρ〈$\overline{{u}^{\prime}{w}^{\prime}}$〉), u′ and w′ are the temporal velocity fluctuations in the streamwise and vertical directions, respectively, and 〈${\overline{\tau}}_{v}$〉 is the SA viscous shear stress (= −ρνd〈ū〉/dz).

_{f}〉 is the governing stress near the gravel-bed [33]. Aberle et al. [34] focused on the 〈τ

_{f}〉 profile influenced by the roughness elements. They analyzed the spatial flow heterogeneity in terms of the 〈τ

_{f}〉 in WGBs for different discharges. Their results infer that the magnitude of 〈τ

_{f}〉 is small away from the crest. However, the 〈τ

_{f}〉 increases as one moves toward the crest in the downward direction. It indicates that the ũ and $\tilde{w}$ near the bed are higher than those away from the bed, resulting in a higher magnitude of 〈τ

_{f}〉. Further, they found that the 〈τ

_{f}〉 profiles are similar for different discharges. Interestingly, the similarity in 〈τ

_{f}〉 profiles is not preserved for different bed slopes. It suggests that for a given bed slope, the 〈τ

_{f}〉 profile is independent of discharge.

_{f}〉, Cooper and Tait [35] analyzed all the terms of Equation (9) in two WGBs created by the unimodal and bimodal sediment mixtures. For the unimodal sediment mixture, the relative submergences varied within the range of 1.2–1.9, while, for bimodal sediment mixture, they varied within 1.3–2. They analyzed the results in terms of forces caused by the shear stresses. In doing so, they considered the fluid force caused by the 〈${\overline{\tau}}_{uw}$〉 at a given vertical distance as 〈${\overline{\tau}}_{uw}$〉ϕA

_{0}, where ϕ is the roughness geometric function (= A

_{f}/A

_{0}, where A

_{f}is the area of fluid in the averaging domain at a given elevation within the total area A

_{0}). Above the roughness crest, ϕ = 1. Similarly, the fluid force caused by the 〈τ

_{f}〉 at given vertical distance was obtained as 〈τ

_{f}〉ϕA

_{0}. They further argued that in addition to these two forces, there exists an additional force called the form drag 〈τ

_{d}〉, which can be computed as $\underset{z}{\overset{{z}_{c}}{\int}}0.5{C}_{d}\rho {\langle \overline{u}\rangle}^{2}{A}_{e}\mathrm{d}z$, where C

_{d}is the drag coefficient and A

_{e}is the exposed frontal area of the grain to the fluid. However, in the analysis, they neglected the force caused by the 〈${\overline{\tau}}_{v}$〉 term considering that it has minimal impact on the turbulent flow. It is pertinent to mention that their analysis mainly focused on the zone below the roughness crest. Analyzing the forces, they inferred that within this zone, the vertical variations of the forces contributed from 〈${\overline{\tau}}_{uw}$〉, 〈τ

_{f}〉 and 〈τ

_{d}〉 with ϕ are similar and thus controlled by the geometry of the roughness elements. Moreover, they observed that with a decrease in vertical distance, the reduction in the force caused by a damping of 〈${\overline{\tau}}_{uw}$〉 is compensated by the addition of the force caused by 〈τ

_{d}〉. Furthermore, their results showed that as the relative submergence increases, the forces contributed from the 〈${\overline{\tau}}_{uw}$〉, 〈τ

_{f}〉, and 〈τ

_{d}〉 increase. It suggests that for a given bed surface topography, the mechanism of momentum transfer between the fluid and particle fairly changes with an increase in relative submergence. When the results of unimodal and bimodal WGBs were compared, they found that for a given vertical distance and relative submergence, the force contributed from the 〈${\overline{\tau}}_{uw}$〉 and 〈τ

_{d}〉 in the unimodal WGB is less than that in the bimodal WGB in the upper portion of the roughness layer and vice versa. Interestingly, in the lower portion of the roughness layers of both beds, the force caused by the 〈τ

_{f}〉 was observed to have different vertical distributions. It indicates that for a given relative submergence, the mechanism of momentum transfer differs owing to the difference in roughness structure.

_{f}〉 for different flow submergence conditions and for gravel-beds with different roughness structures. They observed that the spatial flow variance within the roughness layer is typically 4–5 times higher than that above the roughness layer. In fact, it becomes invariant to the vertical distance at a distance twice the roughness height above the crest. Owing to the increase in relative submergence, the spatial flow variance with respect to 〈τ

_{f}〉 decreases within and above the roughness layer. However, the flow submergence does not have a significant impact on the spatial flow variance with respect to 〈${\overline{\tau}}_{uw}$〉. Further, their study infers that for different bed surface topographies, the spatial flow variance and the 〈τ

_{f}〉 profiles vary, suggesting that the bed geometry possesses a strong control on the spatial flow variance profiles and the vertical organization of the time-averaged flow within the roughness layer.

_{f}〉 were not taken into consideration.

_{f}〉 profiles in a WGB and an SGB. Akin to Pu et al. [30], Padhi et al. [32] found that the roughness height in the WGB was also higher than that in the SGB. However, the results of Padhi et al. [32] do not correspond to those of Pu et al. [30]. In the study by Padhi et al. [32], the 〈${\overline{\tau}}_{uw}$〉 profile in the WGB is higher than that in the SGB owing to a higher roughness height in the former than in the latter (Figure 9). They stated that a higher roughness in the WGB than in the SGB enhances the u′ and w′ values, causing an increased magnitude of 〈${\overline{\tau}}_{uw}$〉 in the WGB. The results are in agreement with those reported in Nezu and Nakagawa [29], Nikora et al. [33], Mignot et al. [37] and Dey and Das [38]. Moreover, the 〈${\overline{\tau}}_{uw}$〉 profile in the WGB collapses on the gravity line at a shorter distance than that in the SGB. It implies that, although the WGB exhibits a higher roughness height than the SGB, owing to the well-organized roughness structure in the WGB, intense flow mixing is restricted to a shorter vertical distance. Further, the 〈τ

_{f}〉 profiles in the WGB and SGB showed that a higher roughness in the WGB than in the SGB produces large values of ũ and $\tilde{w}$ causing an increased magnitude of 〈τ

_{f}〉 in the former than that in the latter (Figure 9). This suggests that in the near-bed flow zone, the flow is more heterogeneous in the WGB than in the SGB.

#### 3.3. Effects of Water-Work on Reynolds Normal Stresses and Form-Induced Normal Stresses

_{uu}〉 = ρ〈$\overline{{u}^{\prime}{u}^{\prime}}$〉, and 〈σ

_{ww}〉 = ρ〈$\overline{{w}^{\prime}{w}^{\prime}}$〉, respectively. Similarly, the streamwise and vertical form-induced normal stresses are 〈σ

_{fuu}〉 = ρ〈$\tilde{u}\tilde{u}$〉 and 〈σ

_{fww}〉 = ρ〈$\tilde{w}\tilde{w}$〉, respectively.

_{fuu}〉 (Figure 10). They observed that, akin to the 〈τ

_{f}〉 profile, the 〈σ

_{fuu}〉 profile is small away from the crest and gradually increases, as one moves downward toward the crest. Interestingly, they found that for a given bed slope and bed roughness structure, the 〈σ

_{fuu}〉 profiles are almost identical for all the discharges. It implies that the shape of the 〈σ

_{fuu}〉 profiles are independent of discharge. Further, they compared the 〈σ

_{fuu}〉 profiles obtained for different roughness structures, but for a constant bed slope. They argued that the shapes of all the 〈σ

_{fuu}〉 profiles are similar, although their absolute magnitudes are different. This suggests that the magnitude of 〈σ

_{fuu}〉 profiles is governed by the roughness structure. Then, they analyzed the 〈σ

_{fuu}〉 profiles for different bed slopes, keeping the roughness structure identical. The comparison of 〈σ

_{fuu}〉 profiles revealed that the variation of bed slope (S

_{0}= 0.001 to 0.01) has a significant impact on the shape of the 〈σ

_{fuu}〉 profiles.

_{fuu}〉 profiles over the original and rotated WGBs. They tested two relative submergences for each bed type: for the original WGB, the relative submergences were taken as 4.4 and 3.2, while, for the rotated WGB, they were 4.5 and 3.3. They noticed that, in the near-bed flow zone, the 〈σ

_{fuu}〉 profile increases with an increase in relative submergence. However, away from the bed, the effects of relative submergence diminish. Cooper et al. [36] examined the impact of the relative submergence on both the 〈σ

_{fuu}〉 and 〈σ

_{fww}〉 profiles in a WGB. In fact, they carried out the analysis for form-induced intensities, 〈σ

_{fuu}〉

^{0.5}and 〈σ

_{fww}〉

^{0.5}. They showed that the SA streamwise form-induced intensity 〈σ

_{fuu}〉

^{0.5}profiles exhibit similar shape for all the values of relative submergences. The spatial flow variance is maximum at the middle of the interfacial sublayer, gradually diminishing away from the crest and continuing up to a vertical distance equaling twice the roughness height above the crest. Further, they observed that between the crest and the vertical distance of twice the roughness height above the crest, the spatial variance is half of its peak value in all the 〈σ

_{fuu}〉

^{0.5}profiles, irrespective of the bed roughness. Analysis of the impact of relative submergence on the 〈σ

_{fuu}〉

^{0.5}profiles revealed that, for a given vertical distance, the magnitude of 〈σ

_{fuu}〉

^{0.5}profile is inversely proportional to the relative submergence. Thus, it confirms that the relative submergence governs the 〈σ

_{fuu}〉

^{0.5}profile. By contrast, the results of SA vertical form-induced intensity 〈σ

_{fww}〉

^{0.5}profiles inferred that although the shapes of 〈σ

_{fww}〉

^{0.5}profiles are similar to those of 〈σ

_{fuu}〉

^{0.5}profiles, there is an insignificant difference in the magnitudes of 〈σ

_{fuu}〉

^{0.5}profiles owing to the difference in relative submergences. Additionally, they analyzed the 〈σ

_{uu}〉

^{0.5}and 〈σ

_{ww}〉

^{0.5}profiles for different relative submergences. Akin to 〈σ

_{fuu}〉

^{0.5}profiles, the magnitudes of 〈σ

_{uu}〉

^{0.5}profiles reduce with an increase in relative submergence, confirming that these profiles are also affected by the relative submergence. Further, they found that the spatial variance in 〈σ

_{uu}〉

^{0.5}profiles is approximately half of the spatial variance in the time-averaged streamwise velocity profiles. Moreover, a small variation in 〈σ

_{ww}〉

^{0.5}profiles was observed owing to the change in relative submergence. It is important to mention that the spatial variance in 〈σ

_{ww}〉

^{0.5}profiles is approximately half of the spatial variance in 〈σ

_{uu}〉

^{0.5}profiles and equals the spatial variance in time-averaged vertical velocity profiles. This implies that the spatial flow variance in the streamwise direction is higher than that in the vertical direction.

_{uu}〉, 〈σ

_{ww}〉, 〈σ

_{fuu}〉 and 〈σ

_{fww}〉 profiles in a WGB and an SGB. Their analysis showed that owing to the higher WGB roughness height, both u′ and w′ enhance, resulting in higher values of 〈σ

_{uu}〉 and 〈σ

_{ww}〉, respectively. Moreover, they also observed that in both the beds, the effects of roughness height are more prominent in the streamwise direction than in the vertical direction. Therefore, the magnitude of 〈σ

_{uu}〉 profile, for a given vertical distance, is greater than that of 〈σ

_{ww}〉 profile. While comparing the 〈σ

_{fuu}〉 and 〈σ

_{fww}〉 profiles in both the beds, they found that a higher roughness in the WGB than that in the SGB enhances the ũ and $\tilde{w}$. As a result, for a given vertical distance, the 〈σ

_{fuu}〉 and 〈σ

_{fww}〉 profiles in the WGB appear to have higher magnitudes than those in the SGB.

#### 3.4. Effects of Water-Work on Conditional Turbulent Events

_{2}(−u′ and +w′) and sweeps Q

_{4}(+u′ and −w′), respectively, are the dominating events, which govern the turbulence mechanism in the flow. On the other hand, those generated from the first and the third quadrants, termed outward interactions Q

_{1}(+u′ and +w′) and inward interactions Q

_{3}(−u′ and −w′), respectively, are the weak events, but they can be effective in the context of sediment entrainment [39].

#### 3.5. Effects of Water-Work on Secondary Currents

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Photograph of a natural gravel-bed stream with a flow direction right to left (

**a**); and close view of the natural gravel-bed stream with a flow direction left to right (

**b**).

**Figure 3.**Probability density functions of bed surface fluctuations with respect to the mean surface level in WGBs (namely, Fed bed 1, Fed bed 2, and Fed bed 3) and an SGB (data extracted from Cooper and Tait [12]).

**Figure 4.**Non-dimensional structure function of a WGB (data extracted from Nikora and Walsh [17]).

**Figure 5.**Variations of scaling exponents ξ of the generalized structure function with the order p (data extracted from Nikora and Walsh [17]).

**Figure 6.**Contours of the second-order structure function for the roughness structure at a discharge of 0.25 m

^{3}s

^{−1}(data extracted from Aberle and Nikora [10]).

**Figure 7.**Variations of non-dimensional streamwise velocity with non-dimensional vertical distance zu

_{*}/ν and (z + Δz)/k

_{s}in smooth and rough beds (WGB and SGB), respectively (data extracted from Pu et al. [30]).

**Figure 8.**Variations of non-dimensional DA streamwise velocity with non-dimensional vertical distance (z + Δz)/Δz in the WGB and SGB. The red and blue broken lines indicate the form-induced sublayers in the WGB and SGB, respectively (data extracted from Padhi et al. [32]).

**Figure 9.**Variations of non-dimensional SA Reynolds shear stress 〈${\overline{\tau}}_{uw}$〉/${u}_{*}^{2}$ and SA form-induced shear stress 〈τ

_{f}〉/${u}_{*}^{2}$ with non-dimensional vertical distance z/h in the WGB and SGB (data extracted from Padhi et al. [32]).

**Figure 10.**Variations of SA form-induced normal stress 〈σ

_{fuu}〉 (=〈$\tilde{u}\tilde{u}$〉/ρ) with z–z

_{0}in the WGB (data extracted from Aberle et al. [34]).

**Figure 11.**Flow structures as examined with the quadrant analysis: (

**a**–

**c**) first quadrant (outward intersections); (

**d**–

**f**) second quadrant (ejections); (

**g**–

**i**) third quadrant (inward intersections); and (

**j**–

**l**) fourth quadrant (sweeps) (data extracted from Hardy et al. [27]).

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Padhi, E.; Dey, S.; Desai, V.R.; Penna, N.; Gaudio, R.
Water-Worked Gravel Bed: State-of-the-Art Review. *Water* **2019**, *11*, 694.
https://doi.org/10.3390/w11040694

**AMA Style**

Padhi E, Dey S, Desai VR, Penna N, Gaudio R.
Water-Worked Gravel Bed: State-of-the-Art Review. *Water*. 2019; 11(4):694.
https://doi.org/10.3390/w11040694

**Chicago/Turabian Style**

Padhi, Ellora, Subhasish Dey, Venkappayya R. Desai, Nadia Penna, and Roberto Gaudio.
2019. "Water-Worked Gravel Bed: State-of-the-Art Review" *Water* 11, no. 4: 694.
https://doi.org/10.3390/w11040694