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The reach-average impacts of frictional forces, which retard flows in man-made channels and natural streams, are basically taken into account by flow resistance coefficients. These coefficients have been commonly treated as either a constant or a variable parameter, while the latter is only feasible through a tedious calibration process considering different flow and channel-boundary conditions. When neither historical records are available nor flow measurement is possible, applying a fixed-value roughness coefficient is practically inevitable. Although variation of Manning’s coefficient (n) with flow characteristics has been established in the literature, it has not been systematically implemented into hydraulic flow routing models, particularly because of the absence of a flow-dependent bed roughness predictor (BRP) suitable for numerical applications. In this study, a new grain roughness predictor, which provides derivations of n in respect with discharge and stage, is proposed. This grain roughness estimator, which enables to consider flow-dependent variation of n, is implemented in casting of governing equations of one-dimensional hydraulic flow routing method. In the numerical experiments designed to assess this implementation, three scenarios for n were considered: (1) constant n, (2) variable n computed using the new roughness predictor, and (3) variable n calculated based on the observed data. The third scenario, which requires a significant amount of field measurements, was considered as the benchmark solution. The obtained results showed that applying the proposed BRP to the hydraulic flow routing improved estimated outflows more than 40% based on the mean absolute relative error. The achieved improvement obviously demonstrates that considering variable resistance coefficient, like the one suggested in this study, may considerably improve the results of the flow-related numerical modeling.

To date, the Smoothed Particle Hydrodynamics (SPH) method has been successfully applied to reproduce the hydrodynamics behind three-dimensional flow-structure interactions. However, as soon as the effect of flow resistance becomes significant, the results obtained are not consistent with observations. This is the case for open channel flows (OCF), in which the water surface is largely influenced by the boundary friction. The roughness generated by the current boundary condition methodologies is solely numerical and cannot be associated to physical values of friction. In light of this challenge, the authors present a novel formulation for the friction boundary condition. The new implementation includes an additional shear stress at the boundaries to reproduce roughness effects, allowing for the adequate three-dimensional simulation of open channel flows using the SPH method. Finally, in order to reduce the high computational cost, typical of the Lagrangian models, without interfering in the representativeness of the SPH simulations, a criterion to define the adequate fluid particle size is proposed.

Dunes form critical agents of bedload transport in all of the world’s big rivers, and constitute appreciable sources of bed roughness and flow resistance. Dunes also generate stratification that is the most common depositional feature of ancient riverine sediments. However, current models of dune dynamics and stratification are conditioned by bedform geometries observed in small rivers and laboratory experiments. For these dunes, the downstream lee-side is often assumed to be simple in shape and sloping at the angle of repose. Here we show, using a unique compilation of high-resolution bathymetry from a range of large rivers, that dunes are instead characterized predominantly by low-angle lee-side slopes (<10°), complex lee-side shapes with the steepest portion near the base of the lee-side slope and a height that is often only 10% of the local flow depth. This radically different shape of river dunes demands that such geometries are incorporated into predictions of flow resistance, water levels and flood risk and calls for rethinking of dune scaling relationships when reconstructing palaeoflow depths and a fundamental reappraisal of the character, and origin, of low-angle cross-stratification within interpretations of ancient alluvial sediments.Dunes in the world’s big rivers are dominated by lee-side slopes with angles of less than 10°, according to a bedform analysis of high-resolution bathymetric datasets.

The present study uses results of eddy‐resolving numerical simulations to investigate the open channel flow over large clusters of freshwater mussels (Unio elongatulus) partially buried in a rough, gravel bed. The density of the mussels forming the array varies from 26 to 500 mussels/m2. The flow structure is analyzed at large distances from the leading edge of the mussel bed, where the flow can be considered fully developed. The effects of changing the mussel bed density, the filtering discharge, the burial level and the roughness of the bed surface in which mussels are burrowed, are investigated in terms of flow field, turbulent structures, drag forces, and bed shear stresses. It is found that strong interactions occur between energetic eddies generated by the larger gravels on the exposed bed surface and by the mussel shells. Simulations results show that for a burial depth close to 50% and a ratio between the average gravel size and the mussel protruding height of 0.13, the shell induced turbulence becomes dominant for mussel bed densities around 50 mussels/m2. The influence of the bed roughness becomes less relevant with increasing mussel density, as the generation of energetic eddies is mostly controlled by mussel‐to‐mussel interactions. For fixed bed roughness, burial level and filtering velocity, the mean streamwise drag force and the associated drag coefficient for the exposed part of each mussel decrease with increasing mussel density, even if strong variations are observed for individual mussels. For constant mussel bed density and burial level, the mean streamwise drag force and the mean drag coefficient decrease slightly with increasing bed roughness. Increasing the burial level decreases not only the drag forces but also the drag coefficients because of the more streamlined shape of the top of the mussels. Strong active filtering acts toward decreasing the mean streamwise force and the mean drag coefficient. The spanwise drag forces contribute significantly to the total drag force, especially for high mussel bed densities. Based on smooth bed calculations, bed‐averaged shear stresses are reduced in highly dense clusters. Key Points Mussel‐to‐mussel interactions are important for dense arrays and influence flow structure and turbulence Eddy resolving simulations showed that the effect of bed roughness become less significant with increasing mussel bed density In dense clusters of mussels, forces on the shells and bed shear stresses are reduced thus favoring mussel stability

The effect of bottom roughness on setup dynamics was investigated using high-resolution observations across a laboratory fringing reef profile with roughness elements scaled to mimic the frictional wave dissipation of a coral reef. Results with roughness were compared with smooth bottom runs across 16 offshore wave and still water level conditions. The time-averaged and depth-integrated force balance was evaluated from observations collected at 17 locations along the flume and consisted of cross-shore pressure and radiation stress gradients whose sum was balanced by quadratic mean bottom stresses. The introduction of roughness had two primary effects. First, for runs with roughness, frictional wave dissipation occurred on the reef slope offshore of the breakpoint, reducing wave heights prior to wave breaking. Second, offshore-directed mean bottom stresses were generated by the interaction of the combined wave–current velocity field with the roughness elements. These two mechanisms acted counter to one another. Frictional wave dissipation resulted in radiation stress gradients that were predicted to generate 18% (on average) less setup on the reef flat for rough runs than for smooth runs when neglecting mean bottom stresses. However, mean bottom stresses increased the predicted setup by 16% on average for runs with roughness. As a result, setup on the reef flat was comparable (7% mean difference) between corresponding rough and smooth runs. These findings are used to assess prior results from numerical modeling studies of reefs and also to discuss the broader implications for how large roughness influences setup dynamics in the nearshore zone.

A theoretically based relationship for the Darcy–Weisbach friction factor$f$for rough-bed open-channel flows is derived and discussed. The derivation procedure is based on the double averaging (in time and space) of the Navier–Stokes equation followed by repeated integration across the flow. The obtained relationship explicitly shows that the friction factor can be split into at least five additive components, due to: (i) viscous stress; (ii) turbulent stress; (iii) dispersive stress (which in turn can be subdivided into two parts, due to bed roughness and secondary currents); (iv) flow unsteadiness and non-uniformity; and (v) spatial heterogeneity of fluid stresses in a bed-parallel plane. These constitutive components account for the roughness geometry effect and highlight the significance of the turbulent and dispersive stresses in the near-bed region where their values are largest. To explore the potential of the proposed relationship, an extensive data set has been assembled by employing specially designed large-eddy simulations and laboratory experiments for a wide range of Reynolds numbers. Flows over self-affine rough boundaries, which are representative of natural and man-made surfaces, are considered. The data analysis focuses on the effects of roughness geometry (i.e. spectral slope in the bed elevation spectra), relative submergence of roughness elements and flow and roughness Reynolds numbers, all of which are found to be substantial. It is revealed that at sufficiently high Reynolds numbers the roughness-induced and secondary-currents-induced dispersive stresses may play significant roles in generating bed friction, complementing the dominant turbulent stress contribution.

This study addressed a research concern that employing a fixed value for the bed roughness coefficient in lowland rivers (mostly sand-bed rivers) is deemed practically questionable in the presence of a mobile bed and time-dependent changes in vegetation patches. Accordingly, we set up 45 cross-sections in four lowland streams to investigate seasonal flow resistance values within a year. The results revealed that the significant sources of boundary resistance in lowland rivers with the lower regime flow were bed forms and aquatic vegetation. The study then used flow discharge as an influential variable reflecting the impacts of the above-mentioned sources of resistance to flow. The studied approach ended up with two new flow resistance predictors which simply connected the dimensionless unit discharge to flow resistance factors, Darcy-Weisbach (f) and Manning (n) coefficients. A comparison of the computed and measured flow resistance values also indicated that 87–89% of the data sets were within ± 20% error bands. The flow resistance predictors were also verified against large independent sets of field and flume data. The obtained predictions using the developed predictors might overestimate flow resistance factors by 40% for other lowland rivers. Based on a different view, according to the findings of this research, seasonal variation of vegetation abundance could show the augmentation in flow resistance values, both f and n, in low summer flows when vegetation covers river bed and side banks. The highest amount of flow resistance was observed during the summer period, during the July–August period.

Stream obstacles, naturally formed like boulders or engineered like weirs, are the major source of flow resistance; however, to quantify their flow resistance, a resistance formula needs to be selected in accordance with the specific obstacle type, that is obstacle type dependency. So far, a unified resistance formula that adequately characterizes the roughness of distinctive obstacle types remains elusive. Here, we conduct flume experiments with various natural and engineered submerged obstacles, including boulders, weirs, log jams, and transverse stones. We combine them with existing data sets containing rigid vegetation, step‐pool, and riffle‐pool to identify a unified metric for a general resistance relation. We test three roughness metrics, the widely used roughness metric D84 (84th percentile of bed grain size distribution), a bathymetric‐line‐based metric σz,centerline (the standard deviation of bed centerline elevation), and a 3D‐bathymetry‐based σz,bed (the standard deviation of elevation of the entire bed) as bed roughness, respectively. σz,bed is adopted to incorporate the roughness inhomogeneity in the transverse direction which widely exists in both natural and engineered channels, complementing the insufficiency of line‐based metric σz,centerline. Using 3‐fold cross validation, we show that the resistance formula based on σz,bed demonstrated a more consistent and superior velocity prediction capacity than those based on D84 and σz,centerline in predicting velocity across almost all obstacle types. Interestingly, when applied to channels with submerged rigid vegetation, the resistance formula based on only σz,bed can compare with those based on multiple vegetation characteristic parameters. This study shows the viability of unifying the flow resistance formula in open‐channels with submerged obstacles, avoiding obstacle‐type dependency.

The dynamic interplay between surface and subsurface flow in the presence of a permeable boundary was investigated using low and high frame-rate particle-image velocimetry measurements in a refractive-index-matching flow environment. Two idealized permeable wall models were considered. Both models contained five layers of cubically packed spheres, but one exhibited a smooth interface with the flow, while the other embodied a hemispherical surface topography. The relationship between the large-scale turbulent motions overlying the permeable walls and the small-scale turbulence just above, and within, the walls was explored using instantaneous and statistical analyses. Although previous studies have indirectly identified the potential existence of amplitude modulation in permeable-wall turbulence (a phenomenon identified in impermeable-wall turbulence whereby the outer large scales modulate the intensity of the near-wall, small-scale turbulence), the present effort provides direct evidence of its existence in flow over both permeable walls considered. The spatio-temporal signatures of amplitude modulation were also characterized using conditional averaging based on zero-crossing events. This analysis highlights the connection between large-scale regions of high/low streamwise momentum in the surface flow, downwelling/upwelling across the permeable interface and enhancement/suppression of small-scale turbulence, respectively, just above and within the permeable walls. The presence of bed roughness is found to intensify the strength and penetration of flow into the permeable bed modulated by large-scale structures in the surface flow, and linked to possible roughness-formed channelling effects and shedding of smaller-scale flow structures from the roughness elements.

Follett et al. (2020a, https://doi.org/10.1029/2020gl089346) developed an analytical model to predict backwater rise by log jams, using the size and packing density of logs and the jam length, as well as river slope and bed roughness. We show that the model formulas can be rewritten using the Froude number instead of river slope and roughness, thus improving their applicability in engineering practice. The equation terms and results of Follett et al. (2020a, https://doi.org/10.1029/2020gl089346) are found to be similar to those of the empirically derived formula by Schalko et al. (2018, https://doi.org/10.1061/(asce)hy.1943‐7900.0001501). However, some differences are identified, calling for further study. Most notably, these distinctions pertain to the effect of accumulation porosity, with additional minor differences in the exponent of the Froude number. Lastly, model implications for some broader applications are explored, showing a methodology to calculate the representative log size for log mixtures, and the expected effect of log orientation on backwater rise. Plain Language Summary Accumulations of wood in rivers (log jams) can block the flow and thereby cause water level rise. Follett et al. (2020a, https://doi.org/10.1029/2020gl089346) developed a theoretical model to predict how this water level rise depends on log jam properties and local river conditions. For the local river conditions, they used the river slope and bottom roughness. In this comment, we show that the Froude number can be used instead, with exactly the same result. The Froude number is a dimensionless number that depends directly on the local river conditions, making the adapted formula easier to apply in practice. The resulting formula shows good agreement with an earlier one based on experimental work by Schalko et al. (2018, https://doi.org/10.1061/(asce)hy.1943‐7900.0001501). Still, some differences were found that raise questions. Most notably, the formulas differ for the effect of accumulation porosity. This becomes especially clear when logs are packed closely together. Next, model implications for slightly different settings than those studied by Follett et al. (2020a, https://doi.org/10.1029/2020gl089346) were explored. This showed how to determine the average log size for a mixture of logs with different sizes, and how the expected water level rise changes with log orientation. Key Points Follett et al. (2020a, https://doi.org/10.1029/2020gl089346) predicted backwater rise by log jams using river slope and roughness. We show the Froude number can be used instead By using the Froude number, the link to the local river conditions becomes stronger, improving formula applicability in engineering practice The resulting formula is shown to be similar to earlier empirical work. But differences in jam porosity effects call for further study