Bed Roughness Research Articles

Uncertainties in Models Predicting Critical Bed Shear Stress of Cohesionless Particles

Our data show large scatter in the critical Shields stress values for initial sediment motion. The main sources of dispersion are related to the methodological procedures defining the inception of movement (i.e., visual observations or extrapolation of sediment transport rate) and to the estimation of the bed shear stress. The threshold for sediment motion varies with many factors related not only to grain size but also to bed composition (e.g., presence of fine sediments in a coarse matrix), arrangement (e.g., bed roughness, grain orientation, and characteristic lengths of bed structures) and slope. New models to estimate the critical Shields number are proposed using grain size or bed slope or a combination of both. Model parameters and uncertainty are estimated through Bayesian inference using prior knowledge of these parameters and measured data. Apart from the uncertainty in observations, two types of uncertainty can be evaluated: one related to the parameter estimation (i.e., parametric) and one related to the choice of the model (i.e., structural). Finally, a four-parameter model based on the grain size and bed slope yields the best results and demonstrates potential interaction between these two parameters. Model uncertainty, however, remains large, which indicates that other input parameters may be needed to improve the proposed model.

Transverse flow distributions in ice‐covered channels

AbstractTraditional discharge measurements in ice‐covered river channels are time‐consuming and costly, thus limiting the elucidation of flow patterns during winter. This study proposes an analytical model for quantifying the transverse distributions of the unit‐width discharge and the depth‐averaged streamwise velocity in ice‐covered channels by extending an existing stream‐tube method to include the effects of cover and bed roughness and cross‐sectional geometry. A new set of equations are obtained for this extended method. An empirical coefficient α is included to lump the effects of the shape and friction factors of the ice cover and the channel bed. The model is compared with flume experiments and field data for fully and partially ice‐covered flows to examine the variation of the coefficient α.

Correction to: Experimental Study of Natural Bed Roughness Effect on Hydraulic Condition and Energy Dissipation Over Chutes

Correction to: Experimental Study of Natural Bed Roughness Effect on Hydraulic Condition and Energy Dissipation Over Chutes

Effect of complex hydraulic variables and physicochemical factors on freshwater mussel density in the largest floodplain lake, China

BackgroundHabitat degradation and flow regime alterations are two of the most prominent and common impact factors to freshwater mussel populations. Knowledge of the correlation between freshwater mussel distribution, density and habitat characteristics is important for maintaining and restoring their biodiversity and ecological functions. Information on predicting habitat suitability of freshwater mussels is lacking in China. Here, we aimed to analyze the correlation between freshwater mussel density and complex hydraulic and physicochemical variables to predict habitat suitability.ResultsThe results showed that four complex hydraulic variables (boundary Reynolds number, critical shear stress, bed roughness and mean sediment particle size) and four physicochemical variables (water temperature, chlorophyll-a, transparency and pH) were key factors for predicting habitat suitability of freshwater mussels. Freshwater mussel density was significantly correlated with Froude number, water temperature and chlorophyll-a.ConclusionsOur results confirmed that higher freshwater mussel density would be associated with areas that are stable in complex hydraulic and physicochemical variables. These results provide an important insight into the conservation of freshwater mussel diversity and their habitat restoration in China and globally.

Simultaneous measurements of inertial acceleration and flow structures during coarse-grain entrainment under steady currents

An instrumented smart sediment particle (SSP) is used to investigate the entrainment of spherical coarse grains resting on a rough bed comprising semi-spherical elements. The SSP contains electronic sensors facilitating the direct measurement of tri-axial accelerations. The instantaneous flow field is measured simultaneously using two-dimensional particle tracking velocimetry (PTV), enabling joint analysis of accelerations and flow structures during entrainment. Two different initial placement positions of the SSP are tested. Both particle vibration and complete entrainment events are observed in experiments. Results show larger maximum acceleration and longer duration of motion with more significant obstruction by surrounding bed roughness, which entails greater momentum transfer at the initiation of entrainment. During vibration events, acceleration can occasionally reach the threshold value but with no entrainment because of the low persistence of relevant flow features inducing energy transfer. Further analysis on instantaneous flow structures indicates that, at the threshold flow condition, the occurrence and persistence of the “sweep-outward interaction” quadrant motion sequence (i.e. Q4-Q1 sequence) in front the particle, combined with the transient increase of vorticity due to the passage of clockwise vortices above the particle, is the key to energy transfer and complete entrainment. The Q4-Q1 sequence may either be caused by the lower half of anti-clockwise vortices or occur independently. Generally, the joint analysis of acceleration and flow structures provides a new perspective to studying coarse grain entrainment, especially a potential to relate near-bed flow structures to the status of particle motion in the future.

Simulation of interactions between dam-break flows and complex downstream beds using Flow 3D model

Dam-break flow simulations are conducted all over the world, especially in the climate change phenomena taking place, complicated and impacting humans’ lives as well as the infrastructures. This paper introduces the interactions between dam-break flows and complex beds using the Flow-3D model. The analytical solution and the physical experiment are implemented to the dam-break flow over the simple and nonrough bed case to calibrate the numerical simulation. Two complex rough beds, which are the hump bed and the solid column bed, are selected to simulate the interactions between dam-break flows and these structures. With the hump bed, the Flow 3D model accurately simulates the flow characteristics over the rough bed and the flow height overtopping the hump. With the solid column bed, the flow velocities before and after a collision are simulated correctly when compared to the experimental data.

Identifying key channel variability functions controlling ecohydraulic conditions using synthetic channel archetypes

AbstractGeometric modelling of river channel topography is a method of design synthesis wherein specific 2D geometric elements of river topography, such as the bed profile, cross‐sectional shape and channel planform contours, are expressed mathematically in isolation and then combined to produce a 3D heightmap. We utilized the geometric modelling framework to synthesize channel terrains that reveal flow–form–function linkages to investigate what roles variability in bed roughness, thalweg elevation and channel width play in defining hydraulic and ecohydraulic conditions of a channel reach from baseflow to bankfull discharge. To achieve a robust inquiry for a range of settings, this study developed four distinct synthetic channel terrain models for each of three stream reaches of different channel types in the South Fork Eel River in northern coastal California, USA. To test the process‐based effects of these diverse terrain synthesis options, we compared the resulting hydraulic patterns and preferred habitat availability for fry/juvenile steelhead trout and coho salmon over a range of discharges. Among thalweg bed undulation, width variation and bed roughness, we found thalweg bed undulation was the key factor affecting the channel ecohydraulic response at baseflow condition. At bankfull condition, thalweg bed elevation had the largest effect in high‐order mainstem streams identified by gravel‐cobble dominated high width‐to‐depth, riffle‐pool sequences, width variation had the largest effect in mid‐order confined channels with gravel‐cobble, high width‐to‐depth ratio with expansions/contractions and bed roughness in low‐order streams with low width‐to‐depth ratio, high‐gradient, cobble‐boulder and step‐pool/cascade channels.

Multi-Branch Deep Neural Network for Bed Topography of Antarctica Super-Resolution: Reasonable Integration of Multiple Remote Sensing Data

Bed topography and roughness play important roles in numerous ice-sheet analyses. Although the coverage of ice-penetrating radar measurements has vastly increased over recent decades, significant data gaps remain in certain areas of subglacial topography and need interpolation. However, the bed topography generated by interpolation such as kriging and mass conservation is generally smooth at small scales, lacking topographic features important for sub-kilometer roughness. DeepBedMap, a deep learning method combined with multiple surface observation inputs, can generate high-resolution (250 m) bed topography with realistic bed roughness but produces some unrealistic artifacts and higher bed elevation values in certain regions, which could bias ice-sheet models. To address these issues, we present MB_DeepBedMap, a multi-branch deep learning method to generate more realistic bed topography. The model improves upon DeepBedMap by separating inputs into two groups using a multi-branch network structure according to their characteristics, rather than fusing all inputs at an early stage, to reduce artifacts in the generated topography caused by earlier fusion of inputs. A direct upsampling branch preserves large-scale subglacial landforms while generating high-resolution bed topography. We use MB_DeepBedMap to generate a high-resolution (250 m) bed elevation grid product of Antarctica, MB_DeepBedMap_DEM, which can be used in high-resolution ice-sheet modeling studies. Moreover, we test the performance of MB_DeepBedMap model in Thwaites Glacier, Gamburtsev Subglacial Mountains, and several other regions, by comparing the qualitative topographic features and quantitative errors of MB_DeepBedMap, BEDMAP2, BedMachine Antarctica, and DeepBedMap. The results show that MB_DeepBedMap can provide more realistic small-scale topographic features and roughness compared to BEDMAP2, BedMachine Antarctica, and DeepBedMap.

Flushing time variability in a short, low-inflow estuary

Flushing time, the time scale for exchange and mixing between embayed and oceanic waters in an estuary, plays an integral role in determining water quality and aquatic ecosystem health. Here, we investigated the spatiotemporal variability of flushing times throughout Morro Bay, a short, low-inflow estuary (LIE) on the California coast, using a calibrated and validated hydrodynamic model (Delft3D). Morro Bay has historically supported an extensive eelgrass (Zostera marina) habitat, which declined substantially from 139 to 5.4 ha during 2007–2017. Eelgrass decline motivated the current research into the role of changing bed roughness and oceanic drivers (i.e., tide and sea-level rise) on estuarine hydrodynamics and flushing times. We found that tidal variability exerts the strongest control on flushing times compared to other effects, i.e., bed roughness or sea-level rise. Additionally, we found that increasing sea level and decreasing bed roughness (associated with declining seagrass coverage) yielded higher rates of mixing (lower flushing times). We detected a strong correspondence between areas having shorter flushing times (e.g., near the estuary mouth) and areas occupied by resilient eelgrass populations in Morro Bay. Our findings further indicated that flushing times in short LIEs are particularly sensitive to several factors (e.g., bed roughness, sea level) that are susceptible to anthropogenic disturbance and future climate change.

Effects of bottom roughness on wave transmission across a submerged reef

This paper presents a laboratory study to investigate the effects of bottom roughness on wave transmission across a submerged coral reef that has a steep fore-reef slope. Experimented models were carried out in wave flumes for four different bed roughness levels: including a smooth bed and three roughness heights. Our investigations showed that there is a significant dissipation of energy in short-period waves (SS-waves), owing to bottom friction, compared with that of infra-gravity waves (IG-waves). In addition, the study found that the IG-wave heights are increased slightly as waves propagate shoreward from the reef-edge surfzone, indicating that a significant portion of energy was transferred from SS-waves to IG-waves. Empirical formulae of wave energy dissipation due to bottom friction and non-linear transfer of energy among the SS- and IG-waves have been derived; these allow for the straightforward determination of wave heights and wave periods on the submerged reef. These local wave parameters can be used to design offshore structures on submerged coral reefs.

The changing rules of the composite roughness in drainage pipelines with sediments

Abstract The deposition of sediments with different roughness increases uncertainty in the prediction of effective Manning's n (also known as composite roughness). In this paper, the changing rules of composite roughness and the influence on the discharge capacity of drainage pipes under different flows and slopes were studied by experimental measurement and numerical simulation. When the Froude number is less than 1, the composite roughness decreases gradually with the increase of flow. When the Froude number is more than 1, the composite roughness increases at first and then decreases with the increase of flow. It also showed that the different bed roughness has a great influence on composite roughness, which affects the hydraulic characteristics of flow. The composite roughness of the drainage pipe increases as the bed roughness increases. The water surface rises and the average velocity decreases under a certain slope and flow. The formulas for calculating the composite roughness are obtained by analogy analysis, which can provide theoretical support for the design of the drainage pipeline.

Plot investigation on rill flow resistance due to path tortuosity

The path tortuosity t is an indicator of rill morphology accounting for the deviation of the thalweg from a straight alignment. The effect of t on flow resistance has been little investigated for rills. This paper reports the results of a plot investigation aimed to establish the suitable accuracy of the rill thalweg measurement to determine the tortuosity parameter and to test the reliability of a theoretical flow resistance law. Four rills were incised in clay soil (CS) and clay-loam soil (LS) and shaped by a clear flow discharge. The three-dimensional Digital Terrain Models were created by the Structure from Motion technique. For rills on LS, an approximate thalweg was tracked by photo-interpretation, and a specific calculation routine was applied to identify the cross sections with a constant spacing d. The actual rill thalweg was obtained as the line joining the lowest points of these cross-sections. Among the different tested d values, d = 0.075 m was chosen to determine t. For both CS and LS, the Darcy-Weisbach friction factor f featured a non-monotonic relation with t, which was explained as the result of three additive components due to bed roughness, sediment transport, and localized energy losses due to curves. The effect of the former two components on f contrasts that of the third, resulting in a linearly decreasing f-t relationship and constant flow velocity for the three lowest tortuosity values, and an increased friction factor and reduced flow velocity for the highest tortuosity value. The flow resistance law was positively tested, and the predicted friction factor was dependent on t.

The effect of ice cover on velocity and shear stress in a riffle‐pool sequence

AbstractDischarge and channel geometry control velocity and bed shear stress within a reach. Channel roughness (e.g., riffles, pools) and ice cover in winter moderates velocity and shear stress at the bed. This study evaluated velocity profiles across a channel segment with variable bed roughness (e.g., riffles, pools) to determine changes in the position of maximum velocity, maximum velocity magnitude, and resulting bed shear stress estimates when ice cover was present. Using acoustic doppler velocimeter (ADV) and acoustic doppler current profiler (ADCP) high resolution velocity profiles were collected during ice cover, open water, and open water with significant increases in vegetation cover through a riffle‐pool sequence in a low‐order channel in southern Ontario Canada in the first half of 2021. Key findings were that in five of the seven cross‐sections, flow direction was significantly different when ice was present. Additionally, maximum velocities were closer to the bed during ice cover, a common finding in modelling and experimental work, and is confirmed in this field setting. Although maximum velocity magnitudes were not significantly different, derived bed shear stress values under ice were larger. Specifically, under ice conditions, riffle bed shear stress ranged 0–16 N/m2 compared to 0–9 N/m2 in ice free conditions. In the pool, bed shear stress ranged 0–6 N/m2 under ice cover, and 0–5 N/m2 in ice free conditions. Further, as flow levels increased through the spring and summer, this coincided with increased in‐stream vegetation cover, which decreased flow velocities near the bed, and thus decreased bed shear stresses to less than 1 N/m2 in both the riffle and pool sections. The findings indicate that channel evolution processes may be more intense during lower‐stage winter flows when ice is present and has significant implications for channel design, restoration and management strategies used in small channels impacted by ice cover.

On the variation of the correction factor of surface velocity with the measurement vertical for shallow flows over rough beds

AbstractConsidering that water flow energy affects the detachment of soil particles, the transport and deposit of the detached particles, the flow velocity is a key variable governing the soil erosion processes at the hillslope scale. The simple dye‐tracer technique for measuring mean flow velocity can be applied in non‐controlled field applications for which some measurement difficulties (e.g. due to sediment transport, and shallow flows) can occur. The correction factor is usually obtained as the ratio between the mean velocity, deriving from measurements of flow discharge and water depth, and surface velocity. Alternatively, the possibility of using the velocity profile in a given vertical to determine a suitable correction factor has not yet been explored. In this article, the flow velocity measurements were carried out in five verticals having a different distance from the wall of a flume whose bed was covered by hemispheres with different concentrations (9%–64%) and organized in two arrangements (square, staggered). Fifteen runs, characterized by different Reynolds and Froude numbers, were performed and the correction factor αvv was calculated for each vertical. For the axial vertical αvv was independent of the arrangement, decreased with the hemisphere concentration, and increased with both the Froude and Reynolds numbers. Furthermore, αvv decreased from the bank to the flume axis as a result of the varying shape of the velocity profile. The analysis showed that the frequency distributions of the ratio between αvv and its mean value αm were overlaid and αm was used to represent the correction factor, accordingly. A relation of αm with the distance from the flume wall was detected. For the measured velocity profiles having a power shape, the analysis also demonstrated that the αvv values, obtained by fitting the power law to the measurements, were close to both those calculated as the ratio between the mean velocity along the vertical and the surface velocity and their averaged values across the hydraulic section. These three methods give comparable average values of the correction factor, in the range of 0.72–0.75, which are close to the commonly applied value of 0.8. Finally, this investigation demonstrated that a single survey of a power velocity profile allows for obtaining the correction factor accounting for different verticals across the entire hydraulic section.

The effect of a local mesh refinement on hydraulic modelling of river meanders

AbstractLarge‐scale river models are generally discretized by relatively large mesh cells resulting in bathymetry discretization errors and numerical effects. These hydraulic models are generally calibrated by altering the bed roughness to compensate for these errors and effects. Consequently, the calibrated roughness values are mesh‐dependent while generally local mesh refinements are executed after model calibration to study the effects of river interventions. This study shows both the errors caused by bathymetry discretization and numerical effects for locally refined meshes. First, schematised river meanders with a flat bed in the transverse flow direction are analysed to isolate the induced numerical effects by the mesh. Afterwards, a case study is considered to verify if similar mesh influences are found in natural river meanders. Curvilinear, triangular and hybrid (combination of curvilinear and triangular cells) meshes are used with different resolutions. The analysis shows that in the schematised river meanders lower depth‐averaged flow velocities and larger water depths are simulated with coarser meshes. In the case study, substantial differences in hydrodynamics between the meshes are obtained suggesting that the bathymetry discretization is more influential than the numerical effects. Finally, it was found that triangular meshes, and rivers with narrow meander bends, are most sensitive to mesh resolution. Especially in these cases, it is desirable to refine the mesh at the desired locations before model calibration.

Sediment vibration characteristics based on accelerometer measurements

The study of the vibration phenomenon of pebbles under turbulence is still a gap despite recent technological advancements in measurement capabilities. In this study, the vibration process of a fully exposed, isolated smart pebble on a rough bed was measured using a miniature inertial accelerometer and combined with simultaneous local measurements of the near-bed velocities. The paper conducts a series of experimental studies with different flow conditions. The test data match well with the manually observed phenomena, indicating the authenticity of the sediment vibration data collected by the measurement system. The test results show that the pebble motion (before entrainment) subjected to turbulence is a nonlinear vibration process, and its vibration types include in-situ vibration and ex-situ strong vibration. The probability distribution for the amplitude of vibration acceleration is well parameterized by the normal distribution. The vibration intensity tends to increase before approaching the threshold, but it weakens when approaching the point. The sediment vibration frequency is within 20–25 Hz, similar to the flow pulsation frequency and belongs to low-frequency vibration. The data indicate that the near-bed flow velocity is most directly related to the particle vibration events.

Maximum energy loss in a vertical drop equipped with horizontal screen with downstream rough and smooth bed

Abstract Screens are one of the recent energy dissipator structures that can be used downstream of small hydraulic structures. In this study, screens were used horizontally at the brinks of the vertical drop with downstream smooth and rough bed to investigate the energy loss of the drop. Experiments were performed on two porosities of screens, a relative critical depth of 0.13–0.39 and a median size of 1.9 cm aggregates. The results showed that for a relative critical depth of more than 0.3 in a vertical drop equipped with a screen with a rough bed, the drop length with respect to smooth bed increases. Compared to applying a Type I stilling basin, a vertical drop equipped with a screen with downstream smooth and rough bed reduces the drop length by approximately 50%. Although a rough bed increases air entrainment, it has no effect on the energy loss and pool depth of a vertical drop equipped with a horizontal screen with smooth bed. The use of horizontal screens at the brinks of the vertical drop causes maximum energy loss in the downstream of drop. Equations were provided to estimate the flow parameters with a R2 value of more than 0.925 and a normalized root mean square error of less than 0.04.

Wake flow field of a wall-mounted pipe with spoiler on a rough channel bed

This research work focuses on the wake flow region of a cylinder with a spoiler on a rough bed under steady flow conditions. The acoustic Doppler velocimetry was used for the measurement of three-dimensional velocity data for two Reynolds numbers in a fully developed turbulent flow around the cylinder with a spoiler. The mean flow velocities, second-order turbulence structures, and conditional statistics were investigated in the wake region of the spoilered cylinder. The flow was separated from the spoiler with the formation of two shear layers between free surface flow and recirculating flow. It is observed that the flow is reattaching to the bed at 11D irrespective of the Reynolds number. Downstream of the cylinder, the mean velocity distributions are asymmetric due to the wall–wake effect, and the point of inflection is observed for each velocity profile at z = 0.40ẟ. The turbulence intensities, Reynolds stresses, and TKE are highly enhanced in the wake region of the cylinder as compared to their respective upstream values for both runs. The turbulence intensities, Reynolds normal stresses, Reynolds shear stresses, and turbulent kinetic energy are attaining peaks at z = 0.4 ẟ for all the streamwise locations, and the peaks are found to be highest at x = 10D. The quadrant analysis results indicate that the sweeps are dominating bursting events in the inner and intermediate layers, while ejections are dominating in the outer layer of the wake region. As the hole size, H increases ejections stress fraction rises as compared to that of the sweeps in the wake region for z = 0.2–0.7 h.

Effects of Boulder Arrangement on Flow Resistance Due to Macro-Scale Bed Roughness

Flow resistance in gravel-bed channels is not only affected by the shape and size of the roughness elements, but also by their arrangement on the channel bed surface (position to flow streamlines, spacing between elements, and their protrusion from the channel bed). Many investigations proved that open channel flow resistance can be obtained by integrating the power velocity profile. For a macro-scale roughness condition, this study aims to investigate the effect of different boulder arrangements on flow resistance. First, for each arrangement, the equation relating Γ function of the power velocity profile, the Froude number, and the channel slope was calibrated using available measurements performed in a flume covered by pebbles with “Random”, “Transversal stripe”, and “Longitudinal stripe” arrangements. For each arrangement, the experimental datasets were divided to consider the effects of boulder concentration Ch. Moreover, the relationship obtained for the “Random” arrangement and element concentration lower than 48% was tested using literature measurements performed in a flume covered by coarse elements randomly arranged. Finally, the effects of the different boulder arrangements on the flow resistance law were investigated by imposing a concentration threshold. The results demonstrated that (i) the Darcy–Weisbach friction factor can be accurately estimated by the proposed flow resistance equation, (ii) the flow resistance increases with Ch for low values (<48%) of concentration, while it does not depend on Ch for high concentrations (≥48%), and (iii) the effect of the boulder arrangement on flow resistance law is more evident for low element concentrations.

Experimental investigation into the boundary layer structure near the tip of a dam-break wave on a dry, rough and horizontal bed

The boundary layer structure near the tip of dam-break waves, swash flow and tsunami, is important for understanding the shape and behavior of their tips and for sediment transport, which is observed under tips on mobile beds. In this study, the boundary layer structure near the dam-break tip on a dry, rough and horizontal bed was investigated experimentally. Horizontal velocities were obtained using advanced image processing techniques, and the concurrent bed shear stress was measured directly with a shear plate. The velocity structure is quantified in terms of the defect scale of horizontal velocity in the vertical direction δ defined by u(z)=u∞[1−e−zδ], while the asymptotic velocity u∞ is defined for each vertical so that the depth-averaged velocity equals the tip's speed of propagation. The experimental results indicate that the shape of the velocity profile changes rapidly with distance s from the contact point. The velocity profile is roughly linear very near the contact point corresponding to a rolling wheel or δ being much greater than the water depth. Further from the contact point, in our case, s/ks≳0.42, where ks is bed roughness, δ is only a fraction of the depth, and this fraction becomes constant, ca. 0.21, at distances greater than s/ks ≈ 1.67. Boundary layer growth as δ(s)∝s is in good agreement with the measured velocity profiles for s/ks ≳ 4. The concurrently measured bed shear stress after its peak can be well predicted with the proposed relationship δ(s)∝s.