Estimation Of Bed Shear Stress Research Articles

Estimation of friction factor and bed shear stress considering bedform effect in rivers

AbstractThe roughness height plays a crucial role, especially in shallow‐water environments with rough‐bed conditions. Specifically, it is a key parameter for predicting flow velocity and bed shear stress. Therefore, an accurate determination of roughness height is essential for precise predictions of hydraulic phenomena. In this study, we propose a method to estimate form roughness height and friction factor using bathymetry data, with a focus on cross‐sectional data in the transverse direction. To overcome the limitations of using lateral direction data, we derived an empirical formula for estimating bedform length from the bed profiles in the streamwise direction. To assess the validity of bedform analysis and estimated form roughness height based on lateral direction data, we compared the characteristics of bedform and form roughness height analysed using lateral direction data with those analysed using the streamwise direction data. Furthermore, we confirmed the importance of considering the form roughness height in estimating bed shear stress through a comparison with bed shear stress calculations considering only grain roughness height.

Experimental Evaluation of Estimating Local Bed Shear Stress Using Log Law in a Straight River Channel

Bed shear stress is a critical parameter in riverine environments, directly influencing sediment transport, erosion, deposition, and flow dynamics. However, direct measurement of bed shear stress in natural rivers is nearly impossible, and estimating bed shear stress by extrapolating the Reynolds stress profile, though known for accuracy, faces practical limitations due to the challenges of measuring turbulence in natural rivers. As alternatives, indirect methods, such as global bed shear stress estimation based on bed slope and hydraulic radius (assuming uniform flow) and local bed shear stress estimation through regression of velocity profiles using the log law, have been employed. The estimation of local bed shear stress using the log law has primarily been derived from laboratory flow conditions due to the limitations in observing detailed turbulence in field conditions. Consequently, the applicability of the log-law method under field conditions has not been sufficiently evaluated. This study aims to assess local bed shear stress using the log law through a dedicated field experiment in a specific river condition, comparing it with methods utilizing the Reynolds stress profile. The experiment was conducted in a straight river channel with a width of approximately 6.5 m, a depth of 0.61 m, and a mean flow velocity of 0.56 m/s. A total of 197 points of regularly distributed velocity and turbulence data for the given cross-section were acquired using micro-acoustic Doppler velocimeter measurements with a duration of 90 s. We found that the log-law method overestimated local bed shear stress by an overall factor of 2.3 compared to the method using Reynolds stress profiles. Thus, the experimental results conclusively indicate that local bed shear stress estimated from the log law in natural river conditions could be overestimated. However, additional research is needed under more diverse flow and geometric conditions to develop a correction formula for applying the log law in estimating local bed shear stress.

Subaqueous silt ripples measured by an echo sounder: Implications for bed roughness, bed shear stress and erosion threshold

Bedforms like ripples are widely distributed in the coastal zone. They influence the bed roughness thus the estimation of bed shear stress and associated sediment transport. An echo sounder was mounted on a bottom-supported tripod intended to measure the erosion and deposition of seabed in the subaqueous Yellow River Delta, China. However, variations in bed elevation are found to be not the net erosion or deposition at the observation site, but the migration of silt ripples which were generated by waves and pushed back and forth or flattened off by the tidal currents. Ripple heights were observed to be within 0.1–0.7 cm and were used for testing the model of Nielsen (1981). The model overestimated the height of silt ripples as it was developed for sands, but the deviation can be well addressed by incorporating a linear modification (R2 = 0.79). Alternatively, a new model specifically for silt ripple height was regressed from the field data with R2 up to 0.78. The existence of silt ripples increases the bed shear stress by 4 times due to the additional bed roughness. A “fluffy layer” overlies the consolidated seabed, therefore, net seabed erosion occurs after the “fluffy layer” is resuspended. A representative critical bed shear stress for net seabed erosion in the study area was found to be 0.8 Pa. The echo sounder can be an alternative tool for observing silt ripples in coastal regions like the Yellow River Delta where the water is too turbid for underwater videos. The proposed model infers silt-ripple features from bed grain size and flow condition and provides a quick estimate for bed roughness improving the understanding on sediment transport.

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.

A comparison of shear stress estimation methods for a single geobag on a rough bed

There are several methods for estimating bed shear stress in the literature, but comprehensive comparisons among them are limited and under specific conditions. This study compared these methods first on a bare smooth bed, and then for a single geobag on a rough bed in the interest of determining the stability of geobags used in riverbank protection structures. The geobag was filled with cement or sand and tested under different open channel flow conditions. The turbulent kinetic energy method appeared to best represent the local bed shear stress on the geobag when using the newly calibrated proportionality constants. The Reynolds stress method via extrapolation was relatively unaffected by changes to the geobags shape and measurement locations, suggesting this method inadequately represents the local bed shear stress. The Patel method and the universal law of the wall method failed to represent local bed shear stress in the rough bed cases due to instrument limitations and the breakdown of the law of the wall. This study highlights the impact of different methods on the bed shear stress estimation.

Estimation of Bed Shear Stress in Shallow Transitional Flows under Condition of Incipient Motion of Sand Particles Using Turbulence Characteristics

In this experimental study, using an ADV, experiments were performed in three different shallow water flows under hydraulically transitional flow condition to estimate the bed shear stress using turbulence characteristics. Vertical distributions of all shear and normal Reynolds stresses as well as TKE were evaluated and simplified in order to estimate bed shear stress under incipient motion of four groups of sand particles. To determine bed shear stress, as the main approach, the linear portion of the −u′w′ profiles were extended towards the channel bed. The necessity of the approach of the vector addition of −u′w′ and −v′w′ in this experimental study was examined. It was found that the bed shear stress can be effectively estimated by multiplying the values of u′20, v′20, w′20 and TKE0 by 0.17, 0.33, 1.24 and 0.2, respectively. However, it was found that these values were slightly proportional to the shear Reynolds number. Additionally, the one-point measurement approach was assessed. The TKE method which applies all three components of Reynolds normal stresses was preferred to the u′2, v′2 and w′2 methods. Results showed that, u′20, v′20 and w′20 have values of 60.5, 31.3 and 8.2 percent of the total, respectively.

Influence of lateral flow contraction on bed shear stress estimation by using measured turbulent kinetic energy

Sedimentation, including erosion, transport, and deposition of river-bed material, is a complex process influenced by several parameters related to flow, materials, and geometries. Evaluation of the bed shear stress under a wide range of flow conditions is the primary step in understanding the sedimentation process. In this study, the bed shear stress is analyzed experimentally near an obstruction where maximum erosion occurs. The local flow conditions near the obstruction are varied by modeling several typical lateral flow contractions in the flume. Through analysis of the results, we discuss the effects of local turbulence on the bed shear stress in terms of Reynolds stress and turbulent kinetic energy that are measured for various ranges of water depth, velocity, and flow contractions. From the findings, we suggest an empirical correction factor that accounts for the local turbulence in calculation of bed shear stress using turbulent kinetic energy. It is concluded from experiments that the empirical correction factor is a function of the flow contraction ratio.

Estimation of bed shear stress and analysis of sediment resuspension in Lake Chaohu, China.

Resuspended sediment is an important carrier of underwater material circulation, and bed shear stress is usually considered to be closely related to sediment resuspension. To analyze the resuspension dynamics in severely eutrophic Lake Chaohu, China, three fixed stations were set up to collect wave, current, and suspended sediment concentrate (SSC) data under windy weather, and two significant sediment resuspension events were recorded. Based on the Gaussian-shaped spectrum characteristics of waves in Lake Chaohu, the wave orbital velocity was estimated by using the wave parameter method. The selection of the general wave spectrum is important for the accurate estimation of wave orbital velocity. The results of the simple linear wave method were very similar to those of the wave parameter method with a Gaussian-shaped spectrum in Lake Chaohu. The total bed shear stress combining waves and currents during the observation period was calculated, and most of it was contributed by wind-driven waves. The bed material of Lake Chaohu has silt-enriched and weak cohesive features, and an examination of critical shear stress showed that the modified Shields curve method was still applicable to Lake Chaohu. When a sediment resuspension event occurred, the vertical gradient of SSC increased significantly, and the peak SSC value depended on the peak value of bed shear stress. As a predictor, bed shear stress only showed a good linear relationship during sediment resuspension events. At other times, the prediction of SSC using bed shear stress may be biased, especially at the time after a significant sediment resuspension event.

Comparison of Methods for Bed Shear Stress Estimation in Complex Flow Field of Bend

Bed shear stress is closely related to sediment transport in rivers. Bed shear stress estimation is very difficult, especially for complex flow fields. In this study, complex flow field measurement experiments in a 60° bend with a groyne were performed. The feasibility and reliability of bed shear stress estimations using the log-law method in a complex flow field were analyzed and compared with those associated with the Reynolds, Turbulent Kinetic Energy (TKE), and TKE-w′ methods. The results show that the TKE, Reynolds, and log-law methods produced similar bed shear stress estimates, while the TKE-w′ method produced larger estimates than the other methods. The TKE-w′ method was found to be more suitable for bed shear stress estimation than the TKE method, but the value of its constant C2 needed to be re-estimated. In a complex, strong, three-dimensional flow field, the height of the measurement point (relative or absolute) should be re-estimated when a single point measurement is used to estimate the bed shear stress. The results of this study provide guidance for experimental measurement of bed shear stress in a complex flow field.

A RANS numerical study of experimental swash flows and its bed shear stress estimation

Quantification of the bed shear stress in the swash zone is subject to much uncertainty due to the very shallow water, complex flow structure and the strong unsteadiness in this zone. This study presents a RANS modeling of experimental dam-break flow generated swash processes, giving numerical reproduction of vertical flow structure of swash flows and thus an opportunity to study the magnitude and features of the bed shear stress. Firstly, numerical solutions (i.e., temporal or spatial variation of the depth-averaged velocity and water surface elevation, the time variations of the swash front, the vorticity structure and the boundary layer thickness) are compared with existing laboratory data and the previous knowledges on swash hydrodynamics. Secondly, using the computed vertical flow structure as input data, performances of four methods (the Reynolds stress method, and the three variants of the log-law method: the depth-averaged variant, the one-position variant, the two-position variant) for estimating the bed shear stress are evaluated. It is shown that the Reynolds stress method produces non-zero bed shear stress during the reversal time, during which the swash flows may be partly stagnant. Among the three variants of the log-law method, the depth-averaged method appears to agree with the measured data much better than the other two variants: those by the two-point log-law method is very sensitive to the selected near-bed positions, and those by the empirical value variant may underestimate (overestimate) the bed shear stress in the early uprush stage (in the initial stage of the backwash).

Application of various shear stress calculation methods with respect to different bridge abutment lengths

When a bridge abutment occupies a significant part of the channel width, the water surface elevation in the upstream of the bridge rises in comparison to that which would occur without the bridge, and this phenomenon is called backwater effect. Due to the backwater in the bridge approach section, several of bed shear stress estimation methods shows an inaccurate result because approach uniform flow might not be assumed depending on the degree of backwater amount. Thus, in this laboratory study, seven widely used shear stress formulas are applied in the bridge approach section subjected to the backwater according to the abutment length, and the results are compared for their validation. For the detailed velocity and turbulence measurements, 3D downlooking Acoustic Doppler Velocimeter (ADV) was used and three different lengths of bridge abutment were constructed in the laboratory to simulate various degree of backwater effect for shear stress calculation in the approach section. The experimental comparison shows that the methods using Reynolds stress and Turbulence Kinetic Energy concept were the most suitable of calculating shear stress in the approach section under severe backwater condition. For other methods leading to inaccurate estimations, the calibrating coefficient is suggeste

Predicting Bed Shear Stresses in Vegetated Channels

AbstractShear stresses on vegetated beds play an important role in driving a wide range of processes at the sediment‐water interface, including sediment transport. Existing methods for the estimation of bed shear stress are not applicable to vegetated beds due to the significant alteration of the near‐bed velocity profile and turbulence intensities by the vegetation. In addition, bed shear stress distributions are highly spatially variable in the presence of vegetation. In this study, computational fluid dynamics simulations were used to investigate the spatial variability of bed shear stresses in the presence of emergent vegetation (modeled as arrays of circular cylinders) and the variation of bed stress with characteristics of both the bulk flow and the array. A recently proposed model that assumes a linear variation of stress in the viscous layer immediately above the bed is shown to be a reliable tool for estimating the spatially averaged bed shear stress over a wide range of flow conditions and vegetation densities. However, application of this model is found to be restrictive due to the lack of a reliable predictive tool for the thickness of the viscous layer. Based on a balance between turbulent kinetic energy production in the vegetation stem wakes and the viscous dissipation of turbulent kinetic energy at the bed, an enhanced formulation is proposed to predict the thickness of the viscous layer, which significantly improves the accuracy of model predictions. This improved model enhances the predictive capability for important benthic processes (such as sediment transport) in vegetated aquatic systems.

Hydromorphological Numerical Model of the Local Scour Process Around Bridge Piers

The aim of this study was to assess the simulation and prediction of scour processes, both hydrodynamically and morphologically, around vertical and inclined piers. A new version of FLOW-3D v. 11.2, including three sediment transport equations, was extensively used for estimating the scour around the pier. The results of the model in terms of water surface, flow velocity, bed shear stress and scour depth were effectively compared with several sets of the experimental and numerical data in the literature. The model provided an accurate estimation of water surface, flow velocity and bed shear stress. However, the results for the vertical velocity upstream of the pier were underestimated. The predictive capabilities of the model were mainly dependent on the pier shape and inclined direction. The downflow, stream-wise velocity, shear stress and local scour depth were significantly reduced at the inclination angle of the circular pier downstream. However, they were nearly equal to those of an inclined perpendicular circular pier. This study strongly demonstrates that a 3D hydromorphological model can be effectively used to predict the scour depth around piers.

Bed Shear Stress Estimation Under Wave Conditions Using near-bottom Measurements: Comparison of Methods

Zhang, Q.; Gong, Z.; Zhang, C.K.; Lacy, J.R.; Jaffe, B.E., and Xu, B.B., 2018. Bed Shear Stress Estimation Under Wavy Condition Using near-bottom Measurements: Comparison of Methods. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 241–245. Coconut Creek (Florida), ISSN 0749-0208.Understanding the influence of waves on bed shear stress is critical for predicting morphodynamical behaviours in coastal areas. Near-bed flow was measured on the middle and lower intertidal mudflats along the Jiangsu coast, China, using a three-dimensional acoustic velocimeter that collected a 3.5-cm vertical profile at 1mm resolution and sample rate of 25 Hz. On the lower and middle tidal flats, velocities from ~2.5–6 cmab (cm above bed) and ~0–3 cmab were measured, respectively. Current-induced bed shear stresses were calculated from turbulent kinetic energy (TKE) at the 11th measurement layer (i.e., 5.1 cm below the probe) using wave-turbulence decomposition and from a logarithmic fit to the horizontal mean velocity profile (LP). A wave boundary layer extended from the bed up to 3 cmab when the significant wave height was 0.23 m; when it was present the near-bed mean velocity profile was non-logarithmic. Waves suppress the development of a vertical velocity gradient and lead to an overestimation of bed shear stress when calculated using the log profile assumption. The TKE method is more accurate than the LP method when waves are present and measurements are at least partially within the wave boundary layer. Accurate calculation of current-induced bed shear stress depends on probe height and wave conditions.

Mean bed shear stress estimation in a rough rectangular channel using a hybrid genetic algorithm based on an artificial neural network and genetic programming

The determination of erosion and deposition patterns in channels requires detailed knowledge and estimations of the bed shear stress. In this investigation, the application of a Genetic Algorithm based Artificial (GAA) neural networkand genetic programming (GP) for predicting bed shear stress in a rectangular channel with rough boundaries. Several input combinations, fitness functions and transfer functions were investigated to determine the best GAA model. Also the effect of various GP operators on estimating bed shear stress was studied. The comparison between the GAA and GP technique abilities in predicting bed shear stress were investigated. The results revealed that the GAA model performs better in predicting the bed shear stress (RMSE = 0.0774), as compared to the GP model (RMSE = 0.0835).

Examining the Generality of τ0/TKE for Gravel and Cobble Beds with Sand Fill

AbstractTurbulence measurements over rough beds are used for a variety of purposes, including studies of habitat diversity for aquatic organisms, stream restoration efforts, and assessment of drag induced by vegetation. Turbulent kinetic energy (TKE) has been used to estimate bed shear stress by use of a proportionality constant of 0.19–0.21. The TKE method of bed shear stress estimation is less sensitive to flow misalignment relative to Reynolds stress or mean velocity measurements, but it has not been tested across a broad range of hydraulic conditions. In the work reported here, TKE was compared to bed shear stresses for gravel (D50=35 mm) and cobble (D50=156 mm) beds with varying discharges and levels of sand fill (D50=0.3 mm). The ratio of bed shear stress (τ0) with TKE was not strongly affected by mean velocity for either the gravel or cobble beds, but it was affected by bed roughness. The mean of the median values of τ0/TKE across three mean velocities was 0.24 for gravel with no sand in the bed...

On the near-wall effects induced by an axial-flow rotor

Laboratory experiments were performed to quantify the near-wall flow characteristics and the bed shear stress in the vicinity of an axial-flow rotor model. It was placed in a smooth-wall open channel flow under subcritical conditions and operated at two heights. A laser Doppler velocimeter was used to collect profiles of the streamwise and vertical velocity at few locations within the rotor symmetry plane as close as one wall unit from the bed. Local estimates of the mean bed shear stress were obtained from the mean velocity profiles in the viscous and logarithmic regions. Results show that the bed shear stress is sensitive to the distance from the rotor and to the relative height of the rotor. Maximum bed shear stress occurred downstream of the rotor with the rotor closer to the bed. Flow statistics shows a reduction of turbulence intensity and turbulent shear stress near the wall and close to the rotor due to flow acceleration and changes in the pressure distribution. Spectral analysis of the streamwise velocity evidences a reduction of the energy content across scales spanning two decades right below the turbine. The increase of bed shear is due to mainly flow accelerating but not to turbulence.

Comparison of bed shear stress in plane and curvilinear bed channel using multiple criteria

Experimental investigation on fluvial hydraulics needs a correct and accurate estimation of bed shear stress, which governs the hydrodynamics of the sediment transport. Present work compares bed shear stress estimated from the reach-averaged bed shear stress, Log profile, Quadratic stress law, Prandtl’s seventh power law, Reynolds shear stress, turbulent kinetic energy and graphical method approaches by doing experimentation on plane bed and curvilinear bed channel. On plane bed condition, the bed shear estimated from Reynolds stresses and Graphical methods are comparable to the reach-averaged bed shear stress (the difference is within 10%). However, all approaches estimate approximately less than 10% from reach-averaged bed shear stress in curvilinear bed channel.

Interaction between flow hydrodynamics and bed roughness in alluvial channel

The present study describes the methods of bed shear stress estimation, numerical estimate of velocity distribution and quadrant events on different hydraulic roughness. Quadrant events of velocity signify the contribution of velocity to generate shear. Experimental data sets of velocities were collected over bed with different hydraulic roughness. In the present work, a turbulent kinetic energy method is anticipated as more reliable to describe the bed shear stress in open channels. These data analysis express that the quadrant events associated with flow is influenced inherently by the bed roughness. Percentage distribution of first and fourth quadrant looks like a wine cup which is wider in the case of hydraulically smooth conditions and getting narrower as the bed roughness increased. It is also a sign of increasing randomness throughout the depth with increased roughness. It is found that at same relative depth for three different roughness conditions, eddy motions are displaying more uncertainty for hydraulically rough condition. Increase in bed roughness augments randomness of Reynolds stress at relative depth 0.05–0.4. The analysis relies on relative depth, which can for imply the local phenomenon and this local phenomenon of velocity on different bed roughness condition was also investigated in this paper.

Momentum transport and bed shear stress distribution in a meandering bend: Experimental analysis in a laboratory flume

The paper concerns the mechanisms underlying the distribution of the bed shear stress in meandering bends. Literature indicates that cross-stream circulation strongly affects the redistribution of the downstream velocity, but the feedback between them is still poorly understood. The aim of this paper is to gain some insight into how the momentum transport by cross-stream circulation contributes to the bed shear stress redistribution. Experimental analysis, based on a detailed dataset collected in a large-amplitude meandering laboratory flume, is presented. From these data an evaluation is made of the terms in the depth-averaged momentum equations and the analysis is especially devoted to terms including the momentum transport by cross-sectional motion. Results confirm that these terms exert an important role in bed shear stress estimation and, thus, they have to be adequately included in the depth-averaged models. Based on measured data, an equation expressing the interrelation between the cross-sectional momentum and the downstream velocity is also introduced.