An analysis of shear stress distribution in circular channels with sediment deposition based on Gene Expression Programming

Knowledge of the boundary shear stress distribution in channels is important because it is a key factor affecting on erosion and sedimentation rates. The presence of sediment deposits in sewers is often reported during operation, and circular channels are frequently used in sewer networks. Gene expression programming(GEP) is applied in this study to determine an equation for evaluating the shear stress distribution along the wetted perimeter of a circular channel with a flat bed, because of the presence of sediment on the bed. In view of the parameters affecting the shear stress distribution, five dimensionless parameters are applied to develop six GEP models to be used with 905 experimental data. The impact of the shear stress parameters is studied using the six GEP models and by dividing the wetted perimeter into wall and bed sections. Two equations are extracted from the GEP models' output to estimate wall and bed shear stresses. The best model results are compared with a well-known equation based on the entropy concept. The GEP model predictions of wall and bed shear stresses are very similar to the experimental outcomes, whereas the entropy-based model overestimates the shear stress distribution.The proposed GEP models demonstrate superior performance in estimating the shear stress distribution with a mean absolute percentage error(MAPE) of 3.79% compared to an existing equation with MAPE of 9.52%.     

An attempt at using the entropy approach to predict the transverse distribution of boundary shear stress in open channel flow

 This paper highlights the similarities between a number of studies which have applied the concept of Shannon's entropy to Hydraulic Engineering. The entropy concept is further developed in an attempt to predict the transverse distribution of boundary shear stress in circular open channels. The approach is also extended and applied to circular channels with a flat bed and trapezoidal channels, and the Lagrange multipliers, λ, found by recourse to empirical equations. Doubts are expressed concerning the value of the entropy approach to such problems.     

The uncertainty of the Shannon entropy model for shear stress distribution in circular channels

The shear stress distribution at alluvial stream beds and banks is one of the essential parameters in channel stability analysis.In the current paper,a novel uncertainty analysis method based on the framework of a Bayesian Forecasting System(BFS) is presented to evaluate the Shannon entropy model for prediction of the shear stress distribution in both circular rigid-bed and alluvial-bed channels.The Johnson and Box-Cox transformation functions were applied to select the optimum sample size(SS) and corresponding transformation factor for determining a 95% confidence bound(CB) for the Shannon entropy model.The Shapiro-Wilk(SW) test is applied according to the SS used to evaluate the power of transformation functions in the data normalization.The results show that the error distribution between predicted and experimental shear stress values generated using the Box-Cox transformation is closer to a Gaussian distribution than the generated using the Johnson transformation.The indexes of the percentage of the experimental values within the CB(N_(in)) and Forecast Range Error Estimate(FREE) are applied for the uncertainty analyses.The lower values of FREE equal to 1.724 in the circular rigid-bed channel represent the low uncertainty of Shannon entropy in the prediction of shear stress values compared to the uncertainty for the circular alluvial-bed channel with a FREE value equal to 7.647.     

Particle image velocimetry evaluation of flow-altering countermeasures for local scour around a submerged circular cylinder

The effect of scour countermeasures on the mechanism of local scour around a cylinder requires clarification in order to develop design methodology for use in practice. Previous investigations on countermeasure performance, though useful, have not provided adequate measurements to support this understanding. In the present investigation, particle image velocimetry(PIV) measurements were acquired at several streamwise-vertical planes in the flow field surrounding a submerged circular cylinder wit...     

NONUNIFORMOPEN CHANNEL FLOW WITH UPWARD SEEPAGE THROUGH LOOSE BEDS

The Reynolds stress and bed shear stress are important parameters in fluvial hydraulics. Steady-nonuniform flow in open channels with streamwise sloping beds having upward seepage through loose beds is theoretically analyzed to estimate the Reynolds stress and bed shear stress. Equations of the Reynolds stress and bed shear stress are developed, assuming a modified logarithmic velocity distribution law due to upward seepage, and using the Reynolds and continuity equations of two-dimensional flow in open channels.     

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.     

One-Dimensional velocity distribution in open channels using Renyi entropy

In this work, the concept of entropy based on probability is applied in modeling the vertical distribution of velocity in open channel turbulent flow. Using the principle of maximum entropy, one-dimensional velocity distribution is derived by maximizing the Renyi entropy subject to some constraints by assuming dimensionless velocity as a random variable. The Renyi entropy-based equation is capable of modeling the velocity distribution from the channel bed to the water surface. The derived velocity distribution is tested with field and laboratory observations and is also compared with existing entropy-based velocity distributions. The present model has shown good agreement with observed data and its prediction accuracy is superior than the other existing models.     

Flow,bed topography,grain size and sedimentary structure in open channel bends: A three-dimensional model

Bed topography and grain size are predicted for steady, uniform flow in circular bends by consideration of the balance of fluid, gravity and frictional forces acting on bed load particles. Uniform flow pattern is adequately described by conventional hydraulic equations, with bed shear defined as that effectively acting on bed load grains. This analysis is used as a basis to predict bed topography and grain size for steady, non-uniform flow in non-circular bends (represented by a ‘sine-generated’ curve). The non-uniform flow pattern is calculated using the method of Engelund (1974a). Equilibrium bed form, hence sedimentary structure, is found by comparison of existing flow conditions with one of the schemes describing the hydraulic stability limits of the various bed forms. The model was compared with bankfull flow observations from a channel bend on the River South Esk, Scotland. Theoretical bed topography and velocity distribution were very close to the observed data. However, bed shear stress showed only a broad agreement, probably because of the use a constant friction coefficient value. Mean grain size distribution showed good agreement, but theory did not account adequately for gravel sizes in the talweg region and on the upstream, inner part of the bar, possibly due to theoretical underestimation of effective bed shear. Bed form and sedimentary structure are predicted well using the familiar stream power-grain size scheme. The behaviour of the model under unsteady uniform flow conditions in circular bends was analyzed, and suggests that any variation of grain size and bed topography with stage is likely to be limited to deeper parts of the channel.     

Investigation of turbulence characteristics in channel with dense vegetation

In this experimental study,the turbulent flow in a channel with vegetation by using sprouts of wheat on channel bed was investigated.Two different aspect ratios of channel were used.An Acoustic Doppler Velocimetry was used to measure parameters of turbulent flow over submerged sprouts of wheat,such as velocity profiles.The log law and the Reynolds shear stress distribution were applied. Results indicate that the position of the maximum turbulence intensity superposes on the inflection point situated over the top of submerged vegetation cover.Quadrant analysis shows that near the vegetation bed,the sweeps and ejections appear to be the most dominant phenomenon,while far from the vegetated bed,the outward is dominant event.Results also show that the aspect ratio plays an important role on the contribution of the different bursting events for Reynolds stress determination.     

MEANDERING OF RIVERS

Abstract

Among various factors that have influence on the meandering of an alluvial channel, the most significant are valley slope, discharge, bed material, and time. The necessary condition for the origin and development of meandering of an alluvial channel is the erosion of bed material and deposition of the eroded material downstream. The criterion for the development of the meandering is that the discharge must be equal to or greater than the critical discharge (i.e., discharge corresponding to critical shear velocity). The initial channel section has an effect on the development of meandering. The meandering in the V-shaped channels starts from the center (deepest point) of the channel and works inside the banks (inside meandering) before it windens the banks, While the meandering in the rectangular channels starts with the widening of the banks (outside meandering). Maender width increases with the increase in the increase discharge and slope, and decreases with the increase in size of bed material. The meander development continues with time the meander reaches the final stage and equilibrium condition.     

EXPERIMENTAL STUDY ON BED SHEAR STRESS AND SEDIMENT TRANSPORT IN A MEANDERING LABORATORY CHANNEL

1 INTRODUCTION River erosion is a complex phenomenon. The rate of bank retreat is determined by flow, bed topography, sediment transport, bank properties, and water quality. Prediction of future river planform changes and the knowledge of river erosion and river meandering are required for land use planning in alluvial river valleys and determining locations for bridges and hydraulic structures. The control of riverbank erosion requires prediction of flow and bed features in a meanderin…     

An analysis of the characteristics of rough bed turbulent shear stresses in an open channel

Entrainment of sediment particles from channel beds into the channel flow is influenced by the characteristics of the flow turbulence which produces stochastic shear stress fluctuations at the bed. Recent studies of the structure of turbulent flow has recognized the importance of bursting processes as important mechanisms for the transfer of momentum into the laminar boundary layer. Of these processes, the sweep event has been recognized as the most important bursting event for entrainment of sediment particles as it imposes forces in the direction of the flow resulting in movement of particles by rolling, sliding and occasionally saltating. Similarly, the ejection event has been recognized as important for sediment transport since these events maintain the sediment particles in suspension. In this study, the characteristics of bursting processes and, in particular, the sweep event were investigated in a flume with a rough bed. The instantaneous velocity fluctuations of the flow were measured in two-dimensions using a small electromagnetic velocity meter and the turbulent shear stresses were determined from these velocity fluctuations. It was found that the shear stress applied to the sediment particles on the bed resulting from sweep events depends on the magnitude of the turbulent shear stress and its probability distribution. A statistical analysis of the experimental data was undertaken and it was found necessary to apply a Box-Cox transformation to transform the data into a normally distributed sample. This enabled determination of the mean shear stress, angle of action and standard error of estimate for sweep and ejection events. These instantaneous shear stresses were found to be greater than the mean flow shear stress and for the sweep event to be approximately 40 percent greater near the channel bed. Results from this analysis suggest that the critical shear stress determined from Shield's diagram is not sufficient to predict the initiation of motion due to its use of the temporal mean shear stress. It is suggested that initiation of particle motion, but not continuous motion, can occur earlier than suggested by Shield's diagram due to the higher shear stresses imposed on the particles by the stochastic shear stresses resulting from turbulence within the flow.     

Modeling depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation

This paper presents an approach to modeling the depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation. The depth-averaged equation of vegetated compound channel flow is given by considering the drag force and the blockage effect of vegetation, based on the Shiono and Knight method (1991) [40]. The analytical solution to the transverse variation of depth-averaged velocity is presented, including the effects of bed friction, lateral momentum transfer, secondary flows and drag force due to vegetation. The model is then applied to compound channels with completely vegetated floodplains and with one-line vegetation along the floodplain edge. The modeled results agree well with the available experimental data, indicating that the proposed model is capable of accurately predicting the lateral distributions of depth-averaged velocity and bed shear stress in vegetated compound channels with secondary flows. The secondary flow parameter and dimensionless eddy viscosity are also discussed and analyzed. The study shows that the sign of the secondary flow parameter is determined by the rotational direction of secondary current cells and its value is dependent on the flow depth. In the application of the model, ignoring the secondary flow leads to a large computational error, especially in the non-vegetated main channel.     

REGIME MORPHOLOGY OF EQUILIBRIUM ALLUVIAL CHANNELS

IINTRODUCTIONThequestfordeterminingthedesigncharacteristicsofregimechannelshasbeengoingonforalongtime.Peoplehavebeenexcavatingnewormodifyingexistingchannelstousethemforirrigation,watersupply,navigation,floodcontrolandotherpurposes.Recently,archeologistsdiscoveredwhatiscurrentlybelievedtobetheoldestman(madecanalsystem.ItwasfoundintheareawhereMesopotamiausedtoexistanditisdatedbacktoabollt4,000BC.Ifachanne]isnotproperlydesigned,erosionofitsbanksordepositionofsedimentwithinitscross-sectionw…     

Morphological signatures of normal faulting in low‐gradient alluvial rivers in south‐eastern Louisiana,USA

We explore the fluvial response to faulting in three low‐gradient, sand‐bed rivers in south‐eastern Louisiana, USA, that flow across active normal faults from footwall (upstream) to hangingwall (downstream). We calculate sinuosity, migration rate and migration direction in order to identify anomalies spatially associated with fault scarps. In two of the rivers we model one‐dimensional steady water flow to identify anomalies in surface water slope, width‐to‐depth ratio, and shear stress. In each of these rivers there is one location where flow modeling suggests potential channel incision through the footwall, as indicated by relatively high surface water slopes and shear stress values. In one of these footwall locations, the river straightens and width‐to‐depth ratios decrease, likely contributing to higher surface water slopes and shear stress. This is in contrast to previous studies that have proposed increased sinuosity across fault footwalls and decreased sinuosity across hangingwalls. However, in two hangingwall locations we also observe relatively less sinuous channels. Other planform changes on the hangingwall include topographic steering of channels along and towards the fault and one example of an avulsion. The most notable anomaly in migration rate occurs on the hangingwall of a fault where a river has cut off a meander loop. Although fluvial response to faulting varies here, comparatively large and small channels exhibit similar responses. Further, Pleistocene fault slip rates are orders of magnitude lower than the channel migration rates, suggesting that faulting should not be a major influence on the fluvial evolution. Nonetheless, notable channel anomalies exist near faults, suggesting that recent fault slip rates are higher than Pleistocene rates, and/or that low‐gradient alluvial channels are more sensitive to faulting than previous studies have suggested. Rivers appear to be influenced by faulting in this setting, however background rates of meander loop cutoff may be just as influential as faulting. Copyright © 2015 John Wiley & Sons, Ltd.     

EXPERIMENTAL STUDY ON INCIPIENT MOTION OF SEDIMENT PARTICLES ON GENERALIZED SLOPING FLUVIAL BEDS

1 INTRODUCTIONWhen water flows over a fluvial bed, hydro-dynandc force induced by the flow is acting on thesediment particles lying on the bed. A further increase in flow velocity results in an increase in themagnitude of this fOrce; and sediment particles begin to move if a situation is eventu8lly reached whenthe hydro-dynandc force exceeds a certain critical value. This initial movement of sediment pallicles istermed inciPient motion. The erosion and sedimentation of nuvial beds can be…     

Currents in a small channel on a sandy tidal flat

Channels affect drainage and bed stresses on tidal flats. Here, near-bottom currents observed on a sandy tidal flat are compared with those observed 35 m away inside a shallow (≈0.3 m deep) channel. For water depths between 0.5 and 2.5 m (when both current meters are submerged), current speeds 0.13 m above the bed on the flat are about 30% greater than those observed 0.13 m above the bed in the channel, and are approximately equal to those observed 0.58 m above the channel bed (0.26 m above the flat elevation). Flow directions on the flat are similar to those in the channel. For flows directed across the channel axis, the ratio of speeds increases from about 1.3 to about 2.2 with increasing water depth. The corresponding ratio of the vertical velocity variances (a proxy for turbulence) decreases from about 1.5 to about 0.2, suggesting that the turbulence near the bed of the channel is greater than that near the bed of the flat for water depths greater than about 1.0 m. Drag coefficients estimated with the vertical velocity variance are approximately 70% larger in the channel than over the visually smoother flat, consistent with prior studies suggesting that channels may increase tidal-flat roughness. For flows directed along the channel axis (in the cross-flat direction), the ratio of speeds (1.2) is similar to the ratio predicted by a cross-flat momentum (along-channel) balance.     

Flow resistance and hydraulic geometry in bedrock rivers with multiple roughness length scales

Many models of incision by bedrock rivers predict water depth and shear stress from discharge; conversely, palaeoflood discharge is sometimes reconstructed from flow depth markers in rock gorges. In both cases, assumptions are made about flow resistance. The depth–discharge relation in a bedrock river must depend on at least two roughness length scales (exposed rock and sediment cover) and possibly a third (sidewalls). A conceptually attractive way to model the depth–discharge relation in such situations is to partition the total shear stress and friction factor, but it is not obvious how to quantify the friction factor for rough walls in a way that can be used in incision process models. We show that a single flow resistance calculation using a spatially averaged roughness length scale closely approximates the partitioning of stress between sediment and rock, and between bed and walls, in idealized scenarios. Both approaches give closer fits to the measured depth–discharge relations in two small bedrock reaches than can be achieved using a fixed value of Manning's n or the Chézy friction factor. Sidewalls that are substantially rougher or smoother than the bed have a significant effect on the partitioning of shear stress between bed and sidewalls. More research is needed on how best to estimate roughness length scales from observable or measurable channel characteristics. © 2019 John Wiley & Sons, Ltd.