Instantaneous Bed Shear Stress Research Articles

Experimental study of coherent structures and bed shear stress on a smooth bed under a solitary wave

The coherent structures induced by a solitary wave on a smooth bed were studied in a wave flume. The solitary wave was near the point of incipient breaking and the wave Reynolds number was in the intermittent turbulent regime. The velocity field inside the bottom boundary layer was measured using a Particle Image Velocimetry (PIV) system. The bed shear stress was obtained from the measured velocities in the viscous sublayer by employing the Newton's law of viscosity. It was found that the generation and maintenance of turbulent coherent structures in a solitary wave boundary layer was like that observed in oscillatory flow boundary layers at similar wave Reynolds numbers, a process that was first described as the bursting phenomenon in the wall boundary layer of steady flows. The effect of coherent structures on the instantaneous velocity profile and bed shear stress was examined. Ejections and sweeps were found to play a crucial role in producing large bed shear stress fluctuations. Quadrant analysis and probability distribution plots of the bed shear stress showed that sweep (Q4) events were responsible for producing instantaneous bed shear stress values as high as four to five times the standard deviation above the mean, while ejection (Q2) events produced bed shear stress values mostly below the mean. Both types of events were more numerous than outward interaction (Q1) and inward interaction (Q3). It was also found that a high proportion of the measured velocity profiles that did not follow the law of the wall were associated with large vortices in the boundary layer. It was shown that the instantaneous velocities did not conform to a law-of-the-wall velocity profile unless the measured velocity field was averaged over an area large compared to the vortices.

Characteristics of instantaneous flow structures of the surface jet over a submerged weir

This paper presents the results of a LES of turbulent surface jets over a submerged weir. The mean flow and turbulent structures are presented for both flat and deformed bed conditions. LES results with the scour hole reveal that the separated shear layer is extended by about three times, locating the reattachment point further downstream. In addition, the presence of the scour hole increases both total and maximum TKE and decreases near-bed TKE. Quantitatively, with the scour hole, the maximum near-bed TKE is decreased by 50%. It turns out that the area of high instantaneous bed shear stress does not match with that of high time-averaged bed shear stress, but does match well with that of the high near-bed TKE. The vortices generated by the weir propagate differently with and without the scour hole and shed light on the generating mechanism of a scour hole.

Near- and far-field structure of shallow mixing layers between parallel streams

Abstract

Channel width, bedform length and turbulence: numerical investigation of flow dynamics over laboratory-scale pool–riffle sequences

Spatial dimensions of bedforms relative to the flow depth are of great interest for both engineers and geoscientists, and continue to be an active area of research. These morphological features are of significant consequence for critical hydrodynamic parameters, which in turn has an impact on sediment and solute transport through the river system. In this study, we present results from three-dimensional large eddy simulation of flows over such bedforms in a straight channel. Rigid three-dimensional pool–riffle structures occupying the full span of the channel were considered as the macro-bedforms. The presence of pool–riffle affects the spatial heterogeneity of the flow parameters such as lateral flow concentration. We observed that the lateral flow concentration increases in convective deceleration (CDF) zone with peak values at the central plane in channels with narrower span. The peak values shift from the central plane towards sidewall in channels with larger width. Flow recovery is found to be faster in narrower channels in the conducted simulations. High-magnitude counter-rotating vortices (HCRVs) in CDF and pool transport the momentum of the flow towards the centre of the channel. Larger channel width ensures persistent presence of HCRV in CDF and pool. Longer riffle length in the streamwise direction is observed to further alter the lateral flow concentration compared to the shorter riffles. Instantaneous bed shear stress mapping reveals the presence of coherent high- and low-velocity streaks on riffles. The coherence of these structures is lost in CDF and pool accompanied with an increase in turbulence represented by an increase in turbulent kinetic energy and Reynolds stress.

Experimental and theoretical study of bed load particle velocity

ABSTRACTThis paper reports an experimental study of sediment particle velocity in the Hydraulic Engineering Laboratory at the University of Arizona. The experiments were performed in a rectangular channel filled with a layer of coarse sand or gravel. The instantaneous particle velocity was measured by using the images captured with a commercial camera. An innovative image processing technique was developed for tracking individual particle motion, which leads to the determination of instantaneous particle velocity vector. Both the mean particle velocity and the distribution of particle velocities were analyzed. It was found that the instantaneous bed shear stress dominated the particle velocity as well as the probability density function of its distribution. This observation is consistent with the theoretically derived equations for particle velocity and its distribution. Furthermore, the Kolmogorov–Smirnov test confirmed the agreement between the distribution of experimental data and that obtained from the theoretical analysis.

Influence of turbulent horseshoe vortex and associated bed shear stress on sediment transport in front of a cylinder

This study concerns the flow and associated sediment transport in front of a cylinder in steady currents. The study comprises (i) flow characteristics induced by the turbulent horseshoe vortex (THV), (ii) bed shear stress within the THV region, and (iii) predicted sediment transport rates. The velocity fields in front of a wall-mounted circular cylinder were measured using time-resolved particle image velocimetry (PIV). The flow characteristics show that two time-averaged THVs are formed, and the dynamics of instantaneous THVs exhibit a quasi-periodic process from generation to death. Both the mean and fluctuations of bed shear stress within the THV region are significantly amplified, and their values are comparable. The probability density function of the instantaneous bed shear stress exhibits a double-peaked distribution and cannot be represented by the normally-used log-normal distribution for uniform channel-open flows. The comparisons of sediment transport rates where turbulent fluctuations in the bed shear stress are, or are not, taken into account show that the sediment transport rates calculated by the mean bed shear stress are under-predicted. Furthermore, a new sediment transport model incorporating the influence of bed shear stress fluctuations is proposed and validated by comparing the initial scour rate in front of the cylinder.

Modeling bedform development under turbulent flows using Large-Eddy-Simulation and Immersed-Boundary-Method

A numerical model was built to study the mechanism of sedimentary bedform development in hydraulically smooth turbulent flows. The model consisted of a module for flows, a module for sediment transport, and a module for bed surface evolution. The flow was unsteady, three-dimensional and modeled by a Large-Eddy-Simulation (LES) method coupled with an Immersed-Boundary-Method (IBM). Governing equations were discretized on a fixed Cartesian grid by Finite Difference Method. Sediment (bedload) transport was estimated by Van Rijn formula corresponding to bed shear stress distribution obtained from the flow solution. The bed surface evolution was adapted to the sediment flux and described by the Exner–Polya equation. Updated bed surface was then used as the boundary for solving the flow field in the next time step. Time-advancement was discretized by the Adams–Bashforth method. The model was first validated by two test cases of bed shear stress and turbulence statistics over fixed sinusoidal bed surfaces. It was then employed to study initiation and development of bedforms from an initially flat bed to fully developed forms. Formation of newly and successively formed bedforms, growing and downstream propagating process of existing bedforms were very close to experimental observations. Instantaneous bed shear stress and corresponding sediment flux around evolving bedforms, which were difficult to observe in experiments, were also well produced by this model.

Structure of turbulent flow at a river confluence with momentum and velocity ratios close to 1: Insight provided by an eddy‐resolving numerical simulation

River confluences are complex hydrodynamic environments where convergence of incoming flows produces complicated patterns of fluid motion, including the development of large‐scale turbulence structures. Accurately simulating confluence hydrodynamics represents a considerable challenge for numerical modeling of river flows. This study uses an eddy‐resolving numerical model to simulate the mean flow and large‐scale turbulence structure at an asymmetrical river confluence with a concordant bed when the momentum ratio between the two incoming streams is close to 1. Results of the simulation are compared with field data on mean flow and turbulence structure. The simulation shows that the mixing interface is populated by quasi‐two‐dimensional eddies. Successive eddies have opposing senses of rotation. The mixing layer structure resembles that of a wake behind a bluff body (wake mode). Strong streamwise‐oriented vortical (SOV) cells form on both sides of the mixing layer, a finding consistent with patterns inferred from the field data. The predicted mean flow fields show that flow curvature has an important influence on streamwise variation of circulation within the cores of the two primary SOV cells. These SOV cells, along with vortices generated by flow over a submerged block of sediment at one of the banks, strongly influence distributions of the streamwise velocity and turbulent kinetic energy downstream of the junction. Comparison of the eddy‐resolving simulation results with predictions from the steady Spalart‐Allmaras RANS model shows that the latter fails to predict important features of the measured distributions of streamwise velocity and turbulent kinetic energy because the RANS model underpredicts the strength of the SOV cells. Analysis of instantaneous and mean bed shear stress distributions indicates that the SOV cells enhance bed shear stresses to a greater degree than the quasi‐two‐dimensional eddies in the mixing interface.

Modeling sediment transport beneath skewed asymmetric waves above a plane bed

A one‐dimensional model solving the Reynolds‐averaged Navier‐Stokes and advection‐diffusion equations in conjunction with a k − ε model for turbulence closure is used to systematically explore net sediment transport rates beneath skewed asymmetric waves under sheet flow conditions. The model, which reproduces net rates obtained in U tube experiments under purely skewed and asymmetric oscillatory flow well, is forced with an analytical expression of free stream oscillatory flow in which we varied the degree of skewness versus asymmetry, the magnitude of the total wave nonlinearity, the oscillatory flow amplitude, and the wave period. We find that for a wide range of conditions sediment entrained into the flow during a particular wave half‐cycle has not completely settled before flow reversal and tends to be transported during the next half‐cycle. Consistent with earlier work, these phase‐lag effects reduce transport rates under oscillatory flow dominated by velocity skewness, while they enhance net transport rates under oscillatory flow dominated by velocity asymmetry. Phase‐lag effects are particularly important in fine‐medium sands (<≈250 μm). For a given grain size phase‐lag effects become more pronounced with an increase in wave nonlinearity and in velocity amplitude, and with a decrease (increase) in wave period under skewed (asymmetric) oscillatory flow. When phase‐lag effects are negligible, transport rates are largest under skewed oscillatory flow containing some asymmetry; otherwise, they are largest under asymmetric flow. Our work implies that nearshore sediment transport equations based on the instantaneous bed shear stress may be restricted in applicability to situations when the grain size exceeds ≈250 μm.

Coherent Structures in the Flow Field around a Circular Cylinder with Scour Hole

Large-eddy simulation (LES) and laboratory-flume visualizations were used to investigate coherent structures present in the flow field around a circular cylinder located in a scour hole. The bathymetry corresponds to equilibrium scour conditions and is fixed in LES. The flow parameters in the simulation correspond to the experimental conditions in which the approach flow is fully turbulent. Detailed consideration is given to the interaction of the horseshoe vortex (HV) system within the scour hole with the detached shear layers formed from the cylinder, and the near bed turbulence. It is found that the overall structure of the HV system varies considerably in space and time, though a large, relatively stable, primary necklace vortex is present at practically all times inside the scour hole. The simulation captures the presence of bimodal chaotic oscillations inside the HV system, as well as the sharp increase in the resolved turbulent kinetic energy levels and pressure fluctuations reported in prior experimental investigations. High levels of the mean bed shear stress are observed beneath the primary necklace vortex, especially over the region where the bimodal oscillations are strong, as well as beneath the small junction vortex at the base of the cylinder. It is also found that the detachment and advection of patches of vorticity from the downstream part of the legs of the necklace vortices can induce large instantaneous bed shear stress values. When the critical bed shear stress value for sediment entrainment on a flat surface is adjusted for bed slope effects, the LES simulation correctly predicts that the distribution of the mean bed shear stress is consistent with equilibrium scour conditions.

Numerical Investigation of Flow Hydrodynamics in a Channel with a Series of Groynes

The flow hydrodynamics in a straight open channel containing a multiple-embayment groyne field on one of its sides is investigated numerically using large eddy simulation. The vertical groynes are fully emerged. The mean flow depth in the groyne region is about half that of the main channel and the length and width of the embayments are much larger than the mean depth in the embayment region. The model is validated using mean velocity and turbulent fluctuations data collected at the free surface in a previous experimental study. It is found that despite the fact that the flow inside the main recirculation eddy in the embayments can be characterized as being quasi-two dimensional, the flow inside the mixing layer region between the embayments and the channel is strongly nonuniform over the depth. As this region controls the mass exchange processes between the groyne field and the main channel, a three-dimensional description of the flow in this area is essential. The large-scale eddies that populate the mixing layer can penetrate the embayment region over lateral distances of the order of the channel depth. These eddies advect with them channel fluid inside the embayment. Eventually, the channel fluid is mixed with the embayment fluid by the small scales. The other main mixing mechanism is due to the injection of patches of high-vorticity mixing-layer fluid near the tip of the downstream groyne and their subsequent convection in the form of a wall-attached jet-like flow into the embayment, first parallel to the downstream groyne face and then to the sidewall. It is shown that on average, most of the fluid leaves the embayment region via the top layer of the embayment-channel interface (upstream half) and enters the embayment region at levels situated around the middepth (practically over the whole length of the embayment) of the interface surface. This explains why the mass exchange coefficients are overestimated when predicted using methods that employ floating particles as a tracer. The instantaneous bed shear stress inside the cavity is found to peak close to the downstream groyne face of each embayment and to show a high variability around the mean values due to the interaction of the mixing layer eddies with the tip of the groynes and the formation of the jet-like flow parallel to the droyne face.

Bed forms created by simulated waves and currents in a large flume

The morphology and evolution of bed forms created by combinations of waves and currents were investigated using an oscillating plate in a 4‐m‐wide flume. Current speed ranged from 0 to 30 cm/s, maximum oscillatory velocity ranged from 20 to 48 cm/s, oscillation period was 8 s (except for one run with 12 s period), and the median grain size was 0.27 mm. The angle between oscillations and current was 90°, 60°, or 45°. At the end of each run the sand bed was photographed and ripple dimensions were measured. Ripple wavelength was also determined from sonar images collected throughout the runs. Increasing the ratio of current to wave (i.e., oscillatory) velocity decreased ripple height and wavelength, in part because of the increased fluid excursion during the wave period. Increasing the ratio of current to waves, or decreasing the angle between current and waves, increased the three‐dimensionality of bed forms. During the runs, ripple wavelength increased by a factor of about 2. The average number of wave periods for evolution of ripple wavelength to 90% of its final value was 184 for two‐dimensional ripples starting from a flat bed. Bed form orientations at the end of each run were compared to four potential controlling factors: the directions of waves, current, maximum instantaneous bed shear stress, and maximum gross bed form normal transport (MGBNT). The directions of waves and of MGBNT were equally good predictors of bed form orientations, and were significantly better than the other two factors.

Experiment study on sediment incipience in backward-facing step flow

Flow over a backward-facing step was studied to investigate the effect of large-scale vortex structures on sediment incipience. The transient flow velocity field at the downstream of the backward-facing step was obtained using the technique of Particle Tracking Velocimetry (PTV). The optical amplification technique was employed to measure the instantaneous flow velocities near the bed and the instantaneous bed shear stress was given. The experimental observations revealed a new insight into the oscillation of the large-scale structure and the three-dimensional characteristics of the flow. In particular, very high turbulence intensity, instantaneous horizontal velocity near the bed and the bed shear stress near the reattachment point were observed. The sediment incipient probability obtained from the sequent images of sediment particles near the bed indicates that the critical instantaneous shear stress of the sediment incipience is independent of flow conditions.

Probability Density Function of Instantaneous Drag Forces and Shear Stresses on a Bed

A probability density function (PDF) of the instantaneous bed shear stress in a turbulent flow is derived in this paper. It is argued that the shape of the PDF is similar to the PDF of the instantaneous drag forces on bed roughness elements. The influence of the near-bed relative turbulence intensity is included in the PDF. The shape of the distribution compares well with our measurements of the instantaneous drag force on a protruding bed element for a range of turbulence intensities. However, deviations are apparent at high turbulence intensities. The PDF also compares well with measurements of shear stresses on a smooth wall.

Effects of wave shape on sheet flow sediment transport

A two‐phase model is implemented to study the effects of wave shape on the transport of coarse‐grained sediment in the sheet flow regime. The model is based on balance equations for the average mass, momentum, and fluctuation energy for both the fluid and sediment phases. Model simulations indicate that the responses of the sheet flow, such as the velocity profiles, the instantaneous bed shear stress, the sediment flux, and the total amount of the mobilized sediment, cannot be fully parameterized by quasi‐steady free‐stream velocity and may be correlated with the magnitude of local horizontal pressure gradient (or free‐stream acceleration). A net sediment flux in the direction of wave advance is obtained for both skewed and saw‐tooth wave shapes typical of shoaled and breaking waves. The model further suggests that at critical values of the horizontal pressure gradient, there is a failure event within the bed that mobilizes more sediment into the mobile sheet and enhances the sediment flux. Preliminary attempts to parameterize the total bed shear stress and the total sediment flux appear promising.

Bed shear stress measurements over a smooth bed in three-dimensional wave-current motion

Wave and current experiments have been carried out with the purpose of measuring the instantaneous bed shear stress over a hydraulically smooth bed, in order to evaluate the extent of the interaction. Measurements have been carried out with a dual-component hot-film probe which, with some constraints, enables the magnitude and direction of the instantaneous bed shear stress to be measured. Results are presented as maximum obtained bed shear stress values over one cycle and the corresponding mean value in the direction of the current for various combinations of waves and current.

Two-dimensional mathematical modelling of local-scour holes

A morphological model for the development of local-scour holes behind structures is developed, based on the 2-D Navier Stokes and convection-diffusion equations. The bed-load (transport) and the concentration at a reference level close to the bed are prescribed using a stochastical approach for the instantaneous bed shear-stress. The standard deviation of the latter is closely related to the turbulence energy in the mixing layer and to the bed turbulence. The computed developments of local-scour holes in scale models and in prototype are compared to measured developments. Reasonable results regarding flow velocities, sediment concentrations and bed configurations as function of time are obtained, promising reliable predictions for local-scour holes in practice.

Hydraulic Interpretation of Grain-size Distributions Using a Physical Model for Bedload Transport

ABSTRACT Grain-size distributions of bedload sediment are modelled by considering the time variation of sediment transport in a unidirectional turbulent flow. A frequency distribution of instantaneous bed shear stress is divided into a large number of shear stress ranges with mean values of oi. Each oi is capable of transporting a range of sediment sizes as bedload; the maximum size is just at its entrainment threshold, the minimum size is just too large to be suspended. Rates of bedload transport are calculated for each size range using a theoretical bedload function, and the proportion of time that these rates occur is obtained by integrating the frequency distribut on between the boundaries of each shear stress range. The relative weights of sediment transported in particular size ranges, determined for all oi values, constitutes the grain-size distribution obtained from bedload sampling at a fixed point on the bed. Cumulative grain-size curves have been simulated using the model in order to demonstrate the effects of the various model parameters (e.g., mean bed shear stress, viscosity). All curves show a distinct break in slope, which represents the maximum grain size transportable in suspension when the shear stress attains its maximum fluctuating value. Examination of many natural bedload distributions shows close qualitative and quantitative agreement with the model, and reasons for discrepancies can be fully explained. Typical grain-size distributions of deposited sediments can be obtained by mixing of different flow-related bedload distributions in various proportions. Thus although deposited sediments may primarily result from bedload transport during a steady flood flow, flow unsteadiness also plays a part. The effects of some deposition directly from suspended load can also be surmised.

Initial Instability of Fine Bed Sand

The initial entrainment characteristics of fine bed sand are objectively defined in terms of the measured distributions of critical instantaneous bed shear stress associated with the observed movement of individual surface grains. Critical flow conditions are then predicted by equating the lower extremes in these characteristic critical shear stress distributions to the upper extremes in the distribution of instantaneous bed shear stress produced by the particular type of background flow under consideration. The method is applied to the case of two-dimensional channel flow over a flat bed and yields sufficiently consistent results to suggest an extension to Shields' curve for small grain Reynolds numbers. The detailed experimental observations clearly illustrate the important role played by bed region turbulence in the interaction process between the fluid and the mobile bed grains constituting the deformable boundary.