Depth-averaged Velocity Research Articles

Flow characteristics of a partially-covered trapezoidal channel

Partial ice covers alter the hydraulic regime of rivers in cold regions. Border ice is a type of partial ice cover that forms on the river banks and grows toward the centre of the channel to form a full ice cover; thereby impacting freeze-up processes. Many studies have been conducted to understand flow characteristics under open channel and full ice cover conditions; however, only a few studies have focused on the effects of partial ice covers on flow characteristics in a rectangular channel. This study goes even further by investigating stream-wise velocity and shear stress distributions in a trapezoidal channel with simulated border ice. This is the very first study to investigate the effects of different border ice coverage ratios and roughness conditions on flow characteristics in a trapezoidal channel. Experiments were conducted under seven different roughness and coverage conditions. High-resolution velocity data were collected using acoustic Doppler velocimeters within the fully-developed region of the flume. The magnitude and shape of the stream-wise velocity contours were significantly altered by the presence of the partial ice and rough boundaries. Moreover, local boundary shear stress distributions were significantly impacted by the coverage and roughness conditions. Generally, stream-wise velocity and local boundary shear stress increased within the open section and decreased within the covered section. For practical purposes, depth-averaged velocity and discharge distributions were investigated for each experiment. Results from this study will improve the current knowledge of the flow in partially covered channels and can be used for design and modelling purposes.

Improved formulae of velocity distributions along the vertical and transverse directions in natural rivers with the sidewall effect

The distribution of flow velocity is a basis for the research into the transport of flow and sediment in natural rivers. Characteristics of velocity distribution in narrow-deep natural rivers are different from those in wide-shallow open channels, and the effect of sidewalls on the distribution of flow velocity is considerable, which leads to a large transverse gradient of the depth-averaged velocity, with the maximum velocity occurring below the water surface. Based on the Reynolds equation of turbulence flow and the analysis of the features of velocity distribution in natural rivers, improved formulae with two empirical parameters α and β have been proposed for the velocity distributions along the vertical and transverse directions, with the effect of sidewalls being considered, through solving the definite solution problem by the method of variable separation. The proposed formulae were validated fully through comparisons between the calculated and measured velocity profiles and depth-averaged velocities at several sections in the Yangtze and Baitarani Rivers, with close agreement between them being obtained. The formula of velocity distribution along the transverse direction in natural rivers with the sidewall effect was also compared with previous studies, and the calculation accuracy of this formula at a section with a narrow-deep geometry was higher than the accuracy of the previous equations. It is confirmed that the proposed formulae can reproduce well the distribution characteristics of flow velocity along the vertical and transverse directions in narrow-deep natural rivers, with a more wide application in practice.

Effects of vegetation patch density on flow velocity characteristics in an open channel

The aquatic plants are often found in natural rivers, and they affect the channel flow structure significantly. To study the effects of the vegetation density a (the frontal area per volume) on the flow velocity characteristics, rigid bamboo circular cylinders are chosen as the model emergent vegetation. In the experiments, the density of the vegetation takes various values while all other flow parameters are kept constant. A 3-D acoustic Doppler velocimeter (ADV) is used to measure the local flow velocities for different vegetation densities. The results show that the existence of the vegetation patch leads to an increase of the depth-averaged velocity on the right and left sides behind the vegetation patch, and it increases monotonically with the vegetation density. For different vegetation densities, the lateral distribution of the stream-wise velocity behind the vegetation patch follows approximately an S-shaped profile when a ≤ 60 m-1, and a logarithmic profile if a > 60 m-1. The vertical distribution of the stream-wise velocity along the channel varies with the vegetation density and also follows an S-shaped distribution in a certain range, with the locations and the ranges being affected by the vegetation density.

Flow resistance in straight gravel bed inbank flow with analytical solution for velocity and boundary shear distribution

ABSTRACT In the present investigation, the roughness characteristics of the gravel bed is tested and modelled for the no-load condition. A straight trapezoidal channel having gravel bed surface of grain size D50 as 13.5 mm for no-load condition is used to carry out the investigation. Depth averaged velocity (DAV) and boundary shear stress (BSS) have been measured for five different depths. An improved model for prediction of friction factor is derived as the function of corresponding hydraulic radius and average diameter of the gravel. This improved model is validated with the models of past investigators. Furthermore, BSS is then calculated using Shiono and Knight Method (SKM), which is dependent on the following hydraulic parameters, such as friction factor f, coefficient of eddy viscosity λ and secondary flow term Г. Since friction factor is modelled for the given channel, same model is used to calculate the value of f over the bed, which tests the reliability of the model while using numerical method. The lateral distribution of DAV and BSS is shown for five different flow depths, which elaborate the bed friction due to the no-load condition. Finally, friction factor model is corroborated on two reaches of the natural river.

Lateral distribution of depth average velocity & boundary shear stress in a gravel bed open channel flow

ABSTRACT Gravel bed flow is so generic condition that its study becomes fascinating as well as critical to apprehend flow characteristic. In this particular study, no bed load movement was maintained using grains of 13.5 mm (D50 value) characterised as no load condition. Depth Average Velocity (DAV) and the Boundary Shear Stress (BSS) has been experimentally estimated for five different depths for the prevailing no load condition. Furthermore, the distribution of streamwise depth-averaged velocity and boundary shear stress at different flow depths of gravel bed are also calculated using different hydraulic software packages such as CES & ANSYS FLUENT. These numerical simulation results have shown reasonably good agreement with experimental data over main channel in inbank flow. Finally, results obtained are corroborated through error analysis. The overall idea of this study was to understand flow characteristic and behaviour of gravel bed having inbank flow through experimental and numerical simulation techniques.

Depth-Average Velocity from Spray Underwater Gliders

AbstractThe depth-average velocity is routinely calculated using data from underwater gliders. The calculation is a dead reckoning, where the difference between the glider’s velocity over ground and its velocity through water yields the water velocity averaged over the glider’s dive path. Given the accuracy of global positioning system navigation and the typical 3–6-h dive cycle, the accuracy of the depth-average velocity is overwhelmingly dependent on the accurate estimation of the glider’s velocity through water. The calculation of glider velocity through water for the Spray underwater glider is described. The accuracy of this calculation is addressed using a method similar to that used with shipboard acoustic Doppler current profilers, where water velocity is compared before and after turns to determine a gain to apply to glider velocity through water. Differences of this gain from an ideal value of one are used to evaluate accuracy. Sustained glider observations of several years off California and Palau consisted of missions involving repeated straight sections, producing hundreds of turns. The root-mean-square accuracy of depth-average velocity is estimated to be in the range of 0.01–0.02 m s−1, consistent with inferences from the early days of underwater glider design.

Depth-averaged simulation of flows in asymmetric compound channels with smooth and rough narrow floodplains

ABSTRACTDepth-averaged hydrodynamic models are predominantly used in numerical simulations of compound channel flows. One of the most popular methods for the depth-averaged simulation is Shiono and Knight method (SKM). This method accounts for the effects of bed friction, lateral turbulence and secondary flows, via three key parameters f, λ and Γ, respectively. The conventional expressions that are developed to calibrate these parameters are generally based on experiments in compound channels with wide floodplains. In this study, the application of SKM to an asymmetric compound channel with a narrow floodplain is examined in terms of the calibration requirements. Two sets of experiments that have smooth and rough floodplains are conducted and then simulated by SKM. In smooth floodplain cases, the results reveal that SKM model with the conventional calibration expressions of f, λ and Г is reasonably capable of predicting the distributions of depth-averaged velocity and boundary shear stress in the main channel. However, in the floodplain region, the expressions recommended for calibrating Г need to be modified to improve the predicted results in that region. In cases of the rough floodplain, the results indicate that only the values of λ in the main channel need to be changed from its conventional values to improve the predictions.

Evaluation of the Secondary Current Parameter and Depth-Averaged Velocity in Curved Compound Open Channels

AbstractSimultaneous effects of centrifugal force, floodplain interferences, and variation of the depth-averaged velocity are combined in an analytical model to derive a relationship for estimating...

Flow structure at the downstream of a one-line riparian emergent tree along the floodplain edge in a compound open-channel flow

This study focuses on the effects of one-line emergent natural tree (Cupressus Macrocarpa) planted at the edge of the floodplain in a compound open-channel flow. The flow velocity and water level are measured and used to analyze the flow structure. The time averaged and depth-averaged streamwise velocity distributions with root mean square (rms) and time series of streamwise velocity distrbution are analyzed. The velocity distribution considerably changes along the compound channel. The streamwise velocity distribution fits with logarithmic distribution in the non-vegetated case, but for vegetated cases, the streamwise velocity distribution shows S shaped profile at the 1/3 part of floodplain (B f / 3) and main channel (B m / 3) close to the boundary between floodplain and main channel. Additionally, it is obtained that the presence of tree line increases turbulence intensity over the compound open-channel. Moreover, an oscillation period is obtained in the flow caused by tree line by analyzing time series of the streamwise velocity distribution. The oscillation is present everywhere in the floodplain and present at almost B m / 3 part of the main channel which is close to the junction between floodplain and main channel.

Lake sturgeon (Acipenser fulvescens) spawning habitat: a quantitative review

The loss of spawning habitat has been identified as a limiting factor to population growth for lake sturgeon, Acipenser fulvescens, the most widely distributed species of the family in North America. While local information exists about lake sturgeon spawning habitat, a synthesis of all available data is needed across its range. Our study used meta-analytical techniques to describe the mean and range of critical spawning habitat characteristics based on data from 48 sites across all major watersheds in which lake sturgeon are found. Data were compiled into univariate habitat suitability indices to describe the spawning niche. Results indicate that peak suitability occurred at depth-averaged velocities of 0.6 m·s−1, depths of 0.55–0.85 m in small rivers (<100 m3·s−1 annual average discharge) and 0.75–5.25 m in large rivers (>100 m3·s−1), over cobble substrates (64–256 mm), and that suitable water temperatures decreased with increasing latitude. This study provides a comprehensive review of critical spawning criteria from which future habitat suitability models can be adapted.

Flow Prediction of Boundary Shear Stress and Depth Average Velocity of a Compound Channel with Narrowing Floodplain

Prediction of boundary shear force distributions in open channel flow is crucial in many critical engineering problems such as channel design, calculation of losses and sedimentation. During floods, part of the discharge of a river is carried by the simple main channel and the rest is carried by the floodplains. For such compound channels, the flow structure becomes complicated due to the transfer of momentum between the deep main channel and the adjoining floodplains. The complexity further increases when dealing with a compound channel with non-prismatic floodplains. Knowledge of momentum transfer at the different interfaces originating from the junction between the main channel and floodplain can be acquired from the distribution of boundary shear in the subsections. The calculation of boundary shear and depth average velocity in non-prismatic compound channel flow is more complex and simple conventional approaches cannot predict the boundary shear and depth average velocity with sufficient accuracy. Hence, in this area, an easily implementable technique, the Artificial Neural Network can be used for predicting the boundary shear and depth average velocity at different sections of a converging compound channel for different geometry and flow conditions. The model’s performance has lead satisfactory results. Statistical error analysis is also carried out to know the degree of accuracy of the model.

Dry granular avalanche impact force on a rigid wall: Analytic shock solution versus discrete element simulations.

The present paper investigates the mean impact force exerted by a granular mass flowing down an incline and impacting a rigid wall of semi-infinite height. First, this granular flow-wall interaction problem is modeled by numerical simulations based on the discrete element method (DEM). These DEM simulations allow computing the depth-averaged quantities-thickness, velocity, and density-of the incoming flow and the resulting mean force on the rigid wall. Second, that problem is described by a simple analytic solution based on a depth-averaged approach for a traveling compressible shock wave, whose volume is assumed to shrink into a singular surface, and which coexists with a dead zone. It is shown that the dead-zone dynamics and the mean force on the wall computed from DEM can be reproduced reasonably well by the analytic solution proposed over a wide range of slope angle of the incline. These results are obtained by feeding the analytic solution with the thickness, the depth-averaged velocity, and the density averaged over a certain distance along the incline rather than flow quantities taken at a singular section before the jump, thus showing that the assumption of a shock wave volume shrinking into a singular surface is questionable. The finite length of the traveling wave upstream of the grains piling against the wall must be considered. The sensitivity of the model prediction to that sampling length remains complicated, however, which highlights the need of further investigation about the properties and the internal structure of the propagating granular wave.

On Strong Nearshore Wind-Induced Currents in Flow-Through Gulfs: Variations on a Theme by Csanady

Csanady’s (1973) model, used to explain the development of strong, wind-induced nearshore currents in long lakes, has been extended to explain the same phenomenon in flow-through semi-enclosed gulfs. As in the original theory, it is predicted that the depth-averaged velocities move with the wind in regions shallower than the characteristic depth and upwind in deeper parts of the basin. The characteristic depth in the modified theory, however, is shown to be larger than the characteristic depth of the original theory, which is the basin mean depth, by a parameter λ, which can be calculated using the wind stress, the cross-section area and the volumetric inflow into the gulf. The theory is further used to examine in detail the scaling of the flow and identify the dimensional parameters underlying the formulation of the Csanady model. By expanding in an appropriately-defined inverse, Rossby number, which can be made arbitrarily large for small times, it is shown that under the influence of the Coriolis force, the free surface assumes a characteristic S-like shape and the shorewise volume flux an M-like shape. It is suggested that the shorewise flux might be of interest in environmental applications. The predictions of both variations of the original model of Csanady have been illustrated by numerical simulations, in pertinent idealized geometries, and have been also used to explain salient features of the wind-induced circulation in the Gulf of Patras in Western Greece.

Performance comparison of four turbulence models for modeling of secondary flow cells in simple trapezoidal channels

Due to the importance of channel flow characteristics in the water conveyance, the study of it is a noteworthy problem for hydraulics experts and much attempts has been accomplished for the modeling of the flow characteristics. One significant problem in this respect is the secondary flow cells and their effect on flow specifications. Widespread experimental and analytical investigations have been accomplished on this phenomenon. However, researchers are trying to replace the expensive and time-consuming experimental approaches and ad hoc analytical models with numerical simulation procedures using computational fluid dynamics (CFD). Selection of the proper turbulence model is one of the most important problems for this type of the numerical modeling. In the present study, after evaluating several turbulence models including k–ε, shear stress transport (SST) and three versions of the Reynolds stress model (RSM) (i.e. LRR-IP, LRR-QI, and SSG models), for the numerical simulation of the secondary flow cells and their effects on trapezoidal channels flow, the more efficient model was selected. Available experimental data and theoretical model was used to validate the selected turbulence model. The results were validated in terms of the free water surface, depth-averaged velocity, and boundary shear stress. The results confirmed the performance and efficiency of SSG version of the Reynolds stress model for the numerical modeling of the secondary flow cells.

3-D Numerical Investigation on Effect of Flow Structure and Water Level on Vegetation Distribution in an Open Channel

Jeon, H.S.; Hur, D.S.; Park, J.R.; Yoon, J.S.; Kim, I.H., and Lee, W.D., 2018. 3-D numerical investigation on effect of flow structure and water level on vegetation distribution in an open channel. 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. 71–75. Coconut Creek (Florida), ISSN 0749-0208.The in-stream vegetation is recognized to have significant ecological and aesthetic importance in managing floods and restoring rivers. However, it also disturbs the velocity of running fluid by increasing the resistance of flow, and raises the water level because of reduced discharge area at times of flood. Therefore, it is very important to study the hydraulic characteristics of vegetation distribution, and this study carried out a numeric simulation for quantitative and qualitative analysis. The simulation applied Navier-Stokes solver based on PBM (Porous Body Model), LES (Large Eddy Simulation) and VOF (Volume of Fluid), and the estimated drag coefficients of vegetation with Reynold's number. A comparison between the measured and calculated water depth and depth-averaged velocity found that conventional and new experiments were highly consistent. A numeric water tank was also used in this study to discuss the hydraulic characteristics of vegetation by measuring the velocity and water level depending on different vegetation zones and incidental conditions. The result showed that full vegetation in an open channel reduced velocity and raised water level because of the drag of vegetation, while half vegetation on one side or at certain part of the channel substantially reduced the hike of water level. Therefore, vegetation should be distributed appropriately when applying that in river management or restoration after an accurate analysis on the hydraulic characteristics of vegetation distribution.

Wave–Current Interaction: A 2DH Model for Turbulent Jet and Bottom-Friction Dissipation

A correct representation of the non-linear interactions between waves and currents is one of the key points when studying the morphological evolution of nearshore environments, in particular close to river mouths or tidal inlets. Undoubtedly, the numerical modelling of similar phenomena can be very complex and computationally demanding, given the size of the domains. In the present paper, a two‐dimensional horizontal (2DH) numerical model is applied to investigate the hydrodynamics of a turbulent jet current interacting with frontal waves, preparatory to the study of morphodynamical processes. The purpose is to reproduce accurately the turbulence of the current flow, which develops in both vertical and horizontal planes, even with the simplifications of depth-averaged velocities. Moreover, the bottom shear stress induces a mechanism of dissipation, which acts both on the jet hydrodynamics and on the wave field. Significant attention is given to this process, which turns out to be crucial in shallow waters. The present model, based on classic shallow-water equations and wave action balance, is applied to a literature test. Comparisons with theoretical and numerical outcomes are shown, the latter obtained with a quasi-3D model.

Application of an Automated Discharge Imaging System and LSPIV during Typhoon Events in Taiwan

An automated discharge imaging system (ADIS), which is a non-intrusive and safe approach, was developed for measuring river flows during flash flood events. ADIS consists of dual cameras to capture complete surface images in the near and far fields. Surface velocities are accurately measured using the Large Scale Particle Image Velocimetry (LSPIV) technique. The stream discharges are then obtained from the depth-averaged velocity (based upon an empirical velocity-index relationship) and cross-section area. The ADIS was deployed at the Yu-Feng gauging station in Shimen Reservoir upper catchment, northern Taiwan. For a rigorous validation, surface velocity measurements were conducted using ADIS/LSPIV and other instruments. In terms of the averaged surface velocity, all of the measured results were in good agreement with small differences, i.e., 0.004 to 0.39 m/s and 0.023 to 0.345 m/s when compared to those from acoustic Doppler current profiler (ADCP) and surface velocity radar (SVR), respectively. The ADIS/LSPIV was further applied to measure surface velocities and discharges during typhoon events (i.e., Chan-Hom, Soudelor, Goni, and Dujuan) in 2015. The measured water level and surface velocity both showed rapid increases due to flash floods. The estimated discharges from ADIS/LSPIV and ADCP were compared, presenting good consistency with correlation coefficient R = 0.996 and normalized root mean square error NRMSE = 7.96%. The results of sensitivity analysis indicate that the components till (τ) and roll (θ) of the camera are most sensitive parameters to affect the surface velocity using ADIS/LSPIV. Overall, the ADIS based upon LSPIV technique effectively measures surface velocities for reliable estimations of river discharges during typhoon events.

Integrating unmanned aerial systems and LSPIV for rapid, cost-effective stream gauging

Quantifying flow in rivers is fundamental to assessments of water supply, water quality, ecological conditions, hydrological responses to storm events, and geomorphological processes. Image-based surface velocity measurements have shown promise in extending the range of discharge conditions that can be measured in the field. The use of Unmanned Aerial Systems (UAS) in image-based measurements of surface velocities has the potential to expand applications of this method. Thus far, few investigations have assessed this potential by evaluating the accuracy and repeatability of discharge measurements using surface velocities obtained from UAS. This study uses large-scale particle image velocimetry (LSPIV) derived from videos captured by cameras on a UAS and a fixed tripod to obtain discharge measurements at ten different stream locations in Illinois, USA. Discharge values are compared to reference values measured by an acoustic Doppler current profiler, a propeller meter, and established stream gauges. The results demonstrate the effects of UAS flight height, camera steadiness and leveling accuracy, video sampling frequency, and LSPIV interrogation area size on surface velocities, and show that the mean difference between fixed and UAS cameras is less than 10%. Differences between LSPIV-derived and reference discharge values are generally less than 20%, not systematically low or high, and not related to site parameters like channel width or depth, indicating that results are relatively insensitive to camera setup and image processing parameters typically required of LSPIV. The results also show that standard velocity indices (between 0.85 and 0.9) recommended for converting surface velocities to depth-averaged velocities yield reasonable discharge estimates, but are best calibrated at specific sites. The study recommends a basic methodology for LSPIV discharge measurements using UAS that is rapid, cost-efficient, and does not require major preparatory work at a measurement location, pre- and post-processing of imagery, or extensive background in image analysis and PIV.

Effect of using guide walls and piers with different geometries on the flow at entrance of a spillway

In the present paper, the effect of guide wall and pier geometry on the flow pattern of a dam spillway was studied. Different scenarios were numerically simulated to optimize the geometry of the guide walls and piers of the spillway in different hydraulic conditions. The RNG and VOF models were used for turbulence and free surface simulations, respectively. Numerical results were validated with experimental data and good agreement was found with an average relative deviation of less than 10%. Results showed that the vertical inclination of the guide wall and pier was the main affecting factor in the approach flow condition through the spillway. A 44% increase in the vertical inclination of the guide wall resulted in a 43% reduction of the turbulence factor and in a 13% increment of the discharge coefficient of the spillway. By increasing the vertical inclination of the piers of the spillway by 28%, the flow behaviour becomes more uniform and the discharge coefficient increases by as much as 11%. Moreover, the results indicate that increasing the straight length of the guide wall leads to a reduction of the depth-averaged velocity and of the turbulence energy in the approach channel.

Experimental Analysis of the Source and Sink Relationship in a Meandering Bend

The source-sink-relationships in natural rivers are compound results of various influencing factors, and correlated fitted equations are kind of qualitative description. Experiment analyses was conducted in a laboratory flume to reach a quantitative description, whose center line follows a sine-generated curve with deflection angle of 30 degree. Three-dimensional velocities, bed deformation and composition of the pool-bar complexes in the meander bend are analyzed. The comparison of deformed bed and the depth-averaged velocities founds that, the maximum depth-averaged velocities of sections around the transition reach occurred at the edge of pool with smaller transverse slope, and the maximum depth-averaged velocities for sections around the apex section occurred at the edge of pool with larger transverse slope. Quantitative analysis of the composition of pool-bar complexes revealed the source-sink relation of moved particles. It shows that, moved particles sourced from the concave bank are mainly come from area down the apex section, and moved particles sourced from the convex bank are mainly come from area upper the apex section. Besides, there exit an area with strong sediment exchange, namely the bar around the convex-side of the apex section.