Water Surface Velocity Research Articles

Hetero-Bäcklund Transformation for a (2+1)-Dimensional Generalized Modified Dispersive Water-Wave System

This work is designed for a (2+1)-dimensional generalized modified dispersive water-wave system for the nonlinear and dispersive long gravity waves travelling along two horizontal directions in the shallow water of uniform depth, with our results as a hetero-B acklund transformation, from that system to a known generalized (2+1)-dimensional dispersive long-wave system. As for the height of the water surface and horizontal velocity of the water wave, our hetero-Backlund transformation depends on the shallow-water coefficients in that system.

Estimating velocity distribution and flood discharge at river bridges using entropy theory – insights from computational fluid dynamics flow fields

Abstract. Estimating the flow velocity and discharge in rivers is of particular interest for monitoring, modeling, and research purposes. Instruments for measuring water level and surface velocity are generally mounted on bridge decks, and this poses a challenge because the bridge structure, with piers and abutments, can perturb the flow field. The current research aims to investigate the applicability of entropy theory to estimate the velocity distribution and the discharge in the vicinity of river bridges. For this purpose, a computational fluid dynamics (CFD) model is used to obtain three-dimensional flow fields along a stretch of the Paglia River (central Italy), where a historical multi-arch bridge strongly affects flood flows. The input data for the entropy model include the cross-sectional bathymetry and the surface velocity provided by the numerical simulations. A total of 12 samples, including three different flow conditions at four cross-sections, one upstream and three downstream of the bridge, are considered. It is found that the entropy model can be reliably applied upstream of the bridge, also when forced with a single (i.e., the maximum) value of the surface velocity, with errors on total discharge below 13 % in the considered case. By contrast, downstream of the bridge, the wakes generated by the bridge piers strongly affect the velocity distribution, both in the spanwise and in the vertical directions and for very long distances. Here, notwithstanding the complex and multimodal spanwise distribution of flow velocity, the entropy model estimates the discharge with error lower than 8 % if forced with the river-wide distribution of the surface velocity. The present study has important implications for the optimal positioning of sensors and suggests the potential of using CFD modeling and entropy theory jointly to foster greater knowledge of river systems.

Siting Considerations for Satellite Observation of River Discharge

AbstractWith growing global capability for satellite measurement of river discharge (flow) comes a need to understand and reduce error in satellite‐based discharge measurements. Satellite‐based discharge estimates are based on measurements of water surface width, elevation, slope, and potentially velocity. Site selection is important for reducing error and uncertainty in both conventional and satellite‐based discharge measurements because geomorphic river characteristics have strong control over the relationships between discharge and width, water surface elevation (or depth), slope, and velocity. A large ground‐truth data set of 8,445 conventional hydraulic measurements, collected by acoustic Doppler current profilers at 503 stations in the United States, was developed and quality assured to examine correlation between river discharge and water surface width, depth, velocity, and cross‐sectional area. A separate database of river surface slope and discharge time‐series was developed from paired continuous monitoring stations to examine slope‐discharge correlations. Results show that discharge correlates most strongly with velocity, cross‐sectional area, depth, width, and slope, in that order. Uncertainty of satellite discharge estimates is affected by observed hydraulic variable and reach‐specific variability in observed variable(s) characteristics including range of variability, georegistration accuracy, and stability over time of relationships between discharge and observed hydraulic variable.

Optimizing Solar Potential: Site Potential Selection for Floating Photovoltaics in the Sepaku Semoi Dam Reservoir

Green energy is considered an essential solution to address the world’s energy scarcity. However, there are several technologies available for producing green energy, including photovoltaics, with a specific focus on floating photovoltaics. The application of photovoltaics on water surfaces can enhance the cooling effect of solar modules, thereby achieving optimal temperatures. The implementation of floating photovoltaics should be approached with careful consideration, for instance, hydrodynamic aspects, reservoir water level fluctuations, forest shadow effects, and safety distance from Dam Facilities. Furthermore, in light of the relocation of the Indonesian National Capital City from Jakarta to Ibu Kota Nusantara (IKN), the city’s green energy options must be thoroughly studied and researched. The Sepaku Semoi Dam is located in Penajam Paser Utara, Kalimantan Timur, and is designated as a flood control and raw rater supplier for IKN. In this research, hydrodynamic simulations using MIKE 21 were conducted to determine water surface velocities. These results were then combined with reservoir depth and the location of areas unaffected by forest shadows. The outcome of this analysis revealed that 15.2% of the water surface area in the Sepaku Semoi Dam Reservoir has the potential for installing floating photovoltaics. With an energy density of floating photovoltaic around 100 MW/km2, Sepaku Semoi Dam Reservoir would produce 50.83 MW. As a result, this research has generated a Potential Location Map for Floating Photovoltaics in Sepaku Semoi Reservoir Dam Reservoir.

Experimental and numerical study of the gated and ungated ogee spillway

This study was carried out by combining numerical modeling and experimental measurements to investigate the hydraulic characteristics of ungated and gated ogee spillways with high head ratios. The primary objective was to validate the use of a numerical model as a complementary approach to the experimental model for simulating the hydraulic behavior of these spillways, providing a more comprehensive understanding of their hydraulic properties under varying conditions of head ratios and relative gate openings. An Acoustic Doppler Velocimeter (ADV) was used to measure the vertical flow velocity distributions, and ultrasonic sensor wave gauges were used to obtain the time history of the water level. The results of the measurements were compared with the simulation results using a model fitted with three different turbulence models (realizable k-ε, RNG k-ε, k-ω SST). The numerical model was developed using OpenFOAM. With respect to the ungated spillway, three different head ratios ranging from 1.4 to 4.6, which correspond to high head ratios, were investigated. Similarly, three different relative gate openings ranging from 0.5 to 2 were investigated for the gated spillway. The results of water surface profiles and velocity profiles suggest that the numerical and experimental models achieve a good agreement for sections located further away from the spillway. For the ungated spillway, the simulation results for the near-spillway sections are enhanced when the head ratio increases. Considering the velocity profiles and error analysis, the realizable k–ε model was found to best predict the results of the experimental model. A discussion about the discharge equation, velocity fields, pressure fields, and the corner separation zone is also included in this study.

Bathymetry Inversion Using a Deep‐Learning‐Based Surrogate for Shallow Water Equations Solvers

AbstractRiver bathymetry is critical for many aspects of water resources management. We propose and demonstrate a bathymetry inversion method using a deep‐learning‐based surrogate for shallow water equations solvers. The surrogate uses the convolutional autoencoder with a shared‐encoder, separate‐decoder architecture. It encodes the input bathymetry and decodes to separate outputs for flow field variables. Utilizing the differentiability of the surrogate, a gradient‐based optimizer is used to perform bathymetry inversion. Two physically based constraints on the ranges of both bed elevation and slope have to be added as inversion loss regularizations to contract the solution space. Using the “L‐curve” criterion, a heuristic approach is proposed to determine the regularization parameters. Both the surrogate model and the inversion algorithm show good performance. The bathymetry inversion progresses in two distinctive stages, which resembles the sculptural process of initial broad‐brush calving and final fine detailing. The inversion loss due to flow prediction error and the two regularizations play dominant roles in the initial and final stages, respectively. The surrogate architecture (whether with both velocity and water surface elevation or velocity only as outputs) does not have significant impact on inversion result. The methodology proposed in this work, an example of differentiable parameter learning, can be similarly used in the inversion of other important distributed parameters such as roughness coefficient.

Satellite Video Remote Sensing for Estimation of River Discharge

AbstractWe demonstrate that river discharge can be estimated by deriving water surface velocity estimates from satellite‐derived video imagery when combined with high‐resolution topography of channel geometry. Large Scale Particle Image Velocimetry (LSPIV) was used to map surface velocity from 28 s of 5 Hz satellite video acquired at a 1.2 m nominal ground spacing over the Darling River, Tilpa, Australia, during a 1‐in‐5‐year flood. We stabilized and assessed the uncertainty of the residual motion induced by the satellite platform, enhancing our sub‐pixel motion analysis, and quantified the sensitivity of image extraction rates on computed velocities. In the absence of in situ observations, LSPIV velocity estimates were validated against predictions from a calibrated 2D hydrodynamic model. Despite the confounding influence of selecting a surface velocity depth‐averaging coefficient, inference of discharge was within 0.3%–15% compared with gauging station measurements. These results provide a valuable foundation for refining satellite video LSPIV techniques.

Improved representation of laminar and turbulent sheet flow in subglacial drainage models

Abstract Subglacial hydrology models struggle to reproduce seasonal drainage patterns that are consistent with observed subglacial water pressures and surface velocities. We modify the standard sheet-flow parameterization within a coupled sheet–channel subglacial drainage model to smoothly transition between laminar and turbulent flow based on the locally computed Reynolds number in a physically consistent way (the ‘transition’ model). We compare the transition model to standard laminar and turbulent models to assess the role of the sheet-flow parameterization in reconciling observed and modelled water pressures under idealized and realistic forcing. Relative to the turbulent model, the laminar and transition models improve seasonal simulations by increasing winter water pressure and producing a more prominent late-summer water pressure minimum. In contrast to the laminar model, the transition model remains consistent with its own internal assumptions across all flow regimes. Based on the internal consistency of the transition model and its improved performance relative to the standard turbulent model, we recommend its use for transient simulations of subglacial drainage.

One-way fluid structure interaction analysis of a static savonius hydrokinetic turbine under different velocity and surface roughness with different blade materials

Hydrokinetic turbines are prone to a harsh hydrodynamic environment with intricate vortical flows that elevate the probability of failure. The degradation of the blade surface caused by corrosion can impact the blade's hydrodynamic and the structural performance. This paper reports a one-way three-dimensional fluid-structure interaction simulation to analyse the performance of a static Savonius hydrokinetic turbine at varying rotor positions, with different surface roughness and water velocities, in terms of coefficients of static torque, static torque, stresses, and blade deformation. The simulations revealed that the optimum position for the highest coefficient of static torque was at 15° (Cst = 0.30) in reference to the water flow. Increasing the water velocity from 0.4 ms−1 to 0.84 ms−1 improved the turbine static torque due to an increase in the kinetic energy. However, the presence of surface roughness has deterioration effects on the static torque coefficient due to a delayed separation which causes a drag reduction. The simulation predicted no structural failure at 0.4 ms−1 and 0.84 ms−1, but varying materials exhibited varying maximum principal stress and deformation, highlighting the significance of the early development of materials selection process. The maximum von Mises stress and deformation was obtained when the turbine is resting at 45° for aluminium blade (σ = 1.05 MPa, ε = 5.6e−4 mm). The results of this study indicate suitable materials from a hydrodynamic and material perspectives for the construction of the Savonius hydrokinetic turbine, which can be implemented in the design process to potentially save cost and minimize turbine downtime.

Comparative Assessment of Different Image Velocimetry Techniques for Measuring River Velocities Using Unmanned Aerial Vehicle Imagery

The accurate measurement of river velocity is essential due to its multifaceted significance. In response to this demand, remote measurement techniques have emerged, including large-scale particle image velocimetry (LSPIV), which can be implemented through cameras or unmanned aerial vehicles (UAVs). This study conducted water surface velocity measurements in the Xihu River, situated in Miaoli County, Taiwan. These measurements were subjected to analysis using five distinct algorithms (PIVlab, Fudaa-LSPIV, OpenPIV, KLT-IV, and STIV) and were compared with surface velocity radar (SVR) results. In the quest for identifying the optimal parameter configuration, it was found that an IA size of 32 pixels × 32 pixels, an image acquisition frequency of 12 frames per second (fps), and a pixel size of 20.5 mm/pixel consistently yielded the lowest values for mean error (ME) and root mean squared error (RMSE) in the performance of Fudaa-LSPIV. Among these algorithms, Fudaa-LSPIV consistently demonstrated the lowest mean error (ME) and root mean squared error (RMSE) values. Additionally, it exhibited the highest coefficient of determination (R2 = 0.8053). Subsequent investigations employing Fudaa-LSPIV delved into the impact of various water surface velocity calculation parameters. These experiments revealed that alterations in the size of the interrogation area (IA), image acquisition frequency, and pixel size significantly influenced water surface velocity. This parameter set was subsequently employed in an experiment exploring the incorporation of artificial particles in image velocimetry analysis. The results indicated that the introduction of artificial particles had a discernible impact on the calculation of surface water velocity. Inclusion of these artificial particles enhanced the capability of Fudaa-LSPIV to detect patterns on the water surface.

Dynamic texture analysis using Temporal Gray scale Pattern Image for water surface velocity measurement

Water surface velocity (WSV) is one of the critical parameters in hydrology. The development of non-intrusive measurement of this parameter using cameras is increasing. Traditionally, measuring WSV using a camera utilizes tracking of moving objects on the water surfaces. Recently, another method has emerged that utilizes the movement of water ripples to estimate the WSV. This paper proposes a novel method for estimating WSV based on camera measurements. The authors call this method Temporal Gray-scale Pattern Image (TGPI) since it extracts Gray-scale patterns of pixels of water flow video in the temporal domain using the XOR operator and create new image. The new image pattern formed is then used to predict WSV using predictor. There are four predictors being compared, namely Multiple Input Linear Regression (MILR), Multiple Input Logistic Regression (MILgR), Convolutional Neural Network Regression (CNN-R), and Convolutional Neural Network Classification (CNN-K). CNN-R and CNN-K predict WSV directly from the results of TGPI. Meanwhile, MILR and MILgR predict WSV from five TGPI features. The five features are the Mean and Median of the Histogram, Mean and Median of the Histogram of Oriented Gradient (HOG), and the Maximum Mid-Value of the Fast Fourier Transform (FFT). MILR and CNN-R are predictors for regression problems, so the testing metrics for them are Trend-Line equation and R2 from the predicted WSV and actual values graph. Meanwhile, for MILgR and CNN-K, which are predictors for classification problems, the testing metrics are Confusion Matrix (CM), Accuracy, Precision, Recall, and F1-Score. To test the four methods without distinguishing their predictor types, a 2-dimensional histogram graph is used. The data-set used for training and testing is video footage of water flow with known WSV. The WSV measurement points used in this study are 1.7 m/s, 3.1 m/s, and 4.2 m/s. The video dataset and these three points are generated by the Mini Open Channel Water Flow Simulator (MOCWFS) developed by the author in this study. From the comparison results, it can be seen that the classification type predictor is superior to the regression type. For the regression type predictor, MILR is better than CNN-R. Meanwhile, for the classification type, CNN-K is superior to MILgR. The best accuracy produced by CNN-K is 98.4%. Although there are shortcomings, the TGPI method is quite feasible for predict Water Surface Velocity.

A Low-Cost Radar-Based IoT Sensor for Noncontact Measurements of Water Surface Velocity and Depth.

We designed an out-of-water radar water velocity and depth sensor, which is unique due to its low cost and low power consumption. The sensor is a first at a cost of less than USD 50, which is well suited to previously cost-prohibited high-resolution monitoring schemes. This use case is further supported by its out-of-water operation, which provides low-effort installations and longer maintenance-free intervals when compared with in-water sensors. The inclusion of both velocity and depth measurement capabilities allows the sensor to also be used as an all-in-one solution for flowrate measurement. We discuss the design of the sensor, which has been made freely available under open-hardware and open-source licenses. The design uses commonly available electronic components, and a 3D-printed casing makes the design easy to replicate and modify. Not before seen on a hydrology sensor, we include a 3D-printed radar lens in the casing, which boosts radar sensitivity by 21 dB. The velocity and depth-sensing performance were characterised in laboratory and in-field tests. The depth is accurate to within ±6% and ±7 mm and the uncertainty in the velocity measurements ranges from less than 30% to 36% in both laboratory and field conditions. Our sensor is demonstrated to be a feasible low-cost design which nears the uncertainty of current, yet more expensive, velocity sensors, especially when field performance is considered.

The influence of hyporheic exchange with spur dikes: Laboratory experiments

It is important to understand heat transfer changes in the hyporheic zone of spur dikes when assessing ecological restoration and sustainability in rivers. To reveal the rule of hyporheic exchange under the action of a spur dike, the sinusoidal temperature change of surface water was set with a period of 24 h. The porous subsurface flow paths under different riverbed forms were plotted through dye tracing. In addition, the influences of surface water velocity (U), river width narrowing ratio (L/B), the number of spur dikes and riverbed shape on hyporheic exchange were also studied using the temperature tracing method. The results show that the hyporheic exchange path presents a trend of diagonal flow downstream, first conducting turbulent diffusion upstream and then sinking, with different riverbed morphologies having different path lengths. The temperature of surface water has a significant controlling effect on the temperature field of the riverbed. The sediment temperature change from the water–sediment interface to 0.3 m depth is closer to the sinusoidal trend. The change in surface water velocity (U) has the most significant effect on the temperature amplitude ratio. The temperature field below spur dikes is more susceptible to the impact of spur dikes and usually presents a “semielliptical” high-temperature area. With the increase in surface water velocity (U), river width narrowing ratio (L/B), and the number of spur dikes, the range of hyporheic exchange under the dam head also increases, which is positively related to the vertical section hyporheic exchange flux at the dam head. The local backwater area generated by spur dikes also affects pressure field distribution near spur dikes, but the changes caused by the fluctuation of the riverbed itself are greater than the impact of spur dikes on the riverbed. The water–sediment interface velocity at the spur dike increases sharply, and the upstream 1 m of the dam head gradually experiences upflow, drops sharply after reaching the maximum at the dam head, and then approaches zero after 1 m. There is no obvious upwelling and downwelling at the whole interface.

An Integrated Interferometric Fiber Optic Sensor Using a 638 nm Semiconductor Laser for Air-Water Surface Velocity Measurements.

An integrated interferometric fiber optic velocimetry sensor has been proposed and demonstrated at the central wavelength of 638 nm. The sensor is based on the principle of two laser-beams' interference. The light signal scattered from the particles or vapor is demodulated to measure the water surface velocity and water vapor velocity. Three velocity measurement experiments are carried out to measure the velocity, and the experimental data shows that the velocity increases linearly in the range of 4 mm·s-1 to 100 mm·s-1, with a slope of linear fitting curve of 0.99777 and the R-Square of 1.00000. The velocity calculated from frequency shift fits well with the reference velocity. The maximum average relative error in the three velocity measurements is less than 2.5%. In addition, the maximum speed of 4.398 m·s-1 is confirmed in the rotating disk calibration experiment, which expands the sensor's velocity measurement range. To solve the problem that it is difficult to directly measure the velocity of small-scale water surface flow velocity, especially from the aspect of the low velocity of air-water surface, the interferometric fiber optic sensor can be applied to the measurement of water surface velocity and wind velocity on the water surface.

Hyporheic exchange law driven by spur dikes: Numerical modeling

The study of hyporheic exchange and the temperature response law driven by spur dikes is helpful to promote the protection of ecological river environments. Taking the river channel course with a spur dike as the research object, the numerical simulation method was used to study the influence of the river width narrowing rate (L/B), spur dike angle (θ), surface water velocity (U), and hydraulic conductivity (K) on the hyporheic exchange characteristics and the temperature response of the hyporheic zone. Research shows that the degree of hyporheic exchange and the spatial range of the temperature response of the hyporheic zone are positively correlated with the river width narrowing rate, surface water velocity and hydraulic conductivity and negatively correlated with the spur dike angle. The temperature response law of the hyporheic zone is affected by spur dikes in different spatial locations in the following ways, from the cross-section, the upstream response area of the spur dike deepens near the dam bank, while the downstream response area deepens on the other side of the spur dikes, and the downstream response area affected by spur dikes is significantly larger than the upstream response area in the vertical range. From the side section, the response area of the curved boundary appears around the spur dike in the central section of the river, and the curvature radius of the response area of the curved boundary around the spur dike in the side section near the dam is smaller. From the longitudinal section, the sensitivity of the temperature response of the shallow section is significantly stronger than that of the deep section. Consequently, we found that the hyporheic exchange law driven by spur dikes. We offer recommendations for future studies seeking to choose the reasonable structure of the spur dam in practical engineering, and optimize the design of the spur dam.

Investigation of flow characteristics in gabion stepped weirs

Abstract Weirs are used to control and regulate the flow in open channels. In gabion structures, the flow conditions are more complex due to the complexity of flow through the porous body of a gabion. The present study aims to investigate the water surface profile, the overflow velocity profile, and both the through-flow and overflow ratios. Six physical models of the three downstream slopes (V:H 1:1, 1:2, and 1:3) and two types of rockfill (crushed stone and rounded gravel) were investigated. Results show that for the same discharge, the milder slope model (1:3) shows higher water surface and higher velocity than the steeper slope (1:1) with about 9 and 8% on average respectively. The water surface was 60% higher on the lower steps than on the upper steps at the nappe flow regime. Moreover, the low porosity models show a slightly higher velocity and flow depth than higher porosity models for all sections. Furthermore, increasing the porosity from 0.38 to 0.42 led to about a 27% increment in the through-flow ratio. Finally, four relationships were developed to estimate the through-flow and overflow ratios at the upstream and inner sections of the gabion weir. The suggested relationships can be considered novel relationships.

Hydrodynamic considerations for improving the design/evaluation of over-topped bridge decks during extreme floods

Flow over an Iranian bridge deck is studied under an actual extreme flood event happening similarly nowadays in many countries due to climate change. Rigorous transient fluid-structure interaction analyses using the realizable k-ε turbulence model and the VOF Method are conducted. Geotechnical and abutments damages are neglected. Water surface profiles, velocity vectors, and hydrodynamic coefficients are determined. Based on the latest hydrological regime, particularly in supercritical flows, the results are partially compared against the latest advanced design codes, to evaluate the performance of their hydrodynamic and hydraulic provisions in similar incidents. It was acknowledged that the flood loads recommended by the Federal Highway Administration (FHWA) are fairly acceptable, Eurocode-1 predicts them rather accurately but not in extreme cases, and the Australian Standard (AS-5100.2) is less effective due to over-estimation of the hydrodynamic loads. Instead, the latter offers comprehensive user-defined hydraulic conditions. Furthermore, upon gradual rise of the water level to thrice the deck height, bridge stability is found to be at risk due to highly turbulent states. It is recommended that due to such threats, re-evaluation of flood regime, as well as its distinct hydrodynamic properties have to be accounted for, when evaluating existing bridges or designing new ones.

Characteristics of air flow driven by the water free surface in a free-flow spillway tunnel

Air is transported downstream by the water flow in a free-flow spillway tunnel, resulting in high negative pressure, which causes gate vibration and cavitation. In this research work, a physical model of a free-flow spillway tunnel was used to investigate the effects of water surface velocity and the area residual of tunnel cross sections on air movements. The results demonstrate that the air velocity distribution forms an S-shaped curve. As the water surface velocity increases or the area residual decreases, the air velocity increases, and the relative action height of the drag force of water flow on the air increases as well. The air velocity distribution is divided into two exponential distributions at the position where the air velocity drops by 0.2 times that of the water surface velocity. Two formulas for calculating the air velocity of the corresponding exponential distributions are developed. Subsequently, an algorithm for the air demand is presented, and the relative error compared to the reference data was less than ±20%. These results provide a reference for free-flow spillway tunnel ventilation shaft design.

Galois field transformation effect on space-time-volume velocimetry method for water surface velocity video analysis

Galois field transformation effect on space-time-volume velocimetry method for water surface velocity video analysis

Investigating Thermal Controls on the Hyporheic Flux as Evaluated Using Numerical Modeling of Flume-Derived Data

The flux of water through the hyporheic zone (HZ) is controlled by stream bedforms, sinuosity, surface water velocity, local water table, seasonality, and hydraulic conductivity (K) of the bed material. Dependent on both the kinematic viscosity and density of water, K values are a function of temperature. In most studies, changes in temperature have been neglected because of the limited effect either density or viscosity has on K values. However, these variations are important given the role of K in HZ flux, which lead to the hypothesis that flow into the HZ would be more efficient (faster rate and greater depth) under warmer conditions than under cool conditions. To discern how water temperature affects flow depth in the HZ, VS2DHI simulations were created to map flow under both warm and cool thermal conditions. The models employed data collected from a series of varying temperature hydrologic flume tests in which the effects of hyporheic flow altering variables such as sinuosity, surface water velocity and volume, and bed-forms were controlled. Results verify that K values in the HZ were larger under warm conditions generating deeper HZ pathways, while the smaller K values under cool conditions produced shallower pathways. The simulations confirmed a faster speed of frontal movement under warm conditions than cool. Péclet numbers revealed a shallower advective extinction depth under cool conditions as opposed to warm.