Depth-averaged Velocity Research Articles

Numerical estimation of wave breaking forces on seawalls

ABSTRACT This paper presents a computationally efficient numerical scheme to estimate wave forces from plunging breakers on vertical rigid seawalls. The approximated velocity equation, an asymptotical solution of the Green-Naghdi equation in the Camassa-Holm scaling, is utilized to obtain the evolution of the free surface and the depth-averaged horizontal velocity over time, leading to the formation of a plunging breaker. The uniform dynamic pressure along the depth is obtained by utilizing the unsteady Bernoulli equation. The wave forces on seawalls are then determined using Froude-Krylov theory, with adjustments for diffraction effects. The results, while being comparable to some existing formulations, notably differ with some others. This highlights the limitations imposed by the inherent assumptions in the existing empirical formulations and underlines the importance of the proposed methodology that is founded on an accurate modelling of the wave breaking process to estimate wave breaking forces on seawalls.

A method for modeling the lateral distributions of depth-averaged velocities behind an emergent vegetation patch

Aquatic vegetation provides ecological, hydrological, and aesthetic functions for rivers, and measuring velocity in vegetated channels is essential for river management. The paper presents a method for modeling the lateral distributions of depth-averaged velocities behind an emergent vegetation patch. Based on SKM, this approach divides the channel behind an emergent vegetation patch into pseudo-vegetation and free-flow regions, offering analytical solutions for the depth-averaged velocities in these two regions. The model incorporates several critical parameters, including the Darcy–Weisbach coefficient, lateral dimensionless eddy viscosity, drag force coefficient, and secondary flow coefficients. These coefficients are associated with bed friction, vegetation-induced resistance, secondary flow effects, and lateral momentum exchange, respectively, affecting the depth-averaged velocities. A comparison with published experimental data validates that the proposed model can predict the lateral distributions of depth-averaged velocities behind an emergent vegetation patch. A steady wake section exists behind an emergent vegetation patch for low-flow blockage. In the steady wake section, the secondary flow coefficients in pseudo-vegetation and free-flow regions remain relatively constant. Upon exiting the stable wake section, the secondary flow coefficient in the pseudo-vegetation region decreases with increasing distance from an emergent vegetation patch, and it in the free-flow region increases with increasing distance from an emergent vegetation patch. A sensitivity analysis of drag coefficient and secondary flow coefficients suggests that secondary flow coefficient in the free-flow region has a more significant effect on the lateral distributions of depth-averaged velocities compared to drag coefficient and secondary flow coefficient in the pseudo-vegetation region.

Comparison of Summer Coastal Currents off the East Coast of Korea in 2021 and 2022

This study investigates the variability of coastal currents off the east coast of Korea, specifically in the Wangdolcho area of the East/Japan Sea, from June 2021 to October 2022. The observations revealed significant fluctuations in depth-averaged current velocity, with a peak of 0.81 m/s in August 2021 and a minimum of −0.05 m/s in August 2022. These year-to-year variations highlight the complex dynamics of coastal currents influenced by regional wind patterns and mesoscale eddies. In the summer of 2021, the development of offshore eddies, coupled with variable alongshore wind stress, led to increased current velocities and alternating upwelling and downwelling conditions, resulting in abrupt changes in current intensity. Conversely, in the summer of 2022, the negative vorticity in the Korea Strait and negative wind stress curl along the coast likely caused the East Korean Warm Current to shift further offshore, resulting in a weakened southward flow along the coast. This study emphasizes the need for long-term monitoring to better understand the coastal current dynamics and their environmental impacts. The anticipated completion of the Wangdolcho Ocean Research Station is expected to greatly improve monitoring capabilities, providing continuous and comprehensive data that will enhance our understanding of coastal currents and their broader impacts on the marine environment.

A novel framework of the lattice Boltzmann model for multilayer shallow water systems

This study proposes a novel framework of the lattice Boltzmann model for multilayer shallow water equations, considering the mass and momentum exchanges between layers (LABMSWE+). Compared with the original LABMSWE model consisting of N two-dimensional lattice Boltzmann method for shallow water equation (LABSWE) models, the new model includes 1+N LABSWE models. The singular LABSWE model with unit relaxation time is introduced to update the total water depth, and thus, the layer water depths can be obtained explicitly through the fixed layer ratios. The N-layer LABSWE models with the multiple-relaxation-time operator evolve the layer velocities. These two modules are coupled by the total water depth and depth-averaged velocities. The constructed model avoids the freely variable layer thicknesses, which is considered as the main source of the instability. In addition, the mass exchanges enable this model to simulate vertical circulation flows, which are beyond the application of the LABMSWE model. Several numerical tests are then conducted to validate the proposed model. The results show that it exactly satisfies the C-property. In addition, the central difference scheme is more stable and accurate than the upwind and nonequilibrium schemes in the computing of the mass exchanges. The numerical results have an excellent agreement with analytical solutions and reference data, while some unstable and nonphysical results are obtained by the original LABMSWE model. Moreover, the computational time is about 40%–60% of that for the MIKE3, a finite volume solver for the three-dimensional shallow water equations by the Danish Hydraulic Institute.

The streamgauging ruler: A low-cost, low-tech, alternative discharge measurement technique

The streamgauging ruler, a.k.a. transparent velocity-head rod, is an inexpensive, easy, and quick tool for conducting wading discharge measurements in open-channel flows. It provides reliable velocity and discharge measurements when the right measuring conditions, especially minimum flow velocity, are met. The principle is simple: depth-averaged velocity can be computed from the water level difference between the upstream and downstream sides of a plastic board placed into the flow perpendicular to the flow direction. The model developed by INRAE (commercially available for €210) is a little more expensive than previously published models but it significantly improves the ease-of-use and measurement quality. Comparison experiments with reference measurements performed in a laboratory flume and at various field sites confirm the accuracy of the semi-empirical velocity rating established by Pike et al. (2016). Over most of the investigated cross-sections, the discharge measurements are generally within 10% of the reference discharge, when the velocity is greater than 0.2 m/s. However, operator-related effects (site selection, number and distribution of verticals, adjustment and reading of the sliding rulers) can lead to larger errors, hence operator training and care are essential.A first evaluation of the velocity uncertainty related to the velocity-head reading is proposed in the form of an equation that can be used in existing methods for calculating discharge measurement uncertainty. As the method is extremely simple and quick, it is well suited for rapid discharge estimates, training or demonstration, citizen science programmes, or cooperation with services with limited resources and/or lacking specialized expertise in hydrometry. As of July 2024, 304 instruments had been built and released to diverse users around the world, along with a simple discharge computing spreadsheet, a video tutorial, and a field memo.

Turbulence and sediment deposition in a channel with floating vegetation

Floating canopies of vegetation alter the vertical profile of flow velocity within and below canopies, which in turn impacts sediment deposition below canopies. This study explored the impacts of channel-average velocity (U0), vegetation density (a), and relative flow depth (hg/H, where hg is the height of the free flow region below the floating canopy and H is the entire flow depth) on the longitudinal distributions of near-bed turbulent kinetic energy (TKE) and sediment deposition in a channel with a floating vegetation canopy. Below a floating canopy, sediment deposition was correlated with the near-bed TKE. For the low-density and low-velocity cases, sediment deposition was spatially uniform across the entire channel because the near-bed TKE was lower than the critical value for sediment resuspension. As the vegetation density and channel-average velocity increased, the near-bed TKE increased and surpassed the critical TKE, which caused resuspension and reduced deposition below the canopy relative to the upstream reference. For the same vegetation density and channel-average velocity, a lower relative flow depth (hg/H) produced a higher below-canopy depth-averaged velocity and near-bed TKE, resulting in less deposition below the canopy. A model was proposed for predicting the longitudinal evolution of near-bed TKE based on the predicted flow velocity below the canopy throughout the channel. The longitudinal evolution of deposition below a floating canopy was predicted by combining the predicted near-bed TKE with the deposition probability. The predicted near-bed TKE and deposition matched laboratory measurements. Finally, the proposed model can be used to predict the longitudinal profile of deposition below a real Eichhornia crassipes canopy.

Impact of flexible vegetation on hydraulic characteristics in compound channels with converging floodplains

ABSTRACT Floodplains in natural rivers are curved and narrow, rather than following a straight path and the presence of vegetation and varying depth of flow affects the flow parameters of the channels. The purpose of this study is to investigate the effects of the convergence of the channel and relative depth of flow on the depth-averaged velocity (DAV) and boundary shear stress (BSS) of a converging compound channel. The effect of vegetation on DAV and BSS was also deliberated. To examine the effect of vegetation, synthetic grass 8 cm in height was used as a flexible vegetation to depict the natural conditions of the rivers. The DAV was calculated using an acoustic Doppler velocimeter (ADV) and the measurement of BSS was done using the Preston tube technique. After analysing the data, it was revealed that as the convergence of floodplains increases, maximum DAV increases. The presence of vegetation reduces the velocity specifically at lower flow depths. BSS increases with the convergence as well as vegetation. This research provides valuable data and results which will be helpful in better flood management, river restoration, and designing effective hydraulic structures.

Reach-Scale Mapping of Surface Flow Velocities from Thermal Images Acquired by an Uncrewed Aircraft System along the Sacramento River, California, USA

An innovative payload containing a sensitive mid-wave infrared camera was flown on an uncrewed aircraft system (UAS) to acquire thermal imagery along a reach of the Sacramento River, California, USA. The imagery was used as input for an ensemble particle image velocimetry (PIV) algorithm to produce near-continuous maps of surface flow velocity along a reach approximately 1 km in length. To assess the accuracy of PIV velocity estimates, in situ measurements of flow velocity were obtained with an acoustic Doppler current profiler (ADCP). ADCP measurements were collected along pre-planned cross-section lines within the area covered by the imagery. The PIV velocities showed good agreement with the depth-averaged velocity measured by the ADCP, with R2 values ranging from 0.59–0.97 across eight transects. Velocity maps derived from the thermal image sequences acquired on consecutive days during a period of steady flow were compared. These maps showed consistent spatial patterns of velocity vector magnitude and orientation, indicating that the technique is repeatable and robust. PIV of thermal imagery can yield velocity estimates in situations where natural water-surface textures or tracers are either insufficient or absent in visible imagery. Future work could be directed toward defining optimal environmental conditions, as well as limitations for mapping flow velocities based on thermal images acquired via UAS.

Assessing Zebra Mussels’ Impact on Fishway Efficiency: McNary Lock and Dam Case Study

The Columbia River Basin faces a threat from the potential invasion of zebra mussels (Dreissena polymorpha), notorious for their ability to attach to various substrates, including concrete, which is common in fishway construction. Extensive mussel colonization within fishways may affect fish passage by altering flow patterns or creating physical barriers, leading to increased travel times, or potentially preventing passage altogether. Many factors affect mussel habitat suitability including vectors of dispersal, water parameters, and various hydrodynamic quantities, such as water depth, velocity, and turbulence. The objective of this study is to assess the potential for zebra mussels to attach to fishway surfaces and form colonies in the McNary Lock and Dam Oregon-shore fishway and evaluate the potential impact of this infestation on the fishway’s efficiency. A computational fluid dynamics (CFD) model of the McNary Oregon-shore fishway was developed using the open-source code OpenFOAM, with the two-phase solver interFoam. Mesh quality is critical to obtain a reliable solution, so the numerical mesh was refined near the free surface and all solid surfaces to properly capture the complex flow patterns and free surface location. The simulation results for the 6-year average flow rate showed good agreement with the measured water column depth over each weir. Regions susceptible to mussel infestation were identified, and an analysis was performed to determine the mussel’s preference to colonize as a function of the depth-averaged velocity, water depth, and wall shear stress. Habitat suitability criteria were applied to the output of the hydraulic variables from the CFD solution and provided insight into the potential impact on the fishway efficiency. Details on the mesh construction, model setup, and numerical results are presented and discussed.

Physical and Numerical Modeling of Flow in a Meandering Channel

In this study, flow behavior in a meandering channel was investigated experimentally and numerically. The experiments were carried out for nine different cases on a channel consisting of 180° and 120° angle bends following successively. Measurements were conducted employing Acoustic Doppler Velocimetry (ADV) at 13 different points in the inner, middle, and outer bends of the sections located at significant bends along the channel. Depth-averaged velocity, velocity profiles, bed shear stress, and turbulence kinetic energy parameters were considered to understand the flow behavior in the meandering channel. A 1:1 scale numerical model of the experimental setup was generated using the Computational Fluid Dynamics (CFD) method through the verified FLOW-3D software (HYDRO 2022R1). It was found to be successful in estimating all parameters and was capable of investigating the flow behavior in the meandering channel. Additionally, a mesh independence study was performed, and four different turbulence models were compared. As a result, as the flow encountered the first meander in the channel, secondary flow occurred, and lateral momentum transfer took place. Therefore, velocity increased by approximately 30% from the first meander of 180° angles to the second meander of 120° angles. Therefore, the most critical zone was the inner bend of the 120-angle meander.

Stability of boulders on cobble streambeds

The placement of boulders in streams enhances aquatic habitat by increasing the heterogeneity of flow conditions. Practical design must ensure the stability of individual boulders, requiring calculation of their incipient movement conditions. The stability of a boulder on a cobble bed is shown experimentally to depend on its size, the bed material size, the degree of embedment of the boulder, the slope of the bed and the flow velocity and depth. An equation is derived through a pivoting analysis for predicting the relationship between the critical ambient depth-averaged velocity and the critical flow depth; this, together with a resistance equation, can be used to predict the flow conditions for boulder stability. The equation is used to develop a simpler form for unsubmerged spherical boulders and cobbles. The stability equation is tested against the experimental data, using an experimentally determined drag coefficient relationship.

Effect of single vanes on turbulent flow

In response to growing environmental and ecological awareness, eco-friendly in-stream structures such as vanes have been implemented in different parts of the world to enhance stream conditions. FLUENT (ANSYS) was used to perform three-dimensional large eddy simulation to investigate the effect of the vanes permeability rate on flow characteristics. To evaluate the numerical model accuracy, numerical and experimental free surface profiles compared. It is observed that simulated free surface profiles agree reasonably well with measured values. The effect of different permeability rates is obvious in the flow characteristics such as depth-averaged velocity distribution, tip velocity variations, formation of the secondary flows in the flow field, turbulent kinetic energy, and mean kinetic energy contours. On average, maximum velocity values in the flow field is 1,54 times the approach velocity. Tip velocity decreases up to 30,6 % for the 70,0 % permeable vane. Maximum turbulent kinetic energy and mean kinetic energy for the 70,0 % permeable vane decrease up to 58,0 % and 43,3 %, respectively. Generally significant velocity and flow pattern variations around the impermeable vane can be attributed to the local effect of the vane structure and channel cross sectional constriction in comparison to the permeable vanes.

A data-driven approach for predicting depth-averaged velocities in the early stages of underwater glider navigation

Predicting the depth-averaged velocities of underwater gliders in the early stages of navigation is crucial for task performance optimization. However, due to the insufficient number of data samples for the depth-averaged velocities of underwater gliders in the early stages of navigation and the complex mechanisms of depth-averaged flow, task performance optimization remains challenging. This study presents a data-driven approach, the CutMix-augmented Extreme Gradient Boosting (CM_XGB) method, to effectively address this issue. Initially, the CutMix method is employed to augment the depth-averaged velocity samples. Then, the XGB method is applied for prediction. The proposed CM_XGB method is compared to five different prediction methods using three real-world depth-averaged velocity datasets and three error evaluation metrics, and its effectiveness in accurately predicting depth-averaged velocities under the same parameter conditions during the early stages of observation missions is demonstrated. This study shows that the CM_XGB method accurately predicts depth-averaged velocities even with limited data. This method is especially useful for underwater glider missions with data challenges in the initial stages. The success of the CM_XGB method highlights its potential for broader applications in oceanographic research and related fields, providing a valuable tool for scientists and researchers working with limited datasets.

Changes in velocity distribution produced by paddlewheels in algae raceway ponds

Open raceway ponds (RWPs) are widely used in large-scale algae production. To improve the performance of these systems, it is crucial to understand the flow structure throughout the ponds. Computational fluid dynamics (CFD) simulations have been widely used to study the flow field in RWPs. However, such studies typically require assumptions about the distribution of velocities at the inlet boundary of the domain (which is usually taken as the cross-section a short distance downstream from the paddlewheel). In this study, laboratory measurements were carried out to study the flow structure in the vicinity of a paddlewheel in a raceway pond model. Results showed that the paddlewheel may induce complex changes to the distribution of depth-averaged velocities, including the complex inversion of the velocity gradient across the channel. The measured non-uniform distribution of velocities was then used as the boundary condition of a CFD simulation to understand the effects of common assumptions on the accuracy of CFD simulations of flows in RWPs. Furthermore, observations in a field (full-scale) installation corroborated that the presence of a paddlewheel significantly affects the velocity distribution in its vicinity, further strengthening the argument that such changes to the flow should not be disregarded in numerical simulations of RWPs.

Prediction of Depth-Averaged Velocity for Flow Though Submerged Vegetation Using Least Squares Support Vector Machine with Bayesian Optimization

Prediction of Depth-Averaged Velocity for Flow Though Submerged Vegetation Using Least Squares Support Vector Machine with Bayesian Optimization

The relationship between linearised 3D and 2DH models for tidally dominated shallow waters

The water motion computed using 3D and 2DH models in tidally dominated shallow waters can, in some cases, differ significantly. In 2DH models, bed friction is typically parametrised in terms of the depth-averaged velocity, whereas in 3D models, typically the near-bed velocity is used. This difference causes the bed shear stress in 2DH models to point towards the depth-averaged velocity, whereas in 3D models, it points towards the near-bed velocity, which are not necessarily the same. Focussing on linearised barotropic models, we derive an exact friction parametrisation for 2DH models such that the same depth-averaged dynamics are described as in the corresponding 3D model. The result is a convolutional friction formulation where the instantaneous friction depends on the present and past velocities, thus modifying the traditional 2DH friction formulation that only depends on the present depth-averaged velocity. In the case of harmonic (tidal) waves, this parametrisation has a clear physical interpretation and shows that the near-bed velocity should be parametrised as a rotated, deformed and phase shifted variant of the depth-averaged velocity. We demonstrate that in certain regions of the parameter space, it may be impossible to calibrate a 2DH model that uses a traditional friction law to reproduce the water levels from a 3D model, showing that the 3D friction formulation can be crucial to capture the 3D dynamics within a depth-averaged model. This phenomenon is explored in detail in a narrow well-mixed estuary.

An Investigation on Hydraulic Aspects of Rectangular Labyrinth Pool and Weir Fishway Using FLOW-3D

Two different arrangements of the weir (i.e., straight weir and rectangular labyrinth weir) were used to evaluate the effects of geometric parameters such as weir shape, weir spacing, presence of an orifice at the weir, and bed slope on the flow regime and the relationship between discharge and depth, variation and distribution of depth-averaged velocity, turbulence characteristics, and energy dissipation at the fishway. Computational fluid dynamics simulations were performed using FLOW-3D® software to examine the effects on flow conditions. The numerical model was validated by comparing the calculated surface profiles and velocities with experimentally measured values from the literature. The results of the numerical model and experimental data showed that the root-mean-square error and mean absolute percentage error for the surface profiles and normalized velocity profiles of plunging flows were 0.014 m and 3.11%, respectively, confirming the ability of the numerical model to predict the flow characteristics of the pool and weir. A plunging flow can occur at values of L/B = 1.83 (L: distance of the weir, B: width of the channel) and streaming flow at L/B = 0.61 for each model. The rectangular labyrinth weir model has larger dimensionless discharge values (Q+) than the conventional model. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q is proportional to 1.56 and 1.47h, respectively (h: the water depth above the weir). The average depth velocity in the pool of a conventional weir is higher than that of a rectangular labyrinth weir. However, for a given discharge, bed slope, and weir spacing, the turbulent kinetic energy (TKE) and turbulence intensity (TI) values are higher for a rectangular labyrinth weir compared to conventional weir. The conventional weir has lower energy dissipation than the rectangular labyrinth weir. Lower TKE and TI values were observed at the top of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall. As the distance between the weirs and the bottom slope increased, the average depth velocity, the average value of turbulent kinetic energy and the turbulence intensity increased, and the volumetric energy dissipation in the pool decreased. The presence of an opening in the weir increased the average depth velocity and TI values and decreased the range of highest TKE within the pool, resulted in larger resting areas for fish (lower TKE), and decreased the energy dissipation rates in both models.

Different effects between cold front and tropical cyclone on short-term morphodynamics in the Changjiang Delta

Global climate change is altering the frequency and intensity of extreme weather events such as typhoons and cold fronts, and this is inducing physical changes and adaptions in estuaries and coasts. We conducted a field campaign on the subaqueous Changjiang Delta front in September 2019 to improve understanding of storm impact on short-term hydro-morphodynamics. Over an 11-day period, during which both typhoon and cold front events occurred, in-situ data including flow velocities, suspended sediment concentrations (SSC), and bed-level changes were acquired using bottom tripod and buoyage systems, Significant wave height reached 5.0 m during the typhoon, and the depth-averaged current velocity increased to 1.7 m/s. The net near-bottom sediment flux was in the same direction as the wind and was 5.5 times of that under calm weather. During the cold-front, significant wave height reached 2.5 m, and the near-bottom SSC increased to 7.0 kg/m3. Bed-level changes were small (<2 cm) under pre-storm weather, while net deposition and erosion reached 15.8 cm and 16.8 cm, respectively, during the typhoon. Short-term changes in the sediment source-to-sink regime were detected in the subaqueous Changjiang Delta. The cold front enhances seaward sediment flushing from the delta towards the sea, while the typhoon drives sediment transport from the subaqueous delta towards Hangzhou Bay. We also observed rapid bed-level recovery following these extreme events. These findings improve our understanding of sediment transport under stormy conditions.

Risk assessment of metro tunnel evacuation in devastating urban flooding events

Due to the increased frequency and magnitude of urban flooding events, there is an urgent need to study evacuation safety and disaster risk reduction in inundated urban underground spaces. In the literature, there is still a lack of methodologies to assess flooding risk in urban underground areas, which can account for the mutual effects of hydrodynamic characteristics, fluid-human interactions, and human behaviors. This study presents a hybrid model to investigate flood-induced evacuation safety in a metro tunnel based on the coupling of the hydrodynamic module, the human instability module, and the human behavior module. Firstly, floodwater conditions and flow characteristics are calculated by the hydrodynamic module. It is found that evacuation speed decreases with an increase in flow velocity and water depth. The water depth obviously increases after the flow passes the train where the flow velocity decreases with an increase in pressure due to the inference of the obstacle. Secondly, both depth-averaged velocity and depth of floodwater are used as the input parameters for the behavior module and stability module, and the flood hazard regimes for children and adults are then determined in an inundated metro tunnel. The relatively safe evacuation moving speeds for a child and an adult is suggested to be less than 0.5 m/s and 0.6 m/s, respectively. This study provides a novel approach to predicting the evacuation process and supports an early warning system in flood-prone underground areas for sustainable cities.

농업용수로의 표면유속 환산계수 산정

The continuous flow velocity monitoring has become a difficult and expensive task in hydrological survey&#x0D; due to unpredictable rainfall patterns. Therefore, the velocity measurements using a non-contact type&#x0D; flowmeter is more effective and easy to use. The generally used average velocity conversion factor 0.85&#x0D; does not take into account the regional characteristics such as curves of a river, bed materials which&#x0D; consequentially affects the vertical flow characteristics. Therefore, considering the those characteristics of&#x0D; irrigation channels of two small reservoirs (Ssangam and Hangye reservoir), results showed that the gentle&#x0D; bed slope of irrigation channel of the Ssangam reservoir, has a velocity conversion factor of 1.06 and the&#x0D; depth-averaged velocity of V0.6, was measured to be higher compared to the surface velocity. On the other&#x0D; hand, velocity conversion factor of 0.83 was computed in case of Hangye reservoir with a relatively sharp&#x0D; bed slope, which is similar to the generally used velocity conversion factor of 0.85. This shows that the&#x0D; bed slope is the dominant factor in affecting the depth-wise velocity characteristics of a waterway.