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We conducted a direct numerical simulation (DNS) study to investigate the impact of surface undulation steepness on rough wall turbulent heat transfer. The flow geometry was turbulent open-channel flow over three-dimensional sinusoidal rough surfaces. To examine the effects of steepness, we systematically varied the streamwise and spanwise wavelengths of the sinusoidal roughness while keeping the roughness height constant. The friction Reynolds number ranged from 180 to 600, and we considered a passive scalar with the fluid Prandtl number was 0.7, assuming air flow conditions. In the fully rough regime, the velocity roughness function is expressed as a function of the inner-scaled equivalent sand grain roughness k s + independent of steepness, whereas the steeper surfaces with shorter wavelengths result in larger temperature roughness functions at the same k s + value. Analysis of the physical mechanisms that increases the roughness function shows that the pressure drag primarily contributes to the increase in the velocity roughness function, while the temperature roughness function is mainly augmented by the roughness-induced wall heat transfer term, correlating with the steepness of the surface undulations. It is also suggested that the effective slope, which quantifies the steepness of rough surfaces, could improve the predictive accuracy of existing correlations for the temperature roughness function. • DNS of turbulent heat transfer over sinusoidal roughness is performed. • Effects of steepness of rough surfaces on turbulent heat transfer are studied. • Spatial and Reynolds averaged equations are analyzed. • Predictive model of temperature roughness function is proposed. [ABSTRACT FROM AUTHOR]

Earthquake induced tsunamis pose devastating threat to coastal communities worldwide. Accurate description of tsunami generation by kinematic fault rupture is of importance to investigate earthquake events and evaluate tsunami impacts. The paper develops a multi-layer non-hydrostatic model with a kinematic bottom boundary condition and conducts comprehensive validation to examine the model's capability in resolving seismic tsunami generation. The two-dimensional governing equations of the multi-layer non-hydrostatic free-surface flow system equipped with kinematic seafloor displacement is first introduced in Cartesian coordinates. A combined finite difference and finite volume scheme is utilized to discretize the governing equations with flow variables arranged on a staggered Arakawa C-grid. Application of pressure correction technique to the discretized formulations yields Poisson-type equations from which the non-hydrostatic pressure is solved for the next time step to complete the temporal integration. Based on existing analytical solutions, four groups of tsunami generation cases considering broad ranges of source parameters, including horizontal scale, rise time, and rupture velocity, are designed to demonstrate performance of the proposed non-hydrostatic model with one-, two-, and three-layers as well as the hydrostatic one. Comparison of 59 generation cases including extreme scenarios indicates the non-hydrostatic model performs better than the hydrostatic model in reproducing the entire waveform and predicting the maximum wave amplitude. High modeling accuracy can be achieved through incorporation of more layers. The proposed multi-layer non-hydrostatic model is a powerful tool for investigating earthquake source mechanisms and evaluating coastal tsunami hazards. • A multi-layer non-hydrostatic model is developed to resolve tsunami generation. • Fifty-nine tsunami generation cases are designed to give comprehensive validation. • The non-hydrostatic model shows good performance in reproducing tsunami waveform. [ABSTRACT FROM AUTHOR]

Flat grooved heat pipes (HPs) have become essential in advanced thermal management solutions across various engineering applications. Modeling these devices, especially multichannel flat grooved HPs, involves significant challenges due to complex phenomena such as phase-change heat transfer and free-surface flow, requiring substantial computational resources, time and expertise. These constraints often limit the full exploration and optimization of HPs' potential in diverse applications. To address this gap, an accelerated 3D computational fluid dynamics (CFD) modeling approach is presented in this study. This novel method begins with a detailed 3D modeling of a single groove, developed using kinetic theory and facilitated by CFD software. The results from this model are then applied as boundary conditions to simulate the entire HP in a multichannel configuration. The importance of this methodology is further highlighted by the alignment of simulation results with experimental observations. The approach significantly enhances computational efficiency by reducing the number of iterations by 10% and computational time by 80%, resulting in a five-fold speed-up. The methodology enables accelerated, comprehensive modeling of multichannel variations and delivers critical insights for optimizing the design of multichannel flat grooved HPs for various engineering applications. • Comprehensive 3D CFD model for multichannel flat grooved heat pipes. • Rigorous thin-film modeling of phase-change heat transfer. • Accelerated modeling reduces iterations and computational time by 80%. • An extended model for multichannel heat pipe adapts single-groove insights. • Validation with experimental data ensures accuracy and reliability. [ABSTRACT FROM AUTHOR]

In order to address the complex moving boundary problem and violent free-surface flows involved in the process of landslide tsunamis, this paper proposes a new low-dissipation Riemann-solver-based smoothed particle hydrodynamics (SPH) numerical model. In this model, the complex fluid-rigid slide interaction and friction effects on landslides are handled by an improved motion boundary approach based on a one-sided Riemann scheme. A weighted essentially non-oscillatory (WENO) reconstruction method is introduced to reduce excessive dissipation of the fluid caused by rigid landslide impact. The kernel gradient accuracy is assured by applying the corrected smoothed particle method (CSPM) into a continuity equation. Single-block and multi-block landslide tsunamis in two-dimensional (2D) or three-dimensional (3D) applications are simulated with different particle resolutions, and the results are compared to those of other numerical models and experimental results. The landslide trajectories obtained from the modified boundary model are in good agreements with the experimental values. Free-surface flows variations during the propagation are properly captured in the current simulations without introducing any artificial viscosity term, and the wave peaks exhibit deviations of −14%–10.5% from the experimental values, thus verifying the usability and robustness of the proposed Riemann-SPH model. • A new low-dissipation Riemann-SPH model is proposed to simulate the generation and propagation of landslide tsunamis. • An improved motion boundary method based on a one-sided Riemann scheme is proposed to handle the moving boundary problem. • The WENO-Z reconstruction is introduced to minimize the numerical dissipation in calculating the fluid force. • The contact force model is improved and a numerical perturbation is introduced. [ABSTRACT FROM AUTHOR]

In this work we present a robust finite element procedure for modeling 3D nonlinear liquid sloshing phenomena using standard potential theory. A well known issue in simulating inviscid free-surface flows is an onset of spurious oscillations ("saw-tooth") caused by numerical instabilities. Here we demonstrate that a novel post-processing procedure, based on the Savitzky–Golay filtering algorithm allows us to overcome this challenge. It is shown that unphysical numerical oscillations are smoothed out and nodal free-surface position along with velocity values are accurately recovered from conventional finite element analysis. Sloshing dynamics (limited to non-overlapping waves) is investigated for a partially filled vertical circular cylinder subjected to a broad range of harmonic and ElCentro seismic excitations. The results compare well with those obtained with finite volume OpenFOAM software. One-way coupling FSI analysis is also included to estimate stress and deflection experienced by cylindrical containers. • Robust FE solution of 3D nonlinear sloshing dynamics modeled by potential theory. • Savitzky-Golay filtering for effective and accurate numerical oscillation smoothing. • One-way FSI analysis which includes stress and deflection parametric study. • Sloshing induced by seismic excitation for small to steep non-overlapping waves. [ABSTRACT FROM AUTHOR]

At weirs and dams, the spillway flow is a high-velocity turbulent motion operating at very-large Reynolds numbers and physical measurements are challenging. In these high-speed free-surface flows, the upstream flow is not aerated and some air entrainment takes place downstream of the inception of free-surface aeration. The state-of-the-art knowledge in large dam spillway hydrodynamics currently reaches a major knowledge gap because of a lack of detailed quantitative field measurements in both the non-aerated and air-water flow regions. In this contribution, a review of prototype observations and measurements is presented based upon optical data sets conducted between 2010 and 2022 during floods at several large dam spillways in eastern Australia, with a focus on the key requirements for successful optical velocity measurements in high-velocity (prototype) spillway flows. The experience and expertise gained in these studies provide new insights into the operation of large dam spillways and their modelling. The intricacy of field measurement techniques is discussed using the experience at dam spillways during large floods, encompassing optical velocity measurements of spillway hydrodynamics at two structures. Overall, the paper presents current challenges on the modelling of large dam spillway flows. • Observations and measurements at large dam spillways are too few. • Prototype observations were successfully gained during 2010-2022 flood events. • A review of field experience and optical velocity measurements was conducted. • Successful optical flow velocity measurements of high-Reynolds-number spillway chutes were achieved. [ABSTRACT FROM AUTHOR]

Numerical simulation of moving boundary flows with topological changes in the fluid domain presents a significant challenge, as traditional mesh-based formulations cannot directly deal with these changes. In this work, we propose a novel position-based Particle Finite Element Method derived from the stationary total mechanical energy principle applied to incompressible Newtonian flows. The use of positions as the main variables instead of velocities might have some advantages in certain scenarios: i. it eliminates the need for an additional step to compute displacements based on particles velocities; ii. it naturally accounts for the geometric non-linearities through the deformation gradient and iii. the resulting approach seems ideal to simulate FSI problems in a monolithic way as hyperelastic materials are usually written in terms of position or displacement. The solution process follows the well-established PFEM, where the entire domain is discretized with particles and a finite element mesh is generated over them to solve the motion equations using the proposed approach. The reference is updated whenever the mesh needs to be reconstructed, resulting in a partially updated Lagrangian description. The incompressibility constraint is enforced using a mixed approach, where pressure is interpolated in the same polynomial basis as the positions. LBB condition is circumvented by applying a Lagrangian version of the pressure stabilization/Petrov–Galerkin (PSPG) technique. The proposed formulation is verified through numerical examples, demonstrating its robustness, accuracy, and applicability. • Position-based PFEM for moving boundary flows with topology changes. • Method for incompressible flows from stationary total mechanical energy principle. • Isoparametric approach with no need for additional step to compute displacements. • Flexible formulation for total, partially updated or updated Lagrangian descriptions. • Easy monolithic coupling with structural solvers using positions as main variables. [ABSTRACT FROM AUTHOR]

We develop a parallel finite element computational framework based on the level set method and adaptive octree meshes for free‐surface flows. The discretized governing formulations are stabilized using a residual‐based variational multiscale method. We redistance the level set field and restore mass conservation after each time step. The octree mesh is adaptively refined according to the interface location, and the load is rebalanced across processes. The adaptive octree‐based level set method is verified and validated using a canonical problem of dam break without obstacle, and a mesh convergence study is carried out in this problem. The surface tension is further considered via a continuum surface force model in the method and validated using a problem of single bubble rising in ambient liquid. A parallel scaling analysis of this method is also performed for the bubble rising problem. The energy equation and Marangoni effect are finally considered in the method and validated using a problem of thermocapillary droplet migration with and without gravity. This work illustrates the ability of the framework to accurately model and predict free‐surface flows under various scenarios. [ABSTRACT FROM AUTHOR]

The emptying process of initially stagnant full-pipe flows in sewer systems and water transmission lines was extensively studied in the literature. The following air intrusion and depressurization wavefronts can cause several issues such as the collapse of pipes, damage to joints, and valves. However, there is a lack of study on the emptying process when the flow has initial velocity. Thus, the present study focuses on the emptying process of a full-pipe flow with an initial flow rate, which decreases during the emptying process. For this purpose, two experiments without and with initial flow rates were performed in a reservoir-circular pipe system. In both experiments, an air cavity intrusion starts downstream of the pipe at the top of the free-surface flow and propagates upstream. It was found that when there is no initial flow rate, the pressure inside the cavity is atmospheric. However, when there is an initial flow rate, at the onset of the air intrusion, a subatmospheric pressure develops inside the air cavity. It was also found that the magnitude of this subatmospheric pressure decreases when the cavity further propagates upstream. In addition, when there is an initial flow rate, the cavity appears at a certain driving pressure. [ABSTRACT FROM AUTHOR]

This study demonstrates an approach to expand and improve the current prediction capability of the National Water Model (NWM). The primary objective is to examine the potential benefit of real-time local stage measurements in streamflow prediction, particularly for local communities that do not benefit from the improved streamflow forecasts due to the current data assimilation (DA) scheme. The proposed approach incorporates real-time local stage measurements into the NWM streamflow DA procedure by using synthetic rating curves (SRC) developed based on an established open-channel flow model. For streamflow DA and its evaluation, we used 6-yr (2016–21) data collected from 140 U.S. Geological Survey (USGS) stations, where quality-assured rating curves are consistently maintained (verification stations), and 310 stage-only stations operated by the Iowa Flood Center and the USGS in Iowa. The evaluation result from NWM's current DA configuration based on the USGS verification stations indicated that DA improves streamflow prediction skills significantly downstream from the station locations. This improvement tends to increase as the drainage scale becomes larger. The result from the new DA configuration including all stage-only sensors showed an expanded domain of improved predictions, compared to those from the open-loop simulation. This reveals that the real-time low-cost stage sensors are beneficial for streamflow prediction, particularly at small basins, while their utility appears to be limited at large drainage areas because of the inherent limitations of lidar-based channel geometry used for the SRC development. The framework presented in this study can be readily applied to include numerous stage-only stream gauges nationwide in the NWM modeling and forecasting procedures. [ABSTRACT FROM AUTHOR]

We present a local analysis of turbulence in open-channel flows, using time-series velocity measurements. The method is based on a local form of the Kolmogorov "4/3-law" of homogeneous turbulence for the third-order moment of velocity increments. Following the Duchon and Robert ["Inertial energy dissipation for weak solutions of incompressible Euler and Navier–Stokes equations," Nonlinearity 13, 249 (2000)] idea, which envisions turbulence dissipation as a lack of smoothness of the Navier–Stokes solutions, we estimate the local energy flux in a laboratory experiment with natural bed flows. Taking advantage of one-dimensional filtering techniques, under reasonable hypothesis, simple expressions of a surrogate of the energy flux are provided. The local energy flux surrogate reveals that, independently of the geometry, turbulence dissipation is highly intermittent. Among a variety of eddies that populate turbulence, dissipative singularities appear in sheet-like, tube, and filament structures, with large amplitude variations and rotations. This simplified technique can be applied to any measurement of hydrodynamic turbulence. [ABSTRACT FROM AUTHOR]

This paper proposes a modification to a previous shock tracking–capturing approach used for simulating transient flows in stormwater systems. Based on the Godunov-type finite-volume (FV) method, this modified approach uses two governing equations for free-surface and pressurized flows discretized. The free-surface flow is simulated using an explicit FV method. However, the pressurized flow is discretized on one control volume and simulated using an implicit FV method. Different examples will be solved to examine the abilities of the proposed modified approach. The examples are pressurized and partially pressurized flows, including the water hammer, the pipe-filling bore advancement, and air pocket entrapment problems. The partially pressurized flow following air pocket entrapment is analyzed under different conditions including various ranges of driving pressure, air and water lengths, as well as dry-bed and with and without air-release conditions. It will be shown that the proposed modification can result in improving the overestimated peak values and the underestimated attenuation of pressure distribution. In addition, it will be shown that the proposed modified approach exhibits less oscillatory behavior, particularly in simulating pipe-filling bore advancement. [ABSTRACT FROM AUTHOR]

Flow resistance is a critical calculation parameter in hydraulic engineering. In this study, the roughness coefficient of a circular drainage pipe with sedimentation was investigated under open-channel flow conditions using experimental measurements and numerical calculations. The ratio of the height of the sediment placed in the pipe to the diameter was defined as the sedimentation degree. The Manning roughness coefficient (n) was determined for pipes with different sedimentation degrees. Moreover, numerical simulations were performed for circular pipes with diameters of 0.152 m and a slope of 0.003, with discharges varying between 1 and 8 L/s. The results of the numerical calculations were validated in terms of the water surface and Manning's n using the corresponding experimental data. Accordingly, an equation in the form of the Moody formula was proposed to estimate the roughness coefficient. Subsequently, the predicted Manning roughness coefficient obtained through the proposed equation was compared with independent experimental results. The results indicate that the equation accurately predicts Manning's n in a pipe with sedimentation, which can provide a theoretical basis for the design of drainage pipelines. [ABSTRACT FROM AUTHOR]

For the purpose of studying the dynamic and inner flow features of an open inlet channel axial flow pump unit, in the present study, numerical calculations using the SST k-ω turbulence model are applied to an open inlet channel axial flow pumping unit based on the NS equation, and experimental validation is then performed. The experimental output indicates that the designed working conditions are Q = 350 L/s, head H = 5.065 m, efficiency η = 79.56%, and the maximum operating head is H = 9.027 m, which is about 1.78 times that of the design head; further, the pump device can operate in a wide range of working conditions. In addition, the design working conditions are within the range of high-efficiency operating conditions. The calculated values and the experimental comparison are all within a 5.0% margin of error; further, the numerical calculations are reliable. The hydraulic loss of the inlet channel under the design condition Q = 350 L/s is 0.0676 m, which satisfies the relationship of the quadratic function. The uniformity of the impeller inlet velocity is 80.675%, and the weighted average angle of the velocity is 79.223°. The hydraulic loss of the outlet channel under the design condition Q = 350 L/s is 0.3183 m, and the hydraulic loss curve is a parabola with an upward opening. The flow state of the pump device is sensitive to changes in the working conditions; additionally, the flow state is optimal under the design working conditions. In this study, the energy and inner flow features of the open inlet axial flow pumping units are revealed, and the research outcomes can be used as a reference for the design and operation of similar pumping units. [ABSTRACT FROM AUTHOR]

In this paper, a free surface flow solver based on an improved coupling method for practical, highly nonlinear, complex free-surface flows is presented. The coupling method which is based on taking the advantages of the continuity and boundedness properties of the conservative level-set (LS) function and the mass conservation property of the VOF approach is integrated into a Navier-Stokes solution to build a new free surface solver. The developed solver is then validated with several practical free surface flows of engineering applications. The test cases are selected so that the developed solver is challenged in simulations of flows with a large scale of density ratio, high-nonlinear, and complicated free surface in a wide range of engineering applications to explore its capability. The simulated flow fields are presented and compared with the available experimental data and of other numerical simulations. Good agreement is achieved implying the capability of the developed solver, and also exhibiting the ability to extend to other applications. [ABSTRACT FROM AUTHOR]

The present work studies the hydro-gasdynamic analogy between a shock wave, occurring in supersonic internal or external compressible flows, and a hydraulic jump, a sort of normal shock occurring in open-channel flows. It consists of an extensive theoretical framework followed by a practical analysis, the aim of which was to experimentally trigger the hydraulic jump, both normal and oblique, while using a low-cost designed lab prototype. The assembly development, called 'water table', arises from the necessity of economical alternatives to expensive supersonic wind tunnels in the experimental study of compressible fluid dynamics. With this objective in mind, a hydraulic canal based on a Laval nozzle was constructed where water flow could accelerate from subcritical to critical to supercritical regime and then return to subcritical regime through a hydraulic jump. In addition, multiple design alternatives were evaluated considering environmental, economic, functional and aesthetics factors. A low-cost implementation was the critical criterion in the design process. The measurements have revealed that the geometry of the nozzle and the wedges designed as obstacles to cause obliquity are the most significant and influential elements in the formation of a hydraulic jump in the experimental set-up. Regarding the experimental variables, the experiments demonstrate the effect of the upstream and downstream heights of the hydraulic jump in the data collection. This experience is a step forward in supporting students in the understanding of compressible flow and its principles by providing an in-house experimental set-up that promotes active learning, motivation and interest in fluid mechanics. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical and numerical analysis of the length required for roll waves to become stationary in a free-surface laminar flow of a Newtonian fluid. Two types of stability analysis are brought to verify flow stability and obtain parameters for wave growth rate in a Saint-Venant like system. Then, numerical simulations are performed of the free-surface laminar transient flow of glycerin. The Navier-Stokes equations were solved using the finite volumes method, Euler schemes and PIMPLE, and the VoF technique to solve the interface. Boundary conditions were specified to obtain a steady and uniform regime given a Froude number. Then, a sinusoidal perturbation with controllable properties was applied to the inlet velocity. From the numerical results, the spatial development of the roll waves was evaluated, focusing on the establishment length as a function of the Froude number and the perturbation amplitude. The analyses performed allowed the verification of the influence of flow hydraulic regime over the establishment length, and it was possible to obtain a new equation as a function of the perturbation amplitude. [ABSTRACT FROM AUTHOR]

Experiments were conducted in open channel flows under near-critical mobility conditions to quantify local evolution of the sediment bed induced by emergent and submerged rectangular vertical porous walls in yawed conditions. The goal was to design minimally invasive hydraulic structures, or vanes, redirecting sediment mass flux to be coupled with intake pipes in dam bypass systems for sustainable sediment redistribution. Theoretical scaling for the maximum scour depth derived from the phenomenological theory of turbulence was extended to our specific emergent vane geometry under varying structure porosity, angle, and size. Most of our attention was devoted to quantifying the asymmetry of the induced bathymetric effects and developing an appropriate metric to identify the most effective vane configuration to steer sedimentation along a desired direction. The orientation angle was shown to significantly affect the geometry and volume of the scour and deposit, the spanwise shift of the deposit volume, and the velocity profiles in the wake, for both emergent and submerged vane configurations. The optimal streamwise and spanwise spacings in yawed, submerged, porous vane arrays were determined based on the spatial evolution of the wake flow, ensuring minimal sheltering effects and maximal lateral directionality of the sediment deposit. We here provide supporting evidence that wind and marine hydrokinetic turbine wake models can be extended to the case of porous planar structures to capture the key physical mechanisms governing sediment deposits. [ABSTRACT FROM AUTHOR]

Elder's equation for the longitudinal dispersion coefficient in two-dimensional solute transport analysis cannot be applied to curved channels because the vertical distribution of the longitudinal velocity does not obey the logarithmic law in the bends of an open channel. In this study, a two-dimensional longitudinal dispersion coefficient based on an equation that can appropriately describe the vertical distribution of flow velocity in open-channel bends is derived theoretically. The proposed equations for the vertical velocity distribution and dispersion coefficient are compared and verified with values measured from two different types of open channels, i.e., a laboratory channel and a natural-like channel. The increase in the longitudinal dispersion coefficient based on the difference in the vertical distribution of the flow velocity is evaluated quantitatively. In terms of the longitudinal dispersion coefficient, no significant difference is observed between the observed dispersion coefficient based on the concentration data and the coefficient value calculated using the equation proposed in this study. The dispersion equation proposed in this study can be easily applied to assign the value of the longitudinal dispersion coefficient for the two-dimensional mixing modelling in bends using basic hydraulic factors. [ABSTRACT FROM AUTHOR]

Hamiltonian variational principles have provided, since the 1960s, the means of developing very successful wave theories for nonlinear free-surface flows, under the assumption of irrotationality. This success, in conjunction with the recognition that almost all flows in the sea are not irrotational, raises the question of extending Hamilton's principle to rotational free-surface flows. The Euler equations governing the bulk fluid motion have been derived by means of Hamilton's principle since the late 1950s. Nevertheless, a complete variational formulation of the rotational water-wave problem, including the derivation of the free-surface boundary conditions, seems to be lacking until now. The purpose of the present work is to construct such a missing variational formulation. The appropriate functional is the usual Hamilton's action, constrained by the conservation of mass and the conservation of fluid parcels' identity. The differential equations governing the bulk fluid motion are derived as usually, applying standard methods of the calculus of variations. However, the standard methodology does not provide enough structure to obtain the free-surface boundary conditions. To overcome this difficulty, differential-variational forms of the aforementioned constraints are introduced and applied to the boundary variations of the Eulerian fields. Under this transformation, both kinematic and dynamic free-surface conditions are naturally derived, ensuring the Hamiltonian variational formulation of the complete problem. An interesting feature, appearing in the present variational derivation, is a dual possibility concerning the tangential velocity on the boundary; it may be either the same as in irrotational flow (no condition) or zero, corresponding to the small-viscosity limit. The deeper meaning and the significance of these findings seem to deserve further analysis. [ABSTRACT FROM AUTHOR]

Investigating the wave hydrodynamics of free-surface flow over rippled bottoms is a continuing concern due to the existence of submarine multiple sandbars and ambient flow in coastal and estuarial areas. More attention to free-surface wave stimulation has been received from the perspective of resonant wave-wave interaction, which is an intensive way for wave energy transfer and a potential way for wave component generation. However, the basic behavior of the triad resonant interaction of this problem is still limited and unclear. In this study, the triad resonant interaction induced by steady free-surface flow over rippled bottoms is numerically investigated by means of the High-Order Spectral (HOS) method. By considering the interactions among free-surface waves, ambient current, and rippled bottoms, the numerical model is applied for this situation based on Zakharov equation with ambient flow term. The temporal evolution of the triad resonant wave amplitude has been numerically investigated and compared well with multiple-scale expansion perturbation theory. Specifically, the temporal evolution behaviors of all six triad resonant wave components are confirmed by both numerical simulation and nonlinear perturbation analysis. [ABSTRACT FROM AUTHOR]

Flow features of a meandering river can vary seasonally and widely in the boreal zone, as seasonal variation in discharges affect the properties of meander bends and the spatial location of flow magnitudes. However, a better understanding of the impacts of consecutive high‐discharge events in the boreal zone requires further analyses. Thus, the impacts of the fluvial processes and their magnitudes on different types of meander bends (e.g., sinuosity, symmetricity) were analysed throughout an open‐channel flow period, using accurate flow measurements and hydrodynamic (two‐dimensional) modelling. In particular, the research compared the impacts of different discharge events in magnitude and length of river evolution, and whether there is a difference in the erosion forces of the rising and falling phases of discharge hydrographs, and which of the phases has the greatest relevance to erosion forces. A case study was carried out in a middle boreal zone meandering river (Koitajoki in eastern Finland) during the 2020 open water season from May to October. Five different types of meander bends were considered in the study area. Flow magnitudes and shear forces were at their strongest during the spring flood peak, which is normally considered as the highest flow event during the hydrological year. Exceptionally, the largest summer discharge event reached a level that was close to the spring floods' maximum erosional capabilities. Bed shear stress values indicated the falling phases of the flood hydrographs are more important to river evolution than during the ascent stage, as the long duration of the flood downstage contributes more strongly to meander bend erosion and development. The smaller the curvature and larger the sinuosity of the bends, the more variation in erosional forces occurs between discharge stages. The study provides new insights into seasonal fluvial processes in boreal river meander bends as well as reinforces results from earlier river studies. [ABSTRACT FROM AUTHOR]

Two decades of research has shown that the global river network emits significant amounts of greenhouse gas. Despite much progress, there is still large uncertainty in the temporal dynamics of gas exchange and thus carbon emissions to the atmosphere. Much of this uncertainty stems from a lack of existing tools for studying the spatiotemporal dynamics of gas exchange velocity k600 ${k}_{600}$ (the rate of this diffusive transport). We propose that the NASA/CNES/UKSA/CSA Surface Water and Ocean Topography (SWOT) satellite can provide new insights to fluvial gas exchange modeling upon launch and subsequent data collection in 2022. Here, we exploit the distinct geomorphology of SWOT‐observable rivers (>50 m wide) to develop a physical model of gas exchange that is remotely sensible and explains 50% of log‐transformed variation across 166 field measurements of k600 ${k}_{600}$. We then couple this model with established inversion techniques to develop BIKER, the "Bayesian Inference of the k600 ${k}_{600}$ Exchange Rate" algorithm. We validate BIKER on 47 SWOT‐simulated rivers without an in‐situ calibration, yielding an algorithm that predicts the k600 ${k}_{600}$ timeseries solely from SWOT observations with a by‐river median Kling‐Gupta Efficiency of 0.21. BIKER is better at inferring the temporal variation of gas exchange (median correlation coefficient of 0.91), than reproducing the absolute rates of exchange (median normalized RMSE of 51%). Finally, BIKER is robust to measurement errors implicit in the SWOT data. We suggest that BIKER will be useful in mapping global‐scale fluvial gas exchange and improving CO2 $\left[\mathrm{C}{\mathrm{O}}_{2}\right]$ emissions estimates when coupled with river CO2 $\left[\mathrm{C}{\mathrm{O}}_{2}\right]$ models. Key Points: BIKER (Bayesian Inference of the k600 ${k}_{600}$ Evasion Rate) algorithm predicts gas exchange velocity from simulated Surface Water and Ocean Topography (SWOT) data without calibrationBIKER is marginally influenced by expected SWOT measurement errorsBIKER and near‐daily SWOT data will allow for the study of gas exchange spatiotemporal dynamics at novel temporal resolutions [ABSTRACT FROM AUTHOR]

In this study, we present a three-dimensional numerical model for the interaction of flow with submerged flexible vegetation, based on a large-eddy simulation and the immersed boundary method. The model innovatively realises the interaction between the flow and highly flexible vegetation with clustered leaves. Besides being a three-dimensional model of motion with full degrees of freedom, this study improves the consideration of the motion of the vegetation in all directions, and in addition the energy and momentum transfer in the spanwise direction. Furthermore, we perform a flume experiment for the flow with submerged flexible vegetation, the results of which are used to validate the simulation effects of the numerical model. It is found that the numerical model can effectively simulate the velocity profiles and the movement of vegetation induced by the flow. Using the model to analyse the flow–vegetation interaction, we find that the movement of vegetation is closely related to the flow velocity. As the flow velocity increases, both the offset angle and the vegetation swaying amplitude increase. Compared to vertical rigid vegetation, the tilting of flexible vegetation does not significantly change the velocity difference and the magnitude of the turbulent kinetic energy between the inside and the outside of the vegetation canopy, but it does weaken the disturbance to flow, thus reducing the resistance to flow. However, the swaying of vegetation dose significantly increase the velocity difference between the inside and the outside of the canopy. It forms Kelvin–Helmholtz hairpin vortices intensifying the turbulence production, and enhancing the disturbance and resistance to flow. [ABSTRACT FROM AUTHOR]

This article investigates two aspects of the generalized Broyden quasi‐Newton method that have a major impact on its convergence: the initial approximation of the Jacobian and the presence of nonlinearities in the secant conditions. After reformulating the common representation of generalized Broyden, a straightforward interpretation is given. This leads to a natural extension of the method in which an application‐dependent physics‐based surrogate model is used as initial approximation of the (inverse) Jacobian. A carefully chosen surrogate has the potential to greatly reduce the required number of iterations. The behavior of generalized Broyden depends strongly on the parameter that determines how many secant conditions are satisfied by the Jacobian approximation. Respecting all secant conditions reduces it to Anderson acceleration; a single one to Broyden's original method. An analysis demonstrates that these two variants behave very differently when nonlinearities are present in the secant conditions: they are ignored by Broyden, but can destabilize Anderson. On the other hand, the analysis shows that Broyden tends to neglect small linear information, possibly reducing convergence speed. To mitigate stability problems with Anderson acceleration, a practical method to detect and remove nonlinear secant information is introduced next. Finally, we solve a steady free‐surface‐flow problem using several generalized Broyden variants, testing the influence of the surrogate, the nonlinearities and the combination thereof. The results agree with the theoretical predictions, showing large differences in convergence behavior. Furthermore, the proposed method effectively negates the problems related to nonlinearities in this case. [ABSTRACT FROM AUTHOR]

Steady plane turbulent free-surface flow over a slightly wavy bottom is considered for very large Reynolds numbers, very small bottom slopes, and Froude numbers close to the critical value 1. As in previous works, the slope and the deviation from the critical Froude number are assumed to be coupled such that turbulence modeling is not required. The amplitudes of the periodic bottom elevations, however, are assumed to be half an order of magnitude larger than in the previous case of bumps or ramps of finite length. Asymptotic expansions give a steady-state version of an extended Korteweg–deVries (KdV) equation for the surface elevation. The extension consists of a forcing term due to the unevenness of the bottom and a damping term due to friction at the bottom. Other flow quantities, such as pressure, flow velocity components, local Froude number and bottom friction force, can be expressed in terms of the surface elevation. Exact solutions of the extended KdV equation, describing stationary cnoidal waves, are obtained for bottoms of particular periodic shapes. As a limiting case, the solitary waves over a bottom ramp are re-obtained in accord with previous results. [ABSTRACT FROM AUTHOR]

In the present work, the flow topologies of a generalized torpedo-like geometry were investigated experimentally via Particle Image Velocimetry (PIV) and dye visualization. The study was conducted at length based on the Reynolds number of Re = 20 × 103 and 40 × 103. The torpedo-like geometry was positioned at ratios of immersion between 0.50 ≤ h/D ≤ 3.50 to investigate the free-surface effect on the present results, comparatively. PIV measurements provided ensemble-averaged velocity fluctuations, turbulent kinetic energy and Reynolds stress correlation with spectral analysis of the vortex-shedding mechanism. It is observed that different vortex shedding mechanism occurs depending on the immersion ratio. At h/D = 0.5, wake flow is characterized by the lower shear layer while upper shear layer dominates it at h/D = 0.75 and 1.00. The influence of the free-surface on flow characteristics is found to be negligible at h/D > 2.00 for both Reynolds numbers. Alternating vortex shedding occurs and the wake regions at h/D = 3.5 became nearly symmetrical. The size of the wake zone is moved closer to the stern of the torpedo-like geometry at Re = 40 × 103 and causes a smaller recirculating region. Spectral analysis of the streamwise velocity revealed a decreasing trend of Strouhal number with increasing immersion ratios. The changing of the Strouhal number showed a significant increase at h/D = 0.75 for Re = 20 × 103 an ever-decreasing trend for Re = 40 × 103. [ABSTRACT FROM AUTHOR]

Thermal stratification can lead to the damping of turbulence, which reduces the mixing of solutes in a fluid body. A series of direct numerical simulation (DNS) solutions sweeping through a range of four different meandering channel curvatures, from a sharp to mild curvature range, are obtained to investigate the effect of curvature on stratification in meandering thermally stratified turbulent open channel flow with an internal heat source that models radiative heating from above. Based on the DNS results, the present paper addresses two issues. First, the influence of changing curvature on the complex bi-cellular pattern of the secondary flow is investigated, including the distribution of the temperature field. Second, the effects of changing curvature on the degree of stratification are analyzed. Stratification can be characterized by the friction Richardson number R i τ and the bulk Richardson number Rib. Stratification can also be viewed in terms of the transfer of energy from mean flow kinetic energy to potential energy via buoyancy fluxes. We study the effect of curvature on stratification by investigating its effect on the friction and bulk Richardson numbers. We also study the transfers between the global potential and kinetic energy reservoirs, including the global available Ea, background Eb, and total potential energy Ep, and the domain-averaged mean kinetic and turbulent kinetic energy. It is found that, in meandering channels, with the increase in curvature, Ep increases and R i τ and Rib decrease, indicating that increasing curvature leads to a decrease in the level of stratification. On the other hand, we also find that a low curvature meandering channel has a higher level of stratification than a straight channel. [ABSTRACT FROM AUTHOR]

The gradually varied open-channel flows (OCF) upstream of a run-of-river (RoR) dam are ubiquitous in natural rivers. In this flow type, the velocity profile shows some similarities to that in uniform open-channel flows, but the turbulence intensity and Reynolds shear stress are slightly greater. However, the presence and properties of very-large-scale motions (VLSMs) in such flows are still unclear. To fill this research gap, time-resolved particle image velocimetry measurements were performed upstream of a modeled RoR dam in an open-channel flume. Based on pre-multiplied spectra analysis, statistical evidence of the presence of VLSMs in the flow type is reported for the first time. The results reveal that although the typical streamwise wavelength of VLSMs in such gradually varied OCF is similar to that in other flows, such as turbulent boundary layers, closed-channel flows, pipe flows, and uniform OCF, the VLSMs in the present gradually varied OCF are stronger and contribute more streamwise turbulent kinetic energy as well as Reynolds shear stress than other flows. [ABSTRACT FROM AUTHOR]

Disintegration of liquid masses in a free-surface flow is still an open question in the field of small-scale spray applications such as dispensing of detergents or sanitizing products. In this context, the pressure-swirl atomizer is widely investigated. It allows to improve several spray characteristics through the formation and breakup of a conical liquid sheet that results in the well-known hollow-cone atomization. From this perspective, the characterization of a small-scale pressure-swirl spray under laminar flow conditions is the focus of this work. The configuration of the device and the physical properties of the discharged liquid are the key parameters that modify the attributes of such multiscale flow. In this regard, the entire picture of the fragmentation process is structured into multiple stages: internal nozzle flow, outer displacement of the liquid–gas interface, droplet spread into the atmosphere, and droplet-wall interactions on a collection surface. Through the computational fluid dynamics, we analyze the influence of the main fluid/packaging parameters on the hollow-cone spray properties, and on the whole atomization process. Reynolds and Ohnesorge numbers are coupled with the Sauter mean diameter to distinguish different breakup mechanisms and spray performances. The solution of the entire spray system is performed by implementing the volume-of-fluid-to-discrete-phase-model, which allows to capture the liquid–gas interface displacement and track the droplets produced downstream the primary atomization, simultaneously. With this Eulerian–Lagrangian hybrid model, we link key features of the hollow-cone spray process to spray pattern and droplet size distribution for both Newtonian and non-Newtonian fluid properties. [ABSTRACT FROM AUTHOR]

Shock waves and granular vacua are important phenomena for studying the behavior of granular materials due to the dramatic change in flow properties across shock wave and the particle-free feature at the boundary of granular vacuum. In this paper, we use experiment and numerical simulation to study the granular free-surface flow past a cylindrical obstacle in an inclined chute, where the time-dependent development of the granular flow impacting the obstacle is analyzed at both microscopic and macroscopic scales using the discrete element method (DEM) and the depth-averaged granular model, respectively. Using high-speed camera results as a benchmark solution, the shock solutions are compared between experiment and simulation. The DEM simulation shows better agreement for its shock formation as it is capable of capturing solid, liquid, and gas behaviors for the shock region, while the depth-averaged model provides closer and simpler agreement for the jump solution across the shock. It is shown from the experiment and simulation that the granular shock wave can give rise to a solid–liquid–gas behavior following the propagation of the flow around the obstacle, where, at the front of the obstacle, the shock region can be regarded as a solid regime as the flow becomes stationary during the primary course of the granular flow. With the flow propagating to the downstream, the shock region extends significantly and exhibits strong liquid and gas behavior. Another mixed liquid and gas behavior of granular flow is also observed following the appearance of the granular vacuum, where a localized μ (I) -rheology is shown to be effective in resolving the vacuum boundary in the numerical simulation. [ABSTRACT FROM AUTHOR]

The impact of obstacles on the hydrodynamic flow structure is of major interest since such flows are representative of flooded urban areas. This study focuses on a pattern depicting a single-family home and garden area, as found in recent suburban development. The purpose herein is to analyze the evolution of the velocity distribution for a densely built area as well as for emerged to slightly submerged situations, which represent various flood situations ranging from commonplace to extreme. Free-surface flows through an in-line distribution of square cylinders were investigated in a laboratory flume, in the aim of assessing the effect of relative submergence on the flow structure within the cylinder array. The results show that the lines of square cylinders channelize the flow. Moreover, the submerged case generated similar flow characteristics below the top of the cylinders, which drastically changed once the water flowed above the square cylinder level. [ABSTRACT FROM AUTHOR]

Open-channel bifurcations are the most common water diversion structures in irrigation districts. In irrigation water conveyance, water transport efficiency and sedimentation are primary concerns. This study accordingly analyzes the influence of open-channel bifurcations on water delivery in irrigation areas. Herein, the three-dimensional flow at an open-channel bifurcation was studied via numerical simulations using FLOW-3D software and including 15 sets of working conditions. The hydraulic characteristics of the recirculation zone and flow structures in the vicinity of the open-channel bifurcation were analyzed. Equations for the flow diversion width of the surface and bottom layers in the trapezoidal channel were then obtained. The flow diversion widths along the water depth were found to differ between trapezoidal and rectangular channels. The results also show that open-channel bifurcations considerably influence the flow velocity in the main channel. The flow velocity in the recirculation zone of open-channel bifurcations was small, but the pulsation velocity and the turbulent kinetic energy were large. The energy dissipated in this area was relatively large, which was not conducive to channel water delivery. This study provides a reference for channel optimization and operation management in irrigation districts. [ABSTRACT FROM AUTHOR]

Flowing lava and water have dramatically different physical properties but can form similar hydraulic structures, including undular hydraulic jumps, or standing wave trains. In water flows, undular hydraulic jumps are evidence of critical flow (Froude number ∼1) and open‐channel hydraulic theory provides a powerful tool for estimating flow depth and velocity. Monitoring these parameters in an active lava channel is inherently challenging, but essential for calculating lava discharge (effusion rate), a primary control on the rate of flow front advance and ultimate flow runout distance. We analyze undular hydraulic jumps in both water and lava flows to assess the conditions under which they form and, by extension, the potential use of critical flow theory to estimate, in real time, lava flow velocity, depth, and discharge. Experimental data for water flows show that these structures mark the transition from supercritical to subcritical flow. Undular hydraulic jumps in the near‐vent lava channel of the 2018 lower East Rift Zone eruption of Kīlauea, Hawaiʻi also reflect critical flow conditions; their wavelengths scale with flow depth and velocity, consistent with hydraulic theory. Calculated lava effusion rates are similar to estimates made using more traditional approaches (Jeffreys', 1925, https://doi.org/10.1080/14786442508634662, equation based on lava viscosity, density, and channel slope) and with lava volumes derived from topographic‐change mapping. From this we conclude that critical flow phenomena show great potential to track flow dynamics and inform hazard assessment for a wide range of geophysical fluids. Plain Language Summary: Flowing water and lava have very different physical properties, but under certain flow conditions, each will form arrays of evenly spaced standing waves (wave trains). In water, these are known to form at "critical flow" when there is a specific ratio between flow depth and flow velocity. However, conditions for forming standing wave trains in lava have not been measured. We investigated the relationship between the spacing of waves in a train, and the flow speed and depth, using both data from experiments with water and measurements made during the 2018 lava flow at Kīlauea volcano. We found that waves form in each fluid at the same ratio of flow speed and depth, and that the spacing of waves in a train shows a fixed mathematical relationship to these parameters. There is considerable practical importance to this finding. During a volcanic eruption, direct measurement of flow speed is difficult and dangerous, and depth is impossible, and yet both are needed to predict how far and how fast lava will travel. The critical flow characteristics of lava, and potentially other hazardous flows such as mudflows, allow assessment of flow behavior and potential hazards in real time. Key Points: Undular hydraulic jumps, or standing wave trains, form in both water and active lava at critical flow (Froude number ∼1)Wavelengths scale with flow depth and velocity following hydraulic theory in water flume experiments and Hawaiian lava flow dataApplication to wave trains in active lava flows provides rapid estimates of key flow parameters and effusion rates for hazard assessment [ABSTRACT FROM AUTHOR]

We have performed high-fidelity simulations of turbulent open-channel flows over submerged rigid canopies made of cylindrical filaments of fixed length $l=0.25H$ ($H$ being the domain depth) mounted on the wall with angle of inclination $\theta$. The inclination is the free parameter that sets the density of the canopy by varying its frontal area. The density of the canopy, based on the solidity parameter $\lambda$ , is a widely accepted criterion defining the ongoing canopy flow regime, with low values ($\lambda \ll 0.1$) indicating the sparse regime, and higher values ($\lambda > 0.1$) the dense regime. All the numerical predictions have been obtained considering the same nominal bulk Reynolds number (i.e. $Re_b=U_b H/\nu = 6000$). We consider nine configurations of canopies, with $\theta$ varying symmetrically around $0^{\circ }$ in the range $\theta \in [\pm 78.5^{\circ }$ ], where positive angles define canopies inclined in the flow direction (with the grain) and $\theta =0^{\circ }$ corresponds to the wall-normally mounted canopy. The study compares canopies with identical solidity obtained inclining the filaments in opposite angles, and assesses the efficacy of the solidity as a representative parameter. It is found that when the canopy is inclined, the actual flow regime differs substantially from the one of a straight canopy that shares the same solidity, indicating that criteria based solely on this parameter are not robust. Finally, a new phenomenological model describing the interaction between the coherent structures populating the canopy region and the outer flow is given. [ABSTRACT FROM AUTHOR]

A rotational version of the fluid-mechanical sewing machine (FMSM) is investigated experimentally. A thin thread of silicon oil was dispensed at a constant flow rate Q from a height H and fell on a table rotating at an angular speed ω , at a distance R from the axis. In all experimental runs, the values of Q and H were kept constant while the radius R was changed manually after each full rotation. Preliminary results show that the usual stitching patterns ensue as the local linear speed V = ω R approaches the critical transition speeds seen in the FMSM scenario but with subtle asymmetries introduced by rotational (centrifugal) effects. In some instances, arcs and loops of the traces were noticeably more pronounced when directed outward compared to those pointing toward the axis of rotation. Moreover, we observed stitching patterns not reported before. Overall, the symmetry-breaking features, while clearly visible, were rather subtle. Their morphological characteristics, such as differences in local curvature of traces relative to those in FMSM, are estimated to be below 10% in most cases. [ABSTRACT FROM AUTHOR]

The use of apparent shear stress at the interface between the adjacent subregions of a cross section to represent the effect of momentum transfer is a common method for the one-dimensional calculation of compound open-channel flow. The apparent shear stress of the dividing lines is affected by the compound geometry and boundary conditions. The expressions of the apparent shear stress established with previous studies are very different. Empirical treatment was proposed in this study to simplify the expressions based on a momentum transfer–equivalent states assumption, in which (1) the apparent shear stress was assumed to be the difference of the momentum transfer from two sides of a dividing line, and (2) two assumed equivalent states were employed to define the equivalent value of the momentum transfer. The apparent shear stress could be calculated based on the deviation of the momentum transfer from its equivalent value. The new expressions were used to calculate the discharges and the boundary shear force. Comparisons between the calculated results based on different methods and the measured data showed that the proposed method improved the calculation of the subregion boundary shear force and the discharges in the compound cross sections. [ABSTRACT FROM AUTHOR]

This paper outlines the implementation of an efficient implicit method for a free surface boundary for solving free surface flows with larger time steps. In this method, the governing equations are solved with dynamic conditions applied to the free surface boundary. The position and shape of the free surface are represented with adaptive boundary grid points. Unlike existing explicit methods, the proposed method solves the space conservation equation implicitly, making the calculations more stable and at a lower computational cost. The approach was implemented numerically by developing a new boundary field in OpenFOAM. Several test cases, including propagations of tidal wave, channel surge and solitary wave, were simulated to demonstrate the method's accuracy. The proposed method accurately predicted the first two cases using larger time steps. The Courant number of the solitary wave case should be less than 1 to reduce numerical errors, which would damp the wave amplitude. [ABSTRACT FROM AUTHOR]

Under a flow in supercritical regime, depending on the pier width to water depth ratio, the flow pattern around a bridge pier can take the form of a wall-jet-like bow wave or a detached hydraulic jump. The present work aims at analysing the maximum scour depth at piers in both flow patterns. A dedicated experimental set-up was used to produce the live-bed scour experiments, varying the inflow velocity and pier diameter. During the experiments, scour developed very rapidly, achieving equilibrium conditions after few minutes. No major differences between the maximum scour depth in the wall-jet-like bow wave and detached hydraulic jump cases were observed. Measured scour depths were of comparable magnitude and followed similar tendencies with controlling parameters as in subcritical flows. Scour formulas for piers in subcritical flow thus achieve a good accuracy in prediction of maximum scour depth at piers in supercritical flows. [ABSTRACT FROM AUTHOR]

Current research investigating ice-covered bridge pier scour has focused on the effects of fully developed ice jams. However, based on observations at various stages of development, ice covers are not always fully developed. This experiment investigated pier scour at various stages of a simulated floating ice jam's development, with a constant flow rate. Various channel-spanning ice cover lengths were tested, along with one circular localized cover, and resulting pier scour was compared to free-surface flow pier scour. Five lengths of downstream initiated ice covers were tested, with lengths upstream of the pier being 0, 0.63, 1.33, 2.66 and 5.32 m. The local cover's diameter was 0.27 m, three times the pier diameter. The 2.66-m ice cover produced the greatest scour and near-bed Reynold stress, with greater scour depth and volume, respectively, by 46.9% and 238% compared to free-surface flow conditions, whereas the local cover produced the smallest scour increase. [ABSTRACT FROM AUTHOR]

Large-eddy simulations (LES) of supercritical flow in a straight-wall, open-channel contraction of 6° and contraction ratio of 2:1 are performed. The LES code solves the filtered Navier-Stokes equations for two-phase flows (water-air) and employs the level-set method. The simulation was validated by replicating a previously reported experiment. Contours of the time-averaged velocities indicate that the flow loses energy and momentum in the contracting channel. Further, secondary currents in the contraction are redistributing momentum and are responsible for local up-and down-flows. The turbulent kinetic energy reaches very high values at the entrance of the contraction, mainly contributed by the streamwise normal stress. The flow contains coherent turbulence structures which are responsible for carrying low-momentum from the bed and the water surface towards the channel centre. Flow deceleration results in significant turbulence anisotropy in the contracted section. It is shown that mainly pressure drag contributes to the energy loss in the contraction. [ABSTRACT FROM AUTHOR]

A Large Eddy Simulation of a fully developed turbulent open-channel flow with a Reynolds number of R e = 71,755 was performed to study dynamics of coherent structures in the vicinity of a stationary sediment particle. The sediment particle was positioned at the bottom on a smooth channel bed. The impulse concept was employed by computing three-dimensional hydrodynamic forces acting on the sediment particle in order to predict the onset of particle motion. Results of quadrant analyses at high impulse events yielded mostly outward and sweep events. Auto- and cross-correlation of the hydrodynamic forces and the flow field were studied and discussed. An identification of coherent structures at high impulse events showed that large-scale, long-lived hairpin-like vortices whose bed-normal lengths are larger than ≈ 100 viscous units were resulting in an increase of lift and drag forces simultaneously, facilitating initiation of particle motion. [ABSTRACT FROM AUTHOR]

Particle image velocimetry (PIV) is a quantitative flow visualization technique, which greatly improves the ability to characterize various complex flows in laboratory and field environments. However, the deployment of reference objects or ground control points (GCPs) for velocity calibration is still a challenge for in situ free-surface velocity measurements. By combining space-time image velocimetry (STIV) with direct sensor orientation (DSO) photogrammetry, a laser distance meter (LDM)-supported photogrammetric device is designed, to realize the GCPs-free surface velocity measurement under an oblique shooting angle. The velocity calibration with DSO is based on the collinear equation, while the lens distortion, oblique shooting angle, water level variation, and water surface slope are introduced to build an imaging measurement model with explicit physical meaning for parameters. To accurately obtain the in situ position and orientations of the camera utilizing the LDM and its embedded tilt sensor, the camera's intrinsic parameters and relative position within the LDM are previously calibrated with a planar chessboard. A flume experiment is designed to evaluate the uncertainty of optical flow estimation and velocity calibration. Results show that the proposed DSO-STIV has good transferability and operability for in situ measurements. It is superior to propeller current meters and surface velocity radars in characterizing shallow free-surface flows; this is attributed to its non-intrusive, whole-field, and high-resolution features. In addition, the combined uncertainty of free-surface velocity measurement is analyzed, which provides an alternative solution for error assessment when comparing measurement failures. [ABSTRACT FROM AUTHOR]