The unsteady three-dimensional (3D), nonaerated, skimming flow over a stepped spillway is investigated by means of a detached eddy simulation (DES). Special emphasis is placed on the description of the instantaneous velocity and vorticity fields on the step cavities, as well as on the 3D, long-term, average flow structure at a Reynolds number of approximately ${10}^5$ . Mean-flow velocities obtained from simulations on both relatively-coarse and fine meshes at different locations in the spillway are in very good agreement with particle image velocimetry (PIV) data published elsewhere. Nondimensional profiles of turbulence intensity and Reynolds stresses are also close to data, although numerical values are larger than the experimental counterparts. Snapshots of velocity vectors reveal that the flow near the pseudo-bottom is continuously flapping, and that it intermittently interacts with ejections of positive vorticity emanating from the cavities. As a result of the interaction between the shear flow and the 3D cavity flow, patches of positive and negative vorticity are carried away downstream, eventually interacting with the free surface. It is also found that the ratios of redistribution among components (terms) of the turbulent kinetic energy (TKE) at the step edges are very similar to those universal values for the intermediate region of open-channel flows. It is additionally shown that large-scale structures extracted from isosurfaces of the $Q$ -criterion correspond primarily to well-organized, randomly-distributed thin tubes of vorticity. The instantaneous flow field revealed in this paper is considered crucial for modeling the even more complex aerated region.

In this paper, we present the simulation results of a Lagrangian particle tracking model that computes the motion of saltating sediment particles, which is considered the most important mode of bedload transport in rivers and channels. The model is one-way coupled to a validated turbulent LES-WALE (Large Eddy Simulation – Wall-Adapting Local Eddy-viscosity) channel flow, i.e., the particles do not affect the computation of the flow velocities and pressures, as suggested for dilute flows. The model addresses the particle trajectories, the collision of the particles with the bottom wall, and collision among particles. The focus of this work is placed on the effect of different particle concentrations and flow intensities (different flow shear stresses) on jump statistics and particle diffusion. Numerical results are validated with experimental laboratory data obtained from the literature for particle diameters in the range of sands. The present results indicate that, at particle concentrations up to 2%, the diffusion coefficients in the streamwise and spanwise directions, ${\gamma }_x$ and ${\gamma }_z$, for the local range are nearly constants with a value close to one, corresponding to the ballistic regime. At a concentration of 4%, the largest concentration studied herein, values of ${\gamma }_x$ and ${\gamma }_z$ for the local range are slightly smaller, with a representative value of 0.9 regardless of flow intensities. For the intermediate regime, it was found that, on average, ${\gamma }_x~1.2{\gamma }_z$ with ${\gamma }_x$ ranging from 0.6 to 0.85 and ${\gamma }_z$ within the range 0.45–0.70. For a fixed flow intensity, both diffusion coefficients increase with the particle concentration, which is an indication of the contribution of the collision among particles to particle diffusion. For highly controlled simulation conditions, the differences in particle velocity at a given concentration may change drastically, which should translate to important fluctuations in the computation of sediment transport rates. Finally, the employed computational resources are described as a function of particle concentration. Although the number of total collisions increases linearly with the number of particles, the number of collisions per particle reaches a plateau, thus indicating that there exists an upper limiting value for the number of collisions per particle.

The classical assumption of self-similarity in flow velocities and turbulence statistics has been successfully validated for fully developed flows in open channels, pipes, and boundary layers. However, its application in developing boundary-layer flows in channels with steep slopes and large roughness elements has not yet been thoroughly scrutinized. This study investigates whether turbulence statistics exhibit self-similar behavior when properly scaled in steep-stepped spillways. Specifically, it explores the influence of roughness height ($k_s$)—representing the cavity size of a steep-stepped spillway—on turbulence statistics in the non-aerated skimming flow region. Numerical simulations, extensively validated against experimental data, were conducted for a stepped spillway with a fixed slope angle of 51.34°, using five roughness heights ($k_s$ = 6.25, 3.12, 1.56, 0.78 and 0.39 cm), corresponding to step height-to-length ratios of 10:8, 5:4, 2.5:2, 1.25:1 and 0.625:0.5, respectively. The results show that the dimensionless profiles of turbulent kinetic energy (TKE) at the step edges collapse onto a single curve when rescaled by a factor of ${\left(\delta /k_s\right)}^n$ with $n~0.4$. Likewise, the dissipation rate of TKE follows a similar collapse with $n~0.3$. For the turbulent eddy viscosity, an exponent of $n~0.5$ was adopted based on dimensional analysis, although the values for the smoothest configuration deviate from the curve.

This study presents a deep learning-enhanced particle tracking velocimetry framework for tracking rod-like particles in a translucent non-Newtonian fluid. The framework addresses conditions under which conventional image-processing techniques fail: particle widths approaching the resolution limit of the imaging system ( ∼ 2 pixels), spatially non-uniform illumination, and progressive inter-particle occlusion. It integrates YOLOv11 instance segmentation with a customized α – β – γ predictive filter to reconstruct the simultaneous translational and rotational trajectories of individual steel fibers in a carbopol yield-stress gel. Segmentation performance was evaluated against Hough transform and SAM baselines: YOLOv11 achieved a precision of 94.7%, a recall of 98.2% and an Intersection over Union of 84.8%, exceeding the Hough transform by more than 90 percentage points in precision. Tracking performance across fiber loadings from 25 to 800 fibers was concentration-dependent, with mean trajectory lengths decreasing from 198 to 68 frames and instantaneous detection ratios ranging from 0.64 to 0.32. Continuous long-duration trajectories are routinely recovered up to approximately 200 fibers, where 5.7%–18.8% of tracks span at least 500 of the 600 frames; above 400 fibers this falls below 2%, and the framework delivers fully resolved Eulerian velocity fields while Lagrangian analysis is restricted to selected trajectories. Regional kinematic analysis resolves statistically distinct velocity, angular velocity and orientation distributions across three geometric zones: the vertical inlet, the 90 ∘ bend and the horizontal outlet. Across the full concentration range tested, the measurements capture a systematic fiber reorientation from predominantly vertical ( 44 ∘ – 57 ∘ ) to predominantly horizontal ( 7 ∘ – 31 ∘ ) alignment. The resulting particle-scale dataset resolves the coupled translational, rotational and orientation dynamics of individual fibers in non-Newtonian suspensions. It advances the quantitative characterization of fiber kinematics in complex multiphase flows and constitutes a direct validation resource for CFD-DEM simulation frameworks of fiber transport. The dominant measurement uncertainties, centroid localization error and orientation-dependent detection bias, were identified and quantified.

The stepped spillway design is widely used globally for its energy dissipation capabilities through its stepped design and air entrainment capacity, crucial for safe hydraulic structure operation. The most common condition found in stepped spillways is the skimming flow regime. This study numerically investigated the influence of the roughness height (K_S) on the distribution of mean flow variables and modeled turbulence statistics in the non-aerated portion of a steep stepped spillway with a constant angle of 51.34°. Three roughness heights of 6.26, 3.13 and 1.57 cm were considered corresponding to a relation step height/horizontal length of 10/8, 5/4 and 2.5/2 (cm/cm), respectively. The results show that profiles of modeled turbulent kinetic energy (TKE) at different step edges can be collapsed into one single curve for relative roughness (Ks/h) smaller than 0.8. For larger ratios of roughness height to water depth, this behavior is not observed and for a given distance away from the wall, values of TKE show a broad range of values, with increasing values as boundary layer grows. A similar trend was obtained for the distribution of TKE along a water column that includes the cavity. The existence of an upper limit for the ratio between the roughness height and the water depth can now be incorporated in the hydraulic design of new steep stepped spillways.