Journal of Hydraulic Engineering

Forum papers are thought-provoking opinion pieces or essays founded in fact, sometimes containing speculation, on a civil engineering topic of general interest and relevance to the readership of the journal. The views expressed in this Forum article do not necessarily reflect the views of ASCE or the Editorial Board of the journal.

We introduce a monolithic/strong, interfacial coupling formulation between two-dimensional (2D) and three-dimensional (3D) shallow water (SW) and transport models. This coupling becomes necessary in regions such as estuaries leading into inundation areas or wetlands where wetting and drying has an effect on baroclinic regions. We present the formulation and verification of a novel method for monolithically coupling 2D and 3D SW and transport equations in an implicit-in-time, streamline upwind Petrov Galerkin (SUPG)-stabilized continuous Galerkin finite-element method (CG-FEM) setting, with a key requirement of mass and momentum conservation across the 2D–3D interface. Solutions of the method are verified against full-2D and full-3D/3D-only models. It is concluded that the formulation is conservative, stable, accurate, convergent, computationally cheaper than full-3D models when noncritical 3D regions are replaced with 2D subdomains, and capable of simulating physics that solely 2D or 3D production models are generally incapable of.

The critical bed-shear stress (cbs) for erosion of mud–sand bed mixtures was studied in laboratory and field conditions with currents, waves, and combined currents and waves. Three types of erosion were distinguished: particle/floc erosion, surface erosion, and mass erosion. Important influencing parameters were found to be sediment composition (percentage clay, silt, and sand), presence of organic and carbonate materials, type of bed (homogeneous, remolded, layered by depositional processes), and the dry bulk density (consolidation stage). The laboratory and field results reveal that the critical bed-shear stress is not much influenced by cohesive effects if the percentage of fines ($<63\mu \mathrm{m}$) is smaller than approximately 15%. For $p_{\text{fines}}>15\%$ up to approximately 50%, the critical bed-shear stress increases for increasing values of $p_{\text{fines}}$ but decreases again for $p_{\text{fines}}>50\%$. The fine fraction includes the clay fraction ($p_{\text{clay}}\cong 0.2$ to 0.4 $p_{\text{fines}}$), which contributes primarily to the cohesive effects. In addition, the bulk density depending on the soil composition (clay, silt, sand content, and consolidation stage) has a strong effect on the cbs for surface erosion. Small bed irregularities (local disturbances) also play an important role by creating local accelerations and decelerations with enhanced turbulence and initiating particle movements. A new empirical relation is suggested to predict the critical bed-shear stress for erosion based on the dry bulk density of the sediment samples. This relation is successfully applied in a morphodynamic model of a schematized tidal basin to represent spatial variations in the erodibility of fines between sandy channels and (relatively) muddy shoals.

In recent years, the research interest in the application of remote sensing technology to highly aerated flows has been increasing because this technology holds the ultimate promise to enable safe and accurate measurements of real-world air–water flows in natural and human-made environments. Despite the increasing number of publications, some fundamental questions, such as “what do we measure” or “what can we measure,” have not been answered conclusively. In this study, we hypothesize that laser distance sensors can measure the concentration of entrapped air, which we demonstrate using two seminal air–water flow types, namely a submerged hydraulic jump and flows down a stepped spillway. By converting our free-surface signals into time series of instantaneous air concentrations, we also show that a dual laser triangulation setup enables the extraction of basic air–water flow parameters of the upper flow region, comprising interface count rates, interfacial velocities, and turbulence levels, whereas we acknowledge that some sensor characteristics, such as beam diameters, can lead to measurement biases. Overall, this study represents a major advancement in the remote measurement of air–water flow properties. Future collective research effort is required to overcome remaining challenges.

The EPA’s Storm Water Management Model (SWMM) has been applied across the globe for citywide stormwater modeling due to its robustness and versatility. Recent research indicated that SWMM, with proper setup, can be applied in the description of more dynamic flow conditions, such as rapid inflow conditions. However, stormwater systems often have geometric discontinuities that can pose challenges to SWMM model accuracy, and this issue is poorly explored in the current literature. The present work evaluates the performance of SWMM 5 in the context of a real-world stormwater tunnel with a geometric discontinuity. Various combinations of spatiotemporal discretization are systematically evaluated along with four pressurization algorithms, and results are benchmarked with another hydraulic model using tunnel inflow simulations. Results indicated that the pressurization algorithm has an important effect on SWMM’s accuracy in conditions of sudden diameter changes. From the tested pressurization algorithms, the original Preissmann slot algorithm was the option that yielded more representative results for a wider range of spatiotemporal discretizations. Regarding spatiotemporal discretization options, intermediate discretization, and time steps that lead to Courant numbers equal to one performed best. Interestingly, the traditional SWMM’s link-node approach also presented numerical instabilities despite having low continuity errors. Results indicated that although SWMM can be effective in simulating rapid inflow conditions in tunnels, situations with drastic geometric changes need to be carefully evaluated so that modeling results are representative.

The transient response of an initially neutral turbulent open channel subject to sudden stable stratification through radiative surface heating is investigated through direct numerical simulations. We find the convergence of the vertical buoyancy and momentum fluxes toward their respective analytical equilibrium values to be a global monotonic process such that locally, buoyancy and momentum flux equilibrium is obtained simultaneously at all locations within the channel. We present scaling arguments to show that the evolution of the flux convergence ratios toward equilibrium scale directly with $R{i}_{\tau }^{-1/2}(t/T_{\tau })$ and reach equilibrium at $R{i}_{\tau }^{-1/2}(t/T_{\tau })\approx 2$, consistent with results from the literature, where $R{i}_{\tau }$ is the friction Richardson number, $T_{\tau }$ is the friction time scale, and $t$ is the measured time from the initial isothermal state. We define the upper laminar layer thickness ${\delta }_i$ and present scaling arguments to show that the laminar layer thickness is well-parameterized by a hybrid bulk parameter such that ${\delta }_i/\delta \approx 0.45(C_R^{1/2}PrR{i}_{\tau }^{-1}R{e}_{\tau }{)}^{-1/2}$ across the full external parameter set. Here $\delta$ is the channel height, $C_R$ is the equilibrium convergence ratio, $Pr$ is the molecular Prandtl number, and $R{e}_{\tau }$ is the friction Reynolds number.

An in-depth understanding of leak behavior in water distribution systems is essential for ensuring the long-term reliability and resilience of critical infrastructure. While previous research has extensively explored leak opening behavior under positive pressure conditions, this study aimed to investigate how leaks behave under negative pressures (e.g., caused by transients, fire flows, etc.). To achieve this, a series of experiments in a 110-mm diameter PVC pipe was conducted, examining various types of leaks under negative pressure conditions. Subsequently, modeling studies were conducted to assess the implications of the observed behavior on intrusion flows through longitudinal cracks considering common pipe materials and properties typical for real water distribution networks, i.e., PVC, PE, AC, and steel. The experimental tests showed consistent head-area slopes for leaks under both positive and negative pressures, with smaller discharge coefficients for intrusion compared to those for leakage flows. This finding suggests that the existing knowledge of leak behavior under positive pressures can be applied in negative pressure conditions. Although round holes and circumferential cracks showed negligible and minimal changes in leak area, respectively, the longitudinal cracks displayed large positive head-area slopes, meaning that their leak areas decreased under negative pressures and sometimes closed, limiting intrusion flows. The study further showed that a leakage exponent (N1) different from 0.5 obtained under positive pressure produces inaccurate results when applied to intrusion flows. The results of modelling studies showed that the intrusion flows in rigid pipe materials such as steel and AC have similar or slightly lower intrusion flows than in the fully rigid case. In contrast, more flexible materials, such as PE and PVC, showed a greater reduction in intrusion flows when subjected to negative pressures.

Abstract

In vegetated flows a reliable estimation of flow scales is crucial to understand and model mixing processes. This study presents velocity maps obtained using particle image velocimetry (PIV) within a cylinder array (diameters $4\le d\le 20\mathrm{mm}$) designed to mimic real emergent vegetation. Tests were undertaken over a comprehensive range of stem Reynolds numbers ($100\le R{e}_d\le 900$), intended to characterize time-dependent hydrodynamic features, including their interactions. Time-averaged flow heterogeneities are found to be independent of $R{e}_d$. Vortex dynamics are seen to dominate turbulent fluxes of momentum, and are the relevant coherent structures driving mass transport. The range of characteristic time- and length-scales from these coherent structures was quantified and shown to be determined by the distribution of spaces between cylinders. This is due to: (1) neighboring cylinders forming clusters, leading to larger flow structures, and (2) the maximum size of the flow structures being constrained by the inter-stem space. It is concluded that the Delaunay criterion provides practitioners with a good approximation to the distribution of flow scales in vegetated flows.

Practical Applications

This study presents the quantification of the scales of flow structures generated in a vegetated flow. These structures play an important role in the quantification of mass transport processes, and estimates of the sizes of these flow structures are necessary to understand the rate of solute transport and therefore provide reliable models for pollutant mixing in vegetated flows. Using state-of-the-art equipment to characterize velocity fields, the present study found that the size of these flow structures is determined by the spacing between cylinders. The authors recommend that for practical applications, engineers quantify the spacing between plant stems using the criteria presented in this paper.

Abstract

This paper presents physics-informed neural networks (PINNs) to approximate the Serre–Green–Naghdi equations (SGNEs) that model steady-state weir flows. Four PINNs are proposed to solve the forward problem and three types of inverse problem. For the forward problem in which continuous and smooth beds are available, we constructed PINN 1 to predict the water depth profile over a weir. Good agreements between the PINN 1 solutions and experimental data demonstrated the capability of PINN 1 to resolve the steady-state weir flows. For the inverse problems with input discretized beds, PINN 2 was designed to output both the water depth profile and the bed profile. The free-surface profiles based on the PINN 2 solutions were in good agreement with the experimental data, and the reconstructed bed profiles of PINN 2 agreed well with the input discretized beds, demonstrating that PINN 2 can reproduce weir flows accurately when only discretized beds are available. For the inverse problems with input measured free surface, PINN 3 and PINN 4 were built to output both the free-surface profile and the bed profile. The output free-surface profiles of PINN 3 and PINN 4 showed good agreement with the experimental data. The inferred bed profiles of PINN 3 agreed generally well with the analytical weir profile or the control points of the weir profile, and the inferred bed profiles of PINN 4 were in good agreement with the analytical weir profile for the investigated test case. These indicate that the proposed PINN 3 and PINN 4 can satisfactorily infer weir profiles. Overall, PINNs are comparable to the traditional numerical models for forward problems, but they can resolve the inverse problems which cannot be solved directly using traditional numerical models.

Practical Applications

There has been tremendous progress in solving governing equations using traditional numerical methods. However, when solving inverse problems, traditional numerical methods usually are time consuming and require new algorithms. Most importantly, traditional numerical methods are unable to resolve problems with missing or noisy initial and boundary conditions. Compared with traditional numerical methods, physics-informed neural networks implement a mesh-free algorithm and are effective and efficient for inverse and even ill-posed problems. Physics-informed neural networks integrate physical governing equations and relevant data, e.g., initial and boundary conditions or measured data, to infer unknown variables for forward and inverse problems, and have been applied to solve various types of governing equations. To the best of our knowledge, no PINNs have been presented to solve weir flows. This paper proposes physics-informed neural networks to solve forward and inverse weir flows. Research findings indicate that physics-informed neural networks are comparable to traditional numerical methods for the forward problem and are capable of resolving the inverse problems in which the discretized bed elevations or the measured free surface are available.

Levee setbacks can create space for side channels, reduce flood impacts, and provide environmental benefits. Guidance is needed on how side channel design affects geomorphic changes over time. This paper explores application of existing research on natural and forced side channels to a levee setback with side channel on the White River (Washington). The side channel maintained a high bifurcation angle into the setback for 2 years. High flows then reset the bifurcation to a lower angle. Flow and sediment volumes and deposition patterns from each 2-year period matched results from existing studies for either a high or low angle. Application of existing research insight into expected flows and sediment patterns was dependent on a static bifurcation angle. In this case study, because the entrance area did not restrict the bifurcation angle and the flow regime included high flows, the bifurcation angle could adjust to maintain the side channel. Designing a large setback entrance enabled the channel to self-adjust to maintain flow and sediment transport into the side channel without the need for engineering intervention.

Flow through cracks in a variety of concrete structures can be problematic for water resources infrastructure. Design of drainage systems to collect and remove such flow requires estimating flow rates through cracks. When the crack is wide or the flow path is relatively short, entrance losses dominate, and discharge may be estimated using orifice equations that neglect friction losses. However, for relatively narrow and long cracks with rough interior surfaces, friction losses can significantly affect discharge. This article reanalyzes data previously collected from tests of flow through a cracked concrete beam to obtain Darcy-Weisbach friction factors and presents them relative to the Reynolds number of the flow through the crack, similar to the Moody diagram commonly used to estimate friction factors in pipe flow. The data are also used to develop an empirical equation for predicting friction factors and to determine the effective roughness of the cracked concrete surfaces. Observations are made regarding unexpected behavior of friction factors for the combination of low Reynolds number and extremely large relative roughness, which is outside the bounds of most previous research on flow resistance.

In the traditional stepped spillways with uniform width, the inception points of air entrainment along the spillway transverse direction generally remain at a similar distance from the spillway entrance, and can therefore be treated as a 2D problem. In the converging stepped spillways, the converging sidewall causes a nonuniform flow distribution along the spillway transverse direction, and a disturbed flow region is generated near the converging sidewall with significantly higher flow depth and discharge and lower air concentration. Their inception points are no longer a 2D problem and were investigated by physical experiments in this study. It was found that the line of the inception points curves downstream in the disturbed flow region and ended at the standing wave with limited air entrainment, while it formed the approximately straight line in the undisturbed flow region away from the converging sidewall. Therefore, the inception line of air entrainment in the converging stepped spillways can be described by the straight and curved lines and two intersections. The effects of the inlet flow discharge and the sidewall convergence angle were tested and analyzed. The expressions for the straight and curved lines and the two intersections are established, which can help to identify the inception line of air entrainment for the converging stepped spillways and make reasonable predictions.