Journal of Hydraulic Engineering

The utilization of mathematical models in hydraulic engineering for the analysis of one-dimensional, unsteady free-surface, and pressurized flows is discussed, with an emphasis when the models performed well as well as when they did not. For illustration purposes, the applications to a number of real-life projects are presented, outlining limitations, successes, and failures.

The two-component pressure approach (TPA) is an alternative to the Preissman slot method (PSM) for modeling highly transient sewer flow, including transitions between free-surface and pressurized conditions. TPA and PSM resolve intralink wave action by discretizing sewers with numerous elements and solving one-dimensional flow equations in contrast to link-node models, such as the popular storm water management model, which resolve only interlink wave action. Here, improvements of TPA are reported to support storm sewer network modeling. These include a source term discretization to preserve stationarity, a wetting and drying scheme, and a local time-stepping scheme to coordinate solution updates across many links and enable coupling to a two-dimensional overland flow model. A unique variant of the Harten, Lax and van Leer (HLL) Riemann solver is also introduced, and a boundary solver is developed to accommodate the wide range of possible flow regimes and transitions. The boundary solver is explicit to facilitate the extension of TPA to large networks and coupling with an overland flow model. Promising results are obtained in a varied set of test problems involving simple sewer networks.

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

Local-uniform-flow (LUF) hypothesis is a simplification of the governing equations describing river morphodynamics, which is needed to determine the evolution of the bed profile and bed-material composition in the case of large time and space scales. This paper presents a rigorous analysis of the full one-dimensional river hydrodynamic and morphodynamic mathematical model compared to its LUF approximation. The analysis establishes two criteria to assess the validity of the LUF hypothesis: (1) a criterion for rivers in equilibrium and (2) a criterion for evolving rivers (i.e., in nonequilibrium). The first criterion is based on the concept of the morphological box. Variations of the river bed longer than the box length are adequately reproduced by the LUF hypothesis, whereas only spatially averaged values are resolved within the box. The second criterion is based on the concept of an evolution window. Temporal variations represented by wave periods larger than the evolution window can be adequately reproduced by the LUF hypothesis, whereas variations with shorter periods are averaged within this window. The minimum size of morphological box and evolution window that limit the error introduced by the LUF hypothesis increases when the Froude number decreases. Further, the minimum size of the evolution window increases for decreasing sediment concentration and increasing mixing layer thickness (i.e., for larger bed forms). The LUF hypothesis is therefore best applied to small mountain rivers for which both the minimum size of the morphological box and the evolution window is relatively small, so that spatial and temporal variations can be resolved in more detail. Applications using the LUF hypothesis for large watersheds (including the lowland portion of the fluvial network) are possible, but are limited to simulations over larger spatial and temporal intervals.

Stream channel restoration can increase flow storage and energy dissipation of passing flood waves. Elements of restoration design that can enhance attenuation include remeandering, which reduces channel slope and increases channel length relative to the floodplain; restoring channel-floodplain connectivity; and revegetating banks and the floodplain. Reestablishment of floodplain hydraulic function is increasingly a goal of restoration programs, yet the approximate magnitude of possible change to attenuation due to reach-scale restoration remains poorly quantified. We examined the efficacy of channel restoration on flood attenuation using restored reaches and synthetic reaches representing median dimensions of channel restoration projects in North Carolina (e.g., $\sim 1\text{km}$ in length). We applied an industry standard dynamic flood routing model (UNET in HEC-RAS) to route floods in impaired and restored reach models. Floods routed through field-based reach models either exhibited very small increases in attenuation, largely due to assumed increases in floodplain roughness, or a decrease in attenuation. Analysis demonstrated that attenuation of peak discharge is overall most sensitive to channel and valley slope, channel and floodplain roughness, and channel and valley length in decreasing order, but is dependent on flood magnitude. Restoration most impacted floods of intermediate magnitude (between 2- and 50-year return interval), particularly those confined to the channel under the impaired morphology but able to access the floodplain under the restored morphology. Restoration may rehabilitate a channel’s ability to attenuate small to intermediate floods by augmenting flood access to the floodplain, changing channel geometry, and enhancing channel and floodplain roughness over time. However, our study shows that the predominantly small scale of current channel restoration will provide minimally quantifiable enhancement to flood attenuation.

In this paper, we investigate the extent to which well-known sediment transport capacity formulas can be used in one-dimensional (1D) numerical modeling of dam-break waves over movable beds. The 1D model considered here is a one-layer model based on the shallow-water equations, a bed update (Exner) equation, a space-lag equation for the nonequilibrium sediment transport and an empirical formula calculating the sediment transport capacity of the flow. The model incorporates a variety of sediment transport capacity formulas proposed by Meyer-Peter and Müller, Bagnold, Engelund and Hansen, Ackers and White, Smart and Jaeggi, van Rijn, Rickenmann, Cheng, Abrahams and Camenen, and Larson. We examine the performance of each formula by simulating four idealized laboratory cases on dam-break waves over sandy beds. Comparisons between numerical results and measurements show that for each case better predictions are obtained using a particular formula, but overall, formulas proposed by Meyer-Peter and Müller (with the factor 8 being replaced by 12), Smart and Jäggi, Cheng, Abrahams and Camenen, and Larson rank as the best predictors for the entire range of conditions studied here. Moreover, results show that in the cases where a bed step exists, implementing a mass failure mechanism in the numerical modeling plays an important role in reproducing the bed and water profiles.

Bed sediment entrainment function is derived based on kinetic theory. The entrainment rate is expressed as an upward flux by integrating the particle velocity over all possible upward motions. The possibility of upward motion is determined by a sediment particle velocity distribution function, which is obtained by solving the Boltzmann equation instead of using a prior assumed distribution. External forces and turbulence intensity of the flow are shown to exert significant influences on the velocity distribution function and, in turn, the entrainment rate. Comparisons between available laboratory data and the entrainment function show that the calculated entrainment rates agree well with the observations. Applications of the entrainment function to the specification of the bottom boundary condition for convection-diffusion equation of suspended load are also presented, which show that the calculated concentration profiles are in good agreement with observations. The study also suggests that kinetic theory is a promising analytical approach for the study of sediment motion near a riverbed.

Aquatic suspended canopies are porous obstacles that extend down from the free-surface but have a gap between the canopy and bed. Examples of suspended canopies include those formed by aquaculture structures or floating vegetation. The major difference between suspended canopies and the more common submerged canopies, which are located on the bottom boundary, is the influence of the bottom boundary layer beneath the suspended canopy. Data from laboratory experiments are presented which explore aspects of the flow through and beneath suspended canopies constructed from rigid cylinders. The experiments, using both acoustic Doppler and two-dimensional (2D) particle tracking velocimetry, give details of the flow structure that may be divided vertically into a bottom boundary layer, a canopy shear layer, and an internal canopy layer. The experimental data show that the penetration of the shear layer into the canopy is limited by the distance between the canopy and bottom boundary layer. Peaks in velocity spectra indicate an interaction between the bottom boundary and canopy shear layer. An analytical model is also developed that can be used to calculate a drag coefficient that includes the effect of both canopy drag and bed friction. This drag coefficient is suitable for use in 2D (depth-averaged) hydrodynamic modeling. The model also allows the average velocity within and beneath the canopy to be calculated, and is used to investigate the effect of canopy density and thickness on both total drag and bottom friction.

The concept of a bottom slot outlet was developed to serve as a combined sewer overflow diversion structure to convey flow to deep tunnel storage under free discharge conditions and pass the remaining volume once storage capacity is exceeded with minimum backwater effects. In order to test the concept, a 1:19.5 scale model was constructed and tested over a range of discharges in order to determine the required slot length to pass a certain discharge. Different bottom slopes and slot widths were tested. For subcritical approach flow, the flow in the structure passed through critical depth at the upstream end of the slot, eliminating the possibility of backwater effects. The results were found to be nearly independent of the bottom slope for typical small slopes in sewer systems, and a simple dimensionless relation was developed to relate the slot length to other parameters. A mathematical model combining continuity and energy relations for the remaining flow in the structure with an orifice relation for flow through the slot was capable of reproducing the observed experimental results.

This note deals with the influence of debris accumulation on scour around bridge piers. Clear-water experiments in different hydraulic conditions have been carried out with three wood debris shapes: rectangular, triangular, and cylindrical. A wide range of debris thickness and width were studied in order to determine their influence on the maximum scour hole depth temporal evolution. The ratio of the pier diameter to the channel width was varied between 0.05 and 0.12 with total bridge contractions up to 20%. A proposed relation presents a simple design procedure to predict the increase in scour depth, which mainly depends on the flow contraction due to the debris accumulation.

A two-dimensional, physical model was constructed to evaluate the air entrainment inception point location in a 4(H):1(V) stepped spillway. Step heights of 38, 76, and 152 mm were evaluated. The physical model was constructed with a broad-crested weir, and model unit discharges ranging from $0.11{\text{m}}^3/\left(\text{s}\cdot \text{m}\right)$ to $0.82{\text{m}}^3/\left(\text{s}\cdot \text{m}\right)$ were tested. Hubert Chanson developed a relationship for predicting the inception point location for primarily steep $\left(\theta \ge 22°\right)$ stepped spillways. In this study, Chanson’s relationship effectively predicts the location of the inception point for slopes as flat as 14° for Froude surface roughness values $\left({\mathsf{F}}_{\ast }\right)>10$ which, in this study, corresponds to model step heights of 38 and 76 mm. A new relationship for predicting the location of the inception point was developed, applicable for flatter sloped $\left(\theta \le 22°\right)$ stepped spillways with $1<{\mathsf{F}}_{\ast }<100$ . This relationship is similar to Chanson’s, but it is optimized for flat-sloped stepped spillways with a broad-crested weir.