Journal of Hydraulic Engineering

This paper presents the results of an experimental investigation on the hydraulic jump on horizontal rough beds. Experiments were carried out to study the effect of bed roughness on both the sequent depth ratio and the roller length. The investigation allowed the writers to positively test the reliability of a new solution of the momentum equation for the sequent depth ratio as a function of the Froude number and the ratio between the roughness height and the upstream supercritical flow depth. The applicability of some empirical relationships for estimating the roller length was also tested.

The process of breach erosion of river embankments depends on the interaction among flow, sediment transport, and the corresponding morphological changes. Levees often consist of noncohesive material with a wide range of grain sizes. The dam material is mainly eroded due to the transport capacity of the overtopping water. Both bed load and suspended load are of importance. For breach formation, the lateral erosion due to slope instabilities has a significant impact. A depth averaged, two-dimensional numerical model was developed to account for these processes. The sensitivity of the discharge through the breach related to different processes and material parameters was investigated and compared to experimental and field data. The results show that the most sensitive parameter of an erosion-based dike-breach simulation is the breach side-slope angle which determines the lateral erosion. The application of the described Model 2dMb to different embankment failures at the Elbe River illustrates its capability in simulating overtopping breaching.

Buoyant surface discharges into ambient water bodies can exhibit multiple complex flow processes, which cover the spatial range from the near field with initial jet mixing to the far field with passive ambient diffusion. Multiple flow phenomena can occur, such as buoyant collapse motions, bottom attachment, deflection by the ambient current, and dynamic shoreline interaction, in the near field, and lateral and/or upstream spreading motions and turbulent diffusion processes, in the far field. Efficient and reliable predictive techniques covering the whole range of these processes are needed for the design and prediction of wastewater effluents that are subject to water quality regulations that can apply in either near and/or far field. A new comprehensive classification framework distinguishes among ten hydrodynamically distinct flow classes within four major flow categories: free jets, shoreline-attached jets, wall jets, and upstream intruding plumes. A prediction methodology for these discharges has been presented that covers the entire spatial domain from the near to the far field. It is based on the linkage of separate predictive modules in form of the expert system CORMIX3. These hydrodynamic modules are implemented by specific flow protocols and transition criteria determine their spatial extent. The methodology, corroborated by numerous detailed laboratory and some field data sources, constitutes a simple and efficient, yet accurate and robust, tool with few data requirements for surface discharge design and mixing analysis.

The near-field region of a buoyant surface discharge into water bodies often displays significant jet-like motions in form of free jets, shoreline-attached jets, and wall jets, respectively, as classified by the CORMIX3 expert system [see Jones et al., (2007, Paper I)]. A new jet integral model CorSurf has been developed that addresses in a single formulation this entire spectrum of jet motions in both deep or shallow environments. The model employs an entrainment closure approach for the separate contributions of entrainment resulting from transverse shear, buoyant damping, advected puff motions, frontal mixing, and interfacial mixing due to lateral spreading. It also contains a quadratic law turbulent drag force mechanism. An alternative model formulation applies to the two-dimensional bottom-attached form of the jet. This formulation contains a deflecting pressure force mechanism as well as the bottom shear force. Specific criteria describe bottom attachment and detachment processes. Finally, a number of confinement effects on the jet dynamics due to shallow water and/or lateral boundaries are included. The model has been validated under a wide range of geometric and dynamic conditions using, in particular, hitherto unavailable high-resolution laboratory data.

Lock-exchange gravity current flows produced by the instantaneous release of a heavy fluid are investigated by means of high-resolution two-dimensional (2D) large-eddy simulation (LES) using a dynamic subgrid scale model for Grashof numbers $\left(\mathsf{Gr}\right)$ up to ${10}^{12}$ . The model is validated using 2D direct numerical simulation results for the classical lock-exchange gravity current flow in an infinite channel with no-slip walls. Then the model is applied to study lock-exchange flows for the case in which the heavier (lock) fluid is initially situated in between a vertical end wall and the lock barrier. Three cases with different aspect ratios of the initial lock fluid are considered for Grashof numbers of the order of ${10}^9–{10}^{10}$ . It is found that 2D LES is able to capture most of the physics observed in experiments including the evolution of the head, as well as the formation of coherent billow structures at the apex of the head due to growth of the Kelvin-Helmholtz (KH) instabilities. However, due to the fact that three-dimensional instabilities cannot develop in 2D simulations, the coherence of these KH billows in the latter stages of the evolution of the current is found to be stronger compared to the experiment where mixing is sensibly higher at the interface between the current and the surrounding fluid. The LES simulations accurately capture the front and bore velocities in the slumping phase and predict that during the inviscid self-similar phase the front speed decay is proportional to $t^{-1∕3}$ , which is consistent with theory, where $t$ =time. A LES simulation at a Grashof number closer to the inviscid range $(\mathsf{Gr}={10}^{12})$ shows that the evolution of the current and the structure of the head region are qualitatively similar to those observed at lower Grashof numbers $(\mathsf{Gr}>{10}^8)$ . The energy balance shows that the higher front velocity in the $\mathsf{Gr}={10}^{12}$ simulation is due to the fact that the amount of mixing (dissipation) decays with the Grashof number. This allows a larger fraction of the potential energy to be converted into kinetic energy. The flow fields are also used to obtain the distributions of the bed shear stress which determine the amount of sediment entrained by a compositional gravity current propagating over a loose bed.

The numerical simulation of unsteady open channel flows is very commonly performed using the one-dimensional shallow-water model. Friction is one of the relevant forces included in the momentum equation. In this work, a generalization of the Gauckler-Manning friction model is proposed to improve the modeling approach in cases of dominant roughness, unsteady flow, and distorted cross-sectional shapes. The numerical stability conditions are revisited in cases of dominant friction terms and a new condition, complementary to the basic Courant-Friedrichs-Lewy condition, is proposed. Some test cases with measured data are used to validate the quality of the approaches.

This investigation considers an approximate formulation of the St. Venant equations for natural channels, in which the fully conservative form is developed by revising the boundary pressure term accounting for the topographic variation in the momentum equation. As such a formulation has the potential to enhance the performance of existing models used in practice, the accuracy implications for this approximate formulation are examined using an error analysis for a simplified case. Further, an energy calculation is performed which illustrates that an earlier formulation actually results in energy gain for some cases. A more general formula for the constant water surface elevation that corrects this is introduced and tested. It is found that the refined formulation presented here is accurate for hydraulic jumps, steep surge waves, and flood wave propagation in natural channels. The shock capturing capability of the approximate formulation is illustrated for both steady- and unsteady-flow situations using the finite-element method, for which this approximate equation formulation adapts naturally. Using the characteristic-dissipative-Galerkin finite-element scheme, good results are obtained for the case of a hydraulic jump in a diverging rectangular channel, with the maximum percent error associated with the approximate formulation determined to be only 0.34%. For the case of dam break wave propagation in a converging and diverging rectangular channel, the model performs similarly well, with the maximum error only 0.0064%. Further, the approximate formulation is used to simulate the flood routing in a natural channel, the Oldman River in southern Alberta. The computational results are in good agreement with the observed data. The arrival time of peak flow is $5\mathrm{h}$ earlier and the magnitude of peak discharge is only 3.8% lower than the observed value.

A new theoretical approach is presented for the derivation of free surface profiles of two-dimensional steady and unsteady flows by solving the Reynolds-averaged Navier-Stokes equations applied to the turbulent flow regime. This approach enables us to compute the steady and unsteady curvilinear flows having small curvatures, such as free overfall and constant velocity surge. In addition, the applications of the theory to the second-order waves are illustrated through the problems of small height bore and second-order tide.

The power law velocity profile has been analyzed in terms of the envelope of the friction factor which gives the friction factor log law. The power law index $\alpha$ and prefactor $C$ are shown as the function of the friction Reynolds number, as well as the function of the alternate variable the nondimensional friction velocity. The fully developed turbulent superpipe flow data of McKeon et al. and fully developed channel flow data of Zanoun et al. have been analyzed and the power law index $\alpha$ and prefactor $C$ data have been estimated, first as a function of the friction Reynolds number and second as function of the nondimensional friction velocity. Based on analysis, several correlations have been proposed that have been supported by the data.

A recent companion paper reported an experimental protocol used to analyze sediment properties. This protocol identified for both freshwater and marine sediments a surface layer with specific dynamic properties (critical erosion shear stresses in the range $0.025–0.05\mathrm{N}{\mathrm{m}}^{-2}$ ) and a second layer with critical erosion shear stresses about ten times larger. The present study compares these former results with recent work which extended the applicability domain of the Shields diagram to very fine particles. The surface layer is shown to consist in fine and unconsolidated sediments that behave like noncohesive material whereas the second layer is characterized as being cohesive. The surface layer is mainly representative of recent deposits of suspended particles. This points out the existence of a fluffy layer of fine sized particles resting near the bed, with specific erosion characteristics, which has to be considered separately when studying sediment properties.