Computational Dam-Break Hydraulics over Erodible Sediment Bed

This paper presents one of the first dedicated studies on mobile bed hydraulics of dam-break flow and the induced sediment transport and morphological evolution. A theoretical model is built upon the conservative laws of shallow water hydrodynamics, and a high-resolution numerical solution of the hyperbolic system is achieved using the total-variation-diminishing version of the second-order weighted average flux method in conjunction with the HLLC approximate Riemann solver and SUPERBEE limiter. It is found that a heavily concentrated and eroding wavefront first develops and then depresses gradually as it propagates downstream. In the early stage of the dam-break, a hydraulic jump is formed around the dam site due to rapid bed erosion, which attenuates progressively as it propagates upstream and eventually disappears. While the backward wave appears to migrate at the same speed as over a fixed bed, the propagation of the forward wavefront shows a complex picture compared to its fixed-bed counterpart as a result of the domination of rapid bed erosion initially, the density difference between the wavefront and the downstream ambient water in the intermediate period, and the pattern of the deformed bed profile in the long term. It is also found that the free surface profiles and hydrographs are greatly modified by bed mobility, which has considerable implications for flood prediction. The computed wave structure in the intermediate period exhibits great resemblance to available experiments qualitatively, and yet the existence of a shear wave is found in lieu of a secondary rarefaction postulated in an existing analysis. Finally, the use of the complete, rather than simplified, conservation equations is shown to be essential for correct resolution of the wave and bed structures, which suggests that previous models need reformulating.     

Dam-Break Wave-Front Celerity

This work is concerned with the role that friction and inertia effects can play on the magnitude of dam-break wave-front celerity. Classic analytical solutions are presented. A large collection of experimental data is used, covering a wide range of different initial conditions: fixed bed or mobile bed (five types of bed material), dry or wet bed downstream, and with or without bed step. To overcome the limitations of analytical solutions, a numerical model is used. The model is based on the shallow-water approach with contact-load dominated sediment transport, and it makes use of developments recently made in the study of sheet flows. The analytical and numerical results are compared with experimental data. It was found that the celerity is mainly dictated by the friction coefficient, by the sediment inertia, by the initial downstream water depth, and by the initial bed step height. For good data fitting, the friction coefficient must be influenced by the type of bed, fixed or mobile. In the latter, the coefficient must vary with the bed material characteristics. The dissimilarities between the experimental, analytical, and numerical results are interpreted.     

Finite-Difference TVD Scheme for Computation of Dam-Break Problems

A second-order hybrid type of total variation diminishing (TVD) finite-difference scheme is investigated for solving dam-break problems. The scheme is based upon the first-order upwind scheme and the second-order Lax-Wendroff scheme, together with the one-parameter limiter or two-parameter limiter. A comparative study of the scheme with different limiters applied to the Saint Venant equations for 1D dam-break waves in wet bed and dry bed cases shows some differences in numerical performance. An optimum-selected limiter is obtained. The present scheme is extended to the 2D shallow water equations by using an operator-splitting technique, which is validated by comparing the present results with the published results, and good agreement is achieved in the case of a partial dam-break simulation. Predictions of complex dam-break bores, including the reflection and interactions for 1D problems and the diffraction with a rectangular cylinder barrier for a 2D problem, are further implemented. The effects of bed slope, bottom friction, and depth ratio of tailwater∕reservoir are discussed simultaneously.     

Applicability of Sediment Transport Capacity Formulas to Dam-Break Flows over Movable Beds

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 J?ggi, 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.     

Numerical Solution of the Dam-Break Problem with a Discontinuous Galerkin Method

A discontinuous Galerkin method for the solution of the dam-break problem is presented. The scheme solves the shallow water equations with spectral elements, utilizing an efficient Roe approximate Riemann solver in order to capture bore waves. The solution is enhanced by a projection limiter that eliminates spurious oscillations near discontinuities. The main advantage of the model is the flexibility in approximating smooth solutions with high-order polynomials and resolving at the same time discontinuous shock waves. Furthermore, the finite element discretization is capable of handling complex geometries and producing correct results near the boundaries. Both the h- and p-type extensions are investigated for the one-dimensional dam break, and the results are verified by comparison with analytical solutions. The application to a two-dimensional dam-break problem shows the efficiency and stability of the method.     

Laminar Water Wave and Current Passing Over Porous Bed

The problem of the dynamic interaction of water waves, current, and a hard poroelastic bed is dealt with in this study. Finite-depth homogeneous water with harmonic linear water waves passing over a semi-infinite poroelastic bed is investigated. In order to reveal the importance of viscous effect for different bed forms, viscosity of water is considered herein. In a boundary layer correction approach, the governing equations of the poroelastic material are decoupled without losing physical generality. The contribution of pressure effect and shear effect to the hard poroelastic bed, which is a valuable indication to the mechanism of ripple formation, is clarified in the present study. This approach will be helpful in saving time and storage capacity when it is applied to numerical computation.     

Dam Break in Channels with 90° Bend

In practice, dam-break modeling is generally performed using a one-dimensional (1D) approach for its limited requirements in data and computation. However, for valleys with multiple sharp bends, such a 1D model may fail for predicting as well the maximum water level as the wave arrival time. This paper presents an experimental study of a dam-break flow in an initially dry channel with a 90° bend, with refined measurements of water level and velocity field. The measured data are compared to some numerical results computed with finite-volume schemes associated with Roe-type flux calculation. The 1D approach reveals the expected limits, while a full two-dimensional (2D) approach provides fine level prediction and rather satisfactory information about the arrival time. A hybrid approach is now proposed, mixing the 1D model for the straight reaches and local 2D models for the bends. The compatibility of the Roe fluxes at the interfaces requires a careful formulation, but the resulting scheme seems able to capture reflection and diffraction processes in such a way that the results are really good in what concerns the water level.     

Numerical Solution of Boussinesq Equations to Simulate Dam-Break Flows

To investigate the effect of nonhydrostatic pressure distribution, dam-break flows are simulated by numerically solving the one-dimensional Boussinesq equations by using a fourth-order explicit finite-difference scheme. The computed water surface profiles for different depth ratios have undulations near the bore front for depth ratios greater than 0.4. The results obtained by using the Saint Venant equations and the Boussinesq equations are compared to determine the contribution of individual Boussinesq terms in the simulation of dam-break flow. It is found that, for typical engineering applications, the Saint Venant equations give sufficiently accurate results for the maximum flow depth and the time to reach this value at a location downstream of the dam.     

Effects of Weakly Nonlinear Water Waves on Soft Poroelastic Bed with Finite Thickness

Since porous material is usually of a finite thickness in nature, the effects of periodically nonlinear water waves propagating over a soft poroelastic bed with finite thickness are hence noticed and studied in this work. The water waves are simulated by potential theory while the porous bed is governed by Biot’s theory of poroelasticity herein. The conventional Stokes expansion of water waves based on a one-parameter perturbation expansion fails to solve the soft poroelastic bed problem; therefore, the boundary layer correction approach combined with a two-parameter perturbation expansion is proposed, which enables us to solve the problem of soft poroelastic bed with finite thickness. The results are compared to the similar problem with an infinite-thickness porous bed. The boundary effects of the impervious rock are significant on wave-induced pore water pressure and effective stresses, but are of very little significance on wave profiles at the free surface and the porous bed surface. However, the rigid boundary is insignificant to the pore water pressure and effective stresses when the thickness of porous bed is larger than about one wavelength.     

Assessment of Methods Used in 1D Models for Computing Bed-Load Transport in a Large River: The Danube River in Slovakia

Comprehensive measurements of bed-load sediment transport through a section of the Danube River, located approximately 70?km downstream from Bratislava, Slovakia, are used to assess the accuracy of bed-load formulas implemented in 1D modeling. Depending on water discharge and water level, significant variations in the distribution of bed load across the section were observed. It appeared that, whatever the water discharge, the bed shear stress τ is always close to the estimated critical bed shear stress for the initiation of sediment transport τcr. The discussion focuses on the methods used in 1D models for estimating bed-load transport. Though usually done, the evaluation of bed-load transport using the mean cross-sectional bed shear stress yields unsatisfactory results. It is necessary to use an additional model to distribute the bed shear stress across the section and calculate bed load locally. Bed-load predictors also need to be accurate for τ close to τcr. From that point of view, bed-load formulas based on an exponential decrease of bed-load transport close to τcr appear to be more appropriate than models based on excess bed shear stress. A discussion on the bed-load formula capability to reproduce grain sorting is also provided.     

Theoretical Solution of Dam-Break Shock Wave

A mathematical model of dam-break shock waves, or flood waves, in channels of trapezoidal cross section is presented. When the model is applied to channels of rectangular cross section, a new theoretical solution expressed using one independent multinominal algebraic equation is derived. In the past, the solution had to be described using three interrelated equations. The new equation indicates that the hydraulic parameters of a shock wave—such as depth and velocity of flow, and velocity of discontinuity—are determined only by the ratio of initial downstream depth to initial upstream depth. The model shows that results from the new equation are completely equivalent to those of the set of old equations. In addition, the flood hydrograph produced by a dam break at any time or any site can be described by a single curve in terms of dimensionless variables.     

Explicit Schemes for Dam-Break Simulations

Dam-break problems involve the formation of shocks and rarefaction fans. The performance of 20 explicit numerical schemes used to solve the shallow water wave equations for simulating the dam-break problem is examined. Results from these schemes have been compared with analytical solutions to the dam-break problem with finite water depth and dry bed downstream of the dam. Most of the numerical schemes produce reasonable results for subcritical flows. Their performance for problems where there is a transition between subcritical and supercritical flows is mixed. Although many numerical schemes satisfy the Rankine-Hugoniot condition, some produce solutions which do not satisfy the entropy condition, producing nonphysical solutions. This was the case for the majority of first-order schemes examined. Numerical schemes which consider critical flow in the solution are guaranteed to produce entropy satisfying solutions. Second-order schemes avoid the generation of expansive shocks; however, some form of flux or slope limiter must be used to eliminate oscillations that are associated with these schemes. These limiters increase the complexity and the computational effort required, but they are generally more accurate than their first-order counterparts. The limiters employed by these second-order schemes will produce monotone or total variation diminishing solutions for scalar equations. Some limiters do not exhibit these properties when they are applied to the nonlinear shallow water wave equations. This comparative study shows that there are a variety of shock-capturing numerical schemes that are efficient, accurate, robust, and are suitable for solving the shallow water wave equations when discontinuities are encountered in the problem.     

Dam-Breach Flood Wave Propagation Using Dimensionless Parameters

An analytical model of flood wave propagation is used to study the sensitivity of dam-breach flood waves to breach-outflow hydrograph volume, peak discharge, and downstream-channel bed slope. Dimensionless parameters are identified for discharge and distance along the channel. A dam-breach Froude number is defined to enable analysis through a wide range of site and flow conditions. It is found that, at a certain distance downstream, the attenuated peak discharge is independent of the magnitude of the discharge at the breach site. This attenuated peak discharge is termed the “ultimate discharge,” and the distance associated with it, the “ultimate distance.” These ultimate values are a function, primarily of the downstream-channel bed slope and, secondarily, of the breach-outflow hydrograph volume.     

Numerical Model for Sediment Transport and Bed Degradation in the Yangtze River Channel Downstream of Three Gorges Reservoir

This paper presents a two-dimensional morphological model for unsteady flow and both suspended-load and bed-load transport of multiple grain size to simulate transport of graded sediments downstream from the Three Gorges Reservoir. The model system includes a hydrodynamic module and a sediment module. The hydrodynamic module is based on the depth-averaged shallow water equations in orthogonal curvilinear coordinates. The sediment module describing nonuniform sediment transport is developed to include nonequilibrium transport processes, bed deformation, and bed material sorting. The model was calibrated using field observations through application to a 63-km-long alluvial river channel on the middle Yangtze River in China. A total of 16 size groups and a loose layer method of three sublayers were considered for the transport of the nonuniform bed materials in a long-term simulation. Predictions are compared with preliminary results of field observations and factors affecting the reliability of the simulated results are discussed. The results may be helpful to the development of more accurate simulation models in the future.     

Generation of Three-Dimensional Fully Nonlinear Water Waves by a Submerged Moving Object

This paper describes a numerical investigation on the generation of three-dimensional (3D) fully nonlinear water waves by a submerged object moving at speeds varied from subcritical to supercritical conditions in an unbounded fluid domain. Considering a semispheroid as the moving object, simulations of the time evolutions of 3D free-surface elevation and flow field are performed. The present 3D model results are found to agree reasonably well with other published vertical two-dimensional (2D) and quasi-3D numerical solutions using Boussinesq-type models. Different from the 2D cases with near critical moving speeds, the 3D long-term wave pattern suggests that in addition to the circularly expanded upstream advancing solitonlike waves, a sequence of divergent and transverse waves are also developed behind the moving object. The velocity distributions and associated fluid-particle trajectories at the free-surface and middle layers are presented to show the 3D feature of the motion. The results under various vertical positions (referred as gap) of a moving object are also compared. It is found the gap has shown a substantial influence on the generated waves, especially in the wake region, when an object moves at a near critical or subcritical speed. However, the results under the case with a high supercritical moving speed indicate the gap has a negligible effect on the generated upstream and downstream waves.     

Cartesian Cut Cell Two-Fluid Solver for Hydraulic Flow Problems

A two-fluid solver which can be applied to a variety of hydraulic flow problems has been developed. The scheme is based on the solution of the incompressible Euler equations for a variable density fluid system using the artificial compressibility method. The computational domain encompasses both water and air regions and the interface between the two fluids is treated as a contact discontinuity in the density field which is captured automatically as part of the solution using a high resolution Godunov-type scheme. A time-accurate solution has been achieved by using an implicit dual-time iteration technique. The complex geometry of the solid boundary arising in the real flow problems is represented using a novel Cartesian cut cell technique, which provides a boundary fitted mesh without the need for traditional mesh generation techniques. A number of test cases including the classical low amplitude sloshing tank and dam-break problems, as well as a collapsing water column hitting a downstream obstacle have been calculated using the present approach and the results compare very well with other theoretical and experimental results. Finally, a test case involving regular waves interacting with a sloping beach is also calculated to demonstrate the applicability of the method to real hydraulic problems.     

Influence of Tailwater Depth and Pile Position on Scour Downstream of Block Ramps

Scour control downstream of hydraulic structures is an important topic in hydraulic engineering. Block ramps or rock chutes are often used to control scour downstream of hydraulic structures and have the peculiarity to be ecofriendly. Although these structures assure great energy dissipation, the rapid passage from supercritical to subcritical flow at the toe results in a scour hole with geometric parameters that have to be evaluated in order to avoid foundation problems. For this reason, the analysis of the scour process and the comprehension of the hydrodynamic mechanisms on which it is based are extremely important. In this paper, the results of systematic experimental tests are shown that analyze both the influence of the stilling basin tailwater depth and the ramp toe stabilizing structures, for both uniform and nonuniform channel bed materials. In fact, block ramps are generally stabilized by inserting piles or micropiles at the toe. The upper edge level of piles or micropiles was found a relevant parameter for the scour hole geometry. Simple novel relationships that account for tailwater depth, pile position, and bed material gradation are developed to evaluate the main lengths of the scour hole, in the case in which a free hydraulic jump in a mobile bed occurs. These simple relationships give engineers helpful instruments in block ramp design.     

Dam-Break Surges with Floating Debris

The effect of floating debris on dam-break surges is studied experimentally. Hexahedron plastic particles having a specific gravity of 0.92 are used as debris. In addition to qualitative investigation of the surge behavior, the speed and height of the surges are plotted for various downstream to upstream depth ratios and debris concentration. The results are compared with the clear-water surges. Deceleration and the increase in height of the surge are more pronounced for smaller initial depths downstream of the gate. In general, the speed of the surge is found to be a function of downstream to upstream depth ratio, the ratio of the mass of the debris per unit surface area to the mass of the water per unit surface area upstream of the gate, and the particle size relative to the upstream depth. The wave height, on the other hand, is found to be a function of the depth and concentration ratios for smaller initial downstream depths. For higher initial downstream depths, the wave height is a function of the depth ratio only.     

Numerical Modeling of Bed Evolution in Channel Bends

A two-dimensional numerical model is developed to predict the time variation of bed deformation in alluvial channel bends. In this model, the depth-averaged unsteady water flow equations along with the sediment continuity equation are solved by using the Beam and Warming alternating-direction implicit scheme. Unlike the present models based on Cartesian or cylindrical coordinate systems and steady flow equations, a body-fitted coordinate system and unsteady flow equations are used so that unsteady effects and natural channels may be modeled accurately. The effective stresses associated with the flow equations are modeled by using a constant eddy-viscosity approach. This study is restricted to beds of uniform particles, i.e., armoring and grain-sorting effects are neglected. To verify the model, the computed results are compared with the data measured in 140° and 180° curved laboratory flumes with straight reaches up- and downstream of the bend. The model predictions agree better with the measured data than those obtained by previous numerical models. The model is used to investigate the process of evolution and stability of bed deformation in circular bends.     

Horizontal Viscous Dam—Break Flow: Experiments and Theory

This paper considers dam-break flow occurring in a horizontal smooth channel. Experiments were carried out with highly viscous Newtonian fluids, e.g., glucose syrup–water solutions. The frontal shape of dam-break flow and its evolution, as well as the free-surface profile, were measured using video-photographic and ultrasonic equipment, respectively. New features of viscous dam-break flow are pointed out. Notably indicated are flow regimes and the effect of reservoir length as well as the effect of fluid viscosity on flow development. Equations describing dam-break flow are derived in nondimensional form, then compared with the results from experiments.