Modelling of flood waves based on wave propagation : algorithms with bed efflux and influx including a coupled-pipe network solver

Flood propagation over urban areas can cause an interaction between the free-surface flow and large underground pipe networks used for storm drainage and sewage, causing outflows and inflows at the bed. The associated waves may collide with each other and the surface waves. In this thesis the shallow water equations are used to model this type of wave interaction over dry or wet beds with bathymetry gradients and friction terms. The proposed shallow water scheme is solved based on finite volume high-resolution Godunov-type methods. The solver is well-balanced and can accurately balance the source terms and flux-gradients for the steady-state solutions. The solver also utilises a new type of Riemann wave speed to provide depth-positive results over nearly dry beds and dry states. Additionally a new type of source term is introduced in the continuity equation to model pipe inflow and outflow conditions at bed connections. For the standard one-dimensional shallow water equations the numerical results are validated with analytical solutions or other reference solutions provided in the literature. This includes the incipient Riemann problems for nearly dry and dry-states, steady flow over a hump in a rectangular channel and the wave propagation problem. Eventually, the generation of dry bed in the middle, over discontinuous topography is considered. Close agreement is achieved between the shallow water scheme and analytical or reference solutions for the above test cases. For the shallow water problems with influx/efflux source terms comparisons are made with STAR-CD, a commercial Navier-Stokes solver for general fluid flow prediction. The shallow water model is first used to simulate vertical flows through finite gaps in the bed. Next, the interaction of the vertical flows with a dam-break flow is considered for both dry and wet beds. An efflux number, En, is defined based on the vertical efflux velocity and the gap length. A parameter study is undertaken to investigate the effect of the one-dimensional approximation of the present model, for a range of non-dimensional efflux numbers. It is found that the shallow flow model gives sensible predictions at all times provided En0.5. Dam break flow over an underground connecting pipe is also considered for the one-dimensional efflux problems. To solve two-dimensional problems the shallow water scheme uses the dimensional-splitting method which solves each one-dimensional Riemann problem in the x- and y-directions separately. The cross-derivative terms for second-order accuracy are incorporated by solving another Riemann problem in the orthogonal direction. For two-dimensional problems first the dam-break problems are considered over wet and dry beds. Then, flood propagation over complex terrain is demonstrated. Next, efflux discharge is modelled in isolation over a dry bed and then with dam-break interaction, comparing with STAR-CD results. Again very good agreement is shown between the two-dimensional shallow water model and STAR-CD for the efflux numbers of En<0.5. For modelling the inundation problem over an underground pipe network the solver is coupled with the general underground pipe network solver to calculate the efflux discharge as the flood waves pass through the pipe network. For analysing the pipe network with unknown effluxes an additional set of equations is incorporated into the solution of a general pipe network solver. The shallow water solver coupled to an underground pipe network is then used to simulate dam-break interaction with pipe networks with 9 and 25 nodes to demonstrate the versatility of the method.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Florida Bay Science Program: a synthesis of research on Florida Bay

This report documents the progress made toward the objectives established in the Strategic Plan revised in 1997 for the agencies cooperating in the program. These objectives are expressed as five questions that organized the research on the Florida Bay ecosystem: Ecosystem History What was the Florida Bay ecosystem like 50, 100, and 150 years ago? Question 1—Physical Processes How and at what rates do storms, changing freshwater flows, sea level rise, and local evaporation and precipitation influence circulation and salinity patterns within Florida Bay and exchange between the bay and adjacent waters? Question 2—Nutrient Dynamics What is the relative importance of the influx of external nutrients and of internal nutrient cycling in determining the nutrient budget for Florida Bay? What mechanisms control the sources and sinks of the bay’s nutrients? Question 3—Plankton Blooms What regulates the onset, persistence, and fate of planktonic algal blooms in Florida Bay? Question 4—Seagrass Ecology What are the causes and mechanisms for the observed changes in the seagrass community of Florida Bay? What is the effect of changing salinity, light, and nutrient regimes on these communities? Question 5—Higher Trophic Levels What is the relationship between environmental and habitat change and the recruitment, growth, and survivorship of animals in Florida Bay? Each question examines different characteristics of the Florida Bay ecosystem and the relation of these to the geomorphological setting of the bay and to processes linking the bay with adjacent systems and driving change.This report also examines the additional question of what changes have occurred in Florida Bay over the past 150 years

A well-balanced unsplit finite volume model with geometric flexibility

A two-dimensional finite volume model is developed for the unsteady, and shallow water equations on arbitrary topography. The equations are discretized on quadrilateral control volumes in an unstructured arrangement. The HLLC Riemann approximate solver is used to compute the interface fluxes and the MUSCL-Hancock scheme with the surface gradient method is employed for second-order accuracy. This study presents a new method for translation of discretization technique from a structured grid description based on the traditional (i, j) duplet to an unstructured grid arrangement based on a single index, and efficiency of proposed technique for unsplit finite volume method. In addition, a simple but robust well-balanced technique between fluxes and source terms is suggested. The model is validated by comparing the predictions with analytical solutions, experimental data and field data including the following cases: steady transcritical flow over a bump, dam-break flow in an adverse slope channel and the Malpasset dam-break in France

two dimensional two phase depth integrated model for transients over mobile bed

AbstractFast geomorphic transients may involve complex scenarios of sediment transport, occurring near the bottom as bed load (i.e., saltating, sliding, and rolling) or as suspended load in the upper portion of the flow. The two sediment transport modalities may even coexist or alternate each other during the same event, especially when the shear stress varies considerably. Modeling these processes is therefore a challenging task, for which the usual representation of the flow as a mixture may result in being unsatisfactory. In the present paper, a new two-phase depth-averaged model is presented that accounts for variable sediment concentration in both bed and suspended loads. Distinct phase velocities are considered for bed load, whereas the slip velocity between the two phases is neglected in the suspended load. It is shown that the resulting two-phase model is hyperbolic, and the analytical expression of the eigenvalues is provided. The entrainment/deposition of sediment between the bottom and the bed ..

Modeling Shallow Water Flows on General Terrains

A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of gravity forces is not exact in the general case of a tilted curved bottom. We claim that an integration path that better adapts to the shallow water hypotheses follows the "cross-flow" surface, i.e., a surface that is normal to the velocity field at any point of the domain. Because of the implicitness of this definition, we approximate this "cross-flow" path by performing depth integration along a local direction normal to the bottom surface, and propose a rigorous derivation of this approximation and its numerical solution as an essential step for the future development of the full "cross-flow" integration procedure. We start by defining a local coordinate system, anchored on the bottom surface to derive a covariant form of the Navier-Stokes equations. Depth integration along the local normals yields a covariant version of the shallow water equations, which is characterized by flux functions and source terms that vary in space because of the surface metric coefficients and related derivatives. The proposed model is discretized with a first order FORCE-type Godunov Finite Volume scheme that allows implementation of spatially variable fluxes. We investigate the validity of our SW model and the effects of the bottom geometry by means of three synthetic test cases that exhibit non negligible slopes and surface curvatures. The results show the importance of taking into consideration bottom geometry even for relatively mild and slowly varying curvatures

Optimal control for studying wave energy in hydraulic systems

A class of novel models for water waves induced by elastic deformation in the topography is developed and analyzed. The depth-averaged shallow water equations including friction terms for the water free-surface and the well-known second-order elastostatic formulation for the bed deformation have been implemented. Friction forces and water hydrostatic pressure distribution are also accounted for in this model. At the interface between the water ow and the bed topography, transfer conditions are implemented. Furthermore, a hybrid nite element/nite volume method for solving free-surface run-up ow problems over deformable beds has been proposed. The deformations in the topography have been generated by a localized force which causes propagations of the water waves with dierent amplitudes and frequencies. Two dierent methods have been proposed for the transfer of informations through the interface. The rst one is the two-mesh procedure; in this method a proper interpolation has been implemented to transfer the data between the surface nodes and the control volumes using uniform nite volume meshes. In the second method, and to avoid the interpolation at the interface, a nite volume method using non-uniform meshes has been implemented. When the shallow water waves approach the coastline they begin to transform as they enter shallow water regime. As each wave begins to experience the seabed, both run-up and overtopping occur. To solve for this, a class of stable, accurate and simple numerical model for moving wet/dry fronts in shallow water equations using the parametrization concept and the point-wise Riemann solver has been proposed. Many parameters of shallow water equations are subject to uncertainties to the inherit randomness of natural processes. To incorporate uncertain parameters into the stochastic shallow water equations, the stochastic properties of dierent parameters that are considered uncertain, namely in ow boundary condition, the bed friction coecients and the domain topography are added to the system. Development of accurate and ecient tools for uncertainty quantication in shallow water ows has been proposed and carefully examined for single-layer, two-layer - nite volume models. To further quantify the uncertainty in shallow water ows the proposed methods have been extended to multi-layer shallow water ows with mass exchange terms subject to stochastic topography, uncertain friction and viscosity coecients. Several test examples and well-established benchmark problems have been used to assess the numerical performance of the proposed models and methods. Comparisons to experimental measurements have also been carried out in this thesis. Finally, an optimal control technique for bed reconstruction has been presented as in many engineering applications this information is not entirely provided

Flow resistance, sediment transport, and bedform development in a steep gravel-bedded river flume

Quantifying flow resistance and sediment transport rates in steep streams is important for flood and debris flow prediction, habitat restoration, and predicting how mountainous landscapes evolve. However, most studies have focused on low gradient rivers and the application of this work is uncertain for steep mountain streams where surface flows are shallow and rough, subsurface flows are not negligible, and there is form-drag from bed- and channel-forms that differs from those in low gradient rivers. To evaluate flow resistance relations and sediment transport rates for steep channel beds, experiments were conducted using a range of water discharges and sediment transport rates in a 12 m long recirculating flume with bed slopes of 10%, 20%, and 30%, and a bed of nearly uniform natural gravel. Flow resistance for planar beds and beds that developed bedforms match empirical models that account for bedload-dependent roughness. Some bedforms were atypical for natural rivers at these bed slopes, such as stepped alternate bars and upstream migrating alternate bars. Total flow resistance increased with decreasing particle submergence and energetic sediment transport and drag on bedforms. Using linear stress partitioning to calculate bed stresses due to grain resistance alone, sediment flux relations developed for lower gradient rivers perform well overall, but they overestimate fluxes at 20% and 30% gradients. Based on previous theory, mass failure of the bed, which did not occur, was predicted for the highest Shields stresses investigated at 20% and 30% bed slopes; instead a concentrated layer, four to ten particle diameters deep, of highly concentrated granular sheetflow was observed

A numerical tool to integrate biophysical diversity of a large regulated river: hydrobiogeochemical bases. The case of the Garonne River (France)

This article presents the bases of a hydrobiogeochemical model of the Garonne River (southwest France) which has been developed to integrate physical and biological processes during summer low-water periods. The physical part of this model is composed of a one-dimensional unsteady hydrodynamic model, allowing the resolution of the Saint-Venant equations, and a transport model which simulates downstream changes in solute concentrations. Biogeochemical processes are considered through the definition of functional compartments which make up the channel bed. These different compartments are defined both by the organisms involved in the solute transformation processes and by the physical and hydraulic characteristics of their habitat. Integration of these functional compartments within the model required investigations at different scales. The scale at which biological processes take place ranges from millimetres to metres. The scale of a reach, at which organization of the functional compartments along the river can be linked to hydrodynamic and morphological characteristics, ranges from 500 m to several kilometres. The regional scale is that at which homogeneous reaches can be integrated. A feedback between numerical results and field experiments has allowed improvements to in situ measurement to increase modelling accuracy. For example, the model allows estimation of variables, such as fluxes, that are difficult to measure in situ. The developed model can integrate various functional compartments and their biogeochemical functioning. Two application examples, focused on dissolved inorganic nitrogen, are presented in order to illustrate the numerical tool functioning: integration of equations on nitrification processes in the water body, and integration of consumption/production terms on epilithic biofilm resulting from in situ experimental mean values. The model we have developed constitutes a promising analytical tool that will be able to integrate previous and future studies

Time domain simulations of dynamic river networks

The problem of simulating a river network is considered. A river network is considered to comprise of rivers, dams/lakes as well as weirs. We suggest a numerical approach with specific features that enable the correct representation of these assets. For each river the flow of water is described by the shallow water equations which is a system of hyperbolic partial differential equations and at the junctions of the rivers, suitable coupling conditions, viewed as interior boundary conditions are used to couple the dynamics. A different model for the dams is also presented. Numerical test cases are presented which show that the model is able to reproduce the expected dynamics of the system. Other aspects of the modelling such as rainfall, run-off, overflow/flooding, evaporation, absorption/seepage, bed-slopes, bed friction have not been incorporated in the model due to their specific nature